Slight mismatching of CASSCF between "Total MCSCF energy" and "MCSCF root 0 energy"

Hello,

I made a strange observation that there is a small discrepancy between the printed energies and psi4’s CURRENT ENERGY in CASSCF. The following is the input I use.

molecule pbenzyne{
  0 1
   C   0.0000000000  -2.5451795941   0.0000000000
   C   0.0000000000   2.5451795941   0.0000000000
   C  -2.2828001669  -1.3508352528   0.0000000000
   C   2.2828001669  -1.3508352528   0.0000000000
   C   2.2828001669   1.3508352528   0.0000000000
   C  -2.2828001669   1.3508352528   0.0000000000
   H  -4.0782187459  -2.3208602146   0.0000000000
   H   4.0782187459  -2.3208602146   0.0000000000
   H   4.0782187459   2.3208602146   0.0000000000
   H  -4.0782187459   2.3208602146   0.0000000000

  units bohr
}

set globals{
  basis                  cc-pvdz
  df_basis_scf           cc-pvdz-jkfit
  reference              rhf
  scf_type               df
  d_convergence          8
  e_convergence          12
  mcscf_type             df
  mcscf_e_convergence    12
  mcscf_r_convergence    10
  mcscf_diis_start       8
  mcscf_max_rot          0.1
  docc                   [5,3,1,1,0,1,5,4]
  restricted_docc        [5,3,0,0,0,0,4,4]
  active                 [1,0,1,2,1,2,1,0]
}
Ecas, wfn = energy('casscf', return_wfn=True)

Here is the part of the output that bothers me.

...
   @DF-MCSCF 16:   -229.495450424074   -1.3379e-09  7.13e-07  0.00e+00   12    1  TS, DIIS
   @DF-MCSCF 17:   -229.495450424145   -7.0315e-11  8.76e-10  0.00e+00   12    1  TS, DIIS
   @DF-MCSCF 18:   -229.495450424145    5.6843e-14  3.93e-10  0.00e+00   12    1  TS, DIIS
   @DF-MCSCF 19:   -229.495450424145   -5.6843e-14  6.15e-11  0.00e+00   12    1  TS, DIIS

          @DF-MCSCF has converged!

   @DF-MCSCF Final Energy: -229.495450424144593

   Computing CI Semicanonical Orbitals

   ==> Energetics <==

    SCF energy =         -229.283874146841754
    Total MCSCF energy = -229.495450424144593

   ==> MCSCF root 0 information <==

    MCSCF Root 0 energy =  -229.495450379691391

The Total MCSCF energy differs from MCSCF Root 0 energy by 4 * 10^-8 and the CURRENT ENERGY uses MCSCF Root 0 energy. It seems to me the problem is the integral transformation step to semicanonical orbitals and re-diagonalizing the Hamiltonian (the latter is probably not necessary), but I am not sure. I tried other molecules (e.g., NH3, N2) but I have not found similar behaviors. Any ideas why this is happening?

Edits: I am using Psi4 1.4a2.dev313.

@francesco anything that you can think of with the semicanonical orbitals here?

Thank you for bringing this up @york0822: I am not sure where the discrepancy comes from. Let me investigate the code that saves the energy to “MCSCF Root 0 energy.”