\textit{Ab Initio} Adiabatic Potential Energy Surfaces and Non-adiabatic Couplings for O$_3$: Construction of Four State Diabatic Hamiltonian

TL;DR

This paper presents highly accurate ab initio potential energy surfaces and non-adiabatic couplings for ozone, employing advanced electronic structure methods and systematic expansions to improve convergence and accuracy for modeling ozone's electronic states.

Contribution

It introduces a comprehensive ab initio approach combining SA-MCSCF and ic-MRCI(Q) with expanded active spaces and basis sets to accurately characterize ozone's electronic states and conical intersections.

Findings

Accurately reproduces ozone dissociation energies and vibrational frequencies.

Locates conical intersections at specific geometries.

Provides detailed non-adiabatic coupling data for ozone.

Abstract

We compute highly accurate first principle based \textit{ab initio} adiabatic potential energy surfaces (PESs) using State-Averaged Multi-Configurational Self-Consistent Field (SA-MCSCF) followed by internally contracted Multi-Reference Configuration Interaction method incorporating fixed-reference Davidson corrections [ic-MRCI(Q)], where a full valence active space of 18 electrons in 12 orbitals and aug-cc-pVQZ basis set are employed for the low-lying four singlet electronic states of ozone ($\tilde{X}^1A'$, $1~^1A''$, $1~^1A'$ and $2^1A''$). It accurately reproduces the dissociation energies of ozone (1.101 eV) as well as the molecular oxygen (5.106 eV) along with vibrational frequencies of O$_3$ in comparison with experimental data. To ensure appropriate accuracy and proper convergence in the interaction as well as asymptotic regions, we (a) extend the number of electronic states in SA-MCSCF calculation (singlet as well as triplet and quintet); (b) systematically expand the active space [(12e,9o) $\rightarrow$ (18e,12o) $\rightarrow$ (24e,15o)] and basis set size (AVDZ $\rightarrow$ AV6Z $\rightarrow$ Complete Basis Set limit); (c) incorporate multi-reference character along with Davidson correction. Conical intersections between the adjacent electronic states (1-2, 2-3 and 3-4) are located at \textit{C}$_{2v}$, \textit{D}$_{3h}$ as well as \textit{C}$_{s}$ geometries through the four-state adiabatic-to-diabatic transformation of non-adiabatic coupling terms (NACTs) computed at Coupled-Perturbed Multi-Configurational Self-Consistent Field (CP-MCSCF) method along the circular contours. Finally, we present: (a) ic-MRCI(Q) calculated minimum energy path of incoming oxygen to the diatom (O$_2$) is devoid of any ``reef'' feature; (b) NACTs and diabatic PES matrix elements as function of hyperangles ($\theta$,$\phi$) at a fixed hyperradius $\rho = 4$ Bohr for a four state sub-Hilbert space.