Excited Electronic States Flashcards
What are excited states important for?
UV-vis absorption
Why are UV-vis absorption peaks broad?
Because of various subsets achievable
(many vibrational energies available for each electronic energy level)
Adiabatic excitation energy
Excitation to the ground state of the electronically excited state
The threshold for the energy transition
Vertical excitation energy
The change in energy to the peak maximum
Computed by assuming ground-state nuclear positions
Where is Eupper (for delta E) computed at for vertical and adiabatic energy?
Ground state geometry for delta E vert.
Excited state geometry for delta E adiab.
When can ordinary methods (for calculating E (excited) used?
If excited state has different spin state or different orbital symmetry
Called the delta SCF approach (for SCF-only methods like HF or DFT)
Variational collapse problem
If electron is excited to a spin-orbital of the same symmetry it had in the ground state, then the excited orbital tends to optimize back to the ground-state orbital
How is variational collapse problem solved?
Matrix diagonalization methods are used, involving a CI matrix
CI Matrix
Has elements Eij = integral( Yi* H Yj dT)
where Yi and Yj are electronic states having different occupations but keeping the same ground state optimized orbitals, which give better state energies when diagnonalized
CI Singles Technique
(1) HF-SCF ground state orbitals (Y, Yi) obtained
(2) CI matrix elements (Eij’s) computed without re-optimizing orbitals, considering only single excitations (Yj’s)
(3) CI matrix is diagonalized, providing several excited-state energies at that molecular geometry (delta E vert, ground state geometry used). Each excited state represented by a linear combination of Slater determinants (just like ground state is in CISD and MCSCF)
Typical errors (CI singles technique)
0.07 eV or 70 kJ/mol
Best for qualitative exploring of excited states
General (more accurate) methods
Excited-state MCSCF
Time-dependent DFT
Excited-state MCSCF
Two modes:
Optimize orbitals for each excited state individually, great for delta E adiab
Hard to do if variational collapse is a threat
State-averaged opt:
Optimize orbitals for the best (lowest) average of several state energies, algorithm converges, generally more accurate than CI
Time-dependent DFT
Uses equations from oscillating electric-field theory to find ‘resonance’ corresponding to excited state energies, accurate for low-lying states
Solvatochromism
UV-vis spectral transitions of solutes, often require consideration of solvent effects
delta E is often increased by solvation (solvatochromism), treated by implicit solvation modelling with excited-state computation
