Generalization of Intrinsic Orbitals to Kramers-Paired Quaternion Spinors, Molecular Fragments, and Valence Virtual Spinors

Abstract

Localization of molecular orbitals finds its importance in the representation of chemical bonding (and anti-bonding) and in the local correlation treatments beyond meanfield 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 arXiv:2009.08671v2 [physics.chem-ph] 10 Feb 2021 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.

Oxidation State Localized Orbitals: A Method for Assigning Oxidation States Using Optimally Fragment-Localized Orbitals and a Fragment Orbital Localization Index

“…[51][52][53] Amongst many such possibilities, Intrinsic Atomic Orbitals (IAOs) are perhaps the simplest, and have been shown to be robust for population analysis. 34,44,54 The basic idea of IAOs is to rely on a projection onto a reference minimal basis to facilitate atom-tagging.…”

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

“…The IFOs and ILMOs are generated in a standalone program called Reduction of Orbital Space Extent (ROSE) [71]. ROSE has been interfaced with DIRAC [66] using quaternion spinors, Psi4 [72] and PySCF [73] using real spinors, as well as the ADF program of the Amsterdam Modeling Suite (AMS) [74] which is based on Slater type orbitals (STO).…”

“…Our current version only works with uncontracted basis sets, so that only the non-relativistic, the exact two-component X2C with or without (i.e., scalar-X2C) spin-orbit coupling, and the molecular mean-field X2C (X2Cmmf) Hamiltonians can be used. The use of ROSE has been detailed in a manual accessible online [71] together with several examples including the interfaces with DIRAC, Psi4, PySCF and ADF.…”

N-electron valence perturbation theory with reference wavefunctions from quantum computing: application to the relative stability of hydroxide anion and hydroxyl radical

“…The combination of VQE and QSE gives an approximation for the ground and excited states of the Born-Oppenheimer Hamiltonian within an active space of valence orbitals and electrons based on intrinsic atomic or-bitals (IAOs) [30][31][32][33][34][35][36][37]. Information from these calculations is then used to compute a perturbative correction to the ground-state energy provided by VQE, that accounts for one-and two-electron transitions from active to inactive orbitals.…”