# Calculate the adiabatic excitation energy difference between two state, Electronic Transition Dipole Emission(ETDE) andElectronic Transition Dipole Absorption (EDMA)

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
\$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:

1. Optimize the geometry of the ground state, note the SCF energy of the equilibrium structure, E0.
2. 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.
3. 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 = 0.00002 + 0.33942 + 0.00002 = 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