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:
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.
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.
A sample input is given in Figure 3.7.
Figure 3.7. Sample input for a CASVB calculation on the lowest
singlet state of CH
.
&seward &end symmetry x y basis set c.sto-3g.... c 0 0 -0.190085345 end of basis basis set h.sto-3g.... h 0 1.645045225 1.132564974 end of basis end of input &scf &end occupied 3 0 1 0 end of input &rasscf &end inactive 1 0 0 0 ras2 3 1 2 0 nactel 6 0 0 lumorb end of input &casvb &end end of input
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 Figure 3.7. 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 in Figure 3.7. 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.
Figure 3.7. Initial part of the CASVB output summarizing the wavefunction definitions.
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, Figure 3.7 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 Yammanouchi-Kotani scheme. Convergence was reached in 7 iterations.
Figure 3.7. The part of the CASVB output relating to wavefunction optimization.
-- 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 (see Figure 3.7) the converged solution is printed; orbital coefficients (in terms of the active CASSCF MOs) and structure coefficients. The overlaps 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.
Figure 3.7. Final part of the CASVB output.
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
In many cases it can be helpful to view the shape of the converged valence bond orbitals, and 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 Molden (in users guide)). Alternatively a CASVB run may be followed by RASREAD (Section rasread (in users guide)) and GRID_IT (Section gridit (in users guide)) with the VB specification, in order to generate necessary files for viewing with Cerius2.