Accurate quantum molecular dynamics for multidimensional systems by the basis expansion leaping multi-configuration Gaussian (BEL MCG) method

Efficient time-dependent vibrational coupled cluster computations with time-dependent basis sets at the two-mode coupling level: Full and hybrid TDMVCC[2]

The computation of the nuclear quantum dynamics of molecules is challenging, requiring both accuracy and efficiency to be applicable to systems of interest. Recently, theories have been developed for employing time-dependent basis functions (denoted modals) with vibrational coupled cluster theory (TDMVCC). The TDMVCC method was introduced along with a pilot implementation, which illustrated good accuracy in benchmark computations. In this paper, we report an efficient implementation of TDMVCC, covering the case where the wave function and Hamiltonian contain up to two-mode couplings. After a careful regrouping of terms, the wave function can be propagated with a cubic computational scaling with respect to the number of degrees of freedom. We discuss the use of a restricted set of active one-mode basis functions for each mode, as well as two interesting limits: (i) the use of a full active basis where the variational modal determination amounts essentially to the variational determination of a time-dependent reference state for the cluster expansion; and (ii) the use of a single function as an active basis for some degrees of freedom. The latter case defines a hybrid TDMVCC/TDH (time-dependent Hartree) approach that can obtain even lower computational scaling. The resulting computational scaling for hybrid and full TDMVCC[2] is illustrated for polyaromatic hydrocarbons with up to 264 modes. Finally, computations on the internal vibrational redistribution of benzoic acid (39 modes) are used to show the faster convergence of TDMVCC/TDH hybrid computations towards TDMVCC compared to simple neglect of some degrees of freedom.

A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde

We developed an approximate method for quantum reaction dynamics simulations, namely, a structure-based Gaussian (SBG) expansion approach, where SBG bases for the expansion of the wave function Ψ, expressed by a product of single-atom Cartesian Gaussians centered at the positions of respective nuclei, are mainly placed around critical structures on reaction pathways such as on the intrinsic reaction coordinate (IRC) through a transition state. In the present approach, the "pseudo-lattice points" at which SBGs are deployed are selected in a perturbative manner so as to make moderate the expansion length. We first applied the SBG idea to a two-dimensional quadruple-well model and obtained accurate tunneling splitting values between the lowest four states. We then applied it to hydrogen tunneling in malonaldehyde and achieved a tunneling splitting of 27.1 cm^-1 with only 875 SBGs at the MP2/6-31G(d,p) level of theory, in good agreement with 25 cm^-1 by the more elaborate multiconfiguration time-dependent Hartree method. Reasonable results were also obtained for singly and doubly deuterated malonaldehyde. We analyzed the tunneling states by utilizing expansion coefficients of individual SBGs and found that 40-45% of the SBGs in Ψ are nonplanar structures and SBGs away from the IRC contribute a little to hydrogen transfer.

Multidimensional Tunneling Dynamics Employing Quantum-Trajectory Guided Adaptable Gaussian Bases

An efficient basis representation of time-dependent wavefunctions is essential for theoretical studies of high-dimensional molecular systems exhibiting large-amplitude motion. For fully coupled anharmonic systems, the complexity of a general wavefunction scales exponentially with the system size; therefore, for practical reasons, it is desirable to adapt the basis to the time-dependent wavefunction at hand. Often times on this quest for a minimal basis representation, time-dependent Gaussians are employed, in part because of their localization in both configuration and momentum spaces and also because of their direct connection to classical and semiclassical dynamics, guiding the evolution of the basis function parameters. In this work, the quantum-trajectory guided adaptable Gaussian (QTAG) bases method [ J. Chem. Theory Comput. 2020, 16, 18-34] is generalized to include correlated, i.e., non-factorizable, basis functions, and the performance of the QTAG dynamics is assessed on benchmark system/bath tunneling models of up to 20 dimensions. For the popular choice of initial conditions describing tunneling between the reactant/product wells, the minimal "semiclassical" description of the bath modes using essentially a single multidimensional basis function combined with the multi-Gaussian representation of the tunneling mode is shown to capture the dominant features of dynamics in a highly efficient manner.