3.3.10. CASVB — A non-orthogonal MCSCF program

CASVB is a program for carrying out quite general types of non-orthogonal MCSCF calculations, offering, for example, all the advantages associated with working within a valence bond formalism.

Warning: as for any general MCSCF program, one may experience convergence problems, (e.g., due to redundant parameters), and the non-orthogonal optimization of orbitals can furthermore give linear dependency problems. Several options in CASVB can help overcoming these difficulties.

This program can be used in two basic modes:

  1. fully variational optimization

  2. representation of CASSCF wavefunctions using overlap- (relatively inexpensive) or energy-based criteria.

CASVB executes the following logical steps: Setup of wavefunction information, starting guess generation, one, or several, optimization steps, various types of analysis of the converged solution.

3.3.10.1. CASVB Input

CASVB attempts to define defaults for as many input quantities as possible, so that in the simplest case no input to the CASVB module is required. Sample input for a CASVB calculation on the lowest singlet state of \(\ce{CH_2}\):

&GATEWAY
coord
3
ch2 molecule
C 0.000000  0.000000 0.000000
H 0.000000  0.892226 0.708554
H 0.000000 -0.892226 0.708554

group= x y; basis= sto-3g
&SEWARD
&SCF
&RASSCF
nactel= 6 0 0; inactive= 1 0 0 0; ras2= 3 1 2 0
lumorb
&CASVB

3.3.10.2. CASVB Output

The amount of output in CASVB depends heavily on the setting of the PRINT levels. In case of problems with convergence behaviour it is recommended to increase these from their rather terse default values.

In the following the main features of the output are outlined, exemplified by the job in the input above. Initially, all relevant information from the previous RASSCF calculation is recovered from the JOBIPH interface file, after which the valence bond wavefunction information is summarized, as shown below. Since spatial configurations have not been specified explicitly in this example, a single covalent configuration is chosen as default. This gives 5 spin-adapted VB structures.

Number of active electrons :   6
          active orbitals  :   6
          Total spin       : 0.0
          State symmetry   :   1

Spatial VB configurations
-------------------------
    Conf. =>   Orbitals
      1   =>    1  2  3  4  5  6

Number of VB configurations :     1
          VB structures     :     5
          VB determinants   :    20

The output from the following optimization steps summarizes only the most relevant quantities and convergence information at the default print level. For the last optimization step, for example, The output below thus states that the VB wavefunction was found by maximizing the overlap with a previously optimized CASSCF wavefunction (output by the RASSCF program), and that the spin adaptation was done using the Yamanuchi–Kotani scheme. Convergence was reached in 7 iterations.

-- Starting optimization - step  3 --------

Overlap-based optimization (Svb).

Optimization algorithm:            dFletch
Maximum number of iterations:           50
Spin basis:                         Kotani

-------------------------------------------
Optimization entering local region.
Converged ... maximum update to coefficient:  0.59051924E-06
Final Svb :    0.9978782695
Number of iterations used:   7

Finally in the output below the converged solution is printed; orbital coefficients (in terms of the active CASSCF MOs) and structure coefficients. The overlap between orbitals are generally of interest, and, as also the structures are non-orthogonal, the structure weights in the total wavefunction. The total VB wavefunction is not symmetry-adapted explicitly (although one may ensure the correct symmetry by imposing constraints on orbitals and structure coefficients), so its components in the various irreducible representations can serve to check that it is physically plausible (a well behaved solution generally has just one non-vanishing component).

Next follows the one-electron density with natural-orbital analysis, again with quantities printed in the basis of the active CASSCF MOs.

Orbital coefficients :
----------------------
          1           2           3           4           5           6
  1  0.43397359 -0.43397359 -0.79451779 -0.68987187 -0.79451780 -0.68987186
  2 -0.80889967  0.80889967 -0.05986171 -0.05516284 -0.05986171 -0.05516284
  3  0.00005587 -0.00005587  0.20401015 -0.20582094  0.20401016 -0.20582095
  4  0.39667145  0.39667145  0.00000000  0.00000000  0.00000000  0.00000000
  5 -0.00000001 -0.00000001 -0.53361427 -0.65931951  0.53361425  0.65931952
  6  0.00000000  0.00000000  0.19696124 -0.20968879 -0.19696124  0.20968879

Overlap between orbitals :
--------------------------
          1           2           3           4           5           6
  1  1.00000000 -0.68530352 -0.29636622 -0.25477647 -0.29636623 -0.25477647
  2 -0.68530352  1.00000000  0.29636622  0.25477647  0.29636623  0.25477646
  3 -0.29636622  0.29636622  1.00000000  0.81994979  0.35292419  0.19890631
  4 -0.25477647  0.25477647  0.81994979  1.00000000  0.19890634  0.04265679
  5 -0.29636623  0.29636623  0.35292419  0.19890634  1.00000000  0.81994978
  6 -0.25477647  0.25477646  0.19890631  0.04265679  0.81994978  1.00000000

Structure coefficients :
------------------------
     0.00000000  0.00000001  0.09455957  0.00000000 -0.99551921

Saving VB wavefunction to file VBWFN.

Saving VB CI vector to file JOBIPH.

Svb :          0.9978782695
Evb :        -38.4265149062

Chirgwin-Coulson weights of structures :
----------------------------------------
VB spin+space (norm   1.00000000) :
     0.00000000  0.00000000 -0.00211737  0.00000000  1.00211737
VB spin only  (norm   0.38213666) :
     0.00000000  0.00000000  0.00894151  0.00000000  0.99105849

Symmetry contributions to total VB wavefunction :
-------------------------------------------------
Irreps 1 to 4 :  0.10000000E+01  0.15118834E-17  0.17653074E-17  0.49309519E-17

Energies for components > 1d-10 :
---------------------------------
Irreps 1 to 4 : -0.38426515E+02  0.00000000E+00  0.00000000E+00  0.00000000E+00

One-electron density :
----------------------
          1           2           3           4           5           6
  1  1.98488829 -0.00021330  0.00011757  0.00000000  0.00000000  0.00000000
  2 -0.00021330  1.90209222 -0.00006927  0.00000000  0.00000000  0.00000000
  3  0.00011757 -0.00006927  0.02068155  0.00000000  0.00000000  0.00000000
  4  0.00000000  0.00000000  0.00000000  0.09447774  0.00000000  0.00000000
  5  0.00000000  0.00000000  0.00000000  0.00000000  1.97572540 -0.00030574
  6  0.00000000  0.00000000  0.00000000  0.00000000 -0.00030574  0.02213479

Natural orbitals :
------------------
          1           2           3           4           5           6
  1 -0.99999668  0.00000000  0.00257629  0.00000000  0.00000000  0.00005985
  2  0.00257628  0.00000000  0.99999668  0.00000000  0.00000000 -0.00003681
  3 -0.00005995  0.00000000 -0.00003666  0.00000000 -0.00000001 -1.00000000
  4  0.00000000  0.00000000  0.00000000  1.00000000  0.00000001  0.00000000
  5  0.00000000  0.99999999  0.00000000  0.00000000  0.00015650  0.00000000
  6  0.00000000 -0.00015650  0.00000000 -0.00000001  0.99999999 -0.00000001

Occupation numbers :
--------------------
          1           2           3           4           5           6
  1  1.98488885  1.97572545  1.90209167  0.09447774  0.02213475  0.02068154

3.3.10.3. Viewing and plotting VB orbitals

In many cases it can be helpful to view the shape of the converged valence bond orbitals. Molcas therefore provides two facilities for doing this. For the Molden program, an interface file is generated at the end of each CASVB run (see also Section 4.3.1). Alternatively a CASVB run may be followed by RASSCF (Section 4.2.44) and GRID_IT (Section 4.2.22) with the VB specification, in order to generate necessary files for viewing with LUSCUS.