Semiclassical Initial Value Representation Calculations Research Articles

Semiclassical Vibrational Spectroscopy of Real Molecular Systems by Means of Cross-Correlation Filter Diagonalization.

We applied the harmonic inversion technique to extract vibrational eigenvalues from the semiclassical initial value representation (SC-IVR) propagator of molecular systems described by explicit potential surfaces. The cross-correlation filter-diagonalization (CCFD) method is used for the inversion problem instead of the Fourier transformation, which allows much shorter propagation time and is thus capable of avoiding numerical divergence issues while getting rid of approximations like the separable one to the pre-exponential factor. We also used the "Divide-and-Conquer" technique to control the total dimensions under consideration, which helps to further enhance the numerical behavior of SC-IVR calculations and the stability of harmonic inversion methods. The technique is tested on small molecules and water trimer to justify its applicability and reliability. Results show that the CCFD method can effectively extract the vibrational eigenvalues from short trajectories and reproduce the original spectra conventionally obtained from long-time ones, with no loss on accuracy while the numerical behavior is much better. This work demonstrates the possibility to apply the combined method of CCFD and SC-IVR to real molecular potential surfaces, which might be a new way to overcome the numerical instabilities caused by the increase of dimensions.

A quantum mechanical insight into SN2 reactions: Semiclassical initial value representation calculations of vibrational features of the Cl-⋯CH3Cl pre-reaction complex with the VENUS suite of codes.

The role of vibrational excitation of reactants in driving reactions involving polyatomic species has been often studied by means of classical or quasi-classical trajectory simulations. We propose a different approach based on investigation of vibrational features of the Cl-⋯CH3Cl pre-reaction complex for the Cl- + CH3Cl SN2 reaction. We present vibrational power spectra and frequency estimates for the title pre-reaction complex calculated at the level of classical, semiclassical, and second-order vibrational perturbation theory on a pre-existing analytical potential energy surface. The main goals of the paper are the study of anharmonic effects and understanding of vibrational couplings that permit energy transfer between the collisional kinetic energy and the internal vibrations of the reactants. We provide both classical and quantum pictures of intermode couplings and show that the SN2 mechanism is favored by the coupling of a C-Cl bend involving the Cl- projectile with the CH3 rocking motion of the target molecule. We also illustrate how the routines needed for semiclassical vibrational spectroscopy simulations can be interfaced in a user-friendly way to pre-existing molecular dynamics software. In particular, we present an implementation of semiclassical spectroscopy into the VENUS suite of codes, thus providing a useful computational tool for users who are not experts of semiclassical dynamics.

Efficient importance sampling in semiclassical initial value representation calculations for time correlation functions

The semiclassical (SC) theory based on an initial value representation (IVR) methodology provides a practical way to describe quantum effects in complex molecular systems. The efficiency of SC–IVR calculations for time correlation functions depends heavily on how to perform the Monte Carlo sampling of initial conditions. Here, we compare a variety of possibilities of sampling initial conditions in the SC calculations by choosing the sampling function to be either time-dependent or time-independent (TI). The implementation of these importance sampling protocols to two benchmark system-bath models demonstrates its advantages over the standard sampling method. In particular, the recently developed TI importance sampling which incorporates path correlation in the bath degrees of freedom shows a great potential in describing many-body quantum dynamics efficiently and accurately.

Time-dependent importance sampling in semi-classical initial value representation calculations for time correlation functions. III. A state-resolved implementation to electronically non-adiabatic dynamics

The recently developed time-dependent (TD) Monte Carlo (MC) importance sampling method [Tao and Miller; JCP 135, 024104 (2011)] provides an efficient implementation of the semi-classical (SC) initial value representation (IVR) methodology for the evaluation of time correlation functions. The key idea in this TD-SC-IVR method is to perform importance sampling of trajectories for the MC averages in the SC calculations with a sampling function that includes information about the final (time-evolved) values of the coordinates and momenta of trajectories in addition to (the usual) information of their initial values. This paper shows how this approach deals with electronically non-adiabatic dynamics, i.e. dynamics that involves coupled multiple electronic states. We suggest that a state-resolved sampling function may facilitate the efficient implementation of TD-SC-IVR for such processes. This is illustrated by application to the calculation of the nuclear momentum distribution function (i.e. the nuclear energy-loss spectrum) for a benchmark non-adiabatic scattering problem.

Communication: Importance sampling including path correlation in semiclassical initial value representation calculations for time correlation functions

Full semiclassical (SC) initial value representation (IVR) for time correlation functions involves a double phase space average over a set of two phase points, each of which evolves along a classical path. Conventionally, the two initial phase points are sampled independently for all degrees of freedom (DOF) in the Monte Carlo procedure. Here, we present an efficient importance sampling scheme by including the path correlation between the two initial phase points for the bath DOF, which greatly improves the performance of the SC-IVR calculations for large molecular systems. Satisfactory convergence in the study of quantum coherence in vibrational relaxation has been achieved for a benchmark system-bath model with up to 21 DOF.

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation

An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions

An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations.

Quantum molecular dynamics of hydrogen bonded complexes of rigid molecules using the semiclassical initial value representation in Cartesian coordinates

Semiclassical initial value representation calculations are performed for the constrained water dimer in Cartesian coordinates. The study represents the first application of a previously reported method [Issak and Roy, J. Chem. Phys. 123, 084103 (2005); 126, 024111 (2007)] to a molecular cluster. Bound state energies are calculated for a dimer of rigid water molecules (H2O)2 as well as its deuterated form (D2O)2. The results show that the approach fares well with respect to accuracy in capturing quantum effects in intermolecular interactions.

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.

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: Accurate reduction in zero-point energy

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

On the semiclassical description of quantum coherence in thermal rate constants

An earlier paper of ours [J. Chem. Phys. 108, 9726 (1998)] used an approximate (linearized) version of the semiclassical initial value representation (SC-IVR) to calculate reactive flux correlation functions for a model of unimolecular isomerization, namely a 1-d double well potential coupled to an infinite set of harmonic oscillators, obtaining excellent agreement with accurate quantum results for this system. Here we analyze this linearized approximation (LA) further, however, and show that it is not capable of describing quantum interference/coherence effects in the longer time recrossing behavior of the isomerization dynamics. (The recrossing effects seen in our earlier work were due to classical mechanics.) To accentuate quantum effects in the recrossing dynamics, the present article considers the double well potential without the harmonic bath, using both the LA and the full SC-IVR. The results of the calculations show that the flux correlation functions given by the LA agrees well with the exact quantum correlation function for times up to ≈ℏβ, meaning that it describes quantum effects in the direct or transition state theory like dynamics accurately. For the longer time recrossing dynamics, however, it agrees with the classical rather than the quantum correlation function, i.e., it does not describe quantum coherence effects on this time scale. The full SC-IVR calculations, however, are in reasonably good agreement with the quantum correlation function for these longer times.