Ab initio centroid path integral molecular dynamics: Application to vibrational dynamics of diatomic molecular systems

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Capturing Deuteration Effects in a Molecular Mechanics Force Field: Deuterated THF and the THF-Water Miscibility Gap

Deuteration is a common chemical modification used in conjunction with experiments such as neutron scattering, NMR, and Fourier-transform infrared for the study of molecular systems. Under the Born-Oppenheimer (BO) approximation, while the underlying potential energy surface remains unchanged by isotopic substitutions, isotopic substitution still alters intramolecular vibrations, which in turn may alter intermolecular interactions. Molecular mechanics (MM) force fields used in classical molecular dynamics simulations are assumed to represent local approximations of the BO potential energy surfaces, and hence, MD simulations using simple isotopic mass substitutions should capture BO-compatible isotope effects. However, standard MM force-field parameterizations do not directly fit to the local harmonic quantum mechanical (QM) Hessian that describes the BO surface, but rather to QM normal-modes and/or mass-dependent internal-coordinate derived distortion energies. Here, using tetrahydrofuran (THF)-water mixtures as our model system, we show that not only does a simple mass-substitution approach fail to capture an experimentally characterized deuteration effect (the loss of the closed-loop miscibility gap associated with the complete deuteration of THF) but also it is necessary to generate new MM force-field parameters that correctly describe isotopic dependent vibrations to capture the experimental deuteration effect. We show that the origin of this failure is a result of using mass-dependent features to fit the THF MM force field, which unintentionally biases the bonded terms of the force field to represent only the isotopologue used during the original force-field parameterization. In addition, we make use of our isotopologue-corrected force field for D₈THF to examine the molecular origins of the isotope-dependent loss of the THF-water miscibility gap.

A Systematic Approach for Computing Zero-Point Energy, Quantum Partition Function, and Tunneling Effect Based on Kleinert's Variational Perturbation Theory

In this paper, we describe an automated integration-free path-integral (AIF-PI) method, based on Kleinert's variational perturbation (KP) theory, to treat internuclear quantum-statistical effects in molecular systems. We have developed an analytical method to obtain the centroid potential as a function of the variational parameter in the KP theory, which avoids numerical difficulties in path-integral Monte Carlo or molecular dynamics simulations, especially at the limit of zero-temperature. Consequently, the variational calculations using the KP theory can be efficiently carried out beyond the first order, i.e., the Giachetti-Tognetti-Feynman-Kleinert variational approach, for realistic chemical applications. By making use of the approximation of independent instantaneous normal modes (INM), the AIF-PI method can readily be applied to many-body systems. Previously, we have shown that in the INM approximation, the AIF-PI method is accurate for computing the quantum partition function of a water molecule (3 degrees of freedom) and the quantum correction factor for the collinear H(3) reaction rate (2 degrees of freedom). In this work, the accuracy and properties of the KP theory are further investigated by using the first three order perturbations on an asymmetric double-well potential, the bond vibrations of H(2), HF, and HCl represented by the Morse potential, and a proton-transfer barrier modeled by the Eckart potential. The zero-point energy, quantum partition function, and tunneling factor for these systems have been determined and are found to be in excellent agreement with the exact quantum results. Using our new analytical results at the zero-temperature limit, we show that the minimum value of the computed centroid potential in the KP theory is in excellent agreement with the ground state energy (zero-point energy) and the position of the centroid potential minimum is the expectation value of particle position in wave mechanics. The fast convergent property of the KP theory is further examined in comparison with results from the traditional Rayleigh-Ritz variational approach and Rayleigh-Schrödinger perturbation theory in wave mechanics. The present method can be used for thermodynamic and quantum dynamic calculations, including to systematically determine the exact value of zero-point energy and to study kinetic isotope effects for chemical reactions in solution and in enzymes.

Interconversion behavior of the C-H bond in the CH4+ radical cation: ab initio molecular dynamics study

Thermal motion of CH4+ is investigated by performing an ab initio molecular dynamics method with the second-order Møller-Plesset (MP2)/6-311G** force field. In the trajectories obtained at 400 K, we have observed rapid interconversion behavior of the geometrical parameters of CH4+ with the frequency of 0.6/ps, where the C-H pair forming the small angle around 55 degrees is switched to another pair on subpicosecond time scale. The switching patterns are found to be classified into the following two types. Type 1: one C-H of the small angled C-H pair is switched to one C-H of the other C-H pair. Type 2: the small angled C-H pair is switched to the other C-H pair, which has been newly observed in the present ab initio MD calculation. The four C-H bonds of CH4+ are characterized by the long and short C-H bonds in a time region of the trajectories, and also for the time-evolution of C-H bonds such interconversion behavior is observed. The switching patterns of the geometrical parameters are compared with those in the interconversion scheme between six equivalent C2v symmetry structures of CH4+ [Paddon-Row, M. N. et al., J Am Chem Soc 1985, 107, 7696]. We have also investigated the electronic energy fluctuation due to thermal motion of CH4+. The standard deviation of total electronic energy at 400 K is evaluated to be 1.2 kcal/mol.

Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range

Fundamental transport properties of liquid para-hydrogen (p-H(2)), i.e., diffusion coefficients, thermal conductivity, shear viscosity, and bulk viscosity, have been evaluated by means of the path integral centroid molecular dynamics (CMD) calculations. These transport properties have been obtained over the wide temperature range, 14-32 K. Calculated values of the diffusion coefficients and the shear viscosity are in good agreement with the experimental values at all the investigated temperatures. Although a relatively large deviation is found for the thermal conductivity, the calculated values are less than three times the amount of the experimental values at any temperature. On the other hand, the classical molecular dynamics has led all the transport properties to much larger deviation. For the bulk viscosity of liquid p-H(2), which was never known from experiments, the present CMD has given a clear temperature dependence. In addition, from the comparison based on the principle of corresponding states, it has been shown that the marked deviation of the transport properties of liquid p-H(2) from the feature which is expected from the molecular parameters is due to the quantum effect.