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The orbital transition contribution in the electronic excitation process

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Author Post
Member
Registered: Jul 2019
Posts: 1
Dear all,

I had run a TDDFT calculation to obtain the vertical excitation energy in various solvents. I want to know how to get the contribution of orbital transition in the electronic excitation process. The following is part of the output file.
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TDDFT Excitation Energies
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Excited state 1: excitation energy (eV) = 2.8755
Total energy for state 1: -1459.39584292 au
Multiplicity: Singlet
Trans. Mom.: 4.2757 X 0.0000 Y 0.0000 Z
Strength : 1.2878838269
X: D( 90) --> V( 1) amplitude = 0.9999

Excited state 2: excitation energy (eV) = 3.3555
Total energy for state 2: -1459.37820286 au
Multiplicity: Singlet
Trans. Mom.: -0.0000 X -0.6336 Y 0.0130 Z
Strength : 0.0330167300
X: D( 89) --> V( 1) amplitude = 0.9852

Excited state 3: excitation energy (eV) = 4.2379
Total energy for state 3: -1459.34577460 au
Multiplicity: Singlet
Trans. Mom.: -0.9262 X -0.0005 Y -0.0000 Z
Strength : 0.0890610106
X: D( 88) --> V( 1) amplitude = 0.9531

Excited state 4: excitation energy (eV) = 4.3111
Total energy for state 4: -1459.34308416 au
Multiplicity: Singlet
Trans. Mom.: 0.0000 X 0.5184 Y -0.0047 Z
Strength : 0.0283839124
X: D( 87) --> V( 1) amplitude = 0.7704
X: D( 90) --> V( 2) amplitude = -0.5454

Excited state 5: excitation energy (eV) = 4.3964
Total energy for state 5: -1459.33994883 au
Multiplicity: Singlet
Trans. Mom.: -0.0000 X -0.2148 Y 0.0100 Z
Strength : 0.0049787277
X: D( 87) --> V( 1) amplitude = 0.5864
X: D( 90) --> V( 2) amplitude = 0.7645

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At first,I think the values of ”amplitude“ are on behalf of the orbital transition contribution of the electronic excitation. But, the total amplitudes of some excited states is not equal to 1. Could someone please answer my following questions? firstly,what does the amplitudes mean? Secondly,how to print the contribution of orbital transition in the electronic excitation process,like the CI coefficient in Gaussian software?

Thanks for your patience and looking for your help.

Best regards.

yingli
Administrator
Registered: Oct 2017
Posts: 22
Dear Yingli,

I am not completely sure what the meaning of "orbital transition contribution" is, but the amplitudes here have exactly the same meaning as CI coefficients. The word "amplitude" is often used in second quantization formulation, and it can be more general. Let's look at the first excited state: X: D( 90) --> V( 1) amplitude = 0.9999 means that in the excited state the orbitals D(90) and V(1) are singly occupied. I suspect you are running a spin-adapted version; in a non-spin-adapted run you can see the separate amplitudes for alpha and beta electrons.

The excited state 4 is more interesting: Here you can see contributions from two different excitations. It means that the wave function is mainly described by two different open-shell spin-adapted configurations (or 4 open-shell determinants).

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