How does MOLPRO choose active orbitals in a CASSCF calculation?

Question

I am trying to calculate electronically excited states for the CO molecule, with the aug-cc-pVTZ basis set, and a CASSCF calculation. The documentation describes how I select the number of orbitals in the closed and active spaces for each symmetry (in the C_2v point group). But I can't find information about the criteria that is used for selecting which orbitals will be the active ones in each symmetry.

Using the command orbprint,12 I can tell that orbitals are not selected simply in increasing energy order (since some unoccupied orbitals have lower energy than the occupied ones).

How does Molpro pick out orbitals for the active space? And, can I control this process if I am not happy with some particular selection?

A condensed version of my input:

***,CASSCF test

MEMORY,2,G

GEOMETRY = {
  C
  O, C, qco
}

basis = aug-cc-pVTZ

dq = 0.125
DO qco = 1, 10, dq
  IF (qco.EQ.1.5) dq = 0.0625
  IF (qco.EQ.3) dq = 0.125
  IF (qco.EQ.4) dq = 0.25
  IF (qco.EQ.5) dq = 0.5
  IF (qco.EQ.6) dq = 1

  CASSCF
    orbprint,12
    closed,2,0,0,0
    occ,6,3,3,2
    wf,14,1,0
      state,5
  
  ! Storing distance, energy, and tr-dip-mom. in memory [..]

END DO

! Saving all computed values to disk [..]

---

For nuclear distance 2.75, these are eight orbitals in each symmetry. Taken from the output file.

Orbital  Occupation       Energy
 1.1        2.00000    -20.72392
 2.1        2.00000    -11.41840
 3.1        1.99027     -1.38533
 4.1        1.93048     -0.81010
 5.1        1.55554     -0.48414
 6.1        0.07730      0.43260
 7.1       -0.00000      0.06413
 8.1       -0.00000      0.08645
 1.2        1.73314     -0.55388
 2.2        0.54582     -0.05416
 3.2        0.01415      0.95790
 4.2       -0.00000      0.09084
 5.2       -0.00000      0.25216
 6.2       -0.00000      0.48245
 7.2       -0.00000      0.57317
 8.2       -0.00000      0.77930
 1.3        1.55073     -0.50443
 2.3        0.39516     -0.01699
 3.3        0.19777      0.09396
 4.3       -0.00000      0.17954
 5.3       -0.00000      0.37646
 6.3       -0.00000      0.50901
 7.3       -0.00000      0.77746
 8.3       -0.00000      1.00082
 1.4        0.00610      1.10176
 2.4        0.00353      2.22594
 3.4       -0.00000      0.47199
 4.4       -0.00000      1.09344
 5.4       -0.00000      1.21291
 6.4       -0.00000      2.37566
 7.4       -0.00000      3.10900
 8.4       -0.00000      3.49887

Answer 1

You fixed the occupation within symmetries by the command "occ,6,3,3,2" and asked the program to make CASSCF for the lowest 5 singlet states of symmetry 1 ($A_1$). And indeed, as you see, the first 6, 3, 3, and 2 orbitals in symmetries 1, 2, 3, 4, respectively, have nonzero occupation numbers, which sum up to 6+8=14, the number of electrons of $\ce{CO}$. These orbitals are ordered by energy, but within symmetries, so the criterion is the orbital energy.

There are many options in the CASSCF Molpro program and it is difficult to advise without knowing what you do not like in your results. You can, e.g., run a HF calculation, use these orbitals as starting orbitals and freeze some orbitals in the subsequent CASSCF calculation. Since you have a linear molecule, you probably would like to select orbitals with "extra" symmetries (i.e. differentiate between orbitals, which are e.g. in the same $A_1$ representation in $C_{2v}$, but in reality they are in different representation in $C_{\infty v}$, look for the EXTRA keyword in the manual). You can also restrict CSFs (so you have RAS, not CAS), by the RESTRICT keyword, e.g. to single and double excitations. Another option is to play with the MERGE command and to prepare initial orbitals from atomic orbitals (there is an example for a $\ce{NO}$ molecule in the Molpro manual, i.e. something very similar to your molecule).

Answer 2

I believe my question is based on a misconception, so this is an answer according to my current understanding. Please, if you find additional misconceptions, comment below and I will try to update accordingly. Okay, let's go!

When you run a CASSCF calculation, note that the coefficients which are building up the orbitals are optimised at the same time as the CI coefficients. So there are no set of predefined orbitals which the calculations picks from (when creating the CI expansion).

Instead, what's happening is that the orbitals are optimised such that they are the best set available—for the chosen basis—to describe the "electron correlation" (i.e. the difference between the product wave-function of the Slater determinant, and the true eigenstate wave-function).

This procedure does not imply that the "selected" orbitals must be the lowest energy ones. What makes the determination is instead how useful their shapes are for describing the electron correlation. Though it can be said that very high energy orbitals are probably not useful.