N$_3^+$: Full-Dimensional Potential Energy Surface, Vibrational Energy Levels and Ground State Dynamics

The fundamentals and higher vibrationally excited states for the N$_3^+$ ion in its electronic ground state have been determined from quantum bound state calculations on 3-dimensional potential energy surfaces (PESs) at the CCSD(T)-F12 and MRCI+Q levels of theory. The vibrational fundamentals are at 1130 cm$^{-1}$ ($ u_1$, symmetric stretch), 807 cm$^{-1}$ ($ u_3$, asymmetric stretch), and 406 cm$^{-1}$ ($ u_2$, bend) on the higher-quality CCSD(T)-F12 surface. For $ u_1$, the calculations are close to the estimated frequency from experiment (1170 cm$^{-1}$) and previous calculationscite{rosmus.n3:1994} which find it at 1190 cm$^{-1}$. Calculations of the vibrational states on the MRCI+Q PES are in qualitative agreement with those using the CCSD(T)-F12 PES. Analysis of the reference CASSCF wave function for the MRCI+Q calculations provides further insight into the shape of the PES and lends support for the reliability of Hartree-Fock as the reference wave function for the coupled cluster calculations. According to this, N$_3^+$ has mainly single reference character in all low-energy regions of its electronic ground state ($^3$A$$) 3d PES.

High-Dimensional Potential Energy Surfaces for Molecular Simulations

An overview of computational methods to describe high-dimensional potential energy surfaces suitable for atomistic simulations is given. Particular emphasis is put on accuracy, computability, transferability and extensibility of the methods discussed. They include empirical force fields, representations based on reproducing kernels, using permutationally invariant polynomials, and neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.