[molpro-user] Saving orbitals to file and natural orbitals

Gerald Knizia knizia at theochem.uni-stuttgart.de
Mon Feb 16 16:06:46 GMT 2009

On Monday 16 February 2009 11:23, Stephen Harrison wrote:
> Firstly, I understand that MOLPRO uses natural orbitals by default at
> MCSCF level, after discussing this with my supervisor we seem slightly
> perplexed by this. Are the MCSCF natural orbitals the same as normal MCSCF
> orbitals? because as far as my understanding goes I thought the 'true'
> natural orbitals only came out during the MRCI level calculation (i.e.
> after MCSCF has already run).

The term "natural orbitals" is used in multiple context. It always denotes a 
set of orbitals which diagonalizes a density matrix[1] , and thus assigns 
each orbital a clear occupation number. However, which density matrix is 
referred to depends on the context. MCSCF natural orbitals diagonalize the 
MCSCF density matrix, MRCI natural orbitals diagonalize the MRCI density 
matrix (and thus the latter contain a large fraction of dynamic correlation, 
while the prior do not). In particular, for the MCSCF density matrix, NOs 
corresponding to closed shell orbitals have occupation number 2.0 and NOs 
referring to external (=virtual) orbitals have occupation number 0.0, neither 
of which is true for a CI wave function.
I hope this clarifies the NO issue.

For the orbital saving issue I don't have advice.

[1]: The matrix of the expectation values gamma_rs = <Psi|e^r e_s|Psi> where 
e^r/e_s are creation/destruction operators, respectively. Psi is ``some wave 
Gerald Knizia

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