A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory

We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian i...

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Main Authors: Meng Wang, Chenyang Li
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Molecules
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Online Access:https://www.mdpi.com/1420-3049/30/9/2082
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author Meng Wang
Chenyang Li
author_facet Meng Wang
Chenyang Li
author_sort Meng Wang
collection DOAJ
description We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme.
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spelling doaj-art-13f56ef3a47546829ccc2f4ade6c048e2025-08-20T02:59:08ZengMDPI AGMolecules1420-30492025-05-01309208210.3390/molecules30092082A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation TheoryMeng Wang0Chenyang Li1Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, ChinaKey Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, ChinaWe present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme.https://www.mdpi.com/1420-3049/30/9/2082driven similarity renormalization groupperturbation theoryspin–orbit coupling effectsexcited states
spellingShingle Meng Wang
Chenyang Li
A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
Molecules
driven similarity renormalization group
perturbation theory
spin–orbit coupling effects
excited states
title A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
title_full A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
title_fullStr A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
title_full_unstemmed A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
title_short A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
title_sort cost effective treatment of spin orbit couplings in the state averaged driven similarity renormalization group second order perturbation theory
topic driven similarity renormalization group
perturbation theory
spin–orbit coupling effects
excited states
url https://www.mdpi.com/1420-3049/30/9/2082
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AT chenyangli acosteffectivetreatmentofspinorbitcouplingsinthestateaverageddrivensimilarityrenormalizationgroupsecondorderperturbationtheory
AT mengwang costeffectivetreatmentofspinorbitcouplingsinthestateaverageddrivensimilarityrenormalizationgroupsecondorderperturbationtheory
AT chenyangli costeffectivetreatmentofspinorbitcouplingsinthestateaverageddrivensimilarityrenormalizationgroupsecondorderperturbationtheory