Quantum chemistry of excited states explores molecules' behavior beyond their ground state. It uses methods like TD-DFT and EOM-CC to calculate energies and properties of higher-energy configurations, crucial for understanding light-matter interactions and photochemical reactions.

This topic delves into excited state dynamics, transitions, and spectroscopy. It covers non-adiabatic processes, conical intersections, and the Franck-Condon principle, providing insights into molecular spectra and photophysical phenomena like fluorescence and phosphorescence.

Quantum Chemistry Methods for Excited States

Time-Dependent Density Functional Theory (TD-DFT)

• Extension of ground-state DFT that allows for the study of excited states and time-dependent phenomena
• Treats the electron density as a function of both space and time, enabling the calculation of excited state properties
• Computationally efficient compared to other excited state methods, making it suitable for larger systems
• Limitations include the accuracy of the exchange-correlation functional and the difficulty in describing charge-transfer and Rydberg states

Wavefunction-Based Methods for Excited States

• Configuration interaction singles (CIS) method generates excited state wavefunctions by promoting a single electron from an occupied to a virtual orbital
• Provides a qualitatively correct description of excited states but lacks dynamic electron correlation, leading to overestimated excitation energies
• Equation-of-motion coupled cluster (EOM-CC) methods describe excited states as linear combinations of the ground state coupled cluster wavefunction
• EOM-CC includes dynamic electron correlation and provides accurate excitation energies and transition properties (oscillator strengths, transition dipole moments)
• Computationally more demanding than TD-DFT but offers higher accuracy for small to medium-sized systems

Linear Response Theory

• General framework for calculating the response of a system to a time-dependent perturbation
• Excited state properties can be obtained from the frequency-dependent linear response function
• Applicable to various quantum chemistry methods, including DFT and coupled cluster theory
• Enables the calculation of excitation energies, transition moments, and polarizabilities
• Provides a unified approach to excited state properties and allows for the inclusion of environmental effects (solvent, electric fields)

Excited State Dynamics and Transitions

Non-Adiabatic Dynamics and Conical Intersections

• Non-adiabatic dynamics involve the coupling between electronic and nuclear motion, leading to transitions between electronic states
• Conical intersections are points in the potential energy surface where two or more electronic states become degenerate
• Play a crucial role in non-adiabatic processes such as photochemical reactions, energy transfer, and charge separation
• Require the use of advanced computational methods (surface hopping, multiple spawning) to accurately describe the dynamics

Franck-Condon Principle and Spectroscopy

• Franck-Condon principle states that electronic transitions occur vertically, without changes in the nuclear coordinates
• Determines the intensity of vibronic transitions in absorption and emission spectra
• Transitions are favored when there is a significant overlap between the vibrational wavefunctions of the initial and final states (Franck-Condon factors)
• Allows for the interpretation of vibronic structure in electronic spectra and the determination of excited state geometries

Jablonski Diagram and Photophysical Processes

• Jablonski diagram is a schematic representation of the electronic states and the transitions between them
• Illustrates the various photophysical processes: absorption, fluorescence, phosphorescence, internal conversion, and intersystem crossing
• Absorption occurs from the ground state to an excited state, followed by relaxation to the lowest vibrational level of the excited state
• Fluorescence is the emission of a photon from an excited singlet state to the ground state (spin-allowed transition)
• Phosphorescence involves emission from an excited triplet state to the ground state (spin-forbidden transition, longer lifetimes)
• Internal conversion is a non-radiative transition between two electronic states of the same spin multiplicity
• Intersystem crossing is a non-radiative transition between two electronic states of different spin multiplicity (singlet to triplet or vice versa)