A NOVEL THEORETICAL APPROACH TO MODEL ELECTRONIC EXCITATIONS IN MOLECULAR CRYSTALS by Feng Xibo Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Dalhousie University Halifax, Nova Scotia May 2021 ⃝c Copyright by Feng Xibo, 2021 \No son molinos, amigo Sancho, que son gigantes." (\They are not windmills, Sancho my friend, they are giants.") { Don Quixote to his loyal servant, Sancho, before charging into battle against an array of windmills. (Don Quixote, Miguel de Cervantes) ii Table of Contents List of Tables .................................. vii List of Figures ................................. ix List of Abbreviations and Symbols Used ................. xi Abstract ..................................... xvii Acknowledgements .............................. xviii Chapter 1 Introduction ......................... 1 1.1 Background . .1 1.2 Contemporary Theoretical Works . .3 1.2.1 The QM/MM Embedding Approach . .4 1.2.2 Applications of QM/MM to Crystalline-Phase Excitations . .7 1.2.3 TDDFT Applied under Periodic-Boundary Conditions . .9 1.3 Thesis Goals . 12 1.4 Layout of the Remaining Chapters . 15 Chapter 2 Theoretical Preparation .................. 16 2.1 Density-Functional Theory . 16 2.2 Time-Dependent Density-Functional Theory . 21 2.2.1 The Runge-Gross Theorem and Kohn-Sham TDDFT . 21 2.2.2 Linear-Response TDDFT . 23 2.3 Becke's Virial Exciton Model . 27 2.4 Periodic-Boundary DFT . 30 2.4.1 The Planewave Basis . 30 iii 2.4.2 Pseudopotentials . 34 2.4.3 The Projector Augmented-Wave (PAW) Method . 35 2.4.4 Spin-Magnetized Calculations . 37 2.4.5 Applied Pressure . 37 2.4.6 Crystalline Band Structure . 38 2.5 The XDM Dispersion Model . 39 Chapter 3 The Effect of Electronic Excitation on London Disper- sion ............................... 44 3.1 Introduction . 45 3.2 Computational Methods . 46 3.2.1 Molecular calculations . 46 3.2.2 Solid-state calculations . 48 3.3 Results and Discussion . 49 3.3.1 Conjugated hydrocarbons . 49 3.3.2 Push-pull chromophores . 50 3.3.3 Intermolecular charge-transfer excitations . 54 3.3.4 Dispersion in crystalline solids . 56 3.4 Summary . 57 Chapter 4 Assessing the Performance of Becke's Virial Exciton Model for Charge-Transfer Excitations ......... 59 4.1 Introduction . 60 4.2 Theory . 62 4.3 Computational Details . 63 4.4 Results and Discussion . 64 4.4.1 C2H4-C2F4: A Classic CT Test . 64 4.4.2 TCNE-Aromatic Dimers and Push-Pull Dye Molecules . 65 iv 4.5 Conclusions . 67 Chapter 5 A Novel Computational Methodology for Modeling Solid-State Excitations: Design & Initial Testing ... 68 5.1 Design of the Computational Framework . 68 5.1.1 Solid-State Calculations: The Ground State . 68 5.1.2 Solid-State Calculations: The First Triplet State . 69 5.1.3 Gas-Phase Calculations . 69 5.1.4 Determination of the First Singlet Excitation Energy . 69 5.2 Preliminary Tests on Ethylene and Nucleobase Crystals . 71 5.2.1 Super-Cell Size Effect . 72 5.2.2 Quantification of Crystalline-Environment Effects . 74 Chapter 6 Computational Modeling of Piezochromism in Molecu- lar Crystals .......................... 77 6.1 Introduction . 77 6.2 Computational Methods . 79 6.3 Results and Discussion . 82 6.3.1 Replication of Piezochromism . 82 6.3.2 Origin of the Universal Red Shift . 84 6.4 Conclusion . 87 Chapter 7 Polymorph- and Coformer-Dependent Electronic Exci- tations in the Solid State: A Theoretical Perspective .................................. 89 7.1 Introduction . 90 7.2 Computational Methods . 92 7.3 Results and Discussion . 95 7.3.1 Polymorph-Dependent Absorption of ROY . 95 v 7.3.2 Coformer-Dependent Emission of 9-ACA Cocrystals . 98 7.4 Conclusions . 101 Chapter 8 Conclusions and Future Work .............. 104 Appendix A Supplementary Material for Computational Modeling of Piezochromism in Molecular Crystals ........ 109 Appendix B Supplementary Material for Polymorph- and Coformer- Dependent Electronic Excitations in the Solid State: A Theoretical Perspective ................... 113 Appendix C Miscellaneous Records ................... 118 C.1 Conference Attendances and Presentations . 118 C.2 Graduate Coursework . 119 C.3 Teaching Assistantship . 119 C.4 Awards and Scholarships . 120 C.5 Program Timeline . 120 Bibliography .................................. 121 vi List of Tables 3.1 Changes in molecular C6 coefficients and overall crystalline dispersion energies. 58 4.1 Calculated excitation energies, and related quantities. 66 5.1 First triplet excitation energies calculated for various super-cell expansions of the test crystals. 74 5.2 Quantification of the effect of the crystalline environment on crystal E0T ................................ 76 5.3 The first singlet excitation energies calculated for the1 × 1 × 1 unit cells of the test crystals. 76 6.1 Experimental PL properties and piezochromism of the investi- gated molecular crystals. 79 6.2 Calculated emission piezochromism, showing both the total red shift (eV) and red shift per unit pressure (eV/GPa). 84 6.3 Molecular S0 and T1 polarizabilities (in a.u.) calculated for the excised molecules at zero pressure. 86 7.1 Experimental structure and absorption data of the 8 investi- gated ROY polymorphs. 93 7.2 Experimental emission data of the 9-ACA crystal and its cocrystals. 93 cryst exp 7.3 Calculated (∆E0S ) vs. experimental (∆Eabs ) absorption energies for the 8 ROY polymorphs under investigation. 96 cryst cryst 7.4 Calculated (∆E0S ) vs experimental (∆E0S ) emission ener- gies for the cocrystals and the pristine crystal of 9-ACA. 99 B.1 Calculated energetics for the absorption of the 8 ROY poly- morphs. 114 B.2 Calculated energetics for the emission of 9-ACA and its cocrystals. 114 B.3 Band structures of the 8 ROY polymorphs. 114 B.4 Band structures of 9-ACA and its cocrystals. 115 vii B.5 The ROY molecule: calculated values of molecular triplet- excitation energies and molecular S1-T1 splittings, across the ◦ 0-180 range of θthio......................... 115 B.6 ROY polymorphs: internal rotation angle values calculated using fixed-cell optimization and variable-cell optimization on ground-state crystal geometries, compared to experiment. 116 B.7 9-ACA and its cocrystals: the amounts of absolute charge per − 9-ACA molecule (e ) in S0 and T1................. 116 viii List of Figures 1.1 Pressure-dependent luminescence (piezochromism) observed for the boron diketonate crystal. .2 1.2 Chemical structure of 1,4-bis(2-cyanostyryl)benzene and its four coformers. 10 1.3 The 3 tautomeric forms of fluorescein. 12 2.1 Schematic sketch of the behavior of the electronic wavefunc- tion in a periodic system. 34 2.2 Schematic diagram of the pseudopotential approximation. 35 2.3 The first Brillouin zone of a face-centered cubic crystal. 39 3.1 The constituents of conjugated-chain set of molecules. 49 3.2 Changes in molecular C6 dispersion coefficients as a function of excitation energy. 51 3.3 Decomposition of the changes in molecular C6 dispersion coefficients. 52 3.4 Calculated intramolecular charge transfer and C6 changes for the set of 4,4'-disubstituted biphenyls. 53 3.5 Calculated properties of the benzene-hexafluorobenzene and benzene-tetracyanoethylene complexes as a function of exact- exchange mixing. 55 3.6 Structures of selected chromophores present in molecular crystals. 57 4.1 The chemical systems investigated in this work. 61 4.2 Calculated S1 excitation energy for the C2H4-C2F4 dimer. 64 4.3 Computed T1-S0 density differences for the TCNE-aromatic dimers and donor-acceptor molecules. 67 5.1 The systems chosen for the preliminary tests. 71 5.2 Density differences between the ground and first triplet and states for the 1 × 1 × 1 unit cells and excised molecules. 73 ix 5.3 Density differences between0 S and T1 states for super cells that converged to a delocalized T1................ 75 6.1 Molecular structures of the investigated piezochromic crystals. 78 6.2 The computational scheme employed in this work. 81 6.3 Calculated emission energies versus applied pressure. 83 6.4 Potential energy curves for the S0 and S1 states of the molecular crystals as functions of applied pressure. 85 6.5 Valence and conduction band edges, and band gaps, of the molecular crystals as functions of applied pressure, using the T1 geometries. 87 7.1 Molecular structure of ROY. 92 7.2 Molecular structures of 9-acetylanthracene and its four co- formers. 92 7.3 Correlation between θthio and the gas-phase singlet-excitation mol (absorption) energy (∆E0S ) of the isolated ROY molecule. 97 7.4 Degrees of intermolecular CT within the cocrystals and the pristine crystal of 9-ACA, as indicated by the absolute charge per molecule. 100 A.1 Calculated absorption energies versus applied pressure. 110 A.2 Calculated polarizabilities of the excised molecules as a func- tion of pressure. 111 A.3 Valence and conduction band edges, and band gaps, of the molecular crystals as functions of applied pressure using the absorption (S0) geometries. 111 A.4 Representative band structures near the valence-conduction band gap, obtained for the S0 geometries at zero pressure. 112 B.1 Calculated energy terms for the ROY molecule. 117 x List of Abbreviations and Symbols Used Abbreviation Description AA Adiabatic Approximation ACQ Aggregation-Caused Quenching ACFDT Adiabatic Connection Fluctuation-Dissipation Theorem AE All-Electron AIE Aggregation-Induced Emission AMBER Assisted Model Building with Energy Refinement APAP Acetaminophen BHandHLYP Becke (1988) exchange Half-and-Half mixing/LYP correlation functional BLYP Becke (1988) exchange/LYP correlation