How to calculate the adiabatic excitation energy difference between two state? I have calculate the ground state and excited state of one molecule, but I don’t know how to extract the difference between ground state and excited state.

Another question is about Electronic Transition Dipole Emission(ETDE) and Electronic Transition Dipole Absorption (EDMA), I don’t know how to extract those from output file of excited state.

```
--------------------------------------------------------------
User input:
--------------------------------------------------------------
$molecule
0 1
C 2.01378700 -1.48849900 0.00000000
C 2.28995100 -0.11795300 0.00000000
C 1.39185800 0.95357400 0.00000000
C 0.78413700 -2.15418400 0.00000000
C 0.00000000 0.93285800 0.00000000
C -0.50398400 -1.61066000 0.00000000
C -0.89316500 -0.27406300 0.00000000
H 2.88919300 -2.13621800 0.00000000
H 3.34387200 0.15083300 0.00000000
H 1.84191300 1.94636000 0.00000000
H 0.83658300 -3.24058400 0.00000000
H -1.32037400 -2.33298500 0.00000000
C -0.84567300 2.05536600 0.00000000
H -0.51364900 3.08694100 0.00000000
C -2.17758700 1.61062700 0.00000000
H -3.04994500 2.25593900 0.00000000
C -2.21340000 0.20656500 0.00000000
H -3.10314400 -0.41207700 0.00000000
$end
$rem
JOBTYPE opt
CIS_STATE_DERIV 1
CIS_N_ROOTS 3
CIS_TRIPLETS FALSE
EXCHANGE B3LYP
BASIS 6-31G(D)
$end
$molecule
read
$end
$rem
JOBTYPE freq
CIS_STATE_DERIV 1
CIS_N_ROOTS 3
CIS_TRIPLETS FALSE
iprint 10000000
EXCHANGE B3LYP
BASIS 6-31G(D)
$end
......
A restricted SCF calculation will be
performed using DIIS
SCF converges when DIIS error is below 1.0e-08
---------------------------------------
Cycle Energy DIIS error
---------------------------------------
1 -388.1119834981 6.18e-02
2 -385.6828076156 5.83e-03
3 -385.5331510776 8.14e-03
4 -385.7556380043 3.72e-03
5 -385.8208564936 4.47e-04
6 -385.8213018226 3.01e-04
7 -385.8216023140 7.51e-05
8 -385.8216234324 1.85e-05
9 -385.8216245684 4.61e-06
10 -385.8216246296 2.31e-06
11 -385.8216246482 3.78e-07
12 -385.8216246486 8.85e-08
13 -385.8216246487 8.02e-09 Convergence criterion met
---------------------------------------
SCF time: CPU 35.93s wall 5.00s
SCF energy in the final basis set = -385.8216246487
Total energy in the final basis set = -385.8216246487
......
---------------------------------------------------
TDDFT/TDA Excitation Energies
---------------------------------------------------
Excited state 1: excitation energy (eV) = 1.6706
Total energy for state 1: -385.76023236 au
Multiplicity: Singlet
Trans. Mom.: 0.0000 X 0.3394 Y -0.0000 Z
Strength : 0.0047155919
D( 34) --> V( 1) amplitude = 0.9900
Excited state 2: excitation energy (eV) = 3.5081
Total energy for state 2: -385.69270494 au
Multiplicity: Singlet
Trans. Mom.: -0.1205 X -0.0000 Y 0.0000 Z
Strength : 0.0012481775
D( 33) --> V( 1) amplitude = -0.6906
D( 34) --> V( 2) amplitude = 0.7072
Excited state 3: excitation energy (eV) = 4.7501
Total energy for state 3: -385.64706164 au
Multiplicity: Singlet
Trans. Mom.: 0.0000 X -0.2693 Y 0.0000 Z
Strength : 0.0084379229
D( 32) --> V( 1) amplitude = -0.5658
D( 33) --> V( 2) amplitude = 0.8002
```

Adiabatic excitation energy is the energy difference between the equilibrium structures in the ground and excited states. The energies must be computed with compatible levels of theory (i.e. HF/CIS, DFT/TDDFT) and could be corrected by ZPE. The steps are as follows:

- Optimize the geometry of the ground state, note the SCF energy of the equilibrium structure, E0.
- Optimize the geometry of the desired excited state, note the absolute CIS energy of the equilibrium structure, E1. This energy is printed under
`Total energy for state X`

in the CIS output. - Compute E(exc) = E1 - E0

If ZPE correction is desired, perform respective vibrational frequencies calculations at steps 1 and 2 and correct E0 and E1 for ZPE.

Thanks a lot, and can you help me explain the Electronic Transition Dipole Emission(ETDE) and Electronic Transition Dipole Absorption (EDMA) in output file of excited state?

Sorry I don’t have much experience computing those properties, but presumably they are just transition dipole moments at the two geometries.

The components of the transition electric dipole vector are given under `Trans. Mom.`

, in your output sample for state 1 for example:

```
Trans. Mom.: 0.0000 X 0.3394 Y -0.0000 Z
```

|mu|^{2} = 0.0000^{2} + 0.3394^{2} + 0.0000^{2} = 0.1152

These quantities are given in atomic units.

Methods for computing electronic couplings are described in the Q-Chem manual here:

https://manual.q-chem.com/4.3/sec-ElCoupl.html

and also in this webinar:

https://www.q-chem.com/webinars/6