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Energy transfer in multichromophoric molecules can be affected by coherences that are induced by the electronic and vibrational couplings between chromophore units. Coherent electron-vibrational dynamics can persist at the subpicosecond time scale even at room temperature. Furthermore, wave-like localized-delocalized motions of the electronic wave function can be modulated by vibrations that actively participate in the intermolecular energy transfer process. Herein, nonadiabatic excited state molecular dynamics simulations have been performed on a rigid synthetic heterodimer that has been proposed as a simplified model for investigating the role and mechanism of coherent energy transfer in multichromophoric systems. Both surface hopping (SH) and Ehrenfest approaches (EHR) have been considered. After photoexcitation of the system at room temperature, EHR simulations reveal an ultrafast beating of electronic populations between the two lowest electronic states. These oscillations are not observed at low temperature and have vibrational origins. Furthermore, they cannot be reproduced using SH approach. This periodic behavior of electronic populations induces oscillations in the spatial localization of the electronic transition density between monomers. Vibrations whose frequencies are near-resonant with energy difference between the two lowest electronic excited states are in the range of the electronic population beating, and they are the ones that contribute the most to the coherent dynamics of these electronic transitions.

We demonstrate how recently developed Boxed Molecular Dynamics (BXD) and kinetics [D. V. Shalashilin et al., J. Chem. Phys. 137, 165102 (2012)] can provide a kinetic description of protein pulling experiments, allowing for a connection to be made between experiment and the atomistic protein structure. BXD theory applied to atomic force microscopy unfolding is similar in spirit to the kinetic two-state model [A. Noy and R. W. Friddle, Methods 60, 142 (2013)] but with some differences. First, BXD uses a large number of boxes, and therefore, it is not a two-state model. Second, BXD rate coefficients are obtained from atomistic molecular dynamics simulations. BXD can describe the dependence of the pulling force on pulling speed. Similar to Shalashilin et al. [J. Chem. Phys. 137, 165102 (2012)], we show that BXD is able to model the experiment at a very long time scale up to seconds, which is way out of reach for standard molecular dynamics.

In many scientific fields, there is an interest in understanding the way in which chemical networks evolve. The chemical networks which researchers focus upon have become increasingly complex, and this has motivated the development of automated methods for exploring chemical reactivity or conformational change in a "black-box" manner, harnessing modern computing resources to automate mechanism discovery. In this work, we present a new approach to automated mechanism generation which couples molecular dynamics and statistical rate theory to automatically find kinetically important reactions and then solve the time evolution of the species in the evolving network. The key to this chemical network mapping through combined dynamics and ME simulation approach is the concept of "kinetic convergence", whereby the search for new reactions is constrained to those species which are kinetically favorable at the conditions of interest. We demonstrate the capability of the new approach for two systems, a well-studied combustion system and a multiple oxygen addition system relevant to atmospheric aerosol formation.

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum-classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

Photo-dissociation dynamics is simulated for vibrationally pre-excited pyrrole molecules using an ab initio multiple cloning approach. Total kinetic energy release (TKER) spectra and dissociation times are calculated. It is found that pre-excitation of N-H bond vibrations facilitates fast direct dissociation, which results in a significant increase in the high-energy wing of TKER spectra. The results are in very good agreement with the recent vibrationally mediated photo-dissociation experiment, where the TKER spectrum was measured for pyrrole molecules excited by a combination of IR and UV laser pulses. Calculations for other vibrational modes show that this effect is specific for N-H bond vibrations: Pre-excitation of other modes does not result in any significant changes in TKER spectra.

We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules. Ministry of Education (MOE) Published version L. Chen acknowledges support from the Max-Planck Gesellschaft via the MPI-PKS visitors program. K. Sun would like to thank the Natural Science Foundation of Zhejiang Province (Grant No. LY18A040005) for support. M. F. Gelin acknowledges the support of Hangzhou Dianzi University through the startup funding. Y. Zhao would like to thank the support of the Singapore Ministry of Education Academic Research Fund Tier 1 (Grant Nos. 2018-T1- 002-175 and 2020-T1-002-075) and Tier 2 (Grant No. MOE2019- T2-1-085). D.V.S. acknowledges EPSRC (Grant No. EP/P021123/1).

We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal. It is shown that a detailed dynamical picture of the singlet fission process can be extracted from the three spectroscopic signals. An increasing temperature leads to lower intensities of the signals and broadened vibrational peaks, which can be attributed to faster singlet-triplet population transfer and stronger bath-induced electronic dephasing at higher temperatures. Ministry of Education (MOE) Submitted/Accepted version L.P.C. acknowledges support from the Max-Planck Gesellschaft via the MPI-PKS visitors program. D.V.S. acknowledges EPSRC (Grant No. EP/P021123/1). Y.Z. thanks the Singapore Ministry of Education Academic Research Fund Tier 1 (Grant Nos. 2018-T1-002-175 and 2020-T1-002-075) for support. M.F.G. acknowledges the support of Hangzhou Dianzi University through startup funding.

We present results obtained using the ab initio multiple cloning (AIMC) method to simulate fully quantum dynamics for imidazole and its structural isomer pyrazole along with their selectively deuterated species. We simulate the ultrafast dissociation of the N-H/D bond for these molecules along the repulsive 1πσ* state which agrees well with previous experimental results. Our results give evidence for a two-stage dissociation of the N-H/D bond on the sub-50 fs regime for imidazole, pyrazole and their selectively deuterated species, and give evidence for the importance of the repulsive 1πσ* state along the N-H/D bond coordinate for the relaxation of both imidazole and pyrazole. The ability of these calculations to reproduce experimental results lends confidence that larger complex systems could be explored with predictive capabilities with the AIMC method. These results also confirm the ability of the AIMC method to add detailed insights into which experiments are blind.

Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner. Previously it has been shown that Zombie States with fractional occupations of spin-orbitals obeyed the correct Fermionic creation and annihilation algebra and presented results for real-time evolution [Dmitrii V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie States and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie States, that allow much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" which removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure.The proposed algorithm of imaginary time propagation on a biased random grids of Zombie States may present an alternative to existing Quantum Monte Carlo methods., Comment: 45 pages, 9 figures, supplementary material 3 pages, submitted to the Journal of Chemical Physics

We present a simple way to incorporate a molecule-field interaction into non-adiabatic molecular dynamics. This makes possible integrated simulation of the photoexcitaion and the ensuing photodynamics, providing accurate initial conditions that are specific for the particular wave-length and duration of the laser pulse. The proposed approach is applied to simulate the dynamics of pyrrole photodissociation. The approach is particularly convenient for the use with ab initio Multiple Cloning approach, but the idea can be implemented in other quantum dynamics methods.

Mechanical signals regulate functions of mechanosensitive proteins by inducing structural changes that are determinant for force-dependent interactions. Talin is a focal adhesion protein that is known to extend under mechanical load, and it has been shown to unfold via intermediate states. Here, we compared different nonequilibrium molecular dynamics (MD) simulations to study unfolding of the talin rod. We combined boxed MD (BXD), steered MD, and umbrella sampling (US) techniques and provide free energy profiles for unfolding of talin rod subdomains. We conducted BXD, steered MD, and US simulations at different detail levels and demonstrate how these different techniques can be used to study protein unfolding under tension. Unfolding free energy profiles determined by BXD suggest that the intermediate states in talin rod subdomains are stabilized by force during unfolding, and US confirmed these results.

We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integrals and exciton-phonon couplings are carefully examined by a detailed comparison with the fully variational multiple Davydov D2 ansatz. It is found that while the MCE approach and the multi-D2 ansatz produce almost exactly the same results for a small transfer integral, the results obtained by the multi-D2 ansatz start to deviate from those by the MCE approach at longer times for a large transfer integral. A large number of coherent state basis functions are required to characterize the delocalized features of the phonon wavefunction in the case of large transfer integral, which becomes computationally too demanding for the multi-D2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate and efficient simulations of polaron dynamics.

The efficiency of the intramolecular energy transfer in light harvesting dendrimers is determined by their well-defined architecture with high degree of order. After photoexcitation, through-space and through-bond energy transfer mechanisms can take place, involving vectorial exciton migration among different chromophores within dendrimer highly branched structures. Their inherent intramolecular energy gradient depends on how the multiple chromophoric units have been assembled, subject to their inter-connects, spatial distances, and orientations. Herein, we compare the photoinduced nonadiabatic molecular dynamics simulations performed on a set of different combinations of a chain of linked dendrimer building blocks composed of two-, three-, and four-ring linear polyphenylene chromophoric units. The calculations are performed with the recently developed ab initio multiple cloning-time dependent diabatic basis implementation of the Multiconfigurational Ehrenfest (MCE) approach. Despite differences in short time relaxation pathways and different initial exciton localization, at longer time scales, electronic relaxation rates and exciton final redistributions are very similar for all combinations. Unlike the systems composed of two building blocks, considered previously, for the larger 3 block systems here we observe that bifurcation of the wave function accounted by cloning is important. In all the systems considered in this work, at the time scale of few hundreds of femtoseconds, cloning enhances the electronic energy relaxation by ∼13% compared to that of the MCE method without cloning. Thus, accurate description of quantum effects is essential for understanding of the energy exchange in dendrimers both at short and long time scales. Fil: Freixas Lemus, Victor Manuel. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Ondarse Alvarez, Dianelys. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina Fil: Tretiak, Sergei. Los Alamos National Laboratory; Estados Unidos Fil: Makhov, D.V.. University Of Leeds; Reino Unido Fil: D. V. Shalashilin. University Of Leeds; Reino Unido Fil: Fernández Alberti, Sebastián. Universidad Nacional de Quilmes. Departamento de Ciencia y Tecnología; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina

The ultrafast photodissociation dynamics of 2-ethylpyrrole (2-EP) is simulated in a fully quantum manner on the S1 and S2 πσ* states by the ab initio multiple cloning (AIMC) method. AIMC treats electrons with accurate electronic structure methods "on the fly", and nuclear dynamics with wavefunction propagation via a basis set of Ehrenfest trajectory guided Gaussian wavepackets. Total kinetic energy release (TKER) spectra are produced, as well as velocity map images and N-H dissociation times. These are compared to results from time-resolved velocity map imaging studies, and the AIMC method is able to provide quantitative reproduction of experimental data, including dissociation times of 50-80 fs. Novel insight into the dissociation mechanism is then obtained, with the experimentally obtained time constant shown to be composed of two components. Firstly, there is a contribution in

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.

We present a new implementation of the Ab Initio Multiple Cloning (AIMC) method, which is applied for non-adiabatic excited-state molecular dynamics simulations of photoinduced processes in conjugated molecules. Within our framework, the multidimensional wave-function is decomposed into a superposition of a number of Gaussian coherent states guided by Ehrenfest trajectories that are suited to clone and swap their electronic amplitudes throughout the simulation. New generalized cloning criteria are defined and tested. Because of sharp changes of the electronic states, which are common for conjugated polymers, the electronic parts of the Gaussian coherent states are represented in the Time Dependent Diabatic Basis (TDDB). The input to these simulations in terms of the excited-state energies, gradients and non-adiabatic couplings, is calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. As a test case, we consider the photoinduced unidirectional electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer between dendritic branches are discussed. Fil: Freixas Lemus, Victor Manuel. Universidad Nacional de Quilmes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Fernández Alberti, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; Argentina Fil: Makhov, Dmitry V.. University of Leeds; Reino Unido. University of Bristol; Reino Unido Fil: Tretiak, Sergei. Los Alamos National High Magnetic Field Laboratory; Estados Unidos Fil: Shalashilin, Dmitrii. University of Leeds; Reino Unido

We present a theoretical framework for the analysis of ultrafast X-ray scattering experiments using nonadiabatic quantum molecular dynamics simulations of photochemical dynamics. A detailed simulation of a pump–probe experiment in ethylene is used to examine the sensitivity of the scattering signal to simulation parameters. The results are robust with respect to the number of wavepackets included in the total expansion of the molecular wave function. Overall, the calculated scattering signals correlate closely with the dynamics of the molecule.

Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method, a new variant of the MCE approach developed by us for dynamics involving multiple electronic states with numerous abrupt crossings. Excited-state energies, gradients and non-adiabatic coupling terms needed for dynamics simulation are calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. A comparative analysis of our results obtained using MCE-TDDB, the conventional Ehrenfest method and the surface-hopping approach with and without decoherence corrections is presented. Fil: Fernández Alberti, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; Argentina Fil: Makhov, Dmitry V.. University Of Leeds.; Reino Unido Fil: Tretiak, Sergei. Los Alamos National Laboratory; Estados Unidos Fil: Shalashilin, Dmitrii V.. University Of Leeds.; Reino Unido

A benchmark calculation is presented for the quantum dynamics of tunnelling through a multidimensional asymmetric double well potential. A model Hamiltonian is used with a 1-dimensional tunnelling mode coupled to an (M−1)-dimensional harmonic bath, a system-bath problem. The benchmark calculation uses a basis set expansion of the wavefunction, with separate basis functions for the system and bath. Indistinguishability of configurations is exploited to greatly reduce the expense of the calculation, and a fully converged result is achieved. Comparison is offered to existing quantum dynamical methods that have tested this model problem, and further benchmark results not previously studied are presented.

We report a detailed computational simulation of the photodissociation of pyrrole using the ab initio Multiple Cloning (AIMC) method implemented within MOLPRO. The efficiency of the AIMC implementation, employing train basis sets, linear approximation for matrix elements, and Ehrenfest configuration cloning, allows us to accumulate significant statistics. We calculate and analyze the total kinetic energy release (TKER) spectrum and Velocity Map Imaging (VMI) of pyrrole and compare the results directly with experimental measurements. Both the TKER spectrum and the structure of the velocity map image (VMI) are well reproduced. Previously, it has been assumed that the isotropic component of the VMI arises from long time statistical dissociation. Instead, our simulations suggest that ultrafast dynamics contributes significantly to both low and high energy portions of the TKER spectrum.

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.

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We present an account of our recent effort to improve simulation of the photodissociation of small heteroaromatic molecules using the Ab Initio Multiple Cloning (AIMC) algorithm. The ultimate goal is to create a quantitative and converged technique for fully quantum simulations which treats both electrons and nuclei on a fully quantum level. We calculate and analyse the total kinetic energy release (TKER) spectra and Velocity Map Images (VMI), and compare the results directly with experimental measurements. In this work, we perform new extensive calculations using an improved AIMC algorithm that now takes into account the tunnelling of hydrogen atoms. This can play an extremely important role in photodissociation dynamics.

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.

Quantum dynamics simulations of HO–SO 2 using the coupled coherent state methodology are described in detail. Motivated by the assumption of fast intramolecular vibrational energy redistribution (IVR) within the nascent collision complex in measurements of the association rate coefficients using the ‘proxy’ method, we examine IVR within HO–SO 2 . Like our earlier classical dynamics calculations [D.R. Glowacki, S.K. Reed, M.J. Pilling, D.V. Shalashilin, E. Martinez-Nunez, Phys. Chem. Chem. Phys. 11 (2009) 963], the quantum dynamics results suggest that OH vibrational excitation is deactivated within HO–SO 2 prior to its dissociation, although the quantum IVR rates are greater than those in the classical simulations. The ubiquitous question of zero point energy in classical dynamics calculations is also considered. Reducing the quantity of zero point energy included in classical dynamics calculations decreases the HO–SO 2 dissociation rate and increases the deactivation of the OH stretch thereby producing vibrational energy distributions for the dissociated OH that more closely resemble those from the quantum dynamics calculations.

In this paper, we present classical and coupled coherent states quantum dynamics simulations to investigate intramolecular vibrational energy redistribution (IVR) from an excited (v = 1-10) OH stretch within the HOSO 2 complex to the other molecular bath modes. Using an analytical PES derived from electronic structure theory calculations, the results obtained from both the classical and quantum simulations are in reasonable agreement. The dynamics results suggest that statistical models overpredict HOSO 2 dissociation k(E)s, and underpredict the amount of vibrational excitation in the nascent OH formed following complex dissociation. In order to understand the dynamics results, we utilize a simple analytical model for describing energy flow from excited modes to bath modes, and show that IVR limits complex dissociation at short times. We also consider qualitative mass affects on IVR, and consider the implications of this work on previous measurements of the OH + SO 2 association k ∞ using the proxy method. © the Owner Societies.

The results of Boxed Dynamics (BXD) fully atomistic simulations of protein unfolding by Atomic Force Microscope (AFM), in both force clamp (FC) and velocity clamp (VC) modes are reported. In AFM experiments the unfolding occurs on time scale which is too long for standard atomistic Molecular Dynamics (MD) simulations, which are usually performed with the addition of forces which exceed those of experiment by many orders of magnitude. BXD can reach the time scale of slow unfolding and sample the very high free energy unfolding pathway, reproducing the experimental dependence of pulling force against extension and extension against time. Calculations show the presence of the pulling force ‘humps’ previously observed in the Velocity Clamp (VC) AFM experiments and allow the identification of intermediate protein conformations responsible for them. Fully atomistic BXD simulations can estimate the rate of unfolding in the Force Clamp (FC) experiments up to the time scale of seconds.

In this article phase space constrained classical mechanics (PSCCM), a version of accelerated dynamics, is suggested to speed up classical trajectory simulations of slow chemical processes. The approach is based on introducing constraints which lock trajectories in the region of the phase space close to the dividing surface, which separates reactants and products. This results in substantial (up to more than 2 orders of magnitude) speeding up of the trajectory simulation. Actual microcanonical rates are calculated by introducing a correction factor equal to the fraction of the phase volume which is allowed by the constraints. The constraints can be more complex than previously used boosting potentials. The approach has its origin in Intramolecular Dynamics Diffusion Theory, which shows that the majority of nonstatistical effects are localized near the transition state. An excellent agreement with standard trajectory simulation at high energies and Monte Carlo Transition State Theory at low energies is demonstrated for the unimolecular dissociation of methyl nitrite, proving that PSCCM works both in statistical and nonstatistical regimes.

The paper reviews the new coupled coherent states (CCS) technique for solution of the time-dependent Schrodinger equation in phase space, as a method for simulating the quantum dynamics of high-dimensional systems. The method is fully quantum although it exploits grids of CS guided by classical mechanics. As distinct from other trajectory guided approaches, the trajectories that carry the coherent states are governed by the classical equivalent of a quantum mechanically ordered Hamiltonian, that ensures optimal cancellation in quantum mechanical coupling terms. The resulting smoothness in the kernel of the integro-differential equation is therefore well adapted for Monte Carlo sampling. The simplest non-unitary version of the theory also obviates the need to invert large overlap matrices. Unitary corrections are also included and the analytical connection with uncoupled semiclassical initial value representation (IVR) techniques is described in detail. A variety of applications are presented.

We extend the technique of quantum propagation on a grid of trajectory guided coupled coherent states to simulate experimental absorption spectra. The approach involves calculating the thermally averaged dipole moment autocorrelation function by means of quantum propagation in imaginary time. The method is tested on simulation of the far infrared spectrum of water trimer based on a three-dimensional model potential. Results are in good agreement with experiment and with other calculations.

A previously developed method of coupled coherent states (CCS) is applied to the simulation of intramolecular vibrational energy redistribution in the CHD3 molecule. All nine modes are taken into account within a fully quantum approach. Emphasis is placed on convergence with respect to the number of coherent states in relation to the desired propagation time, which was taken to be sufficient to resolve Fermi resonance splitting of ∼100 cm−1 at an excitation energy of ∼16 000 cm−1. Fermi-resonance beatings of energy between C–H stretch and two C–H bends as well as slow energy flow to the rest of the molecule are reproduced. Due to the use of Monte Carlo grids the CCS technique scales extremely well with the number of modes and allows fully quantum molecular dynamics simulations of polyatomic systems.

In this paper, we report a version of the coupled-coherent-states method which is able to accurately compute the high-order harmonic generation (HHG) spectrum of an electron in a laser field in one dimension by the use of trajectory-guided grids of Gaussian wave packets. It is shown that by periodic reprojection of the wave function and dynamically altering the basis set size, the method can account for a wave function which spreads out to cover a large area in phase space while still keeping computational expense low and ensuring the preservation of coherence of the wave function. The HHG spectra obtained show good agreement with those from a time-dependent Schr\"odinger equation solver. We show also that the part of the wave function which is responsible for HHG moves along a periodic orbit which is far from that of classical motion. Although this paper is a proof of principle and therefore focused on a simple one-dimensional system, future generalizations for the multielectron case are discussed.

We present a new algorithm for ab initio quantum nonadiabatic molecular dynamics that combines the best features of ab initio Multiple Spawning (AIMS) and Multiconfigurational Ehrenfest (MCE) methods. In this new method, ab initio multiple cloning (AIMC), the individual trajectory basis functions (TBFs) follow Ehrenfest equations of motion (as in MCE). However, the basis set is expanded (as in AIMS) when these TBFs become sufficiently mixed, preventing prolonged evolution on an averaged potential energy surface. We refer to the expansion of the basis set as "cloning," in analogy to the "spawning" procedure in AIMS. This synthesis of AIMS and MCE allows us to leverage the benefits of mean-field evolution during periods of strong nonadiabatic coupling while simultaneously avoiding mean-field artifacts in Ehrenfest dynamics. We explore the use of time-displaced basis sets, "trains," as a means of expanding the basis set for little cost. We also introduce a new bra-ket averaged Taylor expansion (BAT) to approximate the necessary potential energy and nonadiabatic coupling matrix elements. The BAT approximation avoids the necessity of computing electronic structure information at intermediate points between TBFs, as is usually done in saddle-point approximations used in AIMS. The efficiency of AIMC is demonstrated on the nonradiative decay of the first excited state of ethylene. The AIMC method has been implemented within the AIMS-MOLPRO package, which was extended to include Ehrenfest basis functions.

A previous initial value coupled coherent state (CCS) representation is applied to Gaussian wave packet propagation on multidimensional Henon Heiles potentials. Solutions of the time-dependent integro-differential Schrodinger equation are obtained in a basis of trajectory guided Frozen Gaussian Coherent States, with Monte Carlo sampling to ensure a unique capability for propagating multidimensional wave functions. Results, which are obtained for up to 14 D, are compared with those derived by the Herman–Kluk semiclassical initial value representation (IVR) wave packet method.

A previous initial value coherent state representation is applied to Gaussian wave packet propagation on one-dimensional and two-dimensional double well potentials. The method uses a basis of trajectory guided frozen Gaussian coherent states, sampled from a Monte Carlo ensemble, for numerical solutions of the quantum time dependent integro-differential Schrodinger equation. Accurate tunneling splittings are obtained. Comparisons are also made with corresponding results obtained by the Herman–Kluk semiclassical initial value representation wave packet method.

Numerical solutions of the quantum time-dependent integro-differential Schrodinger equation in a coherent state Husimi representation are investigated. Discretization leads to propagation on a grid of nonorthogonal coherent states without the need to invert an overlap matrix, with the further advantage of a sparse Hamiltonian matrix. Applications are made to the evolution of a Gaussian wave packet in a Morse potential. Propagation on a static rectangular grid is fast and accurate. Results are also presented for a moving rectangular grid, guided at its center by a mean classical path, and for a classically guided moving grid of individual coherent states taken from a Monte Carlo ensemble.

We analyze equations of motion which mimic successfully the process of energy transfer in multiple collisions of an atom or molecule with a surface. A Langevin model with a spatially dependent friction coefficient is considered. Similar to our previous model [D.V. Shalashilin, B. Jackson, J. Chem. Phys. 109 (1998) 2856] we assume that the friction is proportional to the repulsive force between the incident particle and the surface. Unlike the standard Langevin equation with constant friction coefficient, the energy dissipation is localized near the region of closest encounter, which is more consistent with the physics of energy exchange. The approach is tested on a flat surface model with a truncated harmonic particle–surface interaction, and on a realistic model describing the scattering of hydrogen atoms from a corrugated copper surface. Quantitative agreement with exact trajectory simulations (full slab calculations) has been achieved over a broad range of temperatures.

Two methods are explored for evolving wavefunctions using short-time propagators of Herman–Kluk form [M.F. Herman, E.K. Kluk, Chem. Phys. 91 (1984) 271]. At each time step the wavefunction is expanded in a set of coherent states distributed in phase space about a guiding trajectory. A harmonic approximation for the potential allows the stability analysis to be done analytically. A Monte Carlo `path integral' form for the long-time propagator is derived and tested for a simple harmonic system. Another approach, where the entire wavefunction is evolved one step at time, is applied to wavepacket motion in a Morse potential.

Quasiclassical molecular dynamics studies are made of H or D atoms incident from the gas phase onto D or H-covered Cu(111) surfaces. Two detailed model potential energy surfaces are used, both based on the results of extensive total energy calculations using the density functional method. The incident H (D) atoms can react directly to form HD via the Eley–Rideal mechanism, or trap onto the surface. These trapped hot atoms can react with the adsorbates to form HD or can eventually dissipate enough energy through collisions with the adsorbates to become immobile. We also observe the formation of D2 (H2). Probabilities for these various processes, as well as the rotational, vibrational, and translational energy distributions of the products are computed and compared with experiment. Hot-atom pathways to product formation are shown to make significant contributions. One of the potentials gives excellent agreement with experiment, while the other is less successful.

A further development of the intramolecular dynamics diffusion theory (IDDT) [J. Chem. Phys. 107, 6204 (1997)] for computing unimolecular reaction rate constants in the IVR-controlled regime is described. The approach is based on Kramers’ energy diffusion theory, with the reaction coordinate taken as the subsystem and the rest of the vibrational modes as the bath. The method provides a practical means of obtaining the rate constants in the IVR-controlled regime at considerable savings of computer time compared to the usual classical trajectory simulations. Its accuracy has been demonstrated in our earlier applications to some simple bond-fission reactions. In the study described here the idea of intrinsic reaction coordinate (IRC) is used to extend the IDDT approach to more complicated systems for which simple reaction coordinates are not easily identifiable. The basic idea is to take the IRC as the subsystem and the transverse vibrational modes as the bath. The method is applied to the unimolecular disso...

A method for computing unimolecular reaction rate constants in the IVR-limited regime is presented. It is based on Kramers’ energy diffusion theory, with the reaction coordinate taken as the subsystem and the rest of the vibrational modes as the bath. Applications to some bond fission reactions demonstrate that the method accurately predicts the rate constants for wide range of energies by using the result of a dynamical calculation of the reaction rate at a single energy to determine the friction coefficient. Examination of the energy exchange in the reaction coordinate provides a qualitative understanding of the validity of the approach for treating unimolecular reactions. Thus, the method provides a practical means of calculating reaction rates in the IVR-limited regime at considerable savings of computer time than that required by standard classical trajectory calculations.

We have performed first-principles total-energy calculations of low-dimensional sections of the electronically adiabatic potential energy surface (PES) that are relevant for the Eley–Rideal (ER) reaction of H atoms on a rigid Cu(111) surface. These calculations were performed within density-functional theory using a plane-wave and pseudopotential method and the generalized gradient approximation for the exchange-correlation energy. The calculated energy points for various configurations of one and two atoms on the Cu(111) surface were used to construct a model PES that can be used in ER reaction dynamics calculations.

The results of a theoretical study of H atoms colliding with a Cu(111) surface are presented. The metal is treated as a five-layer slab of 150 atoms, and all dynamics are classical. The formation of trapped “hot-precursor” atoms on the surface is examined, as well as the nature of their motion on the surface and their energy and momentum dissipation. Connections are made with recent Eley–Rideal experiments, for which hot-atom precursors may play an important role. To facilitate future simulations of Eley–Rideal and hot-atom reactions on metals, simple stochastic models are developed to describe hot-atom energy dissipation. A Fokker–Planck equation is used to model the hot-atom energy distribution. Quasi-Langevin terms, which simulate fluctuation and dissipation consistent with this Fokker–Planck description, are developed for the hot-atom equations of motion. These quasi-Langevin terms are different from the hydrodynamic forms used for Brownian-type motion.

This Letter demonstrates how coherent states can be used to construct an initial value representation for the propagator and classical S -matrix. Advantage is taken of the fact that the coherent state `coordinate' describes trajectories in phase space, resulting in an unusual structure for the propagator. The method, which avoids the usual stability analysis, is successfully applied to nonreactive atom–diatom scattering.

We have performed a quasi-classical molecular dynamics study of the reaction dynamics of HD formation by H or D atoms incident from the gas phase on a D or H-covered Cu(111) surface. A key ingredient has been the construction of a model potential-energy surface (PES) that has been exclusively based on results from total energy calculations using the density functional scheme. Our preliminary study supports the Rettner–Auerbach scenario that a significant fraction of the reactions occurs via hot-atom pathways as opposed to Eley–Rideal pathways, in which the incident atom reacts directly with the adsorbed atom. The calculated reaction probabilities and ro-vibrational distributions are in good agreement with the measured distributions. As observed experimentally on other metal surfaces, we also find that the incident atom induces secondary reactions among the adsorbates, producing either H2 or D2 molecules. The magnitude and the isotope dependence of the calculated secondary reaction probabilities are in good agreement with measured values.

Dynamics simulations were performed to study soft landing of SiNCS + and (CH3)2SiNCS+ ions on a self-assembled monolayer of perfluorinated alkanethiols on gold (F-SAM). Using classical trajectories, the short-time collision dynamics (picosecond scale) were investigated to analyze trapping probabilities for these silyl ions. Thermal desorption of trapped ions was simulated by using "boxed molecular dynamics" (BXD). The simulations predict substantial ion trapping in the collisions of these ions with the F-SAM, especially when the projectile's incident direction is normal to the surface. Desorption of the SiNCS+ ion occurs significantly faster than desorption of the methylated ion, which may explain why soft landing was experimentally observed for the latter ion only [Miller, S. A.; Luo, H.; Pachuta, S. J.; Cooks, R. G. Science 1997, 275, 1447-1450; Luo, H.; Miller, S. A.; Cooks, R. G.; Pachuta, S. J. Int. J. Mass. Spectrom. Ion Processes 1998, 174, 193-217]. The free energy profiles for desorption of these ions show minima at 15 Å above the gold slab, indicating that the silyl ion has a preference to reside on top of the monolayer. Deep penetration of the ion into the monolayer is prevented by a large free energy barrier. However, according to DFT calculations, if this process occurred, the SiNCS+ ion could strongly bind to the Au(111) surface that supports the perfluorinated alkanethiol chains.