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, neural network-learned representations and combinations thereof. Future directions and potential improvements are discussed primarily from a practical, application-oriented perspective.

The fundamental vibrational frequencies and higher vibrationally excited states for the N3+ ion in its electronic ground state have been determined from quantum bound state calculations on three-dimensional potential energy surfaces (PESs) computed at the coupled-cluster singles and doubles with perturbative triples [CCSD(T)]-F12b/aug-cc-pVTZ-f12 and multireference configuration interaction singles and doubles with quadruples (MRCISD+Q)/aug-cc-pVTZ levels of theory. The vibrational fundamental frequencies are 1130 cm−1 (ν1, symmetric stretch), 807 cm−1 (ν3, asymmetric stretch), and 406 cm−1 (ν2, bend) on the higher-quality CCSD(T)-F12b surface. Bound state calculations based on even higher level PESs [CCSD(T)-F12b/aug-cc-pVQZ-f12 and MRCISD+Q-F12b/aug-cc-pVTZ-f12] confirm the symmetric stretch fundamental frequency as ∼1130 cm−1. This compares with an estimated frequency from experiment at 1170 cm−1 and previous calculations [Chambaud et al., Chem. Phys. Lett. 231, 9–12 (1994)] at 1190 cm−1. The remaining disagreement with the experimental frequency is attributed to uncertainties associated with the widths and positions of the experimental photoelectron peaks. Analysis of the reference complete active space self-consistent field wave function for the MRCISD+Q calculations provides deeper insight into the shape of the PES and lends support for the reliability of the Hartree–Fock reference wave function for the coupled cluster calculations. According to this, N3+ has a mainly single reference character in all low-energy regions of its electronic ground state (3A″) PES.

The photodissociation dynamics of N3+ excited from its (linear) 3Σg- /bent 3A'ground to the first excited singlet and triplet states is investigated. Three dimensional potential energy surfaces for the 1A', 1A', and 3A' electronic states, correlating with the 1Δg and 3 Πu states in linear geometry, for N3+ are constructed using high level electronic structure calculations and represented as reproducing kernels. The reference ab initio energies are calculated at the MRCI+Q/aug-cc-pVTZ level of theory. For following the photodissociation dynamics in the excited states, rotational and vibrational distributions P(v') and P(j') for the N2 product are determined from vertically excited ground state distributions. Due to the different shapes of the ground state 3A' PES and the excited states, appreciable angular momentum j' ∼ 60 is generated in the diatomic fragments. The lifetimes in the excited states extend to at least 50 ps. Notably, results from sampling initial conditions from a thermal ensemble and from the Wigner distribution of the ground state wavefunction are comparable.