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.

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.

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.

Enzymes are remarkably efficient catalysts evolved to perform well‐defined and highly specific chemical transformations. Studying the nature of enzymatic rate enhancements is highly important from several aspects, including the rational design of synthetic catalysts and transition‐state inhibitors. Herein, we describe recent progress in our group in the development of multiscale simulation methods and their application to several enzyme systems. In particular, we describe the use of combined quantum mechanics/molecular mechanics (QM/MM) methods in classical and quantum simulations. The development of various novel path‐integral methods is reviewed. These methods are tailor‐made for enzyme systems, where only a few degrees of freedom involved in the chemistry need to be quantized. The application of the hybrid QM/MM quantum‐classical simulation approach to three case studies is presented. The first case involves proton transfer in nitroalkane oxidase, where the enzyme employs tunneling as a catalytic fine‐tuning tool. The second case presented involves orotidine 5′‐monophosphate decarboxylase, where multidimensional free energy simulations together with kinetic isotope effects are combined in the study of the reaction mechanism. Finally, we discuss the monoterpene cyclase bornyl diphosphate synthase, where non‐statistical dynamics is a key component in enzyme function.

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