Quantum Chemistry and Dynamics of Excited States

An introduction to the rapidly evolving methodology of electronic excited states

For academic researchers, postdocs, graduate and undergraduate students, Quantum Chemistry and Dynamics of Excited States: Methods and Applications reports the most updated and accurate theoretical techniques to treat electronic excited states. From methods to deal with stationary calculations through time-dependent simulations of molecular systems, this book serves as a guide for beginners in the field and knowledge seekers alike. Taking into account the most recent theory developments and representative applications, it also covers the often-overlooked gap between theoretical and computational chemistry.

An excellent reference for both researchers and students, Excited States provides essential knowledge on quantum chemistry, an in-depth overview of the latest developments, and theoretical techniques around the properties and nonadiabatic dynamics of chemical systems.

Readers will learn:

• Essential theoretical techniques to describe the properties and dynamics of chemical systems

• Electronic Structure methods for stationary calculations

• Methods for electronic excited states from both a quantum chemical and time-dependent point of view

• A breakdown of the most recent developments in the past 30 years

For those searching for a better understanding of excited states as they relate to chemistry, biochemistry, industrial chemistry, and beyond, Quantum Chemistry and Dynamics of Excited States provides a solid education in the necessary foundations and important theories of excited states in photochemistry and ultrafast phenomena.

Autorentext

Professor Leticia González teaches at the Department of Chemistry at the University of Vienna, Austria. She is a theoretical chemist world-known for her work on molecular excited states and ultrafast dynamics simulations. Besides publishing over 250 papers and several reviews on excited states and dynamics, she has developed the SHARC program package to simulate non-adiabatic dynamics. Professor Roland Lindh currently teaches at Uppsala University, Sweden. He is a member of the editorial board of International Journal of Quantum Chemistry and the MOLCAS quantum chemistry program project. He co-authored the book "Multiconfigurational Quantum Chemistry" and is an expert on method development for multiconfigurational wave function theory.

Inhalt
List of Contributors xix

Preface xxiii

1 Motivation and Basic Concepts **1
*Sandra Gómez, Ignacio Fdez. Galván, Roland Lindh, and Leticia Gonzalez*

1.1 Mission and Motivation 1

1.2 Atomic Units 4

1.3 The Molecular Hamiltonian 5

1.4 Dirac or Bra-Ket Notation 6

1.5 Index Definitions 7

1.6 Second Quantization Formalism 7

1.7 BornOppenheimer Approximation and Potential Energy Surfaces 9

1.8 Adiabatic Versus Diabatic Representations 10

1.9 Conical Intersections 11

1.10 Further Reading 12

1.11 Acknowledgments 12

Part I Quantum Chemistry 13

2 Time-Dependent Density Functional Theory **15
**Miquel Huix-Rotllant, Nicolas Ferre, and Mario Barbatti

2.1 Introduction 15

2.2 TDDFT Fundamentals 16

2.2.1 The RungeGross Theorems 16

2.2.2 The Time-Dependent KohnSham Approach 18

2.2.3 Solutions of Time-Dependent KohnSham Equations 19

2.2.3.1 Real-Time TDDFT 19

2.2.3.2 Linear-Response TDDFT 20

2.3 Linear-Response TDDFT in Action 22

2.3.1 Vertical Excitations and Energy Surfaces 22

2.3.1.1 Vertical Excitations: How Good are They? 23

2.3.1.2 Reconstructed Energy Surfaces: How Good are They? 25

2.3.2 Conical Intersections 28

2.3.3 Coupling Terms and Auxiliary Wave Functions 30

2.3.3.1 The Casida Ansatz 30

2.3.3.2 Time-Derivative Non-Adiabatic Couplings 31

2.3.4 Non-Adiabatic Dynamics 32

2.4 Excited States and Dynamics with TDDFT Variants and Beyond 34

2.5 Conclusions 35

Acknowledgments 36

References 36

3 Multi-Configurational Density Functional Theory: Progress and Challenges **47
*Erik Donovan Hedegård*

3.1 Introduction 47

3.2 Wave Function Theory 50

3.3 KohnSham Density Functional Theory 50

3.3.1 Density Functional Approximations 53

3.3.2 Density Functional Theory for Excited States 54

3.3.2.1 Issues Within the Time-Dependent Density Functional Theory Ansatz 55

3.3.2.2 Self-Interaction Error 55

3.3.2.3 Degeneracies, Near-Degeneracies and the Symmetry Dilemma 56

3.4 Multi-Configurational Density Functional Theory 57

3.4.1 Semi-Empirical Multi-Configurational Density Functional Theory 57

3.4.2 Multi-Configurational Density Functional Theory Based the On-Top Pair Density 58

3.4.2.1 Density Matrices and the On-Top Pair Density 59

3.4.2.2 Energy Functional and Excited States with the On-Top Pair Density 60

3.4.3 Multi-Configurational Density Functional Theory Based on Range-Separation 61

3.4.3.1 Energy Functional and Excited States in Range-Separated Methods 62

3.4.3.2 The Range-Separation Parameter in Excited State Calculations 62

3.5 Illustrative Examples 64

3.5.1 Excited States of Organic Molecules 64

3.5.2 Excited States for a Transition Metal Complex 65

3.6 Outlook 66

Acknowledgments 67

References 67

4 Equation-of-Motion Coupled-Cluster Models **77
**Monika Musia

4.1 Introduction 77

4.2 Theoretical Background 79

4.2.1 Coupled-ClusterWave Function 79

4.2.2 The Equation-of-Motion Approach 80

4.2.3 Similarity-Transformed Hamiltonian 81

4.2.4 Davidson Diagonalization Algorithm 82

4.3 Excited States: EE-EOM-CC 84

4.3.1 EE-EOM-CCSD Model 84

4.3.2 EE-EOM-CCSDT Model 86

4.3.3 EE-EOM-CC Results 87

4.4 Ionized States: IP-EOM-CC 89

4.4.1 IP-EOM-CCSD Model 89

4.4.2 IP-EOM-CCSDT Model 89

4.4.3 IP-EOM-CC Results 90

4.5 Electron-Attached States: EA-EOM-CC 91 4.5.1 EA-EOM-CCSD Model 9...