Subject: TDDFT

From: "Hui-Hsu \(Gavin\) Tsai" <[email-masked]>
Date: Tue, 11 Sep 2001 12:12:53 -0400

Hi CCLers,

Two days ago, I posted a question about TDDFT.
The original email is

Hi CCLers,

      We have a question about excited state calculations by using G98W.
  In the excited state calculation (such as TDDFT), are the coefficients normalized?
Why is the sum of the squared coefficients not equal to 1.0
and sometimes smaller than 0.5? 

    Here is the output of TDDFT calculations of water... 

  Excitation energies and oscillator strengths:
 
  Excited State   1:   Singlet-B1     8.0068 eV  154.85 nm  f=0.0142
       3 -> 14        -0.01126
       5 ->  6         0.69120
       5 -> 11         0.01351
 This state for optimization and/or second-order correction.
 Total Energy, E(RPA) =  -76.1254896781    
 Copying the excited state density for this state as the 1-particle RhoCI density.
 
 Excited State   2:   Singlet-A2    10.0437 eV  123.44 nm  f=0.0000
       5 ->  7         0.70034
       5 ->  8        -0.01585
       5 -> 12         0.01756

   The water example shows that the sum of the squared coefficients is about just 0.5.

   Should we normalize the coefficients by ourselves? 
  
  Hese is the response from Gaussian.

Since the alpha and beta excitation manifold will be identical when
starting from an RHF reference only the alpha excitations are detailed.
So you are getting half of the wavefunction and it should normalize to
a little less than 0.5 because only the largest coefficients are displayed.

  When you start from a UHF reference then both the alpha and beta
manifolds must be displayed because they are generally different.