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Alex Granovsky
gran@classic.chem.msu.su

this part of output is perhaps not well self-explaining...

First, this is TDDFT (or TDHF). In TD, the solution vectors are two-component objects:

X_i + Y_i

Instead of usual CI normalization condition and orthogonality, TD vectors are bi-orthogonal:

X_i⁺*X_i - Y_i⁺*Y_i = 1

X_i⁺*X_j - Y_i⁺*Y_j = 0 for i != j

The X component is what is called "excitations". Roughly speaking, it is similar to single-particle excitations in CIS or TDA/TDDFT.

The Y component is what is called "deexcitations". It is not very trivial to interpret it; however, it is related to two-electron excitations. It is exactly the Y part that allows TD to describe excited states of partially double excited type slightly better
than CIS.

For singly-excited states, X component is large (with norm of X close to unity), while Y is "small".

In the printout section, deexcitations are those that have "from MO" index larger than that of "to MO".

E.g.,

224        230                   0.78233561

and

224        230                  -0.78233561

are excitation regardless of sign of SAP coefficient.

At the same time,  

230        224                  -0.008233561

is deexcitation.

Normally, one should not be too careful tracking signs of SAPs. E.g., if the particular MO changes its sign at some displaced geometry, this causes inversion of signs of all SAPs associated with this MO. So yes, it seems it is still the same state.


As described in the documentation on CIS/TDHF/TDDFT, Firefly has built-in ability to track CIS/TD states over varied geometries. You may be interested to activate this feature.

Hope this helps!
Alex



On Wed Mar 4 '09 2:44pm, Pedro Silva wrote
------------------------------------------
>I am interested in following the energies of several excited states as a specific bond is lenghtened. I have several optimized geometries along this PES, and I have computed the excited states through TDDFT.
>In order to check whether the excited states cross, I have analyzed the EXCITATIONS/DEEXCITATIONS part of the output. In contiguous points of the surface, I find a strange discrepancy in this section:

>Geometry A:
>
>
>          ----------------------------------------------
>          EXCITATIONS & DEEXCITATIONS     SAP COEFFICENT
>          FROM MO     TO MO
>          ----------------------------------------------
>          
>           223        229                  -0.26224016
>          
>           224        230                   0.78233561
>          
>           228        231                   0.40256033

>          ----------------------------------------------
>
>
>Geometry B:
>
>
>          ----------------------------------------------
>          EXCITATIONS & DEEXCITATIONS     SAP COEFFICENT
>          FROM MO     TO MO
>          ----------------------------------------------

>           223        229                   0.16069884
>          
>           224        230                  -0.71201471
>          
>           228        231                  -0.53043190

>          ----------------------------------------------

>As you can see from this truncated output, the involved orbitals seem to be the same (the absolute values of the SAP have not changed much) but the signs of the SAP coefficients have flipped, so that they now are deexcitations instead of excitations...  So my doubt is : are these the same excited state?

>Thanks for any help

>Pedro

>

[ This message was edited on Thu Mar 5 '09 at 0:38am by the author ]