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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 explicitly correlated coupled-cluster singles and doubles with perturbative triples [CCSD(T)]-F12b/aug-cc-pVTZ based potential energy surface in permutationally invariant polynomials (PIPs) of Yu et al. [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 linear regression for potential energy distributions. The MD/α-DMD simulations reveal (i) a strong Raman activity at 260 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 the 500–2000 cm−1 range, assignable to the parallel N⋯H+⋯N proton transfer overtone; and (iii) the presence of a Fermi-like resonance in the Raman spectrum near 2400 cm−1 between the Σg+ N–N stretch fundamental and the Πu overtone corresponding to perpendicular N⋯H+⋯N proton transfer. 

Abstract 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 CH₄PTS, with polarizabilities fitted to 9000 training set points with the energies up to 14,000 cm⁻¹show 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.