Quantum dynamical simulation of the scattering of Ar from a frozen LiF(100) surface based on a first principles interaction potential.

In-plane two and three dimensional diffraction patterns are computed for the vertical scattering of an Ar atom from a frozen LiF(100) surface. Suitable collimation of the incoming wavepacket serves to reveal the quantum mechanical diffraction. The interaction potential is based on a fit to an ab initio potential calculated using density functional theory with dispersion corrections. Due to the potential coupling found between the two horizontal surface directions, there are noticeable differences between the quantum angular distributions computed for two and three dimensional scattering. The quantum results are compared to analogous classical Wigner computations on the same surface and with the same conditions. The classical dynamics largely provides the envelope for the quantum diffractive scattering. The classical results also show that the corrugation along the [110] direction of the surface is smaller than along the [100] direction, in qualitative agreement with experimental observations of unimodal and bimodal scattering for the [110] and [100] directions, respectively.

Quantum Markovian master equation for scattering from surfaces.

We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multi-configurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.

On the fly first principles study of the classical scattering of an Ar atom from the LiF(100) surface.

A density functional theory with dispersion corrections is used to study the scattering of an Ar atom on the LiF(100) surface. On the fly classical trajectories are propagated to study the in-plane angular and energy loss distributions of the scattered Ar atom. The computations are carried out for a frozen surface and a surface in which the crystal atoms are initially at T = 0 K. Two dimensional as well as three dimensional computations are presented. We find that the results agree qualitatively with measured experimental results. These computations show the impact of three dimensional effects on the scattering such as narrowing of the angular distance between rainbow peaks and inversion of asymmetry properties of the angular distribution. The computations also reaffirm the prediction that one should observe energy loss rainbows in the scattering of Ar from the LiF(100) surface.

Path-integral calculations of heavy atom kinetic isotope effects in condensed phase reactions using higher-order Trotter factorizations.

A convenient approach to compute kinetic isotope effects (KIEs) in condensed phase chemical reactions is via path integrals (PIs). Usually, the primitive approximation is used in PI simulations, although such quantum simulations are computationally demanding. The efficiency of PI simulations may be greatly improved, if higher-order Trotter factorizations of the density matrix operator are used. In this study, we use a higher-order PI method, in conjunction with mass-perturbation, to compute heavy-atom KIE in the decarboxylation of orotic acid in explicit sulfolane solvent. The results are in good agreement with experiment and show that the mass-perturbation higher-order Trotter factorization provides a practical approach for computing condensed phase heavy-atom KIE.

Path-Integral Calculations of Nuclear Quantum Effects in Model Systems, Small Molecules, and Enzymes via Gradient-Based Forward Corrector Algorithms.

A practical approach to treat nuclear quantum mechanical (QM) effects in simulations of condensed phases, such as enzymes, is via Feynman path integral (PI) formulations. Typically, the standard primitive approximation (PA) is employed in enzymatic PI simulations. Nonetheless, these PI simulations are computationally demanding due to the large number of discretizations, or beads, required to obtain converged results. The efficiency of PI simulations may be greatly improved if higher order factorizations of the density matrix operator are employed. Herein, we compare the results of model calculations obtained employing the standard PA, the improved operator of Takahashi and Imada (TI), and several gradient-based forward corrector algorithms due to Chin (CH). The quantum partition function is computed for the harmonic oscillator, Morse, symmetric, and asymmetric double well potentials. These potentials are simple models for nuclear quantum effects, such as zero-point energy and tunneling. It is shown that a unique set of CH parameters may be employed for a variety of systems. Additionally, the nuclear QM effects of a water molecule, treated with density functional theory, are computed. Finally, we derive a practical perturbation expression for efficient computation of isotope effects in chemical systems using the staging algorithm. This new isotope effect approach is tested in conjunction with the PA, TI, and CH methods to compute the equilibrium isotope effect in the Schiff base-oxyanion keto-enol tautomerism in the cofactor pyridoxal-5'-phosphate in the enzyme alanine racemase. The study of the different factorization methods reveals that the higher-order actions converge substantially faster than the PA approach, at a moderate computational cost.