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In continuation with Paper I [S. R. Reddy et al., J. Chem. Phys. 151, 054303 (2019)], the vibronic structure and dynamics of the 1 Σ u + electronic state of C15, C17, C19, and C21 chains in the coupled manifold of 1 Σ u + –1Πg–1Πu– 1 Σ g + electronic states have been investigated in this paper. The model vibronic Hamiltonian developed through extensive ab initio quantum chemistry calculations in Paper I is employed, and first principles nuclear dynamics calculations are carried out to obtain the photoabsorption band of the 1 Σ u + electronic state. Both time-independent and time-dependent quantum mechanical calculations are carried out to precisely locate the vibrational levels, assign them with the progression of vibrational modes, and elucidate the impact of both Renner-Teller and pseudo-Renner-Teller couplings on them. The nonradiative decay of the 1 Σ u + electronic state is studied, and it is found that the decay rate is comparable with the prediction made for them to be qualified as a carrier of diffuse interstellar bands in the literature. The theoretical results are found to be in good accord with the available experimental results. [ABSTRACT FROM AUTHOR]

In Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], we presented the ring-polymer instanton with explicit friction (RPI-EF) method and showed how it can be connected to the ab initio electronic friction formalism. This framework allows for the calculation of tunneling reaction rates that incorporate the quantum nature of the nuclei and certain types of non-adiabatic effects (NAEs) present in metals. In this paper, we analyze the performance of RPI-EF on model potentials and apply it to realistic systems. For a 1D double-well model, we benchmark the method against numerically exact results obtained from multi-layer multi-configuration time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for medium and high friction strengths and less accurate for extremely low friction values. We also show quantitatively how the inclusion of NAEs lowers the crossover temperature into the deep tunneling regime, reduces the tunneling rates, and, in certain regimes, steers the quantum dynamics by modifying the tunneling pathways. As a showcase of the efficiency of this method, we present a study of hydrogen and deuterium hopping between neighboring interstitial sites in selected bulk metals. The results show that multidimensional vibrational coupling and nuclear quantum effects have a larger impact than NAEs on the tunneling rates of diffusion in metals. Together with Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], these results advance the calculations of dissipative tunneling rates from first principles. [ABSTRACT FROM AUTHOR]

In this paper, we present a comprehensive account of quantum dissipation theories with the quadratic environment couplings. The theoretical development includes the Brownian solvation mode embedded hierarchical quantum master equations, a core-system hierarchy construction that verifies the extended dissipaton equation of motion (DEOM) formalism [R. X. Xu et al., J. Chem. Phys. 148, 114103 (2018)]. Developed are also the quadratic imaginary-time DEOM for equilibrium and the λ(t)-DEOM for nonequilibrium thermodynamics problems. Both the celebrated Jarzynski equality and Crooks relation are accurately reproduced, which, in turn, confirms the rigorousness of the extended DEOM theories. While the extended DEOM is more numerically efficient, the core-system hierarchy quantum master equation is favorable for "visualizing" the correlated solvation dynamics. [ABSTRACT FROM AUTHOR]

Over the last century, quantum theories have revolutionized our understanding of material properties. One of the most striking quantum phenomena occurring in heterogeneous media is the quantum tunneling effect, where carriers can tunnel through potential barriers even if the barrier height exceeds the carrier energy. Interestingly, the tunneling process can be accompanied by the absorption or emission of light. In most tunneling junctions made of noble metal electrodes, these optical phenomena are governed by plasmonic modes, i.e., light-driven collective oscillations of surface electrons. In the emission process, plasmon excitation via inelastic tunneling electrons can improve the efficiency of photon generation, resulting in bright nanoscale optical sources. On the other hand, the incident light can affect the tunneling behavior of plasmonic junctions as well, leading to phenomena such as optical rectification and induced photocurrent. Thus, plasmonic tunneling junctions provide a rich platform for investigating light–matter interactions, paving the way for various applications, including nanoscale light sources, sensors, and chemical reactors. In this paper, we will introduce recent research progress and promising applications based on plasmonic tunneling junctions. [ABSTRACT FROM AUTHOR]

Fewest-switches surface hopping (FSSH) has emerged as one of the leading methods for modeling the quantum dynamics of molecular systems. While its original formulation was limited to adiabatic populations, the growing interest in the application of FSSH to coherent phenomena prompts the question of how one should construct a complete density matrix based on FSSH trajectories. A straightforward solution is to define adiabatic coherences based on wavefunction coefficients. In this paper, we demonstrate that inconsistencies introduced in the density matrix through such treatment may lead to a violation of positivity. We furthermore show that a recently proposed coherent generalization of FSSH results in density matrices that satisfy positivity while yielding improved accuracy throughout much (but not all) of parameter space. [ABSTRACT FROM AUTHOR]

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ ‖ H ‖ | t | + ln (1 / ϵ) + ln (1 / δ) . Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields. [ABSTRACT FROM AUTHOR]

The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels that are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper, we study the approximate solution of the GQME, obtained by calculating the kernels with two methods: Ehrenfest mean-field theory and spin-mapping. We test the approaches on a range of spin–boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin-mapping outperforms Ehrenfest for all the systems studied. The problem of unphysical negative electronic populations affecting spin-mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite. [ABSTRACT FROM AUTHOR]

The generalized quantum master equation (GQME) provides a general and formally exact framework for simulating the reduced dynamics of open quantum systems. The recently introduced modified approach to the GQME (M-GQME) corresponds to a specific implementation of the GQME that is geared toward simulating the dynamics of the electronic reduced density matrix in systems governed by an excitonic Hamiltonian. Such a Hamiltonian, which is often used for describing energy and charge transfer dynamics in complex molecular systems, is given in terms of diabatic electronic states that are coupled to each other and correspond to different nuclear Hamiltonians. Within the M-GQME approach, the effect of the nuclear degrees of freedom on the time evolution of the electronic density matrix is fully captured by a memory kernel superoperator, which can be obtained from short-lived (compared to the time scale of energy/charge transfer) projection-free inputs. In this paper, we test the ability of the M-GQME to predict the energy transfer dynamics within a seven-state benchmark model of the Fenna–Matthews–Olson (FMO) complex, with the short-lived projection-free inputs obtained via the Ehrenfest method. The M-GQME with Ehrenfest-based inputs is shown to yield accurate results across a wide parameter range. It is also found to dramatically outperform the direct application of the Ehrenfest method and to provide better-behaved convergence with respect to memory time in comparison to an alternative implementation of the GQME approach previously applied to the same FMO model. [ABSTRACT FROM AUTHOR]

Exact nonadiabatic quantum evolution preserves many geometric properties of the molecular Hilbert space. In the first paper of this series ["Paper I," S. Choi and J. Vaníček, J. Chem. Phys. 150, 204112 (2019)], we presented numerical integrators of arbitrary-order of accuracy that preserve these geometric properties exactly even in the adiabatic representation, in which the molecular Hamiltonian is not separable into kinetic and potential terms. Here, we focus on the separable Hamiltonian in diabatic representation, where the split-operator algorithm provides a popular alternative because it is explicit and easy to implement, while preserving most geometric invariants. Whereas the standard version has only second-order accuracy, we implemented, in an automated fashion, its recursive symmetric compositions, using the same schemes as in Paper I, and obtained integrators of arbitrary even order that still preserve the geometric properties exactly. Because the automatically generated splitting coefficients are redundant, we reduce the computational cost by pruning these coefficients and lower memory requirements by identifying unique coefficients. The order of convergence and preservation of geometric properties are justified analytically and confirmed numerically on a one-dimensional two-surface model of NaI and a three-dimensional three-surface model of pyrazine. As for efficiency, we find that to reach a convergence error of 10−10, a 600-fold speedup in the case of NaI and a 900-fold speedup in the case of pyrazine are obtained with the higher-order compositions instead of the second-order split-operator algorithm. The pyrazine results suggest that the efficiency gain survives in higher dimensions. [ABSTRACT FROM AUTHOR]

Nuclear dynamics in the coupled electronic states of mono-, di-(ortho and meta), and pentafluorobenzene molecules is investigated here. Attempts are specifically made to understand the complexity and broadening of the recorded gas phase electronic absorption spectra of these molecules. Justification is also provided for the low quantum yield of fluorescence emission with increasing number of fluorine substitutions. The nuclear dynamics is simulated from first principles both by time-independent and time-dependent quantum mechanical methods. Potential energy surfaces of the low-lying excited electronic states of these molecules constructed in Paper I [Mondal and Mahapatra, J. Chem. Phys. 133, 084304 (2010)] are employed for the purpose. Theoretical results presented in this paper are compared with the available experimental data and the agreement between the two is found to be excellent. While structured electronic absorption bands are observed for the S1 state of mono- and difluorobenzene molecules, the same for the pentafluorobenzene is broad and structureless. Occurrence of S1-S2 conical intersections in pentafluorobenzene leads to a nonradiative internal conversion of the S1 state in ∼165 fs and contributes to the broadening of the S1←S0 absorption band and a biexponential decay of its fluorescence emission. [ABSTRACT FROM AUTHOR]

In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition, Ψ=Ψ1+Ψ2, was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ1 and Ψ2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Ψ itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well behaved, even when Ψ has many nodes or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step potential, and square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a companion paper [C. Trahan and B. Poirier, J. Chem. Phys. 124, 034116 (2006), following paper]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom. [ABSTRACT FROM AUTHOR]

In this paper, we discuss extending the sub-system embedding sub-algebra coupled cluster formalism and the double unitary coupled cluster (DUCC) ansatz to the time domain. An important part of the analysis is associated with proving the exactness of the DUCC ansatz based on the general many-body form of anti-Hermitian cluster operators defining external and internal excitations. Using these formalisms, it is possible to calculate the energy of the entire system as an eigenvalue of downfolded/effective Hamiltonian in the active space, which is identifiable with the sub-system of the composite system. It can also be shown that downfolded Hamiltonians integrate out Fermionic degrees of freedom that do not correspond to the physics encapsulated by the active space. In this paper, we extend these results to the time-dependent Schrödinger equation, showing that a similar construct is possible to partition a system into a sub-system that varies slowly in time and a remaining sub-system that corresponds to fast oscillations. This time-dependent formalism allows coupled cluster quantum dynamics to be extended to larger systems and for the formulation of novel quantum algorithms based on the quantum Lanczos approach, which has recently been considered in the literature. [ABSTRACT FROM AUTHOR]

In this paper, multidimensional dissipative quantum dynamics is studied within a system–bath approach in the Markovian regime using a model Lindblad operator. We report on the implementation of a Monte Carlo wave packet algorithm in the Heidelberg version of the Multi-Configuration Time-Dependent Hartree (MCTDH) program package, which is henceforth extended to treat stochastic dissipative dynamics. The Lindblad operator is represented as a sum of products of one-dimensional operators. The new form of the operator is not restricted to the MCTDH formalism and could be used with other multidimensional quantum dynamical methods. As a benchmark system, a two-dimensional coupled oscillators model representing the internal stretch and the surface–molecule distance in the O2/Pt(111) system coupled to a Markovian bath of electron–hole-pairs is used. The simulations reveal the interplay between coherent intramolecular coupling due to anharmonic terms in the potential and incoherent relaxation due to coupling to an environment. It is found that thermalization of the system can be approximately achieved when the intramolecular coupling is weak. [ABSTRACT FROM AUTHOR]

This work follows a companion article, which will be referred to as Paper I [Campeggio et al., J. Chem. Phys. 158, 244104 (2023)] in which a quantum-stochastic Liouville equation for the description of the quantum-classical dynamics of a molecule in a dissipative bath has been formulated in curvilinear internal coordinates. In such an approach, the coordinates of the system are separated into three subsets: the quantum coordinates, the classical relevant nuclear degrees of freedom, and the classical irrelevant (bath) coordinates. The equation has been derived in natural internal coordinates, which are bond lengths, bond angles, and dihedral angles. The resulting equation needs to be parameterized. In particular, one needs to compute the potential energy surfaces, the friction tensor, and the rate constants for the nonradiative jumps among the quantum states. While standard methods exist for the calculation of energy and dissipative properties, an efficient evaluation of the transition rates needs to be developed. In this paper, an approximated treatment is introduced, which leads to a simple explicit formula with a single adjustable parameter. Such an approximated expression is compared with the exact calculation of transition rates obtained via molecular dynamics simulations. To make such a comparison possible, a simple sandbox system has been used, with two quantum states and a single internal coordinate (together with its conjugate momentum). Results show that the adjustable parameter, which is an effective decoherence time, can be parameterized from the effective relaxation times of the autocorrelation functions of the conjugated momenta of the relevant nuclear coordinates., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

This paper reports the release of PathSum, a new software suite of state-of-the-art path integral methods for studying the dynamics of single or extended systems coupled to harmonic environments. The package includes two modules, suitable for system-bath problems and extended systems comprising many coupled system-bath units, and is offered in C++ and Fortran implementations. The system-bath module offers the recently developed small matrix path integral (SMatPI) and the well-established iterative quasi-adiabatic propagator path integral (i-QuAPI) method for iteration of the reduced density matrix of the system. In the SMatPI module, the dynamics within the entanglement interval can be computed using QuAPI, the blip sum, time evolving matrix product operators, or the quantum-classical path integral method. These methods have distinct convergence characteristics and their combination allows a user to access a variety of regimes. The extended system module provides the user with two algorithms of the modular path integral method, applicable to quantum spin chains or excitonic molecular aggregates. An overview of the methods and code structure is provided, along with guidance on method selection and representative examples., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Non-fullerene acceptor materials have posed new paradigms for the design of organic solar cells , whereby efficient carrier generation is obtained with small driving forces, in order to maximize the open-circuit voltage (VOC). In this paper, we use a coarse-grained mixed quantum–classical method, which combines Ehrenfest and Redfield theories, to shed light on the charge generation process in small energy offset interfaces. We have investigated the influence of the energetic driving force as well as the vibronic effects on the charge generation and photovoltaic energy conversion. By analyzing the effects of the Holstein and Peierls vibrational couplings, we find that vibrational couplings produce an overall effect of improving the charge generation. However, the two vibronic mechanisms play different roles: the Holstein relaxation mechanism decreases the charge generation, whereas the Peierls mechanism always assists the charge generation. Moreover, by examining the electron–hole binding energy as a function of time, we evince two distinct regimes for the charge separation: the temperature independent excitonic spread on a sub-100 fs timescale and the complete dissociation of the charge-transfer state that occurs on the timescale of tens to hundreds of picoseconds, depending on the temperature. The quantum dynamics of the system exhibits the three regimes of the Marcus electron transfer kinetics as the energy offset of the interface is varied. [ABSTRACT FROM AUTHOR]

The common basis sets constructed for use in electronic structure calculations have been found inadequate for the representation of electrons participating in nonadiabatic time-dependent dynamics calculations. In this paper we outline an approach to construct electronic bases better suited for dynamical processes such as energy deposition and charge transfer in binary collisions of ions, atoms, and molecules. Since electrons of many-atom systems commonly are represented by orbitals formed as linear combinations of atomic orbitals, the focus is on atomic basis sets. The main idea is to construct basis sets that adequately reproduce the first few excitation energies of neutral atoms. In this paper we outline a method for such basis set construction of various levels of accuracy for first-row atoms and give a few illustrative examples. [ABSTRACT FROM AUTHOR]

In a previous paper [J. Theo. Comput. Chem. 2, 65 (2003)], one of the authors (B.P.) presented a method for solving the multidimensional Schrödinger equation, using modified Wilson-Daubechies wavelets, and a simple phase space truncation scheme. Unprecedented numerical efficiency was achieved, enabling a ten-dimensional calculation of nearly 600 eigenvalues to be performed using direct matrix diagonalization techniques. In a second paper [J. Chem. Phys. 121, 1690 (2004)], and in this paper, we extend and elaborate upon the previous work in several important ways. The second paper focuses on construction and optimization of the wavelength functions, from theoretical and numerical viewpoints, and also examines their localization. This paper deals with their use in representations and eigenproblem calculations, which are extended to 15-dimensional systems. Even higher dimensionalities are possible using more sophisticated linear algebra techniques. This approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where differential equations are involved. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

By extending an earlier study [Gianturco et al., J. Chem. Phys. 154, 054311 (2021)] on the purely rotational excitation of HeH+ by He atoms, we report in this paper integral cross sections and rate coefficients for rovibrational excitation and de-excitation processes in HeH+ due to collisions with He. The data were obtained using a new ab initio potential energy surface that includes the vibrational degree of freedom. The results are compared with those computed using the earlier potential energy surface by Panda and Sathyamurthy [J. Phys. Chem. A 107, 7125 (2003)] that additionally accounts for the proton-exchange reaction between HeH+ and He. It is shown that the exchange channel contributes nearly as much as the inelastic channel to the vibrational excitation and de-excitation processes and that the total rate constants pertaining to the purely inelastic processes are largely of the same magnitude as those obtained when both inelastic and reactive channels are included in the dynamics. The inelastic rovibrational rate coefficients involving this astrophysical cation are also found to be much larger than those obtained for anions present in similar interstellar environments. [ABSTRACT FROM AUTHOR]

The multistate vibronic dynamics in the &Xtilde;²E[sub 1g]-&Etilde;²B[sub 2u] electronic states of the benzene radical cation is investigated theoretically by an ab initio quantum-dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from the previous Paper I. Vibronic line spectra are obtained with the Lanczos procedure. Extensive calculations on wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Up to five coupled electronic potential energy surfaces and 13 vibrational degrees of freedom have been included in these calculations. As a result, the impact of a third electronic state (&Xtilde; or &Btilde;) on a strongly coupled manifold (&Btidel;-&Ctilde; or &Dtilde;-&Etilde; states) is quantitatively assessed. It leads to a restructuring of the spectral envelope which is stronger for the &Btilde;-&Dtilde;-&Etilde; than for the &Xtilde;-&Btilde;-&Ctilde; system. The internal conversion dynamics is characterized by a stepwise transfer of electronic population to the lowest electronic state on a time scale of ∼100 fs, if the system is prepared initially on the highest potential energy surface. Companion calculations have also been performed for the case when the system is prepared in the intermediate state at t = 0; they show a branching of the electronic populations. These are all novel findings which are discussed in terms of a series of conical intersections between the various potential energy surfaces. The importance of such multistate vibronic interactions for the photophysics and photochemistry of medium-sized systems is pointed out. [ABSTRACT FROM AUTHOR]

Within the well-established optical response function formalism, a new strategy with the central idea of employing the forward-backward stochastic Schrödinger equations in a segmented way to accurately obtain the two-dimensional (2D) electronic spectrum is presented in this paper. Based on the simple excitonically coupled dimer model system, the validity and efficiency of the proposed schemes are demonstrated in detail, along with the comparison against the deterministic hierarchy equations of motion and perturbative second-order time-convolutionless quantum master equations. In addition, an important insight is provided in this paper that the characteristic frequency of the overdamped environment is an extremely crucial factor to regulate the lifetimes of the oscillating signals in 2D electronic spectra and of quantum coherence features of system dynamics. It is worth noting that the proposed scheme benefiting from its stochastic nature and wavefunction framework and many other advantages of substantially reducing the numerical cost has a great potential to systematically investigate various quantum effects observed in realistic large-scale natural and artificial photosynthetic systems. [ABSTRACT FROM AUTHOR]

For molecules with more than three atoms, it is difficult to fit or interpolate a potential energy surface (PES) from a small number of (usually ab initio) energies at points. Many methods have been proposed in recent decades, each claiming a set of advantages. Unfortunately, there are few comparative studies. In this paper, we compare neural networks (NNs) with Gaussian process (GP) regression. We re-fit an accurate PES of formaldehyde and compare PES errors on the entire point set used to solve the vibrational Schrödinger equation, i.e., the only error that matters in quantum dynamics calculations. We also compare the vibrational spectra computed on the underlying reference PES and the NN and GP potential surfaces. The NN and GP surfaces are constructed with exactly the same points, and the corresponding spectra are computed with the same points and the same basis. The GP fitting error is lower, and the GP spectrum is more accurate. The best NN fits to 625/1250/2500 symmetry unique potential energy points have global PES root mean square errors (RMSEs) of 6.53/2.54/0.86 cm−1, whereas the best GP surfaces have RMSE values of 3.87/1.13/0.62 cm−1, respectively. When fitting 625 symmetry unique points, the error in the first 100 vibrational levels is only 0.06 cm−1 with the best GP fit, whereas the spectrum on the best NN PES has an error of 0.22 cm−1, with respect to the spectrum computed on the reference PES. This error is reduced to about 0.01 cm−1 when fitting 2500 points with either the NN or GP. We also find that the GP surface produces a relatively accurate spectrum when obtained based on as few as 313 points. [ABSTRACT FROM AUTHOR]

An accurate system-bath model to investigate the quantum dynamics of hydrogen atoms chemisorbed on graphene is presented. The system comprises a hydrogen atom and the carbon atom from graphene that forms the covalent bond, and it is described by a previously developed 4D potential energy surface based on density functional theory ab initio data. The bath describes the rest of the carbon lattice and is obtained from an empirical force field through inversion of a classical equilibrium correlation function describing the hydrogen motion. By construction, model building easily accommodates improvements coming from the use of higher level electronic structure theory for the system. Further, it is well suited to a determination of the system-environment coupling by means of ab initio molecular dynamics. This paper details the system-bath modeling and shows its application to the quantum dynamics of vibrational relaxation of a chemisorbed hydrogen atom, which is here investigated at T = 0 K with the help of the multi-configuration time-dependent Hartree method. Paper II deals with the sticking dynamics. [ABSTRACT FROM AUTHOR]

The Direct Dynamics variational Multi-Configurational Gaussian (DD-vMCG) method provides a fully quantum mechanical solution to the time-dependent Schrödinger equation for the time evolution of nuclei with potential surfaces calculated on-the-fly using a quantum chemistry program. Initial studies have shown its potential for flexible and accurate simulations of non-adiabatic excited-state molecular dynamics. In this paper, we present developments to the DD-vMCG algorithm that improve both its accuracy and efficiency. First, a new, efficient parallel algorithm to control the DD-vMCG database of quantum chemistry points is presented along with improvements to the Shepard interpolation scheme. Second, the use of symmetry in describing the potential surfaces is introduced along with a new phase convention in the propagation diabatization. Benchmark calculations on the allene radical cation including all degrees of freedom then show that the new scheme is able to produce a consistent non-adiabatic coupling vector field. This new DD-vMCG version thus opens the route for effectively and accurately treating complex chemical systems using quantum dynamics simulations. [ABSTRACT FROM AUTHOR]

The concept of instantaneous normal modes in liquids is extended into the quantum regime using the Feynman path centroid perspective in quantum statistical mechanics. To accomplish this goal, the variational quadratic approximation for the effective centroid potential is recast in a general multidimensional phase space form. In the context of the effective quadratic approximation, the velocity autocorrelation functions of liquids can then be predicted based on a set of instantaneous quantum normal modes. Representative applications are presented for quantum Lennard-Jones liquids and a quantum particle solvated in a classical fluid. The quantum effective phonon spectrum leads to some revealing observations and interpretations for these systems. [ABSTRACT FROM AUTHOR]

In this paper we report new developments in the expansion and partial resummation of the evolution operator. Higher order resummations allow derivation of an effective one-dimensional potential which accurately represents quantum dynamics for even strongly coupled low-frequency modes. This allows a system bath approximation which can accurately reproduce multidimensional quantum mechanics. In addition the formulation presented in this paper should prove significantly easier to extend to many-body problems than previous formulations we have derived. The accuracy of the method for even highly nonadiabatic applications, and the ease of implementation suggests that this approach will be useful in the calculation of the quantum dynamics of many dimensional systems. [ABSTRACT FROM AUTHOR]

In this paper we report a new method for resummation of operator expansions of the evolution operator. These resummation techniques are applied to the Feynman propagator and then to the derivation of an effective Schrödinger equation for general system–bath problems. This paper presents a significant advance over work previously reported by us [J. Chem. Phys. 96, 5952 (1992)], and it provides a highly accurate way to calculate quantum mechanical data for many dimensional systems. We then apply this new analytic resummation technique to the calculation of flux–flux correlation functions for two, three, and four dimensional problems in order to study the range of applicability of the approach. For moderate frequencies and coupling strengths, not only is the resummed operator calculational method essentially exact, it also requires a fraction of the computer time that the exact calculation consumes. For truly many dimensional problems this approach should provide the first accurate quantum mechanics of rate processes. [ABSTRACT FROM AUTHOR]

Canonical Coherent States (CSs) of Harmonic Oscillator have been extensively used as a basis in a number of computational methods of quantum dynamics. However, generalising such techniques for fermionic systems is difficult because Fermionic Coherent States (FCSs) require complicated algebra of Grassmann numbers not well suited for numerical calculations. This paper introduces a coherent antisymmetrised superposition of “dead” and “alive” electronic states called here Zombie State (ZS), which can be used in a manner of FCSs but without Grassmann algebra. Instead, for Zombie States, a very simple sign-changing rule is used in the definition of creation and annihilation operators. Then, calculation of electronic structure Hamiltonian matrix elements between two ZSs becomes very simple and a straightforward technique for time propagation of fermionic wave functions can be developed. By analogy with the existing methods based on Canonical Coherent States of Harmonic Oscillator, fermionic wave functions can be propagated using a set of randomly selected Zombie States as a basis. As a proof of principles, the proposed Coupled Zombie States approach is tested on a simple example showing that the technique is exact. [ABSTRACT FROM AUTHOR]

We use one-electron non-adiabatic mixed quantum/classical simulations to explore the temperature dependence of both the ground-state structure and the excited-state relaxation dynamics of the hydrated electron. We compare the results for both the traditional cavity picture and a more recent non-cavity model of the hydrated electron and make definite predictions for distinguishing between the different possible structural models in future experiments. We find that the traditional cavity model shows no temperature-dependent change in structure at constant density, leading to a predicted resonance Raman spectrum that is essentially temperature-independent. In contrast, the non-cavity model predicts a blue-shift in the hydrated electron's resonance Raman O-H stretch with increasing temperature. The lack of a temperature-dependent ground-state structural change of the cavity model also leads to a prediction of little change with temperature of both the excited-state lifetime and hot groundstate cooling time of the hydrated electron following photoexcitation. This is in sharp contrast to the predictions of the non-cavity model, where both the excited-state lifetime and hot ground-state cooling time are expected to decrease significantly with increasing temperature. These simulationbased predictions should be directly testable by the results of future time-resolved photoelectron spectroscopy experiments. Finally, the temperature-dependent differences in predicted excited-state lifetime and hot ground-state cooling time of the two models also lead to different predicted pumpprobe transient absorption spectroscopy of the hydrated electron as a function of temperature. We perform such experiments and describe them in Paper II [E. P. Farr et al., J. Chem. Phys. 147, 074504 (2017)], and find changes in the excited-state lifetime and hot ground-state cooling time with temperature that match well with the predictions of the non-cavity model. In particular, the experiments reveal stimulated emission from the excited state with an amplitude and lifetime that decreases with increasing temperature, a result in contrast to the lack of stimulated emission predicted by the cavity model but in good agreement with the non-cavity model. Overall, until ab initio calculations describing the non-adiabatic excited-state dynamics of an excess electron with hundreds of water molecules at a variety of temperatures become computationally feasible, the simulations presented here provide a definitive route for connecting the predictions of cavity and non-cavity models of the hydrated electron with future experiments. [ABSTRACT FROM AUTHOR]

The hierarchical equations of motion (HEOMs) have developed into an important tool in simulating quantum dynamics in condensed phases. Yet, it has recently been found that the HEOM may become numerically unstable in simulations using discrete harmonic oscillator modes [I. S. Dunn, et al., J. Chem. Phys. 150, 184109 (2019)]. In this paper, a new set of equations of motion are obtained based on the equivalence between the HEOM for discrete harmonic oscillator modes and the mixed quantum-classical Liouville equation. The new set of equations can thus be regarded as the expansion of the same phase space partial differential equation using different basis sets. It is shown that they have similar structures as the original HEOM but are free from the problem of numerical instability. The new set of equations are also incorporated into the matrix product state method, where it is found that the trace of the reduced density operator is not well conserved during the propagation. A modified time-dependent variational principle is then proposed to achieve better trace conservation. [ABSTRACT FROM AUTHOR]

In this paper, we present the theory and implementation of nuclear magnetic resonance shielding constants with gauge-including atomic orbitals for the hybrid multiconfigurational short-range density functional theory model. As a special case, this implementation also includes Hartree-Fock srDFT (HF-srDFT). Choosing a complete-active space (CAS) wave function as the multiconfigurational parameterization of the wave function, we investigate how well CAS-srDFT reproduces experimental trends of nuclear shielding constants compared to DFT and complete active space self-consistent field (CASSCF). Calculations on the nucleobases adenine and thymine show that CAS-srDFT performs on average the best of the tested methods, much better than CASSCF but only marginally better than HF-srDFT. The performance, compared to regular DFT, is similar when functionals containing exact exchange are used. We generally find that the inclusion of exact exchange is important for an accurate description of the shielding constants. In cases where no exact exchange is included, we observe that the HF- and CAS-srDFT often outperform regular DFT. For calculations on transition metal nuclei in organometallic compounds with significant static correlation, the CAS-srDFT method again outperforms CASSCF compared to experimental shielding constants, and the change from HF-srDFT is substantial. In conclusion, the static correlation posed by the metal complexes seems to be captured by CAS-srDFT, which is promising since this type of correlation is not well described by regular DFT.

In this second paper of a two part series, we present extensive benchmark results for two different inchworm Monte Carlo expansions for the spin-boson model. Our results are compared to previously developed numerically exact approaches for this problem. A detailed discussion of convergence and error propagation is presented. Our results and analysis allow for an understanding of the benefits and drawbacks of inchworm Monte Carlo compared to other approaches for exact real-time non-adiabatic quantum dynamics. [ABSTRACT FROM AUTHOR]

Line mixing effects have been calculated in the ν1 parallel band of self-broadened NH3. The theoretical approach is an extension of a semi-classical model to symmetric-top molecules with inversion symmetry developed in the companion paper [Q. Ma and C. Boulet, J. Chem. Phys. 144, 224303 (2016)]. This model takes into account line coupling effects and hence enables the calculation of the entire relaxation matrix. A detailed analysis of the various coupling mechanisms is carried out for Q and R inversion doublets. The model has been applied to the calculation of the shape of the Q branch and of some R manifolds for which an obvious signature of line mixing effects has been experimentally demonstrated. Comparisons with measurements show that the present formalism leads to an accurate prediction of the available experimental line shapes. Discrepancies between the experimental and theoretical sets of first order mixing parameters are discussed as well as some extensions of both theory and experiment. [ABSTRACT FROM AUTHOR]

In open quantum system dynamics, rich information about the major energy relaxation channels and corresponding relaxation rates can be elucidated by monitoring the vibrational energy flow among individual bath modes. However, such calculations often become tremendously difficult as the complexity of the subsystem–bath coupling increases. In this paper, we attempt to make this task feasible by using a mixed quantum–classical method, the Poisson-bracket mapping equation with non-Hamiltonian modification (PBME-nH) [H. W. Kim and Y. M. Rhee, J. Chem. Phys. 140, 184106 (2014)]. For a quantum subsystem bilinearly coupled to harmonic bath modes, we derive an expression for the mode energy in terms of the classical positions and momenta of the nuclei, while keeping consistency with the energy of the quantum subsystem. The accuracy of the resulting expression is then benchmarked against a numerically exact method by using relatively simple models. Although our expression predicts a qualitatively correct dissipation rate for a range of situations, cases involving a strong vibronic resonance are quite challenging. This is attributed to the inherent lack of quantum back reaction in PBME-nH, which becomes significant when the subsystem strongly interacts with a small number of bath modes. A rigorous treatment of such an effect will be crucial for developing quantitative simulation methods that can handle generic subsystem–bath coupling. [ABSTRACT FROM AUTHOR]

We show two more approaches for generating trajectory-based dynamics in the phase space formulation of quantum mechanics: 'equilibrium continuity dynamics' (ECD) in the spirit of the phase space continuity equation in classical mechanics, and 'equilibrium Hamiltonian dynamics' (EHD) in the spirit of the Hamilton equations of motion in classical mechanics. Both ECD and EHD can recover exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Both ECD and EHD conserve the quasi-probability within the infinitesimal volume dxtdpt around the phase point (xt, pt) along the trajectory. Numerical tests of both approaches in the Wigner phase space have been made for two strongly anharmonic model problems and a double well system, for each potential auto-correlation functions of both linear and nonlinear operators have been calculated. The results suggest EHD and ECD are two additional potential useful approaches for describing quantum effects for complex systems in condense phase. [ABSTRACT FROM AUTHOR]

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase. [ABSTRACT FROM AUTHOR]

The non-Markovian approach developed in the companion paper [Hughes et al., J. Chem. Phys. 131, 024109 (2009)], which employs a hierarchical series of approximate spectral densities, is extended to the treatment of nonadiabatic dynamics of coupled electronic states. We focus on a spin-boson-type Hamiltonian including a subset of system vibrational modes which are treated without any approximation, while a set of bath modes is transformed to a chain of effective modes and treated in a reduced-dimensional space. Only the first member of the chain is coupled to the electronic subsystem. The chain construction can be truncated at successive orders and is terminated by a Markovian closure acting on the end of the chain. From this Mori-type construction, a hierarchy of approximate spectral densities is obtained which approach the true bath spectral density with increasing accuracy. Applications are presented for the dynamics of a vibronic subsystem comprising a high-frequency mode and interacting with a low-frequency bath. The bath is shown to have a striking effect on the nonadiabatic dynamics, which can be rationalized in the effective-mode picture. A reduced two-dimensional subspace is constructed which accounts for the essential features of the nonadiabatic process induced by the effective environmental mode. Electronic coherence is found to be preserved on the shortest time scale determined by the effective mode, while decoherence sets in on a longer time scale. Numerical simulations are carried out using either an explicit wave function representation of the system and overall bath or else an explicit representation of the system and effective-mode part in conjunction with a Caldeira–Leggett master equation. [ABSTRACT FROM AUTHOR]

The observation of long-lived electronic coherence in photosynthetic excitation energy transfer (EET) by Engel et al. [Nature (London) 446, 782 (2007)] raises questions about the role of the protein environment in protecting this coherence and the significance of the quantum coherence in light harvesting efficiency. In this paper we explore the applicability of the Redfield equation in its full form, in the secular approximation and with neglect of the imaginary part of the relaxation terms for the study of these phenomena. We find that none of the methods can give a reliable picture of the role of the environment in photosynthetic EET. In particular the popular secular approximation (or the corresponding Lindblad equation) produces anomalous behavior in the incoherent transfer region leading to overestimation of the contribution of environment-assisted transfer. The full Redfield expression on the other hand produces environment-independent dynamics in the large reorganization energy region. A companion paper presents an improved approach, which corrects these deficiencies [A. Ishizaki and G. R. Fleming, J. Chem. Phys. 130, 234111 (2009)]. [ABSTRACT FROM AUTHOR]

In previous articles [J. Chem. Phys. 121, 4501 (2004); J. Chem. Phys. 124, 034115 (2006); J. Chem. Phys. 124, 034116 (2006); J. Phys. Chem. A 111, 10400 (2007); J. Chem. Phys. 128, 164115 (2008)] an exact quantum, bipolar wave decomposition, ψ=ψ++ψ-, was presented for one-dimensional stationary state and time-dependent wavepacket dynamics calculations, such that the components ψ± approach their semiclassical WKB analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well behaved, even when ψ has many nodes or is wildly oscillatory. In this paper, both the stationary state and wavepacket dynamics theories are generalized for multidimensional systems and applied to several benchmark problems, including collinear H+H2. [ABSTRACT FROM AUTHOR]

The multistate vibronic dynamics in the X-D electronic states of all three difluorobenzene radical cations are investigated theoretically by an ab initio quantum dynamical approach. The vibronic coupling scheme and the ab initio values of the system parameters are adopted from Paper I [S. Faraji and H. Köppel, J. Chem. Phys. 129, 074310 (2008)]. Extensive calculations by wave-packet propagation have been performed with the aid of the multiconfiguration time-dependent Hartree method. Five coupled electronic potential energy surfaces and 10 (11 in the case of the orthoisomer) vibrational degrees of freedom have been included in these calculations. The nonadiabatic interactions lead to the restructuring of the photoelectron spectral envelopes. Ultrafast internal conversion processes within the electronic manifolds in question demonstrate the strength of the nonadiabatic coupling effects and complement the analogous findings for the electronic spectra. The internal conversion dynamics is characterized by a stepwise transfer of the electronic population to the lowest electronic state on a time scale of femtoseconds to picoseconds. A difference between the three isomers is found to be related to the weaker interaction between the sets of X-Ã and B-C-D states (with high-energy conical intersections) in the meta isomer, as compared to the other isomers. The implications of these findings for the qualitative understanding of the fluorescence dynamics of fluorinated benzene radical cations are discussed. [ABSTRACT FROM AUTHOR]

In this paper, quantum fluctuations of a carbonyl sulfide molecule in helium-4 clusters are studied as a function of cluster size N in a small-to-large size regime (2≤=N≤=64). The molecular rotation of the dopant shows nonmonotonic size dependence in the range of 10≤=N≤=20, reflecting the density distribution of the helium atoms around the molecule. The size dependence on the rotational constant shows a plateau for N>=20, which is larger than the experimental nanodroplet value. Superfluid response of the doped cluster is found to show remarkable anisotropy especially for N≤=20. The superfluid fraction regarding the axis perpendicular to the molecular axis shows a steep increase at N=10, giving the significant enhancement of the rotational fluctuation of the molecule. On the other hand, the superfluid fraction regarding the axis parallel to the molecular axis reaches 0.9 at N=5, arising from the bosonic exchange cycles of the helium atoms around the molecular axis. The anisotropy in the superfluid response is found to be the direct consequence of the configurations of the bosonic exchange cycles. [ABSTRACT FROM AUTHOR]

We have recently reported a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization [M. P. de Miranda and F. Javier Aoiz, Phys. Rev. Lett. 93, 083201 (2004)]. This paper presents a detailed account of the derivation outlined in that paper, and discusses the implications of the new results. These include (i) a new expression of the role of the uncertainty principle in the broadening of angular momentum distributions, (ii) the attribution of azimuthal fluctuations of angular momentum distributions to spatial quantum beats, (iii) the definition of a new Fourier transform of the density matrix, distinct from those suggested in the past, that provides an alternative view of how the quantum description of angular momentum polarization approaches the classical one in the correspondence principle limit, (iv) a prescription for the determination of a quasiclassical angular momentum distribution function that does not suffer from problems encountered with its purely classical counterpart, and (v) a description of how angular momentum distributions commonly visualized with recourse to the classical vector model can be depicted with exact and well-defined quantum mechanics.© 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Accurate calculation of the energies and widths of the resonances of HOCl—an important intermediate in the O(1D)HCl reactive system—poses a challenging benchmark for computational methods. The need for very large direct product basis sets, combined with an extremely high density of states, results in difficult convergence for iterative methods. A recent calculation of the highly excited OH stretch mode resonances using the filter diagonalization method, for example, required 462 000 basis functions, and 180 000 iterations. In contrast, using a combination of new methods, we are able to compute the same resonance states to higher accuracy with a basis less than half the size, using only a few hundred iterations—although the CPU cost per iteration is substantially greater. Similar performance enhancements are observed for calculations of the high-lying bound states, as reported in a previous paper [J. Theo. Comput. Chem. 2, 583 (2003)]. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In this paper, we extend and elaborate upon a wavelet method first presented in a previous publication [B. Poirier, J. Theo. Comput. Chem. 2, 65 (2003)]. In particular, we focus on construction and optimization of the wavelet functions, from theoretical and numerical viewpoints, and also examine their localization properties. The wavelets used are modified Wilson-Daubechies wavelets, which in conjunction with a simple phase space truncation scheme, enable one to solve the multidimensional Schrödinger equation. This approach is ideally suited to rovibrational spectroscopy applications, but can be used in any context where differential equations are involved. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

For a model of the B850 band in the light harvesting complex 2 of purple bacteria, the main quantum mechanical characteristics of the single complex line shapes are studied based on the theory of the preceding paper. The model consists of single exciton states coupled to harmonic oscillator bath, with the inclusion of both static and quasistatic disorder within the exciton Hamiltonian. A closed form line shape expression is derived that can account for the non-Markovian nature of the bath for a general spectral density. The calculation of the line shape only requires the inversion of a small matrix with dimension equal to the number of exciton levels, at each frequency. For two examples of site energy modulation with definite symmetries, we examine the dependencies of the line shape on the polarization of the radiation, on the type of exciton-bath coupling, and on temperature. For a plausible example of disorder, we simulate the line shapes of the ensemble and single complex spectroscopies. Simulation of single complex line shapes suggests that the quasistatic disorder is responsible for large spectral jumps (spectral diffusion) of the lowest exciton state and make the widths of the two brightest peaks comparable. [ABSTRACT FROM AUTHOR]

The multistate vibronic interactions in the benzene radical cation are investigated theoretically, employing the framework of a linear vibronic coupling scheme. The five lowest electronic states are included in the treatment; in view of the degeneracy of some states, this amounts to eight coupled potential energy surfaces. Different types of ab initio calculations have been performed for the system parameters and been found to be in good mutual agreement, thus supporting each other. The calculations reveal a whole sequence of low-energy conical intersections between the potential energy surfaces of different states. Their importance for the nuclear dynamics in this prototypical organic radical cation is pointed out. Wave-packet dynamical simulations for these coupled potential energy surfaces will be presented in the following paper (Paper II). [ABSTRACT FROM AUTHOR]

This paper extends work previously presented [J. Chem. Phys. 113, 2648 (2000)] to establish a rigorous expression for the angular momentum resolved microcanonical reactive flux. A kinetic energy expression in terms of the angular momentum, based on the coordinate system described in the above reference, is derived. Analytic integration over momenta conjugate to the coordinates that describe the relative orientation of the fragments is effected at the canonical level. The Laplace transform relation between canonical and microcanonical coefficients is then exploited to yield the angular momentum dependent microcanonical reactive flux. Evaluation of the resulting rate expression involves a numerical integral whose dimension, in most cases, is the same as the integrals in corresponding canonical and standard microcanonical forms. [ABSTRACT FROM AUTHOR]

We report quantum-mechanical calculations on the formation of aligned rotational wave packets in the ground state of I[sub 2], following the excitation of a rotationally cold sample of molecules with an intense picosecond laser pulse. Using these calculations, we have studied (1) the dynamic alignment during or shortly after the intense pump pulse, (2) the alignment at characteristic revival times following the laser excitation, and (3) the alignment between the revivals, as a function of the laser-pulse duration and peak intensity and the initial rotational temperature of the molecular beam. We conclude that the alignment at a revival is maximum for intermediate pulse durations (∼3 ps for I[sub 2]) that are long enough to get efficient population transfer out of the initially populated state, yet short enough for the interaction to remain partially diabatic and partially adiabatic. The alignment at the revivals increases with laser intensity, although the time-dependent structure of the revivals becomes increasingly complicated as the laser intensity is increased, and the maximum degree of alignment that is obtained is eventually limited by the initial rotational temperature of the molecular beam. The findings in this paper qualitatively agree with experimental results on short-pulse laser-induced alignment that were presented in our experimental article (preceding paper). © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The self-consistent quantum mode-coupling theory developed in the preceding paper [J. Chem. Phys. 116, 6271 (2002)] is applied to the study of density fluctuations and transport in liquid para-hydrogen. The method combines exact static input generated by a path-integral Monte Carlo method, and an approximate form of the quantum memory function, for the solution of the exact quantum generalized Langevin equation under consideration. The approach provides exact results for any correlation function at short times, and is expected to provide accurate results at long times. The quantum mode-coupling theory is compared with experimental observations for a variety of dynamical correlations in liquid para-hydrogen. We find that the quantum mode-coupling theory provides quantitative agreement with experiments. Improvement of the methodology and future applications are discussed. [ABSTRACT FROM AUTHOR]

A generalized Frenkel–Holstein Hamiltonian is constructed to describe exciton migration in oligo(para-phenylene vinylene) chains, based on excited state electronic structure data for an oligomer comprising 20 monomer units (OPV-20). Time-dependent density functional theory calculations using the ωB97XD hybrid functional are employed in conjunction with a transition density analysis to study the low-lying singlet excitations and demonstrate that these can be characterized to a good approximation as a Frenkel exciton manifold. Based on these findings, we employ the analytic mapping procedure of Binder et al. [J. Chem. Phys. 141, 014101 (2014)] to translate one-dimensional (1D) and two-dimensional (2D) potential energy surface (PES) scans to a fully anharmonic, generalized Frenkel–Holstein (FH) Hamiltonian. A 1D PES scan is carried out for intra-ring quinoid distortion modes, while 2D PES scans are performed for the anharmonically coupled inter-monomer torsional and vinylene bridge bond length alternation modes. The kinetic energy is constructed in curvilinear coordinates by an exact numerical procedure, using the TNUM Fortran code. As a result, a fully molecular-based, generalized FH Hamiltonian is obtained, which is subsequently employed for quantum exciton dynamics simulations, as shown in Paper II [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)]. [ABSTRACT FROM AUTHOR]

This paper provides a detailed account of the numerical implementation of the stochastic equation of motion (SEOM) method for the dissipative dynamics of fermionic open quantum systems. To enable direct stochastic calculations, a minimal auxiliary space (MAS) mapping scheme is adopted, with which the time-dependent Grassmann fields are represented by c-number noises and a set of pseudo-operators. We elaborate on the construction of the system operators and pseudo-operators involved in the MAS-SEOM, along with the analytic expression for the particle current. The MAS-SEOM is applied to study the relaxation and voltage-driven dynamics of quantum impurity systems described by the single-level Anderson impurity model, and the numerical results are benchmarked against those of the highly accurate hierarchical equations of motion method. The advantages and limitations of the present MAS-SEOM approach are discussed extensively. [ABSTRACT FROM AUTHOR]

The time dependent density matrix renormalization group (TD-DMRG) has become one of the cutting edge methods of quantum dynamics for complex systems. In this paper, we comparatively study the accuracy of three time evolution schemes in the TD-DMRG, the global propagation and compression method with the Runge-Kutta algorithm (P&C-RK), the time dependent variational principle based methods with the matrix unfolding algorithm (TDVP-MU), and with the projector-splitting algorithm (TDVP-PS), by performing benchmarks on the exciton dynamics of the Fenna-Matthews-Olson complex. We show that TDVP-MU and TDVP-PS yield the same result when the time step size is converged and they are more accurate than P&C-RK4, while TDVP-PS tolerates a larger time step size than TDVP-MU. We further adopt the graphical processing units to accelerate the heavy tensor contractions in the TD-DMRG, and it is able to speed up the TDVP-MU and TDVP-PS schemes by up to 73 times. [ABSTRACT FROM AUTHOR]

The Wigner thermal density is a function of considerable interest in the area of approximate (linearized or semiclassical) quantum dynamics where it is employed to generate initial conditions for the propagation of appropriate sets of classical trajectories. In this paper, we propose an original approach to compute the Wigner density based on a generalized Langevin equation. The stochastic dynamics is nontrivial in that it contains a coordinate-dependent friction coefficient and a generalized force that couples momenta and coordinates. These quantities are, in general, not known analytically and have to be estimated via auxiliary calculations. The performance of the new sampling scheme is tested on standard model systems with highly nonclassical features such as relevant zero point energy effects, correlation between momenta and coordinates, and negative parts of the Wigner density. In its current brute force implementation, the algorithm, whose convergence can be systematically checked, is accurate and has only limited overhead compared to schemes with similar characteristics. We briefly discuss potential ways to further improve its numerical efficiency. [ABSTRACT FROM AUTHOR]

Previously, we introduced two versions of the Multiconfigurational Ehrenfest (MCE) approach to high dimensional quantum dynamics. It has been shown that the first version, MCEv1, converges well to the existing benchmarks for high dimensional model systems. At the same time, it was found that the second version, MCEv2, had more difficulty converging in some regimes. As MCEv2 is particularly suited for direct dynamics, it is important to facilitate its convergence. This paper investigates an efficient method of basis set sampling, called Quantum Superposition Sampling (QSS), which dramatically improves the performance of the MCEv2 approach. QSS is tested on the spin-boson model, often used for modeling of open quantum systems. It is also shown that the quantum subsystem in the spin-boson model can be conveniently treated with the help of two level system coherent states. Generalized coherent states, which combine two level system coherent states for the description of the system and Gaussian coherent states for description of the bath, are introduced. Various forms of quantum equations of motion in the basis of generalized coherent states can be developed by analogy with known quantum dynamics equations in the basis of Gaussian coherent states; in particular, the multiconfigurational Ehrenfest method becomes a version of coupled generalized coherent states, and QSS can then be viewed as a generalization of a sampling method known for the existing coupled coherent states method which uses Gaussian coherent states. [ABSTRACT FROM AUTHOR]

A recent paper of ours compared an analytical, liquid-theory-based set of predictions for electronic band structure in liquids with the results of explicit computer simulation. In the interim, we discovered both an error in one of the figures from this paper and some new ways of using solid-state physics perspectives to remove finite-size simulation artifacts. The results that one obtains after correcting the error, and after applying the new lessons, demonstrate that the liquid-theory predictions are even more accurate than our previous work had indicated, especially for p bands. [ABSTRACT FROM AUTHOR]

This paper reports further applications of the recently developed interaction representation form of infinite order operator corrections to adiabatic evolution operators. Previous work derived the form of the correction, and applied the methodology to a bilinearly coupled system bath model. In this paper we present results on coupled quantum systems in which the coupling is highly nonlinear. The method is both easy to implement and numerically accurate. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The use of a discrete variable representation (DVR) and absorbing boundary conditions (ABC) to construct the outgoing Green’s function G(E+)≡limε→0(E+iε-H)-1, and its subsequent use to determine the cumulative reaction probability for a chemical reaction, has been extended beyond our previous work [J. Chem. Phys. 96, 4412 (1992)] in several significant ways. In particular, the present paper gives a more thorough derivation and analysis of the DVR-ABC approach, shows how the same DVR-ABC Green’s function can be used to obtain state-to-state (as well as cumulative) reaction probabilities, derives a DVR for the exact, multidimensional Watson Hamiltonian (referenced to a transition state), and presents illustrative calculations for the three-dimensional H+H2 reaction with zero total angular momentum. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to quantum evolution in the presence of a quantum bath. We develop an equation of motion for an observed system evolving under the influence of an unobserved quantum bath. The methodology we follow uses operator expansions of the Feynman propagator. Corrections to the zeroth order approximation are corrections to an adiabatic approximation. In this paper we explicitly develop an approximation which is infinite order in bath and system coupling, but first order in system degree of freedom. This infinite order approximation is found through a resummation of an infinite class of terms in the operator expansion. We first present a simplified single time (Markovian) version of the theory. We then present a derivation for including the effects of memory. The approach developed in this paper also has the potential for systematic improvement. In other words, while the bath and system coupling in this calculation is treated to infinite order, the system itself is only treated to first order. We will briefly discuss how these higher order corrections can be found. Finally, we present a test calculation of the our approach with comparison to exact results. For a two-dimensional test problem with potential much like that for collinear H+H2 the effective one-dimensional approximation we apply produces essentially exact results. [ABSTRACT FROM AUTHOR]

A recently formulated density corrected quantum Boltzmann equation emphasizes the need to explicitly include pair correlations and the conversion of kinetic energy to potential energy as important effects in the kinetic theory of moderately dense gases. This paper first considers an appropriate evolution equation for the pair correlations which includes their decay via interactions with other particles in the gas. The molecular description is given of such a gas close to local thermal equilibrium, together with expressions for the associated hydrodynamic variables. Wigner functions are used to uniquely separate macroscopic and microscopic properties. An accompanying paper solves the combination of linearized Boltzmann and correlated pair equations to obtain expressions for the transport coefficients. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Geometric integrators of the Schrödinger equation conserve exactly many invariants of the exact solution. Among these integrators, the split-operator algorithm is explicit and easy to implement but, unfortunately, is restricted to systems whose Hamiltonian is separable into kinetic and potential terms. Here, we describe several implicit geometric integrators applicable to both separable and nonseparable Hamiltonians and, in particular, to the nonadiabatic molecular Hamiltonian in the adiabatic representation. These integrators combine the dynamic Fourier method with the recursive symmetric composition of the trapezoidal rule or implicit midpoint method, which results in an arbitrary order of accuracy in the time step. Moreover, these integrators are exactly unitary, symplectic, symmetric, time-reversible, and stable and, in contrast to the split-operator algorithm, conserve energy exactly, regardless of the accuracy of the solution. The order of convergence and conservation of geometric properties are proven analytically and demonstrated numerically on a two-surface NaI model in the adiabatic representation. Although each step of the higher order integrators is more costly, these algorithms become the most efficient ones if higher accuracy is desired; a thousand-fold speedup compared to the second-order trapezoidal rule (the Crank-Nicolson method) was observed for a wavefunction convergence error of 10−10. In a companion paper [J. Roulet, S. Choi, and J. Vaníček, J. Chem. Phys. 150, 204113 (2019)], we discuss analogous, arbitrary-order compositions of the split-operator algorithm and apply both types of geometric integrators to a higher-dimensional system in the diabatic representation. [ABSTRACT FROM AUTHOR]

Magnetic field effects on radical pair reactions arise due to the interplay of coherent electron spin dynamics and spin relaxation effects, a rigorous treatment of which requires the solution of the Liouville-von Neumann equation. However, it is often found that simple incoherent kinetic models of the radical pair singlet-triplet intersystem crossing provide an acceptable description of experimental measurements. In this paper, we outline the theoretical basis for this incoherent kinetic description, elucidating its connection to exact quantum mechanics. We show, in particular, how the finite lifetime of the radical pair spin states, as well as any additional spin-state dephasing, leads to incoherent intersystem crossing. We arrive at simple expressions for the radical pair spin state interconversion rates to which the functional form proposed recently by Steiner et al. [J. Phys. Chem. C 122, 11701 (2018)] can be regarded as an approximation. We also test the kinetic master equation against exact quantum dynamical simulations for a model radical pair and for a series of PTZ•+–Phn–PDI•− molecular wires. [ABSTRACT FROM AUTHOR]

The molecular dynamics following the electronic B Π u 3 0 + ⟵ X Σ g + 1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I2Kr18 cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I2 energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < RI–I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I2-krypton system addressed in Paper II. [ABSTRACT FROM AUTHOR]

In a recent communication [N. Makri, J. Chem. Phys. 148, 101101 (2018)], it was shown that the locality of interactions in many systems of interest allows a decomposition of the path integral and its evaluation via sequential linking of the paths of relatively small "modules" (e.g., chemical groups or monomers). The present paper describes the modular path integral methodology for simulating dynamical properties by propagating the density matrix in real time. The procedure is first presented for the simple topology of a single-file arrangement of units interacting via nearest neighbor couplings and subsequently extended to the calculation of two-particle correlations in arrays that may also contain some long-range interactions, to the treatment of systems with side chains or cyclic structures, to the simulation of internal dynamics in long organic molecules, and to the modifications required for coupling of one or several units of a system to dissipative environments. Illustrative applications to the dynamics of interacting two-level-systems are presented. [ABSTRACT FROM AUTHOR]

The role of vibrational excitation of reactants in driving reactions involving polyatomic species has been often studied by means of classical or quasi-classical trajectory simulations. We propose a different approach based on investigation of vibrational features of the Cl−⋯CH3Cl pre-reaction complex for the Cl− + CH3Cl SN2 reaction. We present vibrational power spectra and frequency estimates for the title pre-reaction complex calculated at the level of classical, semiclassical, and second-order vibrational perturbation theory on a pre-existing analytical potential energy surface. The main goals of the paper are the study of anharmonic effects and understanding of vibrational couplings that permit energy transfer between the collisional kinetic energy and the internal vibrations of the reactants. We provide both classical and quantum pictures of intermode couplings and show that the SN2 mechanism is favored by the coupling of a C–Cl bend involving the Cl− projectile with the CH3 rocking motion of the target molecule. We also illustrate how the routines needed for semiclassical vibrational spectroscopy simulations can be interfaced in a user-friendly way to pre-existing molecular dynamics software. In particular, we present an implementation of semiclassical spectroscopy into the VENUS suite of codes, thus providing a useful computational tool for users who are not experts of semiclassical dynamics. [ABSTRACT FROM AUTHOR]

Advances in experimental methodology aligned with technological developments, such as 3rd generation light sources, X-ray Free Electron Lasers, and High Harmonic Generation, have led to a paradigm shift in the capability of X-ray spectroscopy to deliver high temporal and spectral resolution on an extremely broad range of samples in a wide array of different environments. Importantly, the complex nature and high information content of this class of techniques mean that detailed theoretical studies are often essential to provide a firm link between the spectroscopic observables and the underlying molecular structure and dynamics. In this paper, we present approaches for simulating dynamical processes in X-ray spectroscopy based upon on-the-fly quantum dynamics with a Gaussian basis set. We show that it is possible to provide a fully quantum description of X-ray spectra without the need of precomputing highly multidimensional potential energy surfaces. It is applied to study two different dynamical situations, namely, the core-hole lifetime dynamics of the water monomer and the dissociation of C F 4 + recently studied using pump-probe X-ray spectroscopy. Our results compare favourably to previous experiments, while reducing the computational effort, providing the scope to apply them to larger systems. [ABSTRACT FROM AUTHOR]

Semiclassical (SC) vibrational spectroscopy is a technique capable of reproducing quantum effects (such as zero-point energies, quantum resonances, and anharmonic overtones) from classical dynamics runs even in the case of very large dimensional systems. In a previous study [Conte et al. J. Chem. Phys. 151, 214107 (2019)], a preliminary sampling based on adiabatic switching has been shown to be able to improve the precision and accuracy of semiclassical results for challenging model potentials and small molecular systems. In this paper, we investigate the possibility to extend the technique to larger (bio)molecular systems whose dynamics must be integrated by means of ab initio "on-the-fly" calculations. After some preliminary tests on small molecules, we obtain the vibrational frequencies of glycine improving on pre-existing SC calculations. Finally, the new approach is applied to 17-atom proline, an amino acid characterized by a strong intramolecular hydrogen bond.

We present an ab initio quantum study of the photoelectron spectra of sulfur dioxide, based on wavepacket propagations on manifolds of ionic, and excited/Rydberg states. We obtain excellent agreement for two different cases. First, the one photon ionization case where we can reproduce all details of the experimental spectrum and demonstrate the influence of the conical intersection between two of the ionic states. Then the multiphoton ionization regime, in which the dynamics of the wave packet on the two lowest singlet states is directly mapped in the spectra via a pump-probe scheme, as proposed in the experimental companion paper [I. Wilkinson et al., J. Chem. Phys. 140, 204301 (2014)]. [ABSTRACT FROM AUTHOR]

In this paper, we compare and contrast basis set sampling techniques recently developed for use in the ab initio multiple cloning method, a direct dynamics extension to the multiconfigurational Ehrenfest approach, used recently for the quantum simulation of ultrafast photochemistry. We demonstrate that simultaneous use of basis set cloning and basis function trains can produce results which are converged to the exact quantum result. To demonstrate this, we employ these sampling methods in simulations of quantum dynamics in the spin boson model with a broad range of parameters and compare the results to accurate benchmarks. [ABSTRACT FROM AUTHOR]

We use the "generalized hierarchical equation of motion" proposed in Paper I [C.-Y. Hsieh and J. Cao, J. Chem. Phys. 148, 014103 (2018)] to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher-order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two kinds of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of localized nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are distributed in an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as ~1/ √NB where NB is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justifies the linear response approximations in the thermodynamic limit. For the nuclear/electron spin bath models, system-bath couplings are directly deduced from spin-spin interactions and do not necessarily obey the 1/ √NB scaling. It is not always possible to justify the linear response approximations in this case. Furthermore, if the spin-spin Hamiltonian is highly symmetrical, there exist additional constraints that generate highly non-Markovian and persistent dynamics that is beyond the linear response treatments. [ABSTRACT FROM AUTHOR]

The speed and angular distribution of O atoms arising from the photofragmentation of C5H8-O2, the isoprene-oxygen van der Waals complex, in the wavelength region of 213-277 nm has been studied with the use of a two-color dissociation-probe method and the velocity map imaging technique. Dramatic enhancement in the O atoms photo-generation cross section in comparison with the photodissociation of individual O2 molecules has been observed. Velocity map images of these 'enhanced' O atoms consisted of five channels, different in their kinetic energy, angular distribution, and wavelength dependence. Three channels are deduced to be due to the one-quantum excitation of the C5H8-O2 complex into the perturbed Herzberg III state (3Δu) of O2. This excitation results in the prompt dissociation of the complex giving rise to products C5H8+O+O when the energy of exciting quantum is higher than the complex photodissociation threshold, which is found to be 41740 ± 200 cm-1 (239.6±1.2 nm). This last threshold corresponds to the photodissociation giving rise to an unexcited isoprene molecule. The second channel, with threshold shifted to the blue by 1480 ± 280 cm-1, corresponds to dissociation with formation of rovibrationally excited isoprene. A third channel was observed at wavelengths up to 243 nm with excitation below the upper photodissociation threshold. This channel is attributed to dissociation with the formation of a bound O atom C5H8-O2 + hv → C5H8-O2(3Δu) → C5H8O + O and/or to dissociation of O2 with borrowing of the lacking energy from incompletely cooled complex internal degrees of freedom C5H8*-O2 + hv → C5H8*-O2(3Δu) → C5H8 + O + O. The kinetic energy of the O atoms arising in two other observed channels corresponds to O atoms produced by photodissociation of molecular oxygen in the excited a 1Δg and b 1Σg+ singlet states as the precursors. This indicates the formation of singlet oxygen O2(a 1Δg) and O2(b 1Σg+) after excitation of the C5H8-O2 complex. Cooperative excitation of the complex with a simultaneous change of the spin of both partners 1X-3O2 + hν → 3X-1O2 → 3X + 1O2 is suggested as a source of singlet oxygen O2(a 1Δg) and O2(b 1Σg+). This cooperative excitation is in agreement with little or no vibrational excitation of O2(a 1Δg), produced from the C5H8-O2 complex as studied in the current paper as well as from the C3H6-O2 and CH3I-O2 complexes reported in our previous paper [Baklanov et al., J. Chem. Phys. 126, 124316 (2007)]. The formation of O2(a 1Δg) from C5H8-O2 was observed at λpump = 213-277 nm with the yield going down towards the long wavelength edge of this interval. This spectral profile is interpreted as the red-side wing of the band of a cooperative transition 1X-3O2 + hν → 3X(T2)-1O2(a 1Δg) in the C5H8-O2 complex. [ABSTRACT FROM AUTHOR]

We study the dynamics of quantum excitations inside macromolecules which can undergo conformational transitions. In the first part of the paper, we use the path integral formalism to rigorously derive a set of coupled equations of motion which simultaneously describe the molecular and quantum transport dynamics, and obey the fluctuation/dissipation relationship. We also introduce an algorithm which yields the most probable molecular and quantum transport pathways in rare, thermally activated reactions. In the second part of the paper, we apply this formalism to simulate the propagation of a quantum charge during the collapse of a polymer from an initial stretched conformation to a final globular state. We find that the charge dynamics is quenched when the chain reaches a molten globule state. Using random matrix theory we show that this transition is due to an increase of quantum localization driven by dynamical disorder. We argue that collapsing conducting polymers may represent a physical realization of quantum small-world networks with dynamical rewiring probability. [ABSTRACT FROM AUTHOR]

In this paper, control of open quantum systems with emphasis on the control of surface photochemical reactions is presented. A quantum system in a condensed phase undergoes strong dissipative processes. From a theoretical viewpoint, it is important to model such processes in a rigorous way. In this work, the description of open quantum systems is realized within the surrogate Hamiltonian approach [R. Baer and R. Kosloff, J. Chem. Phys. 106, 8862 (1997)]. An efficient and accurate method to find control fields is optimal control theory (OCT) [W. Zhu, J. Botina, and H. Rabitz, J. Chem. Phys. 108, 1953 (1998); Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. 120, 5509 (2004)]. To gain control of open quantum systems, the surrogate Hamiltonian approach and OCT, with time-dependent targets, are combined. Three open quantum systems are investigated by the combined method, a harmonic oscillator immersed in an ohmic bath, CO adsorbed on a platinum surface, and NO adsorbed on a nickel oxide surface. Throughout this paper, atomic units, i.e., h = me = e = a0 = 1, have been used unless otherwise stated. [ABSTRACT FROM AUTHOR]

We investigate the vibrational shift of beryllium oxide (BeO) in Xe matrix as well as in Ar matrix environments by mixed quantum-classical simulation and examine the origin of spectral shift in details. BeO is known to form strong chemical complex with single rare gas atom, and it is predicted from the gas phase calculations that vibrational frequencies are blueshifted by 78 cm-1 and 80 cm-1 upon formation of XeBeO and ArBeO, respectively. When the effects of other surrounding rare gas atoms are included by Monte Carlo simulations, it is found that the vibrational frequencies are redshifted by 21 cm-1 and 8 cm-1 from the isolated XeBeO and ArBeO complexes, respectively. The vibrational shift of XeBeO in Ar matrix is also calculated and compared with experimental data. In all simulations examined in this paper, the calculated vibrational frequency shifts from the isolated BeO molecule are in reasonable agreement with experimental values. The spectral shift due to the rare-gas-complex formation of RgBeO (Rg = Xe or Ar) is not negligible as seen in the previous studies, but it is shown in this paper that the effects of other surrounding rare gas atoms should be carefully taken into account for quantitative description of the spectral shifts and that these two effects are competing in vibrational spectroscopy of BeO in matrix environments. [ABSTRACT FROM AUTHOR]

The mixed quantum-classical formulation derived in our companion paper [D. Bousquet, K. H. Hughes, D. Micha, and I. Burghardt, J. Chem. Phys. 134, 064116 (2011)], which is based upon a hydrodynamic representation of the classical sector, is applied to nonequilibrium nonpolar solvation dynamics as exemplified by the solvation of the electronically excited NO molecule in a rare gas environment. Derived from a partition of the Hamiltonian into a primary (quantum) part and a secondary (classical) part the hydrodynamic equations are formulated for multi-quantum states and result in explicit equations of motion for populations and coherences. The hierarchy of hydrodynamic equations is truncated by the following approximate closure schemes: Gauss-Hermite closure, dynamical density functional theory approximation, and a generalized Maxwellian closure. A comparison of the dynamics using these three closure methods showed that the suitability of a particular closure scheme was dependent on the initial conditions and the nonequilibrium character of the dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we examine how and when quantum evolution can be approximated in terms of (generalized) classical dynamics in calculations of correlation functions, with a focus on the symmetrized time correlation function introduced by Schofield. To that end, this function is expressed as a path integral in complex time and written in terms of sum and difference path variables. Taylor series expansion of the path integral's exponent to first and second order in the difference variables leads to two original developments. The first order expansion is used to obtain a simple, path integral based, derivation of the so-called Schofield's quantum correction factor. The second order result is employed to show how quantum mechanical delocalization manifests itself in the approximation of the correlation function and hinders, even in the semiclassical limit, the interpretation of the propagators in terms of sets of guiding classical trajectories dressed with appropriate weights. [ABSTRACT FROM AUTHOR]

Gas-phase atomic anions lack bound electronic excited states, yet in solution many of these anions exhibit intense absorption bands due to the presence of excited states, referred to as charge-transfer-to-solvent (CTTS) states that are bound only by the presence of the solvent. CTTS spectra thus serve as delicate probes of solute-solvent interactions, but the fact that they are created by the interactions of a solute with many solvent molecules makes them a challenge to describe theoretically. In this paper, we use mixed quantum/classical molecular dynamics with the two-electron Fourier-grid (2EFG) electronic structure method presented in the previous paper [W. J. Glover, R. E. Larsen, and B. J. Schwartz, J. Chem. Phys. 132, 144101 (2010)] to simulate the CTTS states of a sodium anion in liquid tetrahydrofuran, Na-/THF. Since our 2EFG method is based on configuration interaction with single and double excitations in a grid basis, it allows for an exact treatment of the two valence electrons of the sodium anion. To simulate Na-/THF, we first develop a new electron–THF pseudopotential, and we verify the accuracy of this potential by reproducing the experimental absorption spectrum of an excess electron in liquid THF with near quantitative accuracy. We also are able to reproduce the CTTS spectrum of Na-/THF and find that the CTTS states of Na- exhibit a Rydberg-like progression due to the pre-existing long-range solvent polarization around the anion. We also find that the CTTS states are highly mixed with the disjoint electronic states supported by naturally occurring solvent cavities that exist in liquid THF. This mixing explains why the solvated electrons that are ejected following CTTS excitation appear with their equilibrium absorption spectrum. The mixing of the CTTS and solvent-cavity states also explains why the recombination of the electron and its geminate Na0 partner occurs on slower time scales when photoexciting in the blue compared to in the red of the CTTS band: blue excitation accesses CTTS states whose charge densities lies further from the position of the anion, whereas red excitation accesses CTTS states that lie primarily within the anion’s first solvation shell. Finally, we see that the radial character of the CTTS states near the Na+ core matches that of Na0, explaining why the spectrum of this species appears instantly after photoexciting Na-. [ABSTRACT FROM AUTHOR]

In this paper we propose an iterative method for solving the inhomogeneous systems of linear equations associated with density fitting. The proposed method is based on a version of the conjugate gradient method that makes use of automatically built quasi-Newton preconditioners. The paper gives a detailed description of a parallel implementation of the new method. The computational performance of the new algorithms is analyzed by benchmark calculations on systems with up to about 35 000 auxiliary functions. Comparisons with the standard, direct approach show no significant differences in the computed solutions. [ABSTRACT FROM AUTHOR]

We address the problem of establishing which is the proper form of quantum master equation generating a survival probability identical to that corresponding to the nonergodic sequence of “light on” and “light off” fluorescence fluctuations in blinking quantum dots. We adopt a theoretical perspective based on the assumption that the abrupt transitions from the light on to light off state are the results of many collisions between system and environment, properly described by the Lindblad equation, and that between two consecutive collisions the system dynamics are frozen. This generates a quantum master equation belonging to the recently proposed class of generalized Lindblad equations, with a time convoluted structure, involving in the specific case of this paper both the unitary and the nonunitary contribution of the Lindblad equation. This is the property that under the low-frequency condition makes the new class of generalized Lindblad equation generates the required survival probability. We make the conjecture that this equation corresponds to the cooperative dynamics of many units that, in isolation, are described by the ordinary Lindblad equation. When the time scale of the unitary term of the Lindblad equation is shorter than the dephasing time, the cooperation generates a surprisingly extended macroscopic coherence. [ABSTRACT FROM AUTHOR]

Disorder plays an important role in the photophysics of conjugated polymers such as poly(para-phenylene vinylene) (PPV). The dipole moments measured by electroabsorption spectroscopy for a centrosymmetric system such as PPV provide a direct quantitative measure of disorder-induced symmetry breaking. Although inner-sphere (structural) disorder is present, outer-sphere (environmental) disorder dominates the symmetry breaking in PPV. This paper develops and compares six models of outer-sphere disorder that differ in their representation of the electrostatic environment of PPV in glassy solvents. The most detailed model is an all-atom description of the solvent glass and this model forms the basis for comparison of the less detailed models. Four models are constructed in which multipoles are placed at points on a lattice. These lattice models differ in the degree to which they include correlation between the lattice spacings and the orientations of the multipoles. A simple model that assigns random Gaussian-distributed electrostatic potentials to each atom in the PPV molecule is also considered. Comparison of electronic structure calculations of PPV in these electrostatic environments using the all-atom model as a benchmark reveals that dipole and quadrupole lattices provide reasonable models of organic glassy solvents. Including orientational correlation among the solvent molecules decreases the effects of outer-sphere disorder, whereas including correlation in the lattice spacings increases the effects. Both the dipole and quadrupole moments of the solvent molecules can have significant effects on the symmetry breaking and these effects are additive. This additivity provides a convenient means for predicting the effects of various glassy solvents based on their multipole moments. The results presented here suggest that electrostatic disorder can account for the observed symmetry breaking in organic glasses. Furthermore, the lattice models are in general agreement with the dipole and quadrupole lattice models used to explain the Poole–Frenkel behavior in charge transport through disordered organic materials. [ABSTRACT FROM AUTHOR]

This paper presents dielectric relaxation data for organic glass-forming liquids compiled from different groups and supplemented by new measurements. The main quantity of interest is the “minimum slope” of the α dielectric loss plotted as a function of frequency in a log-log plot, i.e., the numerically largest slope above the loss peak frequency. The data consisting of 347 spectra for 53 liquids show prevalence of minimum slopes close to -1/2, corresponding to approximate t dependence of the dielectric relaxation function at short times. The paper studies possible correlations between minimum slopes and (1) temperature (quantified via the loss peak frequency); (2) how well an inverse power-law fits data above the loss peak; (3) degree of time-temperature superposition; (4) loss peak half width; (5) deviation from non-Arrhenius behavior; (6) loss strength. For the first three points we find correlations that show a special status of liquids with minimum slopes close to -1/2. For the last three points only fairly insignificant correlations are found, with the exception of large-loss liquids that have minimum slopes that are numerically significantly larger than 1/2. We conclude that—excluding large-loss liquids—approximate t relaxation appears to be a generic property of the α relaxation of organic glass formers. [ABSTRACT FROM AUTHOR]

We have constructed free-time and fixed end-point optimal control theory for quantum systems and applied it to entanglement generation between rotational modes of two polar molecules coupled by dipole-dipole interaction. The motivation of the present work is to solve optimal control problems more flexibly by extending the popular fixed time and fixed end-point optimal control theory for quantum systems to free-time and fixed end-point optimal control theory. As a demonstration, the theory that we have constructed in this paper will be applied to entanglement generation in rotational modes of NaCl–NaBr polar molecular systems that are sensitive to the strength of entangling interactions. Our method will significantly be useful for the quantum control of nonlocal interaction such as entangling interaction, which depends crucially on the strength of the interaction or the distance between the two molecules, and other general quantum dynamics, chemical reactions, and so on. [ABSTRACT FROM AUTHOR]

Conventional quantum chemical solvation theories are based on the mean-field embedding approximation. That is, the electronic wavefunction is calculated in the presence of the mean field of the environment. In this paper a direct quantum mechanical/molecular mechanical (QM/MM) analog of such a mean-field theory is formulated based on variational and perturbative frameworks. In the variational framework, an appropriate QM/MM free energy functional is defined and is minimized in terms of the trial wavefunction that best approximates the true QM wavefunction in a statistically averaged sense. Analytical free energy gradient is obtained, which takes the form of the gradient of effective QM energy calculated in the averaged MM potential. In the perturbative framework, the above variational procedure is shown to be equivalent to the first-order expansion of the QM energy (in the exact free energy expression) about the self-consistent reference field. This helps understand the relation between the variational procedure and the exact QM/MM free energy as well as existing QM/MM theories. Based on this, several ways are discussed for evaluating non-mean-field effects (i.e., statistical fluctuations of the QM wavefunction) that are neglected in the mean-field calculation. As an illustration, the method is applied to an SN2 Menshutkin reaction in water, NH3+CH3Cl→NH3CH3++Cl-, for which free energy profiles are obtained at the Hartree–Fock, MP2, B3LYP, and BHHLYP levels by integrating the free energy gradient. Non-mean-field effects are evaluated to be <0.5 kcal/mol using a Gaussian fluctuation model for the environment, which suggests that those effects are rather small for the present reaction in water. [ABSTRACT FROM AUTHOR]

Optical response functions are known to reflect quantum dynamics in a superposition state and as such, lack a well-defined classical limit. In a previous paper we considered the importance of accounting for the quantum nature of the dynamics by comparing the linear absorption spectrum and homodyne-detected time-integrated two-pulse photon-echo signal as calculated via the semiclassical forward-backward approach, linearized semiclassical approach, and standard approach which is based on equilibrium ground state dynamics [Shi and Geva, J. Chem. Phys. 122, 064506 (2005)]. In the present paper, we extend the comparison to the case of heterodyne-detected and time-resolved nonlinear time-domain rephasing and nonrephasing signals generated in three-pulse experiments and the corresponding frequency-domain two-dimensional spectra. The comparison is performed in the context of a two-state chromophore solvated in a nonpolar liquid. It is shown that the inherent insensitivity of the standard method to the nonequilibrium dynamics on the excited state potential surface gives rise to two-dimensional spectra which are symmetrical relative to the diagonal. In contrast, accounting for the effect of nonequilibrium excited state dynamics, as is the case within the forward-backward and linearized semiclassical methods, is found to give rise to two-dimensional spectra that become increasingly asymmetrical relative to the diagonal as the waiting time between the second and third pulses becomes larger. It is argued that the emergence of the asymmetry provides a useful probe of nonequilibrium solvation on the excited state potential surface. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to propagating the density matrix based on a time stepping procedure arising from a Trotter factorization and combining the forward and backward incremental propagators. The sums over intermediate states of the discrete quantum subsystem are implemented by a Monte Carlo surface hopping-like procedure, while the integrals over the continuous variables are performed using a linearization in the difference between the forward and backward paths of these variables leading to classical-like equations of motion with forces determined by the quantum subsystem states. The approach is tested on several models and numerical convergence is explored. [ABSTRACT FROM AUTHOR]

We re-examine the analysis of the equilibrium limits of the fewest switches surface hopping algorithm for mixed quantum-classical dynamics. In contrast with previously reported results, we show that surface hopping does not, in general, exactly yield Boltzmann equilibrium, but that in practice the observed deviations are quite small. We also demonstrate that surface hopping does approach the exact equilibrium distribution in both the limits of small adiabatic splitting and/or strong nonadiabatic coupling. We verify these analytical results with numerical simulations for a simple two-level quantum system connected to a bath of classical particles. [ABSTRACT FROM AUTHOR]

In previous articles [B. Poirier J. Chem. Phys. 121, 4501 (2004); C. Trahan and B. Poirier, ibid. 124, 034115 (2006); 124, 034116 (2006); B. Poirier and G. Parlant, J. Phys. Chem. A 111, 10400 (2007)] a bipolar counterpropagating wave decomposition, ψ=ψ++ψ-, was presented for stationary states ψ of the one-dimensional Schrödinger equation, such that the components ψ± approach their semiclassical Wentzel–Kramers–Brillouin analogs in the large action limit. The corresponding bipolar quantum trajectories are classical-like and well behaved, even when ψ has many nodes, or is wildly oscillatory. In this paper, the method is generalized for time-dependent wavepacket dynamics applications and applied to several benchmark problems, including multisurface systems with nonadiabatic coupling. [ABSTRACT FROM AUTHOR]

Several features and the performance of the recently published [P. Jankowski and M. Ziólkowski, Mol. Phys. 104, 2293 (2006)] three-dimensional intermolecular potential energy surface for the Ar–HF complex have been investigated. This full-dimensional surface has been obtained using the method of the local expansion of the exact interaction energy surface [P. Jankowski, J. Chem. Phys. 121, 1655 (2004)] in the Taylor series with respect to intramolecular coordinates. The interaction energies have been calculated with the coupled-cluster supermolecular method with single, double, and noniterative triple excitations. The convergence of the interaction energy with respect to the size of the basis set is discussed. The two-dimensional surfaces resulting from averaging of the full-dimensional surface over the intramolecular vibration of HF have been obtained and directly compared to the empirical H6(4,3,2) set of surfaces proposed by Hutson [J. Chem. Phys. 96, 6752 (1992)]. A very good agreement has been observed. The averaged potentials have been used to calculate the rovibrational energy levels of the Ar–HF and Ar–DF complexes and compared to the experimental data. The accuracy of rovibrational calculations achieved with the new surface is much better than with any of the ab initio surfaces available so far. Predictions of the rovibrational energy levels and spectroscopic constants have also been done for Ar–HF with HF in the v=4,5 vibrational states, and for Ar–DF and DF in the v=3,4 states. The full-dimensional surface studied in this paper is the first ab initio surface which is fully compatible with the empirical H6(4,3,2) surface proposed by Hutson. [ABSTRACT FROM AUTHOR]

While closed-loop control of quantum dynamics in the laboratory is proving to be broadly successful, the control mechanisms induced by the fields are often left obscure. Hamiltonian encoding (HE) was originally introduced as a method for understanding mechanisms in quantum dynamics in the context of computational simulations, based on access to the system wavefunction. As a step towards laboratory implementation of HE, this paper addresses the issues raised by the use of observables rather than the wavefunction in HE. The goal of laboratory based HE is to obtain an understanding of control mechanism through a sequence of systematic control experiments, whose collective information can identify the underlying control mechanism defined as the set of significant amplitudes connecting the initial and final states. Mechanism is determined by means of observing the dynamics of special sequences of system Hamiltonians encoded through the control field. The proposed algorithm can handle complex systems, operates with no recourse to dynamical simulations, and functions with limited understanding of the system Hamiltonian. As with the closed-loop control experiments, the HE control mechanism identification algorithm performs a new experiment each time the dynamical outcome from an encoded Hamiltonian is called for. This paper presents the basic HE algorithm in the context of physical systems described by a finite dimensional Hilbert space. The method is simulated with simple models, and the extension to more complex systems is discussed. [ABSTRACT FROM AUTHOR]

This article is a continuation of our previous paper on schemes of energy decompositions of molecular systems in the real space [D. R. Alcoba et al., J. Chem. Phys. 122, 074102 (2005)] now using correlated state functions. We study, according to physical arguments, the appropriate management of the density cumulant arising from the second-order reduced density matrix at correlated level, whose contributions can be assigned to one-center or to two-center terms in the energy partitioning. Our treatments are applied within two physical space partitioning schemes: the Bader partitioning into atomic basins and the fuzzy atom procedure. The results obtained in selected molecules are analyzed and discussed in detail. [ABSTRACT FROM AUTHOR]

A previously developed nonadiabatic semiclassical surface hopping propagator [M. F. Herman J. Chem. Phys. 103, 8081 (1995)] is further studied. The propagator has been shown to satisfy the time-dependent Schrödinger equation (TDSE) through order h, and the O(h2) terms are treated as small errors, consistent with standard semiclassical analysis. Energy is conserved at each hopping point and the change in momentum accompanying each hop is parallel to the direction of the nonadiabatic coupling vector resulting in both transmission and reflection types of hops. Quantum mechanical analysis and numerical calculations presented in this paper show that the h2 terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the h2 terms are analyzed for the nonadiabatic semiclassical propagator. It is shown that the propagator can satisfy the TDSE for multidimensional systems by including another type of nonclassical trajectories that reflect on the same surfaces. This h2 analysis gives three conditions for these three types of trajectories so that their coefficients are uniquely determined. Besides the nonadiabatic semiclassical propagator, a numerically useful quantum propagator in the adiabatic representation is developed to describe nonadiabatic transitions. [ABSTRACT FROM AUTHOR]

A numerical solution for the quantum dynamics of the spin boson problem is obtained using the semiclassical initial value series representation approach to the quantum dynamics. The zeroth order term of the series is computed using the new forward-backward representation for correlation functions presented in the preceding adjacent paper. This leads to a rapid convergence of the Monte Carlo sampling, as compared to previous attempts. The zeroth order results are already quite accurate. The first order term of the series is small, demonstrating the rapid convergence of the semiclassical initial value representation series. This is the first time that the first order term in the semiclassical initial value representation series has been converged for systems with the order of 50 degrees of freedom. [ABSTRACT FROM AUTHOR]

This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer. Optimal control fields are shown to be capable of cooperating or fighting with observations to achieve a good yield, and the nature of the observations may be optimized to more effectively control the quantum dynamics. Quantum observations also can break dynamical symmetries to increase the controllability of a quantum system. The quantum Zeno and anti-Zeno effects induced by observations are the key operating principles in these processes. The results indicate that quantum observations can be effective tools in the control of quantum dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys. 120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed. [ABSTRACT FROM AUTHOR]

Protonation and subsequent intramolecular hydrogen bonding as methods to control chain structure and tune luminescence in heteroatomic conjugated polymers were reported experimentally [A. P. Monkman et al., J. Am. Chem. Soc. 124, 6049 (2002)]. In this paper, the structure and photophysical properties of the model teraryl compound of phenylene-pyridylene copolymer before and after protonation are theoretically studied with quantum chemistry methods. From the optimized ground states, intramolecular hydrogen bonding to the adjacent oxygen atom in the alkoxy substituent planarizes the backbone of the molecules, and the optimized detailed results of compound 9 before and after protonation, such as the dihedral angles between the central benzene and the two pyridyl rings, the bond lengths, and the bond angles, are consistent with the experimental results. From the results of the calculated excited states, the protonation and subsequent intramolecular hydrogen bonding result in the redshifts of the absorption, the increase of the ionization energy, the increase of the electron affinity, the decrease of the energy difference of the highest occupied molecular orbital and lowest unoccupied molecular orbital, the decrease of the binding gap, and the delocalization of the electron-hole coherence. The photophysical properties of compound 9 before and after protonation are further studied with a three-dimensional real-space analysis method of transition and charge difference densities (study transition dipole moment and charge transfer in the absorption and fluorescence processes) and two-dimensional real-space analysis method of transition density matrices (study the electron-hole coherence and the excitation delocalization). The calculated results show theoretically an insight understanding on the influence of the protonation and subsequent intramolecular hydrogen bonding to chain structure and photophysical properties. [ABSTRACT FROM AUTHOR]

In a recent paper [D. Babikov, J. Chem. Phys. 121, 7577 (2004)], quantum optimal control theory was applied to analyze the accuracy of quantum gates in a quantum computer based on molecular vibrational eigenstates. The effects of the anharmonicity parameter of the molecule, the target time of the pulse, and the penalty function on the accuracy of the qubit transformations were investigated. We demonstrate that the effects of all the molecular and laser-pulse parameters can be explained utilizing the analytical pulse area theorem, which originates from the standard two-level model. Moreover, by analyzing the difference between the optimal control theory results and those obtained using the pulse area theorem, it is shown that extremely high quantum gate fidelity can be achieved for a qubit system based on vibrational eigenstates. [ABSTRACT FROM AUTHOR]

This paper presents a new tracking method where the target observable 〈O(s,T)〉 at the final dynamical time T follows a predefined track P(s) with respect to a homotopy tracking variable s>=0. The procedure calculates the series of control fields E(s,t) required to accomplish observable homotopy tracking by solving a first-order differential equation in s for the evolution of the control field. Controls produced by this technique render the desired track for all s without encountering field singularities. This paper also extends the technique to the case where the field-free Hamiltonian and dipole moment operator change with s in order to explore the control of new physical systems along the track. Several simulations are presented illustrating the various uses for this quantum tracking control technique. [ABSTRACT FROM AUTHOR]

A method for constructing diabatic potential-energy matrices from ab initio quantum chemistry data is described and tested for use in exact quantum reactive scattering. The method is a refinement of that presented in a previous paper, in that it accounts for the presence of the nonremovable derivative coupling. The accuracy of quantum dynamics on this type of diabatic potential is tested by comparison with an analytic model and for an ab initio description of the two lowest-energy states of H3. [ABSTRACT FROM AUTHOR]

Modern spectroscopical techniques allow the efficient experimental investigation of highly excited vibrational states in molecular systems. On the theoretical side, powerful computational methods have also been developed for the calculation of the corresponding energy levels and wave functions, and their interpretation. In this paper we use a combination of two such methods, namely, the distribution of zeroes in the Husimi function and energy-level correlation diagrams, to discuss a classification scheme, for the lowest hundred vibrational levels of the LiNC/LiCN floppy molecular system, based on their dynamical characteristics. [ABSTRACT FROM AUTHOR]