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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]