THE UNIVERSITY OF CHICAGO ELECTRONIC STRUCTURE OF MOLECULES AND MATERIALS FROM QUANTUM SIMULATIONS A DISSERTATION SUBMITTED TO THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES IN CANDIDACY FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF CHEMISTRY BY HE MA CHICAGO, ILLINOIS DECEMBER 2020 ProQuest Number:28153743 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent on the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. ProQuest 28153743 Published by ProQuest LLC (2020). Copyright of the Dissertation is held by the Author. All Rights Reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, MI 48106 - 1346 Copyright c 2020 by He Ma All Rights Reserved To my family TABLE OF CONTENTS LIST OF FIGURES . vi LIST OF TABLES . xiii ACKNOWLEDGMENTS . xvii ABSTRACT . xviii 1 INTRODUCTION . 1 2 THEORETICAL BACKGROUND . 5 2.1 The electronic structure problem . 5 2.2 Density functional theory . 7 2.3 Many-body perturbation theory . 9 3 FINITE FIELD ALGORITHM FOR MANY-BODY PERTURBATION THEORY 12 3.1 Finite field calculation of response functions . 13 3.1.1 Introduction . 13 3.1.2 The finite-field approach . 16 3.1.3 GW calculations . 24 3.1.4 Technical details . 35 3.1.5 Conclusions . 48 3.2 Bethe-Salpeter equation . 49 3.2.1 Introduction . 49 3.2.2 Method . 51 3.2.3 Results . 55 3.2.4 Technical details . 59 3.2.5 Conclusions . 78 4 QUANTUM EMBEDDING AND QUANTUM SIMULATIONS OF STRONGLY- CORRELATED ELECTRONIC STATES . 79 4.1 Introduction . 80 4.2 Formalism . 82 4.2.1 General strategy . 82 4.2.2 Embedding theory . 82 4.2.3 Derivation of the embedding formalism . 85 4.3 Application of embedding theory to spin-defects . 89 4.3.1 Excitation energies of defects . 94 4.3.2 Convergence of the active space size . 95 4.4 Quantum simulations . 96 4.5 Technical details . 99 4.6 Discussion . 101 iv 5 FIRST-PRINCIPLES CALCULATION OF SPIN PROPERTIES OF MOLECULES AND MATERIALS . 103 5.1 All-electron calculation of spin properties using finite-element DFT . 104 5.1.1 Introduction . 104 5.1.2 Formalism . 107 5.1.3 Results . 111 5.1.4 Technical details . 121 5.1.5 Conclusions . 128 5.2 Mixed all-electron-pseudopotential calculation of spin properties . 130 6 FIRST-PRINCIPLES SIMULATION OF SPIN-DEFECTS FOR QUANTUM IN- FORMATION SCIENCE . 133 6.1 Discovery of novel spin qubits in silicon carbide and aluminum nitride . 135 6.1.1 Introduction . 135 6.1.2 Methods . 138 6.1.3 Results . 141 6.1.4 Conclusions . 154 6.2 First-principles study of strongly-correlated states for spin-defects in diamond 156 6.2.1 Introduction . 156 6.2.2 Methods . 159 6.2.3 Results . 162 6.2.4 Technical details . 168 6.2.5 Conclusion . 176 6.3 Microscopic theory for spin-phonon interactions in silicon carbide . 177 6.3.1 Introduction . 177 6.3.2 Experimental control of divacancy spins using surface accoustic waves 179 6.3.3 First-principles theory of spin-strain coupling . 188 6.3.4 Conclusions . 195 6.4 Quantum dynamics simulation of spin-defects . 197 7 CONCLUSION . 201 A PUBLICATIONS . 204 B SOFTWARE . 205 B.1 PyZFS: A Python package for first-principles calculations of zero-field splitting tensors . 206 B.2 PyCDFT: A Python package for constrained density functional theory . 209 B.2.1 Introduction . 209 B.2.2 Computational methodology . 214 B.2.3 Software . 218 B.2.4 Verification . 220 B.2.5 Conclusions . 225 REFERENCES . 226 v LIST OF FIGURES 3.1 Workflow of finite-field calculations. The WEST code performs an iterative di- ~ ~ agonalization of K (~χ0,χ ~RPA,χ ~). In GW calculations beyond the RPA, fxc is computed from Eq. 3.12, which requires computing the spectral decomposition ofχ ~0 and evaluatingχ ~ in the space ofχ ~0 eigenvectors. Finite-field calculations are carried out by the Qbox code. If the Hartree (VH) and exchange correlation potential (Vxc) are updated self-consistently when solving Eq. 3.10, one obtains K = χ; if Vxc is evaluated at the initial charge density n0 and kept fixed during the SCF procedure, one obtains K = χRPA; if both Vxc and VH are evaluated for n0 and kept fixed, one obtains K = χ0. The communications of δn and δV between WEST and Qbox is carried through the filesystem. 21 3.2 Comparison of the eigenvalues(a) and eigenfunctions(b) ofχ ~RPA obtained from density functional perturbation theory (DFPT) and finite-field (FF) calculations. Three approaches are used: diagonalization ofχ ~0 by DFPT, diagonalization of χ~0 by FF (denoted by FF(0)) and diagonalization ofχ ~RPA by FF (denoted by FF(RPA)). In the case of DFPT and FF(0), Eq. 3.6 was used to obtain the eigenvalues ofχ ~RPA from those ofχ ~0. In (b) we show the first 32 × 32 elements of the hξDFPTjξFF(0)i and hξDFPTjξFF(RPA)i matrices (see Eq. 3.7). 22 3.3 Comparison of eigenvalues(a) and eigenfunctions(b) ofχ ~ andχ ~RPA obtained from finite-field calculations. In (b), the first 32 × 32 elements of the hξRPAjξfulli matrices are presented. 23 3.4 Average relative differences ∆fxc (see Eq. 3.13) between diagonal elements of the f~xc matrices computed analytically and numerically with the finite-field approach. Calculations were performed with the LDA functional. 24 3.5 Difference (∆E) between vertical ionization potential (VIP) and vertical electron fxc affinity (VEA) of molecules in the GW100 set computed at the G0W0 /G0W0Γ0 RPA level and corresponding G0W0 results. Mean deviations (MD) in eV are shown in brackets and represented with black dashed lines. Results are presented for three different functionals (LDA, PBE and PBE0) in the top, middle and bottom panel, respectively. 32 3.6 Vertical ionization potential (VIP), vertical electron affinity (VEA) and electronic RPA fxc gap of molecules in the GW100 set computed at G0W0 , G0W0 and G0W0Γ0 levels of theory, compared to experimental and CCSD(T) results (black dashed lines). 33 3.7 GW quasiparticle corrections to the valance band maximum (VBM) and the RPA conduction band minimum (CBM). Circles, squares and triangles are G0W0 , fxc G0W0 and G0W0Γ0 results respectively; red, blue, green markers correspond to calculations with LDA, PBE and DDH functionals. 34 jδn(ai)−δn(aj)j 3.8 Relative difference ∆ij = , where j:::j is the 2-norm of δn's (see Eq. jδn(aj)j 3.34) defined on a real space grid. 39 3.9 Relative difference between δn(NSCF) and the converged result δn0. δn0 is com- puted with NSCF = 50. See Eq. 3.34 for the definition of δn. 40 vi RPA 3.10 Comparison of VIP and VEA for the GW100 set obtained at the G0W0 @PBE level, with χ0 computed with either the finite-field (FF) approach or DFPT. Diagonal dash lines are DFPT results, dots are FF results. 41 3.11 First 32 × 32 matrix elements of the exchange-correlation kernel in PDEP basis (the space ofχ ~0 eigenvectors) for Ar, SiH4 and CO2 molecule. 41 3.12 Quasiparticle energies of Si (64-atom supercell, PBE functional) computed with ~ RPA and without the head of fxc. VBM obtained at G0W0 level is set as the zero of energy. 44 ~ ~ −1 3.13 Diagonal elements ofχ ~0, fxc, [1 − χ~0(1 + fxc)] ,χ ~RPA,χ ~ andχ ~Γ for the SiH4 molecule. 45 3.14 Diagonal elements of un-renormalized (nr) and renormalized (r) f~xc matrices and resultingχ ~Γ matrices for the SiH4 molecule and bulk Si. 46 3.15 Convergence of GW quasiparticle gaps of SiH4 and Si as a function of NPDEP, using either un-renormalized (nr) or renormalized (r) f~xc matrices. 47 3.16 The lowest singlet excitation energies of the 28 molecules of the Thiel's set com- puted by solving the Bethe Salpeter equation in finite field (FF-BSE) with (green) and without (blue) the Random Phase Approximation (RPA), using the PBE and the PBE0 hybrid functional (red). Results are compared (∆E) with the best theory estimates obtained using quantum chemistry methods [343, 344]. The horizontal lines denote the maximum, mean, and minimum of the distribution of results, compared with quantum chemistry methods. χ denotes the response function computed with and without the RPA. The numerical values are reported in Section 3.2.4. 56 3.17 Optical absorption spectra of C60 in the gas phase computed by solving the BSE with.