Search

In this paper, we report a new algorithm for creating an adaptive basis set in the Multiconfigurational Ehrenfest (MCE) method, which is termed Full Cloning (FC), and test it together with the existing Multiple Cloning (MC) using the spin-boson model at zero-temperature as a benchmark. The zero-temperature spin-boson regime is a common hurdle in the development of methods that seek to model quantum dynamics. Two versions of MCE exist. We demonstrate that MC is vital for the convergence of MCE version 2 (MCEv2). The first version (MCEv1) converges much better than MCEv2, but FC improves its convergence in a few cases where it is hard to converge it with the help of a reasonably small size of the basis set. [ABSTRACT FROM AUTHOR]

We present the result of our calculations of ultrafast electron diffraction (UED) for cyclobutanone excited into the S2 electronic state, which is based on the non-adiabatic dynamics simulations with the Ab Initio Multiple Cloning (AIMC) method with the electronic structure calculated at the SA(3)-CASSCF(12,12)/aug-cc-pVDZ level of theory. The key features in the UED pattern were identified, which can be used to distinguish between the reaction pathways observed in the AIMC dynamics, although there is a significant overlap between representative signals due to the structural similarity of the products. The calculated UED pattern can be compared with the experiment. [ABSTRACT FROM AUTHOR]

Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that 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 [D. 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 allows 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" that 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 biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [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]

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

In this paper, a two-layer scheme is outlined for the coupled coherent states (CCS) method, dubbed two-layer CCS (2L-CCS). The theoretical framework is motivated by that of the multiconfigurational Ehrenfest method, where different dynamical descriptions are used for different subsystems of a quantum mechanical system. This leads to a flexible representation of the wavefunction, making the method particularly suited to the study of composite systems. It was tested on a 20-dimensional asymmetric system-bath tunnelling problem, with results compared to a benchmark calculation, as well as existing CCS, matching-pursuit/split-operator Fourier transform, and configuration interaction expansion methods. The two-layer method was found to lead to improved short and long term propagation over standard CCS, alongside improved numerical efficiency and parallel scalability. These promising results provide impetus for future development of the method for on-the-fly direct dynamics calculations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The vibrational predissociation of the Ne2Br2(B) van der Waals complex has been investigated using the quasi-classical trajectory method (QCT), in the range of vibrational levels v′ = 16-23. Extensive comparison is made with the most recent experimental observations [Pio et al., J. Chem. Phys. 133, 014305 (2010)], molecular dynamics with quantum transitions simulations [Miguel et al., Faraday Discuss. 118, 257 (2001)], and preliminary results from 24-dimensional Cartesian coupled coherent state (CCCS) calculations. A sequential mechanism is found to accurately describe the theoretical dynamical evolution of intermediate and final product populations, and both QCT and CCCS provide very good estimates for the dissociation lifetimes. The capabilities of QCT in the description of the fragmentation kinetics are analyzed in detail by using reduced-dimensionality models of the complexes and concepts from phase-space transport theory. The problem of fast decoupling of the different coherent states in CCCS simulations, resulting from the high dimensionality of phase space, is tackled using a re-expansion scheme. QCT ro-vibrational product state distributions are reported. Due to the weakness of the van der Waals couplings and the low density of vibrational states, QCT predicts a larger than observed propensity for Δv′ = -1 and -2 channels for the respective dissociation of the first and second Ne atoms. [ABSTRACT FROM AUTHOR]

In this article, we describe coupled coherent states (CCS) simulations of vibrational predissociation of weakly bounded complexes. The CCS method is implemented in the Cartesian frame in a manner that is similar to classical molecular dynamics. The calculated lifetimes of the vibrationally excited Ne-Br2(ν) complexes agree with experiment and previous calculations. Although the CCS method is, in principle, a fully quantum approach, in practice it typically becomes a semiclassical technique at long times. This is especially true following dissociation events. Consequently, it is very difficult to converge the quantum calculations of the final Br2 vibrational distributions after predissociation and of the autocorrelation functions. However, the main advantage of the method is that it can be applied with relative ease to determine the lifetimes of larger complexes and, in order to demonstrate this, preliminary results for tetra- and penta-atomic clusters are reported. [ABSTRACT FROM AUTHOR]

This article proposes an improved version of recently developed multiconfigurational Ehrenfest approach to quantum dynamics. The idea of the approach is to use frozen Gaussians (FG) guided by Ehrenfest trajectories as a basis set for fully quantum propagation. The method is applied to simulation of nonadiabatic dynamics of pyrazine and shows that nonadiabatic dynamics on two coupled electronic states S2 and S1, which determines pyrazine absorption spectrum, can be simulated with the help of a basis comprised of very small number of trajectory guided basis functions. For the 24 dimensional (24D) model, good results were obtained with the basis of only 250 trajectories guided FG per electronic state. The efficiency of the method makes it particularly suitable for future application together with direct dynamics, calculating potentials on the fly. [ABSTRACT FROM AUTHOR]

In this article a method of numerical solution of the Schrödinger equation is proposed. The approach corrects the Ehrenfest approximation by using several trajectories/configurations with their amplitudes coupled within and across configurations, thus making the method formally exact. Accurate results are obtained for the spin-boson model with up to 2000 bath modes treated on fully quantum level without approximations. [ABSTRACT FROM AUTHOR]

In this article, two coherent-state based methods of quantum propagation, namely, coupled coherent states (CCS) and Gaussian-based multiconfiguration time-dependent Hartree (G-MCTDH), are put on the same formal footing, using a derivation from a variational principle in Lagrangian form. By this approach, oscillations of the classical-like Gaussian parameters and oscillations of the quantum amplitudes are formally treated in an identical fashion. We also suggest a new approach denoted here as coupled coherent states trajectories (CCST), which completes the family of Gaussian-based methods. Using the same formalism for all related techniques allows their systematization and a straightforward comparison of their mathematical structure and cost. [ABSTRACT FROM AUTHOR]

The paper provides a systematic account of simple sampling techniques used in the multidimensional quantum dynamical method of coupled coherent states. For the sampling techniques based on a Gaussian distribution, it is noticed that faster convergence is achieved if “compression” of the basis set decreases as the basis size is increased. Good results are obtained for the autocorrelation functions of wave packets propagated in Henon-Heiles potentials with up to 32 degrees of freedom. Further test calculations are performed by employing trains of coherent states sampled on the same classical trajectory with successive time delays. [ABSTRACT FROM AUTHOR]

As a preliminary to future work on the behavior of atoms and molecules in strong time-dependent fields, we apply the coupled coherent-states (CCS) technique of multidimensional phase-space quantum dynamics to obtain Born–Oppenheimer energy levels of electrons in molecules. Unlike traditional approaches based on atomic and molecular-orbital basis sets and time-independent Schrödinger equation the CCS method exploits the solution of the time-dependent Schrödinger equation in the basis of Monte Carlo-selected trajectory-guided coherent states, which treat classical electron correlations exactly. In addition the CCS trajectories move over averaged potentials, which remove the Coulombic singularities. [ABSTRACT FROM AUTHOR]

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrödinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space. [ABSTRACT FROM AUTHOR]

As a preliminary to future work on the behavior of atoms and molecules in strong time-dependent fields, we apply the coupled coherent-states (CCS) technique of multidimensional phase-space quantum dynamics to obtain Born–Oppenheimer energy levels of electrons in molecules. Unlike traditional approaches based on atomic and molecular-orbital basis sets and time-independent Schrödinger equation the CCS method exploits the solution of the time-dependent Schrödinger equation in the basis of Monte Carlo-selected trajectory-guided coherent states, which treat classical electron correlations exactly. In addition the CCS trajectories move over averaged potentials, which remove the Coulombic singularities. [ABSTRACT FROM AUTHOR]

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrödinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space. [ABSTRACT FROM AUTHOR]

In this work we apply the coupled coherent states technique of quantum molecular dynamics to simulation of the absorption spectrum of pyrazine. All 24 vibrational modes are taken into account. The nonadiabatic coupling obetween the S1 and S2 electronic states is treated by a mapping approach that adds two extra degrees of freedom to the effective vibronic Hamiltonian. The results are in a good agreement with experiment and with previous calculations by quantum multiconfigurational time dependent Hartree and semiclassical Herman-Kluk methods. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A previously developed method of coupled coherent states (CCS) is applied to the simulation of intramolecular vibrational energy redistribution in the CHD[sub 3] 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[sup -1] at an excitation energy of ∼16 000 cm[sup -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. [ABSTRACT FROM AUTHOR]

Describes an intramolecular dynamics diffusion theory approach to complex unimolecular reactions. Energy diffusion theory for unimolecular reactions; Application for the dissociation of RDX; Potential energy surfaces.

Presents a method for computing unimolecular reaction rate constants in the IVR-limited regime. Details of the method based on Kramer's energy diffusion theory; Application to unimolecular reactions; Reaction rate constants; Validity of the theory.

The nonstatistical behavior of a unimolecular reaction at energies well in excess of the threshold is examined. This behavior is sometimes referred to as ‘‘intrinsically non-Rice–Ramsperger–Kassel–Marcus’’ (RRKM). It is well known that microcanonical unimolecular rates computed by using classical mechanics can deviate from the predictions of statistical theories, particularly at high energies. The simplest manifestation of this behavior is that rate constants as a function of energy cannot be represented by simple expressions such as the RRK equation, k(E)=ν(1-E*/E)s-1, with a single set of parameter values over a wide energy range; more specifically, fits of the classical RRK expression to trajectory results frequently yield values for the effective number of degrees of freedom s that are significantly smaller than the ‘‘theoretical’’ values 3N-6. In the present study, rates were calculated for the unimolecular dissociation of dimethylnitramine, (CH3)2NNO2, by simple N–N bond rupture over wide energy ranges by using classical trajectories and Monte Carlo transition-state theory. The formalism of a diffusional theory of chemical reactions is used to develop a model that relates classical reaction rates to intramolecular vibrational energy redistribution (IVR). This model is based on the assumption that the molecular modes can be separated into reaction coordinate and energy reservoir modes. It is shown how this model can be used to extrapolate high-energy, nonstatistical classical trajectory rates to the low-energy, statistical region. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents the results of a study on the collision of hydrogen atoms with Cu(111) surface. Examination of the formation of trapped hot-precursor atoms on the surface; Development of stochastic models to describe hot-atom energy dissipation; Importance of the Fokker-Planck equation.

Focuses on intramolecular dynamics diffusion theory based on diffusion theory for calculating unimolecular reaction rates at high energies where reaction is limited by the intramolecular vibrational energy redistribution rate. Use of short-time classical trajectory results to determine the characteristic times for the evolution of an initial microcanonical distribution.

In this article we report the formalism and first implementation of the ab initio multiconfigurational Ehrenfest (AI-MCE) method for simulation of ultrafast nonadiabatic dynamics, which uses the MOLPRO electronic structure program to calculate the potential energy surfaces on the fly. The approach is tested on the benchmark of the excited ππ* state dynamics of ethylene producing the dynamics which agree with previous simulations by ab initio multiple spawning technique. The AI-MCE seems to be robust, stable and efficient. [ABSTRACT FROM AUTHOR]

Molecular dynamics (MD) methods are increasingly widespread, but simulation of rare events in complex molecular systems remains a challenge. We recently introduced the boxed molecular dynamics (BXD) method, which accelerates rare events, and simultaneously provides both kinetic and thermodynamic information. We illustrate how the BXD method may be used to obtain high-resolution kinetic data from explicit MD simulations, spanning picoseconds to microseconds. The method is applied to investigate the loop formation dynamics and kinetics of cyclisation for a range of polypeptides, and recovers a power law dependence of the instantaneous rate coefficient over six orders of magnitude in time, in good agreement with experimental observations. Analysis of our BXD results shows that this power law behaviour arises when there is a broad and nearly uniform spectrum of reaction rate coefficients. For the systems investigated in this work, where the free energy surfaces have relatively small barriers, the kinetics is very sensitive to the initial conditions: strongly non-equilibrium conditions give rise to power law kinetics, while equilibrium initial conditions result in a rate coefficient with only a weak dependence on time. These results suggest that BXD may offer us a powerful and general algorithm for describing kinetics and thermodynamics in chemical and biochemical systems. [ABSTRACT FROM AUTHOR]

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 Schro¨dinger 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. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

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 Schro¨dinger 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. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Numerical solutions of the quantum time-dependent integro-differential Schro¨dinger 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. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

As a preliminary to future work on the behavior of atoms and molecules in strong time-dependent fields, we apply the coupled coherent-states (CCS) technique of multidimensional phase-space quantum dynamics to obtain Born-Oppenheimer energy levels of electrons in molecules. Unlike traditional approaches based on atomic and molecular-orbital basis sets and time-independent Schrodinger equation the CCS method exploits the solution of the time-dependent Schrodinger equation in the basis of Monte Carlo-selected trajectory-guided coherent states, which treat classical electron correlations exactly. In addition the CCS trajectories move over averaged potentials, which remove the Coulombic singularities.

We report a new version of the diffusion Monte Carlo (DMC) method, based on coherent-state quantum mechanics. Randomly selected grids of coherent states in phase space are used to obtain numerical imaginary time solutions of the Schrodinger equation, with an iterative refinement technique to improve the quality of the Monte Carlo grid. Accurate results were obtained, for the appropriately symmetrized two lowest states of the hydrogen molecule, by Monte Carlo sampling and six-dimensional propagation in the full phase space.