Development of Selected Configuration Interaction Methods for Problems in Strong Correlation translation missing: zh.hyrax.visibility.files_restricted.text

Schriber, Jeffrey (Spring 2019)

Permanent URL: https://etd.library.emory.edu/concern/etds/kp78gh24w?locale=zh
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Abstract

In this dissertation, we develop and apply the adaptive configuration interaction (ACI) method to enable computations on large chemical systems with potentially many strongly correlated electrons. ACI is a new variant of selected CI methods that provides the user with a priori control over the error in the total energy by an iterative, cumulative determinant screening algorithm. We benchmark the ACI on the dissociation of N2 and on the singlet-triplet splittings of oligoacenes up to decacene, achieving sub kcal/mol accuracy in comparison to density matrix renormalization group data. We then extend the ACI to compute excited states both by optimizing determinantal spaces for each electronic state, and by using a single determinantal space optimized for several states. We test these methods using excited states of methylene, the avoided crossing in LiF, and challenging excited states in long polyenes. To connect the ACI to a dynamical correlation treatment, we then use ACI as an affordable substitute for complete active space CI (CASCI) in combination with the multireference driven similarity renormalization group perturbatively expanded to second order (ACI-DSRG-MRPT2). The ACI-DSRG-MRPT2 uses specialized techniques to recover both static and dynamical electron correlations, and we are able to treat active spaces with as many as 30 electrons in 30 orbitals in a total basis of 1350 orbitals. We apply this method to the oligoacenes and achieve good agreement with experimental singlet-triplet splittings, and the dynamical correlation treatment causes a significant reduction in the observed radical character compared to active space methods. Finally, we introduce a real time-dependent ACI (TD-ACI) which uses ACI to generate a fixed basis for propagating an initial state in real time. We apply the TD-ACI to study charge migration dynamics following ionization, and we can reproduce experimental migration frequencies in iodoacetylene with minimal computational effort. 

Table of Contents

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

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

1.2 Electronic Structure Theory......................... 3

1.2.1 Second Quantization ........................ 5

1.2.2 An exact solution.......................... 6

1.2.3 Single-referenceApproaches.................... 8

1.3 Multireference Methods........................... 11

1.3.1 Active Space Treatments...................... 13

1.3.2 Multireference Methods for Dynamical Correlation . . . . . . . . 18

1.3.3 The Driven Similarity Renormalization Group . . . . . . . . . . . 22

1.4 Selected Configuration Interaction..................... 25

1.4.1 Early Selected CI Methods..................... 26

1.4.2 Modern Selected CI......................... 28

1.5 Prospectus.................................. 31

2 The Adaptive Configuration Interaction Method. . . . . . . . . . . . . . . 44

2.1 Introduction................................. 44

2.2 The Adaptive Configuration Interaction Method. . . . . . . . . . . . . . 45

2.3 Numerical Tests and Applications ..................... 48

2.3.1 The Dissociation of N2 ....................... 48

2.3.2 Singlet-Triplet Splittings in Oligoacenes . . . . . . . . . . . . . . 50

2.4 Conclusions................................. 52

3 ACI for Computing Challenging Excited States . . . . . . . . . . . . . . . 58

3.1 Introduction................................. 58

3.2 Theory.................................... 62

3.2.1 Brief review of ground-state ACI.................. 62

3.2.2 Excited State Methods in ACI ................... 66

3.3 Results and Discussion........................... 72

3.3.1 Methylene.............................. 72

3.3.2 LiF avoided crossing........................ 75

3.3.3 Extended polyenes ......................... 79

3.4 Conclusions................................. 84

4 Combining ACI with DSRG.......................... 96

4.1 Introduction................................. 96

4.2 Theory.................................... 98

4.2.1 Adaptive CI............................. 98

4.2.2 Implementation of RDMs...................... 100

4.2.3 DSRG-MRPT2........................... 101

4.3 The Oligoacenes............................... 105

4.3.1 Computational Details ....................... 106

4.3.2 Singlet-Triplet Splittings...................... 109

4.3.3 Emergent Radical Character .................... 113

4.3.4 Analysis of Spin-Spin Correlation ................. 115

4.4 Conclusions................................. 117

5 Real-Time Propagation of Selected Configuration Interaction Wave Functions Applied to Charge Migration....................... 126

5.1 Introduction................................. 126

5.2 Theory.................................... 129

5.2.1 Time-Dependent ACI........................ 129

5.3 Results and Discussion........................... 133

5.3.1 Valence Ionization of Benzene................... 133

5.3.2 Charge Migration in Iodoacetylene. . . . . . . . . . . . . . . . . 136

5.4 Conclusions and Future Challenges..................... 140

6 Conclusions and Future Directions ...................... 150

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