ROHF Theory Made Simple

TL;DR

This paper introduces a simplified, mathematically constrained formulation of ROHF theory called CUHF, which eliminates ambiguities and spin contamination, providing physically meaningful orbitals and energies with good experimental agreement.

Contribution

It presents a new, parameter-free CUHF approach that simplifies ROHF theory and resolves longstanding ambiguities and issues with orbital energies.

Findings

CUHF eliminates spin contamination in ROHF.

CUHF orbitals and energies are physically meaningful.

Benchmarks show good agreement with experiments.

Abstract

Restricted open-shell Hartree-Fock (ROHF) theory is formulated as a projected self-consistent unrestricted HF (UHF) model by mathematically constraining spin density eigenvalues. The resulting constrained UHF (CUHF) wave function is identical to that obtained from Roothaan's effective Fock operator. Our $\alpha$ and $\beta$ CUHF Fock operators are parameter-free and have canonical orbitals and orbital energies that are physically meaningful as in UHF, except for eliminating spin contamination. The present approach removes ambiguities in ROHF orbital energies and the non-uniqueness of methods that build upon them. We present benchmarks to demonstrate CUHF physical correctness and good agreement with experimental results.