Automatic active space selection for the driven similarity renormalization group method Open Access

Abstract

We proposed a convenient automatic active space selection scheme for the driven similarity renormalization group truncated to second order (DSRG-PT2) [C. Li and F. A. Evangelista, J.Chem. Theory Comput. 11, 2097 (2015)]. It is based on stateaveraged conguration singles (CIS) natural orbitals and the following DSRG computations become a black-box procedure. The scheme is tested for valence excited states calculations with three DSRG methods: valence CI singles (VCIS) and VCIS with doubles (VCISD) wave functions improved with a second-order perturbation theory (VCIS/VCISD-DSRG-PT2) [C. Li and F. A. Evangelista, J. Chem. Phys. 147, 074107 (2017)], and stateaveraged multireference driven similarity renormalization group [(SA)-MRDSRG] second-order perturbation theory (SA-DSRGPT2) [C. Li and F. A. Evangelista, J. Chem. Phys. 148, 124106 (2018)]. Results are benchmarked on a set of 24 organic molecules. The scheme is also tested for H2O core excitations with the complete-active-space (CAS) DSRG method.

Table of Contents

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Density Matrix and Natural Orbitals . . . . . . . . . . . . . . . . . . 3

1.3 Static and Dynamical Correlation . . . . . . . . . . . . . . . . . . . . 4

1.4 Conguration Interaction Singles (CIS) . . . . . . . . . . . . . . . . . 5

1.5 Automatic Active Space Selection . . . . . . . . . . . . . . . . . . . . 7

1.5.1 Generate State Averaged (SA)-CIS One Body Reduced Density Matrix . . . 7

1.5.2 Active Orbitals Selection Based on NO Occupancy. . . . . . . 8

1.5.3 Construct New Coecient Matrix C . . . . . . . . . . . . . . . 10

2 CIS-NO For Valence Excited States . . . . . . . . . . . . . . 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 VCIS/VCISD-DSRG-PT2 . . . . . . . . . . . . . . . . . . . . . 13

2.2.2 SA-DSRG-PT2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.3 Computational Details. . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.4.1 Threshold Dependence of Active Space . . . . . . . . . . . . . 18

2.4.2 Comparison with Manual Selection. . . . . . . . . . . . . . . . 22

2.4.3 Comparison with Established Excited State Methods . . . . . 24

2.4.4 Comparison with CAS Space . . . . . . . . . . . . . . . . . . . 26

2.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 CIS-NO Work On Core Excitation . . . . . . . . . . . . . . . 34

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.2 Computational Details. . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3.1 H2O Core Excitation Energy Calculations with Dierent Methods ...36

3.3.2 H2O Core Excitation Energy Calculations with Dierent Orbitals ... 38

3.3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3.4 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

About this Master's Thesis

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School	Laney Graduate School
Department	Chemistry
Degree	M.S.
Submission	Master's Thesis
Language	English
Research Field	Chemistry, Physical
Keyword	Driven Similarity Renormalization Group Active Space
Committee Chair / Thesis Advisor	Evangelista, Francesco, Emory University
Committee Members	Bowman, Joel, Emory University Kindt, James, Emory University

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