Search

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]

The generalized quantum master equation (GQME) approach provides a powerful general-purpose framework for simulating the inherently quantum mechanical dynamics of a subset of electronic reduced density matrix elements of interest in complex molecular systems. Previous studies have found that combining the GQME approach with quasiclassical mapping Hamiltonian (QC/MH) methods can dramatically improve the accuracy of electronic populations obtained via those methods. In this paper, we perform a complimentary study of the advantages offered by the GQME approach for simulating the dynamics of electronic coherences, which play a central role in optical spectroscopy, quantum information science, and quantum technology. To this end, we focus on cases where the electronic coherences predicted for the spin-boson benchmark model by direct application of various QC/MH methods are inaccurate. We find that similar to the case of electronic populations, combining the QC/MH methods with the GQME approach can dramatically improve the accuracy of the electronic coherences obtained via those methods. We also provide a comprehensive analysis of how the performance of GQMEs depends on the choice of projection operator and electronic basis and show that the accuracy and feasibility of the GQME approach can benefit from casting the GQME in terms of the eigen-basis of the observable of interest. [ABSTRACT FROM AUTHOR]

An important class of methods for modeling dynamics in open quantum systems is based on the well-known influence functional (IF) approach to solving path-integral equations of motion. Within this paradigm, path-filtering schemes based on the removal of IF elements that fall below a certain threshold aim to reduce the effort needed to calculate and store the influence functional, making very challenging simulations possible. A filtering protocol of this type is considered acceptable as long as the simulation remains mathematically stable. This, however, does not guarantee that the approximated dynamics preserve the physics of the simulated process. In this paper, we explore the possibility of training Generative Flow Networks (GFlowNets) to produce filtering protocols while optimizing for mathematical stability and for physical accuracy. Trained using the trajectory balance objective, the model produces sets of paths to be added to a truncated initial set; it is rewarded if the combined set of paths gives rise to solutions in which the trace of the density matrix is conserved, the populations remain real, and the dynamics approach the exact reference. Using a simple two-level system coupled to a dissipative reservoir, we perform proof-of-concept simulations and demonstrate the elegant and surprising filtering solutions proposed by the GFlowNet. [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 report a new algorithm for creating an adaptive basis set in the Multiconfigurational Ehrenfest (MCE) method, which is termed Full Cloning (FC), and test it together with the existing Multiple Cloning (MC) using the spin-boson model at zero-temperature as a benchmark. The zero-temperature spin-boson regime is a common hurdle in the development of methods that seek to model quantum dynamics. Two versions of MCE exist. We demonstrate that MC is vital for the convergence of MCE version 2 (MCEv2). The first version (MCEv1) converges much better than MCEv2, but FC improves its convergence in a few cases where it is hard to converge it with the help of a reasonably small size of the basis set. [ABSTRACT FROM AUTHOR]

Quantum dynamics simulation and computational spectroscopy serve as indispensable tools for the theoretical understanding of various fundamental physical and chemical processes, ranging from charge transfer to photochemical reactions. When simulating realistic systems, the primary challenge stems from the overwhelming number of degrees of freedom and the pronounced many-body correlations. Here, we present Kylin-V, an innovative quantum dynamics package designed for accurate and efficient simulations of dynamics and spectroscopic properties of vibronic Hamiltonians for molecular systems and their aggregates. Kylin-V supports various quantum dynamics and computational spectroscopy methods, such as time-dependent density matrix renormalization group and our recently proposed single-site and hierarchical mapping approaches, as well as vibrational heat-bath configuration interaction. In this paper, we introduce the methodologies implemented in Kylin-V and illustrate their performances through a diverse collection of numerical examples. [ABSTRACT FROM AUTHOR]

Electron transfer reactions play an essential role in many chemical and biological processes. Fermi's golden rule (GR), which assumes that the coupling between electronic states is small, has formed the foundation of electron transfer rate theory; however, in short range electron/energy transfer reactions, this coupling can become very large, and, therefore, Fermi's GR fails to make even qualitatively accurate rate predictions. In this paper, I present a simple modified GR theory to describe electron transfer in the Marcus inverted regime at arbitrarily large electronic coupling strengths. This theory is based on an optimal global rotation of the diabatic states, which makes it compatible with existing methods for calculating GR rates that can account for nuclear quantum effects with anharmonic potentials. Furthermore, the optimal GR (OGR) theory can also be combined with analytic theories for non-adiabatic rates, such as Marcus theory and Marcus–Levich–Jortner theory, offering clear physical insights into strong electronic coupling effects in non-adiabatic processes. OGR theory is also tested on a large set of spin-boson models and an anharmonic model against exact quantum dynamics calculations, where it performs well, correctly predicting rate turnover at large coupling strengths. Finally, an example application to a boron-dipyrromethane–anthracene photosensitizer reveals that strong coupling effects inhibit excited state charge recombination in this system, reducing the rate of this process by a factor of 4. Overall, OGR theory offers a new approach to calculating electron transfer rates at strong couplings, offering new physical insights into a range of non-adiabatic processes. [ABSTRACT FROM AUTHOR]

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111-1–214111-13 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understand how energy is dissipated in realistic open quantum system dynamics. [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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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 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]

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]

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]