Subject: summary of CAS questions

From: "Varnai Peter" <[email-masked]>
Date: Tue, 12 Dec 1995 19:24:15 GMT+100

Dear CClers,

A little late, but I send You the summary. My thanks to those (Frank 
Jensen, Mathias Bock, Doug Fox) who sent me their comments. Yes, it is 
not an easy question how to select the active space of an e.g. 
transition state. In my view there are some methods, but none of them 
is always applicable: 1, visualization (what is the chemical problem) 
2, orbitals weights in CI calculations  3, occupancy number of the 
orbitals. Important to check the orbitals of the structures around 
your initial structure to create a consistent active space!  Be 
careful, sometimes occ. number or weights tell you chemically not 
important orbitals eg pi-orbitals in a sigmatropic shift (hard to 
answer whether it is a mistake to include those beyond the essential 
orbitals; whether CAS is ONLY for the non-dynamic part of the 
correlation energy etc). Gaussian 94 is indeed have a new routine 
which seems to converge better, but allow you to create nonsense as 
well. But, don't lose the chk file, hard to recover it! In case 
somebody has new ideas, those are always welcome! Here follows the 
original letter and the answers. Again, thank You!

Peter Varnai

???????????????????????????????????????????????????????????????
 I would need Your help to understand the practical tricks in CASSCF 
calculations. 

1, One needs to define an active space. 
    -At this point quantum chemists start to think as the 
    conventional organic chemist,in localized orbitals. Here 
    those orbitals needed -in view of a chemist- that are 
    involved in a eg. reaction (forming/breaking orbitals). 
    -A more exact answer would be that those orbitals needed 
     which are important in "excitation" to give configurations 
     that contribute to the total energy significantly.
So: -according to the first approach one would visualize the MOs. 
Here he/she would realize that in MO theory the orbitals are spread 
all over the molecule, so the needed eg C-C bond will appear in 
at least 3 MOs. Which one should be used then? Let's use all 
(unfortunately, the valence MOs  usually can't be all involved in 
the active space)? Let's localize the MOs with standard methods? 
Pick one random and what happens (the one is better than the other if 
using it the SCF energy is lower)?
    -according to the more "mathematical" approach let's calculate a 
CISD wavefunction  [in the absence of the full CI :(]  and involve 
the orbitals which are involved in large coefficient (say 0.03<) 
determinants? And what if the HF reference function was not a good 
approximation and some important determinants are missed? 
     -If I am right CAS should be used as the correction to the non-
dynamic electron correlation (through the the right geometry and 
wavefunction). What happens then when CISD tells you that an orbital 
energetically important though not needed in view of the reaction, 
description of the radical etc. it would be some parts of the 
dynamic correlation effect then?!

2,  CASSCF in Gaussian 92 for me (and I guess for several others) 
stopped with the error message: rotation larger than 45 degree... If 
I understand well either a smaller step in wavefunction optimization 
would have been desirable or the active space was not well chosen and 
a non-selected orbital was crucial in the active space. Yet, I 
haven't 
got error message like this with the G94 routine, only warnings that 
large rotations are scaled and something like: I J=     12      26. I 
don't really understand the meaning of these numbers (i,if these are 
MO numberings, I have to say that eg MO- 12 was not selected to be in 
the active space, ii, in MOLCAS for example the user can define only 
the number and symmetry of the active orbitals, the exact MO not, how 
will then the routine pick the right orbital? iii, is it allowed to 
change orbitals of the active space during SCF). 

3, In case one loses the chk file and would like to keep it for 
further use, is the following way is correct to create the same chk 
file? 1, Calculate the HF-MOs at the starting geometry once again 
and picking the same MOs 2, converging the CAS wavefunction as it 
was done in the previous calculation and 3, reading in the 
wavefunction (to have the same active space) and having the 
converged CAS-geometry (not to redo the whole previous calculation). 
If it is correct can anyone tell me why I did not reproduce the 
same stationary point, but locating an other one (higher in 
energy). (As I know this method is used when one tries to find the 
right active space in a supermolecule by isolating it to fragments).

If You had the patience and read my letter through, and You can help 
me in using CAS smoothly: THANK YOU!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    Varnai,
    one of the 'modern' ways of selecting the active MOs
in a CASSCF is from the natural orbital occupation numbers,
i.e. first do a MP2 or CISD and diagonalize the density matrix
to giv ethe natural orbitals. Then select the orbitals
which have occupation number 'significantly' different from
0 or 2. How far away depends on your problem (and hardware!)
but typically orbitals with occ. >0.05 and < 1.95 must
be included, and >0.03 and < 1.97 is desireable. Since
CASSCF wave functions often are used for many different
geometries (like a reaction), you need to do this at
several points, and select a 'consistent' space, i.e.
the smallest which include all the 'important' orbitals
at each geometry. In some cases it will be difficult
to make a consistent choice.
    So, as you can se from the 'quotes', CASSCF
orbital selection is not easy.
    Frank
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Hallo Peter,

your CASSCF questions were quite familar to me, unfortunetaly I
am not able to answer them totally, maybe the specific G9x answers
will come from [email-masked] if you havenot already done so.

First of all, I should prefer to use several CI-methods to look
for the most important configurations to be included. You can
decide whether static correlation is included at a minimum of cost.

In G92 CASSCF/6-31G gave nice results, even for open-shell molecules.
The choice of orbitals was crucial. Sometimes I used sophisticated
pre-runs to get starting orbitals. But this is no garanty to converge
even from a converged ground state to reach convergence for an excited
state. G94 will not care as much as G92, so don't get slippy  !
Running small basis sets, gives an easy initial choice, but it 
happened not
to give SCF-convergence, until another starting geometry was given.
Good starting geometries were given by UHF/3-21G or RMP2/6-31G*.

The open-shell UHF/ROHF gives you another riddle, as the UHF-functions
don#t give reliable wave functions. The use of CISD seems necessary to
annihilate spin contamination. Also try an RHF-guess first by changing
charge and multiplicity.

I hope a summary of answer will go to net. If not, I would 
appreciate a copy. Thanks .

Mathias Brock

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
  Peter,

  The choice of active space is the most challenging part of getting
a CASSCF right.  WE have changed the code with G94 to make failures
like "rotation larger than 45 degrees" go away but with an 
intellectual
cost.  The meaning of this error, as I think we have discussed, is to
switch a pair of orbitals changing the active space.  To avoid this
G94 damps this rotation to keep it from switching and force a solution
within the chosen active space.

  The reason behind not adapting MolCAS's behavior is that you most 
often
want to study a particular state or reaction with a CAS wavefunction.
This may well not be the lowest energy solution and if the active 
space
is allowed to change you may well end up with the wrong state or 
with the wrong active space for the reaction of interest.  For example
if you are looking at formaldehyde loosing H2 the lowest energy 
solution
is to include the pi orbitals but these play no part in proper 
dissociation
to H2 + CO.  The penalty for not allowing the switch is a poor initial
guess may end up not describing the orbital you wanted or an ill 
chosen
guess can include orbitals which don't interact with the orbitals that
define/control the reaction/state of interest.

  Thus for G94 what you want to do is pick your active space as well 
as
possible and then examine the result of a single point calculation.  
Make
sure that there are not orbitals with double or zero occupancy.  Use 
#P
to get this printed out.  If there are then the eigenvector for that 
state, key back to the list of configurations printed earlier, can let
you see which orbitals are likely candidates either to be removed or
switched.  The goal is to make the solution match your state of 
interest
not simply a lowest energy solution.

  Restarting can be a bit of a problem.  First, you may well have 
moved
to a  part of the surface where the RHF solution is a lousy 
representation.
Using STABLE=OPT to make sure that you get the best single determinant
is worthwhile.  Your plan of starting from the initial orbitals and 
then
leaping to the final structure seems reasonable as well.  There are
changes to the orbitals as the optimization progresses.  These changes
may make the difference between the "excited" state you found and the 
state you optimized to.  Is your case small enough that you can try 
the
CASSCF(QC) option, requires writting AO integrals to disk, this may
well be able to get past the problem.

  Doug Fox
[email-masked]

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!