Assignment of Infrared-Active Combination Bands in the Vibrational Spectra of Protonated Molecular Clusters Using Driven Classical Trajectories: Application to N4H+ and N4D. J Phys Chem A 2019;123:5613-5620. [PMID: 31244119 DOI: 10.1021/acs.jpca.9b04480]

Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis

A linearly parameterized functional form for a Cartesian representation of molecular dipole polarizability tensor surfaces (PTS) is described. The proposed expression for the PTS is a linearization of the recently reported power series ansatz of the original Applequist model, which by construction is non-linear in parameter space. This new approach possesses (i) a unique solution to the least-squares fitting problem; (ii) a low level of the computational complexity of the resulting linear regression procedure, comparable to those of the potential energy and dipole moment surfaces; and (iii) a competitive level of accuracy compared to the non-linear PTS model. Calculations of CH₄ PTS, with polarizabilities fitted to 9000 training set points with the energies up to 14,000 cm^-1 show an impressive level of accuracy of the linear PTS model obtained with ~1600 parameters: ~1% versus 0.3% RMSE for the non-linear vs. linear model on a test set of 1000 configurations.

Observing Intramolecular Vibrational Energy Redistribution via the Short-Time Fourier Transform

Intramolecular vibrational energy relaxation (IVR) is important in many problems in chemical physics. Here, we apply the short-time Fourier transform method for analyzing IVR with classical dynamics. Calculating time-dependent Fourier transforms to perform such an analysis requires extending the usual Fourier transform method, and we do that here. The guiding concept behind the generalization is that if there is a shift of vibrational energy from one frequency range to another, we see a difference between the spectrum before the shift and the spectrum after the shift. We use time-window functions to transform the power spectrum of a trajectory into a time-dependent density spectrum of the average kinetic energy. The time-dependent average kinetic energy for each interval of the spectrum becomes an indicator to monitor the extent and nature of the energy transfer into and out of the corresponding modes. We illustrate this method for the H₂O molecule. By analyzing cases with different initial conditions, we show that the short-time Fourier transform method can distinguish trends in IVR that depend on the initial distribution of energy and not just on the total energy.

Intramolecular Proton Transfer in the Hydrogen Oxalate Anion and the Cooperativity Effects of the Low-Frequency Vibrations: A Driven Molecular Dynamics Study

We report first-principles molecular dynamics (MD) and dipole-driven molecular dynamics (μ-DMD) simulations of the hydrogen oxalate anion at the MP2/aug-cc-pVDZ level of theory. We examine the role of vibrational coupling between the OH stretching bands, that is, the fundamental and a few combination bands spanning the 2900-3100 cm^-1 range, and several of the low-frequency bending and stretching fundamental modes. The low-frequency modes between 300 and 825 cm^-1 play a crucial role in the proton-transfer motion. Strong involvement of CO₂ and CCO bending and the CC stretching vibrations indicate that these large amplitude motions cause the shortening of the O···O distance and thus promote H⁺ transfer to the other oxygen by bringing it over the 3.4 kcal/mol barrier. Analysis of resonant μ-DMD trajectories shows that the complex spectral feature near 825 cm^-1, closely corresponding to both an overtone of two quanta of 425 cm^-1 and a combination band of low-frequency CO₂ rocking (300 cm^-1) and CCO bending (575 cm^-1) modes, is involved in the proton transfer. μ-DMD shows that exciting the system at these mode combinations leads to faster barrier activation than exciting at the OH fundamental mode.

Analysis of the Proton Transfer Bands in the Infrared Spectra of Linear N2H+···OC and N2D+···OC Complexes Using Electric Field-Driven Classical Trajectories

In this work, we describe ab initio calculations and assignment of infrared (IR) spectra of hydrogen-bonded ion-molecular complexes that involve a fluxional proton: the linear N₂H⁺···OC and N₂D⁺···OC complexes. Given the challenges of describing fluxional proton dynamics and especially its IR activity, we use electric field-driven classical trajectories, i.e., the driven molecular dynamics (DMD) method that was developed by us in recent years and for similar applications, in conjunction with high-level electronic structure theory. Namely, we present a modified and a numerically efficient implementation of DMD specifically for direct (or "on the fly") calculations, which we carry out at the MP2-F12/AVDZ level of theory for the potential energy surface (PES) and MP2/AVDZ for the dipole moment surfaces (DMSs). Detailed analysis of the PES, DMS, and the time-dependence of the first derivative of the DMS, referred to as the driving force, for the highly fluxional vibrations involving H⁺/D⁺ revealed that the strongly non-harmonic PES and non-linear DMS yield remarkably complex vibrational spectra. Interestingly, the classical trajectories reveal a doublet in the proton transfer part of the spectrum with the two peaks at 1800 and 1980 cm^-1. We find that their shared intensity is due to a Fermi-like resonance interaction, within the classical limit, of the H⁺ parallel stretch fundamental and an H⁺ perpendicular bending overtone. This doublet is also observed in the deuterated species at 1360 and 1460 cm^-1.