Subject: CCL:G98 TD/CIS Opposite sign of the components of length- a

From: "Jens Spanget-Larsen" <[email-masked]>
Date: Mon, 10 Jun 2002 16:05:14 +0100

Hi Peter,
hello again:

> I have some questions regarding the output os CIS and TD jobs in G98
> (Rev. A7). I can't find anything on these issues in Gaussian
> documentation or past CCL posts, although the questions are rather
> simple. So I hope it makes sense...
> 
> The output of TD and CIS calculations give the x, y, and z
> components of the "Ground to excited state Transition electric
> dipole moments", "Ground to excited state transition velocity dipole
> Moments", and the "Ground to excited state transition magnetic
> dipole Moments". 
> 
> 1) Why are the components of the electric and velocity derived
> transition dipole moments oppositely signed? I thought that they
> should be identical in a complete basis. I would have thought that
> the sign ought to be the same. Which values should I trust? 

The "dipole length" and "dipole velocity" electronic transition 
moments, <m|r|n> and <m|p|n>, are far from identical (even in a 
complete basis); e.g., For a one-electron system we have r = {x,y,z} 
and p = -i{d/dx,d/dy,d/dz} (a.u.). <m|p|n> is thus an imaginary 
quantity and Gaussian98 outputs the imaginary part, im[<m|p|n>]. For 
the operators x and d/dx the following relations are valid for EXACT 
wavefunctions (since [H,x] = -d/dx):

<m|d/dx|n>  =  (En - Em)<m|x|n>

==>   im[<m|p|n>] = -(En - Em)<m|r|n>

Hence, <m|r|n> and im[<m|p|n>] should indeed have different signs, as 
printed by Gaussian98.

Yours, Jens >--<

NB! Please note new mail address: <[email-masked]>
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