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Thomas
thomaspijper@hotmail.com

In addition to the merits and drawback earlier mentioned, I would like to mention a few as well.

One big advantage of state-averaged (SA) MCSCF is that SCF convergence is usually better when working with excited states. For example, when one is interested in the first excited state, one could do the calculation state-specific (SS) by specifying

WSTATE(1)=0,1

in $DET or $GUGDM2 (depending on whether one is using ALDET or GUGA MCSCF code). However, SCF convergence is usually already much better when a bit of ground state 'character' is introduced in the orbitals. For example:

WSTATE(1)=0.1,1.0

One can even use:

WSTATE(1)=1,1

in order to describe both the ground state and the first excited state. Note that one should not compare the MCSCF energies of different states when different fractions were used in WSTATE for each state. For example, using WSTATE=1.0,0.2 for the ground state and WSTATE(1)=0.5,1.0 for the first excited state makes it not possible to compare the SCF energies. Instead, when using WSTATE(1)=0.5,1.0 for the first excited state, one should use WSTATE(1)=1.0,0.5 for the ground state.

What is important to note with respect to SS/SA-MCSCF in Firefly is that analytical gradients (needed for geometry optimization and such) are only available for SS-MCSCF. For SA-MCSCF, gradients are obtained in a semi-numerical way which requires three energy evaluations. This makes the calculation of SA-MCSCF gradients roughly three times slower than SS-MCSCF. In addition, because of this semi-numerical approach, it is needed to increase the accuracy of the calculation. Tighter convergence criteria, integral cutoffs, etc., should be used. In addition, INTTYP=HONDO is highly recommended. I usually use the following keywords for increasing accuracy when doing SA-MCSCF with the ALDET code:

 $CONTRL INTTYP=HONDO ICUT=11 $END 
 $MOORTH NOSTF=.T. NOZERO=.T. SYMS=.T. SYMDEN=.T. SYMVEC=.T. TOLSYM=1D-7 $END 
 $DET CVGTOL=1D-7 $END
 $TRANS CUTTRF=1D-15 $END 
 $MCSCF ACURCY=1D-7 $END 

You either can loosen or should tighten the above values depending on your calculation. Obviously, higher accuracy has a serious impact on the speed of the calculation (making the difference in gradient calculation times between SS- and SA-MCSCF even bigger).

One more important thing about SS/SA-MCSCF: for SS-MCSCF, one should not use the ISTATE keyword. This is because ISTATE selects different routines in Firefly which should only be used for SA-MCSCF. To give an example, if one uses SS-MCSCF and is interested in the first excited state, one could specify:

 $MCSCF CISTEP=ALDET $END 
 $DET GROUP=C1 NCORE=30 NACT=8 NELS=8 NSTATE=5 WSTATE(1)=0,1 $END

Here, ISTATE is not needed as the WSTATE keyword already tells Firefly which state to use. However, doing this calculation with SA-MCSCF, one should specify:

 $MCSCF CISTEP=ALDET ISTATE=2 $END 
 $DET GROUP=C1 NCORE=30 NACT=8 NELS=8 NSTATE=5 WSTATE(1)=1,1 $END

>What are the merits and drawbacks of using state averaging in MCSCF calculation? Similarly, What are the merits and drawbacks of MCSCF calculaton without state averaging?

>Thanks!

>Patrick

[ This message was edited on Wed Oct 10 '12 at 9:51am by the author ]