Discrepancy of one-electron integral in FCI dump

[Li Yuan]

Dear all,

I have one question on the one-electron integral calculated from FCI dump program. Basically, I am trying to print the one- and two-electron integrals by defining different occupied and frozen-core orbitals. Starting with the very simple case CO2, there are in total 11 occupied orbitals. I tried with two different FCI input:

1): {fci,dump=10.fcidump; orbital,set=2;occ, 12; core,10}

2) :{fci,dump=0.fcidump;   orbital,set=2;occ, 12; core,0}

If I compare the fcidump files of these two setups:

fcidump file of setup 1):

  0.6749792190779742E+00   1   1   1   1
 -0.8740929811623456E-01    2   1   1   1
  0.5657582443643333E-01    2   1   2   1
  0.4208276606818894E+00   2   2   1   1
  0.1269907293158428E-01    2   2   2   1
  0.4349180192779021E+00   2   2   2   2
 -0.1296840359814508E+01   1   1   0   0
  0.8740943988656774E-01     2   1   0   0
 -0.5692356756040545E+00    2   2   0   0
 -0.1857220591732645E+03    0   0   0   0

The two-electron integral here 0.6749792190779742E+00   1   1   1   1 corresponding to the orbitals of 11 in setup 2) and integral is exactly same 0.6749792190779742E+00  11  11  11  11. The same consistency can found for other two-electron integrals. 

The question here is for one-electron integral, for example,  -0.1296840359814508E+01   1   1   0   0 in setup 1) is not equal to the one-electron integral -0.1054243218844784E+02  11  11   0   0 in setup 2). I want to know how to understand this discrepancy. May someone help on this. Thank you very much!

Best regards,

Yuan

[Peter Knowles]

In the case of a frozen core, the one electron integrals in the FCIdump are the matrix elements of the Fock operator formed using the density of the frozen orbitals. The ‘zero-electron’ integral is, similarly, the nuclear repulsion energy plus half the trace over the core space of the bare 1-electron hamiltonian plus core Fock. This is just what you want for a hamiltonian expressed only in terms of the orbitals that are not in the core.

Peter

On 8 Sep 2023, at 16:10, Li Yuan <yli2...@gmail.com> wrote:

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[Li Yuan]

Hi Peter,

Thanks for your explanation. It is very helpful. I was wondering what is the input command for getting the one- and two-electron integral of different spin, i.e., alpha and beta spin, after CASSCF calculation in molpro program? 

Best regards,

Yuan

[Peter Knowles]

CASSCF in Molpro works with spin-restricted orbitals only, and so the integrals are not spin-dependent.

If you do uhf;fci,dump=… you will see that FCIdump file does contain the different spin cases. They can be parsed as in https://github.com/molpro/fcidump/tree/master/examples .

Best regards,

Peter  

On 20 Sep 2023, at 01:26, Li Yuan <yli2...@gmail.com> wrote:

Hi Peter,

Thanks for your explanation. It is very helpful. I was wondering what is the input command for getting the one- and two-electron integral of different spin, i.e., alpha and beta spin, after CASSCF calculation in molpro program? 

Best regards,

Yuan