We describe an approach to constructing an analytic Cartesian representation of the molecular dipole polarizability tensor surface in terms of polynomials in interatomic distances with a training set of ab initio data points obtained from a molecular dynamics (MD) simulation or by any other available means. The proposed formulation is based on a perturbation treatment of the unmodified point dipole polarizability model of Applequist [J. Am. Chem. Soc.1972942952] and is shown here to be, by construction (i) free of short-range or other singularities or discontinuities, (ii) symmetric and translationally invariant, and (iii) nonreliant on a body-fixed coordinate system. Permutational invariance of like nuclei is demonstrated to be readily applicable, making this approach useful for highly fluxional and reactive systems. Derivation of the method is described in detail, adding brief didactic numerical examples of H2 and H2O and concluding with an MD simulation of the Raman spectrum of H5O2 + at 300 K with the polarizability tensor fitted to CCSD­(T)/aug-cc-pVTZ data obtained using the HBB-4B potential [044308J. Chem. Phys.2005122].

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 CH 4 PTS, with polarizabilities fitted to 9000 training set points with the energies up to 14,000 cm À1 show an impressive level of accuracy of the linear PTS model

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 N 2 H + •••OC and N 2 D + •••OC complexes. Given the challenges of describing fluxional proton dynamics and especially its IR activity, we use electric fielddriven 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 .

We present molecular dynamics (MD), polarizability driven MD (α-DMD) and pump-probe simulations of Raman spectra of the protonated nitrogen dimer N4H+, and some of its isotopologues, using the CCSD(T)-F12b/aug-cc-pVTZ based potential energy surface in permutationally invariant polynomials (PIP) due to Yu and co-workers [J. Phys. Chem. A 119, 11623, (2015)] and a corresponding PIP-derived CCSD(T)/aug-cc-pVTZ-tr (N: spd, H: sp) polarizability tensor surface (PTS), the latter reported here for the first time. To represent the PTS in terms of a PIP basis, we utilize a recently described formulation for computing the polarizability using a many-body expansion in the orders of dipole-dipole interactions while generating a training set using a novel approach based on a linear regression for potential energy distributions. The MD/α-DMD simulations reveal: (i) a strong Raman activity at 260 cm-1 and 2400 cm-1 corresponding to the symmetric N-N...H bend and symmetric N-N stretch modes, respectively; (ii) a very broad spectral region in 500-2000 cm-1 range assignable to the parallel N...H+...N proton transfer overtone, and (iii) presence of a Fermi-like resonance in the Raman spectrum near 2400 cm-1 between the 1Σg+ N-N stretch fundamental and the Πu overtone corresponding to perpendicular N...H+...N proton transfer.