Q. What is the
definition of the excitation energy ? Is it the
relative energy from the SAC state (closed-shell singlet state) or the lowest
state in each spin-symmetry?
A. The result of
the diagonalization of the SAC-CI Hamiltonian matrix
would be printed out as follows.
### 1-st ###
--- 1st state in this
spin multiplicity ---
This state is being
used for optimizations.
Total energy in au
= -137.984448
Correlation energy in
au =
-0.211509
Excitation energy in au
=
0.067464 in eV = 1.835777
*SINGLE EXCITATION
8 9 0.95882
8 13 -0.20786
7 9 -0.05952
4 9 -0.03690
Here,
“Excitation energy” is the relative energy from the SAC state. The same is for the other spin
multiplicities. On the other hand, you would have the result for the transition
property of the singlet states as followings.
Transition dipole moment of singlet state from SAC ground
state
-------------------------------------------------------------------------------
Symmetry Solution Excitation Transition dipole
moment (au)
Osc.
energy (eV) X
Y
Z strength
-------------------------------------------------------------------------------
A1
0
0.0
Excitations are from this state.
A1
1
10.7545
0.0000
0.0000 0.6593 0.1145
A1
2 19.1017 0.0000 0.0000 -0.7882 0.2907
A2
1
10.7291
0.0000
0.0000 0.0000 0.0000
A2
2
26.5243
0.0000
0.0000 0.0000 0.0000
B1
1
8.5939
0.2738 0.0000 0.0000 0.0158
B1
2
24.9801
0.0961
0.0000
0.0000 0.0056
B2
1
13.2224
0.0000
-0.6270
0.0000
0.1273
B2
2
15.9912
0.0000
1.1672
0.0000 0.5337
-------------------------------------------------------------------------------
As
you see in the output, the excitation energy is calculated as the relative
energy from the SAC ground state.
However, for the other spin-multiplicities, the excitation energy is
calculated from the energy of the lowest state in each spin-multiplicity. See
an example shown below. The excitation energies of the double ionized states
are calculated from the 12B1 state which the lowest state
within the SAC-CI result.
Transition
dipole moment of ionized
state from symmetry B1
1-th state
-------------------------------------------------------------------------------
Symmetry Solution Excitation Transition dipole
moment (au)
Osc.
energy (eV) X
Y
Z
strength
-------------------------------------------------------------------------------
A1
1
1.7771
-0.1919
0.0000
0.0000 0.0016
A1
2
22.9129
0.2647 0.0000 0.0000 0.0393
A1
3
27.5008
0.1943
0.0000
0.0000 0.0254
B1
1
0.0
Excitations are from this state.
B2
1
7.1924
0.0000
0.0000 0.0000 0.0000
-------------------------------------------------------------------------------