Herman-Kluk semiclassical dynamics of molecular rotations in laser fields

The action-angle mapping algorithm [R. Saha and M. Ovchinnikov, J. Chem. Phys. 124, 204112 (2006)] is utilized to provide a Herman-Kluk semiclassical initial value representation (SC-IVR) treatment of quantum dynamics of systems with non-Cartesian degrees of freedom. The non-Cartesian system under investigation is a linear rotor molecule in static electric and pulsed laser field. The results demonstrate that the SC-IVR procedure described in this work provides an accurate representation of quantum rotational dynamics of the system.     

Forward-backward semiclassical initial value series representation of quantum correlation functions

The forward-backward (FB) approximation as applied to semiclassical initial value representations (SCIVR's) has enabled the practical application of the SCIVR methodology to systems with many degrees of freedom. However, to date a systematic representation of the exact quantum dynamics in terms of the FB-SCIVR has proven elusive. In this paper, we provide a new derivation of a forward-backward phase space SCIVR expression (FBPS-SCIVR) derived previously by Thompson and Makri [Phys. Rev. E 59, R4729 (1999)]. This enables us to represent quantum correlation functions exactly in terms of a series whose leading order term is the FBPS-SCIVR expression. Numerical examples for systems with over 50 degrees of freedom are presented for the spin boson problem. Comparison of the FBPS-SCIVR with the numerically exact results of Wang [J. Chem. Phys. 113, 9948 (2000)] obtained using a multiconfigurational time dependent method shows that the leading order FBPS-SCIVR term already provides an excellent approximation.     

Quantum and semiclassical theories for nonadiabatic transitions based on overlap integrals related to fast degrees of freedom

Alternative treatments of quantum and semiclassical theories for nonadiabatic dynamics are presented. These treatments require no derivative couplings and instead are based on overlap integrals between eigenstates corresponding to fast degrees of freedom, such as electronic states. Derived from mathematical transformations of the Schr?dinger equation, the theories describe nonlocal characteristics of nonadiabatic transitions. The idea that overlap integrals can be used for nonadiabatic transitions stems from an article by Johnson and Levine [Chem. Phys. Lett. 13, 168 (1972)]. Furthermore, overlap integrals in path-integral form have been recently made available by Schmidt and Tully [J. Chem. Phys. 127, 094103 (2007)] to analyze nonadiabatic effects in thermal equilibrium systems. The present paper expands this idea to dynamic problems presented in path-integral form that involve nonadiabatic semiclassical propagators. Applications to one-dimensional nonadiabatic transitions have provided excellent results, thereby verifying the procedure. In principle these theories that are presented can be applied to multidimensional systems, although numerical costs could be quite expensive.     

Nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation method revisited: applications to Tully's three model systems

The nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method for nonadiabatic problems is reformulated. The method has the same spirit as Tully's surface hopping technique [J. Chem. Phys. 93, 1061 (1990)] and almost keeps the same structure as the original single-surface HK SC-IVR method except that trajectories can hop to other surfaces according to the hopping probabilities and phases, which can be easily integrated along the paths. The method is based on a rather general nonadiabatic semiclassical surface hopping theory developed by Herman [J. Chem. Phys. 103, 8081 (1995)], which has been shown to be accurate to the first order in h and through all the orders of the nonadiabatic coupling amplitude. Our simulation studies on the three model systems suggested by Tully demonstrate that this method is practical and capable of describing nonadiabatic quantum dynamics for various coupling situations in very good agreement with benchmark calculations.     

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: excited states

The authors show that a recently proposed approach [J. Chem. Phys. 123, 084103 (2005)] for the inclusion of geometric constraints in semiclassical initial value representation calculations can be used to obtain excited states of weakly bound complexes. Sample calculations are performed for free and constrained rare gas clusters. The results show that the proposed approach allows the evaluation of excited states with reasonable accuracy when compared to exact basis set calculations.     

Quantum dynamics study of H+NH3-->H2+NH2 reaction

We report in this paper a quantum dynamics study for the reaction H+NH3-->NH2+H2 on the potential energy surface of Corchado and Espinosa-Garcia [J. Chem. Phys. 106, 4013 (1997)]. The quantum dynamics calculation employs the semirigid vibrating rotor target model [J. Z. H. Zhang, J. Chem. Phys. 111, 3929 (1999)] and time-dependent wave packet method to propagate the wave function. Initial state-specific reaction probabilities are obtained, and an energy correction scheme is employed to account for zero point energy changes for the neglected degrees of freedom in the dynamics treatment. Tunneling effect is observed in the energy dependency of reaction probability, similar to those found in H+CH4 reaction. The influence of rovibrational excitation on reaction probability and stereodynamical effect are investigated. Reaction rate constants from the initial ground state are calculated and are compared to those from the transition state theory and experimental measurement.     

Two-dimensional optical three-pulse photon echo spectroscopy. I. Nonperturbative approach to the calculation of spectra

The nonperturbative approach to the calculation of nonlinear optical spectra of Seidner et al. [J. Chem. Phys. 103, 3998 (1995)] is extended to describe four-wave mixing experiments. The system-field interaction is treated nonperturbatively in the semiclassical dipole approximation, enabling a calculation of third order nonlinear spectroscopic signals directly from molecular dynamics and an efficient modeling of multilevel systems exhibiting relaxation and transfer phenomena. The method, coupled with the treatment of dynamics within the Bloch model, is illustrated by calculations of the two-dimensional three-pulse photon echo spectra of a simple model system-a two-electronic-level molecule. The nonperturbative calculations reproduce well-known results obtained by perturbative methods. Technical limitations of the nonperturbative approach in dealing with a dynamic inhomogeneity are discussed, and possible solutions are suggested. An application of the approach to an excitonically coupled dimer system with emphasis on the manifestation of complex exciton dynamics in two-dimensional optical spectra is presented in paper II Pisliakov et al. [J. Chem. Phys. 124, 234505 (2006), following paper].     

Recovering the Crooks equation for dynamical systems in the isothermal-isobaric ensemble: a strategy based on the equations of motion

The Crooks equation [Eq. (10) in J. Stat. Phys. 90, 1481 (1998)] relates the work done on a system during a nonequilibrium transformation to the free energy difference between the final and the initial state of the transformation. Recently, the authors have derived the Crooks equation for systems in the canonical ensemble thermostatted by the Nose-Hoover or Nose-Hoover chain method [P. Procacci et al., J. Chem. Phys. 125, 164101 (2006)]. That proof is essentially based on the fluctuation theorem by Evans and Searles [Adv. Phys. 51, 1529 (2002)] and on the equations of motion. Following an analogous approach, the authors derive here the Crooks equation in the context of molecular dynamics simulations of systems in the isothermal-isobaric (NPT) ensemble, whose dynamics is regulated by the Martyna-Tobias-Klein algorithm [J. Chem. Phys. 101, 4177 (1994)]. Their present derivation of the Crooks equation correlates to the demonstration of the Jarzynski identity for NPT systems recently proposed by Cuendet [J. Chem. Phys. 125, 144109 (2006)].     

Reconciling semiclassical and Bohmian mechanics. V. Wavepacket dynamics

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, psi = psi(+) + psi(-), was presented for stationary states psi of the one-dimensional Schrodinger equation, such that the components psi(+/-) 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 psi 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.     

Semiclassical calculation of nonadiabatic thermal rate constants: application to condensed phase reactions

The nonadiabatic transition state theory proposed recently by Zhao et al. [J. Chem. Phys. 121, 8854 (2004)] is extended to calculate rate constants of complex systems by using the Monte Carlo and umbrella sampling methods. Surface hopping molecular dynamics technique is incorporated to take into account the dynamic recrossing effect. A nontrivial benchmark model of the nonadiabatic reaction in the condensed phase is used for the numerical test. It is found that our semiclassical results agree well with those produced by the rigorous quantum mechanical method. Comparing with available analytical approaches, we find that the simple statistical theory proposed by Straub and Berne [J. Chem. Phys. 87, 6111 (1987)] is applicable for a wide friction region although their formula is obtained using Landau-Zener [Phys. Z. Sowjetunion 2, 46 (1932); Proc. R. Soc. London, Ser. A 137, 696 (1932)] nonadiabatic transition probability along a one-dimensional diffusive coordinate. We also investigate how the nuclear tunneling events affect the dependence of the rate constant on the friction.     

Long-time and unitary properties of semiclassical initial value representations

We numerically compare the semiclassical "frozen Gaussian" Herman-Kluk propagator [Chem. Phys. 91, 27 (1984)] and the "thawed Gaussian" propagator put forward recently by Baranger et al. [J. Phys. A 34, 7227 (2001)] by studying the quantum dynamics in some nonlinear one-dimensional potentials. The reasons for the lack of long-time accuracy and norm conservation in the latter method are uncovered. We amend the thawed Gaussian propagator with a global harmonic approximation for the stability of the trajectories and demonstrate that this revised propagator is a true alternative to the Herman-Kluk propagator with similar accuracy.     

Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: applications to condensed phase systems

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.     

Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions

The thermal Gaussian approximation (TGA) recently developed by Frantsuzov et al. [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-betaH) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the "forward-backward semiclassical dynamics" approximation developed by Shao and Makri [J. Phys. Chem. A 103, 7753 (1999); 103, 9749 (1999)]. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and calculation of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.     

Understanding Molecular Dynamics with Stochastic Processes via Real or Virtual Dynamics

Molecular dynamics with the stochastic process provides a convenient way to compute structural and thermodynamic properties of chemical, biological, and materials systems. It is demonstrated that the virtual dynamics case that we proposed for the Langevin equation[J. Chem. Phys. 147 , 184104 (2017)] in principle exists in other types of stochastic thermostats as well. The recommended "middle" scheme[J. Chem. Phys. 147 , 034109 (2017)] of the Andersen thermostat is investigated as an example. As shown by both analytic and numerical results, while the real and virtual dynamics cases approach the same plateau of the characteristic correlation time in the high collision frequency limit, the accuracy and efficiency of sampling are relatively insensitive to the value of the collision frequency in a broad range. After we compare the behaviors of the Andersen thermostat to those of Langevin dynamics, a heuristic schematic representation is proposed for understanding efficient stochastic thermostatting processes with molecular dynamics.     

Electronic excitation dynamics in multichromophoric systems described via a polaron-representation master equation

We derive a many-site version of the non-Markovian time-convolutionless polaron master equation [Jang et al., J. Chem Phys. 129, 101104 (2008)] to describe electronic excitation dynamics in multichromophoric systems. By treating electronic and vibrational degrees of freedom in a combined frame (polaron frame), this theory is capable of interpolating between weak and strong exciton-phonon coupling and is able to account for initial non-equilibrium bath states and spatially correlated environments. Besides outlining a general expression for the expected value of any electronic system observable in the original frame, we also discuss implications of the Markovian and Secular approximations highlighting that they need not hold in the untransformed frame despite being strictly satisfied in the polaron frame. The key features of the theory are illustrated using as an example a four-site subsystem of the Fenna-Mathews-Olson light-harvesting complex. For a spectral density including a localised mode, we show that oscillations of site populations may only be observed when non-equilibrium bath effects are taken into account. Furthermore, we illustrate how this formalism allows us to identify the electronic and vibrational components of the oscillatory dynamics.     

A justification for a nonadiabatic surface hopping Herman-Kluk semiclassical initial value representation of the time evolution operator

A justification is given for the validity of a nonadiabatic surface hopping Herman-Kluk (HK) semiclassical initial value representation (SC-IVR) method. The method is based on a propagator that combines the single surface HK SC-IVR method [J. Chem. Phys. 84, 326 (1986)] and Herman's nonadiabatic semiclassical surface hopping theory [J. Chem. Phys. 103, 8081 (1995)], which was originally developed using the primitive semiclassical Van Vleck propagator. We show that the nonadiabatic HK SC-IVR propagator satisfies the time-dependent Schrodinger equation to the first order of variant Planck's over 2pi and the error is O(variant Planck's over 2pi(2)). As a required lemma, we show that the stationary phase approximation, under current assumptions, has an error term variant Planck's over 2pi(1) order higher than the leading term. Our derivation suggests some changes to the previous development, and it is shown that the numerical accuracy in applications to Tully's three model systems in low energies is improved.     

Path integral calculation of thermal rate constants within the quantum instanton approximation: application to the H + CH4 --> H2 + CH3 hydrogen abstraction reaction in full Cartesian space

The quantum instanton approximation for thermal rate constants of chemical reactions [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)], which is modeled after the earlier semiclassical instanton approach, is applied to the hydrogen abstraction reaction from methane by a hydrogen atom, H + CH4 --> H2 + CH3, using a modified and recalibrated version of the Jordan-Gilbert potential surface. The quantum instanton rate is evaluated using path integral Monte Carlo approaches based on the recently proposed implementation schemes [Yamamoto and Miller, J. Chem. Phys. 120, 3086 (2004)]. The calculations were carried out using the Cartesian coordinates of all the atoms (thus involving 18 degrees of freedom), thereby taking explicit account of rotational effects of the whole system and also allowing the equivalent treatment of the four methane hydrogens. To achieve such a treatment, we present extended forms of the path integral estimators for relevant quantities that may be used for general N-atom systems with any generalized reaction coordinates. The quantum instanton rates thus obtained for the temperature range T = 200-2000 K show good agreement with available experimental data, which gives support to the accuracy of the underlying potential surface used.     

Semiclassical initial value representation treatment of a hydrogen bonded complex of rigid water molecules from a single trajectory in Cartesian coordinates

A semiclassical initial value representation approach for molecular systems in Cartesian coordinates is combined with a recently proposed time averaging technique [J. Chem. Phys. 118, 7174 (2003)]. It is shown that a single trajectory can yield the zero-point energy of the water dimer with good accuracy for the model chosen when compared to fully constrained Cartesian semiclassical calculations. The convergence with respect to the number of averaging time origins is discussed.