# CI wavefunction norm in Gaussian

Dear fellow netters,
I am running CI(SD) calculations using G90, and I
am trying to extract the coefficient of the HF
configuration. The manual says (page 165) that "Norm(A1)
- 1 gives a measure of the correlation correction to the
wavefunction." But what exactly is the coefficient for
the HF configuration? My guess is that it is given by
1/Norm(A1), but I am not sure. Any comments?
Thank you,
Gernot Frenking
frenking { *at * } dmrhrz11.bitnet
Your guess is correct. This is one of the most commonly asked questions,
and the G92 manual has the equation for Norm(A) in an attempt to make the
relationship clearer. The wavefunction is stored in intermediate
normalization. That is:
Psi(CISD) = Psi(0) + Sum(ia) Tia Psi(i-->a) + Sum (ijab) Tijab
Psi(ij-->ab)
Where Psi(0) is the Hartree-Fock determinant and has a coefficient of 1
(that's what intermediate normalization means). Norm(A) is the factor
by which to divide the wavefunction as given above to fully normalize it.
Thus
Norm(A) = Sqrt (1 + Sum(ia) Tia*Tia + Sum(ijab) Tijab*Tijab)
The coefficient of the Hartree-Fock determinant in the fully normalized
wavefunction is then 1/Norm(A), the coefficient of singly excited
determinant Psi(i-->a) is Tia/Norm(A), etc.
Another pitfall to be careful of is that the sum over the doubly-excited
determinants is really restricted to the unique determinants. It is
really
Sum(i<j,a<b) Psi(ij-->ab ijab all alpha spin) +
Sum(all ijab) Psi(ij-->ab i,a alpha j,b beta) +
Sum(i<j,a<b) Psi(ij-->ab ijab all beta spin)
For closed shell, the all beta coefficients are equal to the all alpha
coefficients and if you request that the coefficients be printed (using
IOP(9/28=N) to get coefficients larger than 10^-N or IOP(9/28=-1) to get all
coefficients) only the alpha-alpha and alpha-beta coefficients will be
printed.
Mike Frisch
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