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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MDPI AG
2025-05-01
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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. |
| format | Article |
| id | doaj-art-13f56ef3a47546829ccc2f4ade6c048e |
| institution | DOAJ |
| issn | 1420-3049 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
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| series | Molecules |
| 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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