Generalization of intrinsic orbitals to Kramers-paired quaternion spinors, molecular fragments and valence virtual spinors

TL;DR

This paper extends intrinsic atomic and bonding orbitals to relativistic contexts using quaternion spinors and molecular fragments, enabling localized virtual orbitals in complex heavy-element systems.

Contribution

It introduces a generalized method for localizing orbitals with relativistic effects and molecular fragments, broadening the applicability of intrinsic orbitals.

Findings

Successfully applied to molecules like benzene, ferrocene, and acrylic-acid.

Enabled localization in heavy-element complexes with relativistic effects.

Implemented in a standalone program interfaced with quantum chemistry packages.

Abstract

Localization of molecular orbitals finds its importance in the representation of chemical bonding (and anti-bonding) and in the local correlation treatments beyond mean-field approximation. In this paper, we generalize the intrinsic atomic and bonding orbitals [G. Knizia, J. Chem. Theory Comput. 2013, 9, 11, 4834-4843] to relativistic applications using complex and quaternion spinors, as well as to molecular fragments instead of atomic fragments only. By performing a singular value decomposition, we show how localized valence virtual orbitals can be expressed in this intrinsic minimal basis. We demonstrate our method on systems of increasing complexity, starting from simple cases such as benzene, acrylic-acid and ferrocene molecules, and then demonstrating the use of molecular fragments and inclusion of relativistic effects for complexes containing heavy elements such as tellurium, iridium and astatine. The aforementioned scheme is implemented into a standalone program interfaced with several different quantum chemistry packages.