A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
Abstract
1. Introduction
2. Theory
2.1. State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory
2.2. Incorporating Spin–Orbit Coupling in SA-DSRG-PT2
3. Implementation
4. Numerical Results
4.1. Calibration of the Parameters of BP1-SA-DSRG-PT2c
4.2. Main-Group Atoms and Diatomic Molecules
4.3. Transition-Metal Elements: Cu, Ag, and Au
4.4. Actinide Oxides: [UO2]+ and [NpO2]2+
4.5. Mononuclear Single-Molecule Magnet: (PMe3)2FeCl3
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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System | SA-DSRG-PT2c a | QD-NEVPT2 b | 4c-DSRG-MRPT2 c | Experiment | ||
---|---|---|---|---|---|---|
ZFS | Ref. | |||||
B | 14.7 | 14.9 | 15.0 | 13.99 | 15.3 | [85] |
Al | 104.0 | 105.8 | 107.6 | 106.70 | 112 | [85] |
Ga | 844.0 | 865.7 | 887.4 | 743.28 | 826 | [85] |
In | 2459.6 | 2470.5 | 2560.8 | 2213 | [85] | |
Tl | 11,591.0 | 12,065.6 | 12,475.8 | 7793 | [85] | |
F | 401.5 | 401.5 | 401.5 | 384.70 | 404 | [85] |
Cl | 789.7 | 789.7 | 789.7 | 867.69 | 882 | [85] |
Br | 3574.4 | 3574.4 | 3574.4 | 3546.46 | 3685 | [85] |
I | 8150.1 | 8150.1 | 8150.0 | 7603 | [85] | |
CH | 27.8 | 28.5 | 29.0 | 27 | [86] | |
SiH | 131.2 | 131.9 | 128.0 | 142 | [86] | |
GeH | 880.4 | 864.1 | 864.1 | 892 | [86] | |
SnH | 2433.1 | 2311.8 | 2286.3 | 2178 | [86] | |
OH | 139.8 | 149.2 | 152.5 | 139 | [86] | |
SH | 354.7 | 374.4 | 375.6 | 377 | [86] | |
SeH | 1742.9 | 1832.7 | 1836.7 | 1763 | [87] | |
TeH | 4080.9 | 4271.0 | 4293.5 | 3816 | [88] | |
FO | 187.8 | 180.0 | 180.0 | 197 | [89] | |
ClO | 270.0 | 280.3 | 299.7 | 322 | [90] | |
BrO | 741.4 | 853.2 | 961.9 | 975 | [91] | |
IO | 1593.3 | 1871.7 | 2303.8 | 2091 | [92] |
System | State | SA-CASSCF a | SA-DSRG-PT2c a | CASPT2 b | DMRG c | Exp. d |
---|---|---|---|---|---|---|
Cu | 2D (no SOC) | 1.66 | 1.36 | 1.49 | ||
2D5/2 | 1.55 | 1.26 | 1.43 | 1.31 | 1.39 | |
2D3/2 | 1.81 | 1.52 | 1.69 | 1.57 | 1.64 | |
ZFS | 0.26 | 0.26 | 0.26 | 0.26 | 0.25 | |
Ag | 2D (no SOC) | 4.46 | 3.98 | 3.97 | ||
2D5/2 | 4.23 | 3.75 | 3.75 | |||
2D3/2 | 4.80 | 4.33 | 4.30 | |||
ZFS | 0.58 | 0.58 | 0.55 | |||
Au | 2D (no SOC) | 2.30 | 1.74 | 1.58 | 1.62 | 1.74 |
2D5/2 | 1.61 | 1.05 | 0.97 | 1.02 | 1.14 | |
2D3/2 | 3.33 | 2.77 | 2.49 | 2.55 | 2.66 | |
ZFS | 1.72 | 1.72 | 1.51 | 1.53 | 1.52 |
Method | 2Δ3/2u | 2Φ7/2u | 2Δ5/2u |
---|---|---|---|
SA-DSRG-PT2c a,b | 0.35 | 0.85 | 0.99 |
QD-NEVPT2 a,c | 0.36 | 0.80 | 0.98 |
CASPT2 a,d | 0.32 | 0.83 | 0.98 |
QD-NEVPT2 a,e | 0.35 | 0.76 | 0.95 |
IHFSCCSD f | 0.34 | 0.71 | 0.81 |
Exp. g | 0.33 |
Method | 2Δ3/2u | 2Φ7/2u | 2Δ5/2u |
---|---|---|---|
SA-DSRG-PT2c a,b | 0.38 | 1.02 | 1.16 |
QD-NEVPT2 a,c | 0.45 | 1.00 | 1.15 |
XMS-CASPT2 a,d | 0.45 | 0.98 | 1.18 |
CASPT2 a,e | 0.38 | 1.00 | 1.15 |
QD-NEVPT2 a,f | 0.45 | 0.94 | 1.11 |
IHFSCCSD g | 0.44 | 0.90 | 1.11 |
SHCI h | 0.43 | 0.89 | 1.10 |
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Wang, M.; Li, C. A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory. Molecules 2025, 30, 2082. https://doi.org/10.3390/molecules30092082
Wang M, Li C. A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory. Molecules. 2025; 30(9):2082. https://doi.org/10.3390/molecules30092082
Chicago/Turabian StyleWang, Meng, and Chenyang Li. 2025. "A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory" Molecules 30, no. 9: 2082. https://doi.org/10.3390/molecules30092082
APA StyleWang, M., & Li, C. (2025). A Cost-Effective Treatment of Spin–Orbit Couplings in the State-Averaged Driven Similarity Renormalization Group Second-Order Perturbation Theory. Molecules, 30(9), 2082. https://doi.org/10.3390/molecules30092082