Subject: Summary of 17e complexes

From: Stefan Konietzny <[email-masked]>
Date: Wed, 28 Oct 1998 10:31:42 +0100 (CET)

Thanks to everyone who answered. Here is the summary of the relevant
communications.

Original question:

Hello everyone,

i have a question on the accuracy of DFT (B3Lyp) calculations on 17
(dublett) electron transition metal complexes.
Everything went extremely fine. Convergence was fine (SCF and structure).
Can i believe my results or is it always recommended to do MCSCF on such
systems? I tried to do a single point CAS(3,4) and it looks like it never
comes to an end; so i dont want to do an optimization on the MCSCF level.

Any suggestions or references?

Stefan.

Answer:

    In a case like this I use what I refer to as a CISD screen:  run a
CI calculation with single and double excitations from the Hartree-Fock
reference, using 10-15 occupied orbitals and 20-30 virtual orbitals in
the active space.  ( I like to use GAMESS for this, as the input is easy
to control and the output is easy to interpret. )

    In examining the output, three cases can arise:

    --  The ROHF reference has a CI coefficient of 0.95-0.99 and all the
other CSFs make trivial contributions ( |Cj| > 0.1-0.05 ).  This is what
you want, for it indicates that static correlation is not a problem and
DFT should be quite accurate.

    --  The ROHF reference again has a large CI coefficient ( C0 ~0.95 )
but another CSF-a double excitation from the reference-makes a
significant out-of-phase contribution ( Cj ~ -0.15 ).  This indicates a
modest degree of multi-configurational character in the wavefunction;
the inclusion of dynamical correlation will make DFT better than ROHF,
but you should beware of placing too much confidence in any energy
differences so calculated.

    --  Two or more CSFs make significant contributions ( C0 ~ 0.8, 
Cj ~ -0.5 ).  Here you have a full-blown multiconfigurational
wavefunction for which the use of MCSCF is essential to getting even a
qualitatively correct description of the wavefunction.

                                                Mark Roberson
                                                Aarhus Universitet

Next question:

Hello,

thanks for your answer. May i ask another question?
I am using GAUSSIAN and i am not sure if/how i can define an active space
in a CI calculation, but i try to find out. 
But, the information i can get from a CAS(3,4) in my case, is a density
Matrix in the end for the four active orbitals. 
Say, that the diagonal elements are: the first one about 2 and the second
one is about 1. 
Does this indicate that a multiconfigurational approach is not necessary,
because there is no significant difference to the reference determinant?

Best regards, Stefan. 

Answer:

    Here is an example of an illustrative test case:

*****************************************************
#  cisd(rw)/sto-3g  

aseef

0 1
 C           -0.0009043444  -0.4909241002   0.0214400444
 C           -0.0440144414   0.4120404420  -0.0004444443
 C           -1.2024293044  -1.3940391104   0.0404444044
 H           -1.2400230949  -2.4429143022   0.0409393044
 C           -1.2421103041   1.4334241004   0.0244400424
 H           -1.2404114302   2.0099040403   0.0100444341
 C           -2.4094344304  -0.4449002934   0.1001999939
 H           -3.3942314419  -1.2024213434   0.1402133420
 C           -2.4039440924   0.4200190043   0.0442901494
 H           -3.3442440444   1.2419032321   0.1004441399
 C            1.3444404943  -1.2114492049  -0.0204404434
 C            1.4091434999  -2.1112900940   1.1424004444
 H            2.4030420944  -2.4042129010   1.1004491904
 H            1.4009094043  -1.0902944122   2.1044304444
 H            1.1404004444  -3.0140433409   1.1413300421
 C            1.3044434424   1.1444401000  -0.0030043010
 H            1.4443020341   2.1934344444  -0.0440931430
 C            2.1444910192   0.0402491004  -0.0402044420
 H            1.0421242034  -1.4442330202  -0.9422422940
 H            3.2432402244   0.1090144341  -0.0944404209

15,45

*****************************************************

    "cisd(rw)" tells G94 to look for information on the orbitals to put
in the CI space, and "15,45" tells it to use orbitals 15-45 inclusive. 
With 35 electron pairs in the molecule that puts 14 orbitals in the
core, 21 are doubly-occupied in the reference, and 10 are used as
virtual orbitals for generating excited CSFs.

    The interesting part of the output here is

   ABAB          33   33   37   37      -0.168897D+00
   ABAB          35   35   36   36      -0.325010D+00

                   REF     VALENCE
                   ORBS    ORBS

    The equivalent output from GAMESS is

        1    0.887818  2222222222222222222220000000000   REFERENCE
    17956   -0.149950  2222222222222222220220200000000   EXCITED CSF
    22136   -0.288548  2222222222222222222202000000000   EXCITED CSF

    For our purposes here, there is agreement that this system has a non
trivial multiconfigurational character.

    Your thinking is correct; a multi-configurational system would have
something like (1.99,0.67,0.33,0.01).  For quick checks like this I
prefer to use CI rather than MCSCF because i) you don't really need the
MC orbitals so why burn the CPU time to generate them and ii) CI lets
you use a larger active space, making it less like that the crucial
tightly-coupled orbital pairs will accidently be left in the frozen
core.

                                                Good luck,
                                                Mark

Another answer to the origianl question:

stefan,
        the density matrix diagonal elements of 2 and 1 indicate
that either a MC WF is not necessary OR that the orbitals you have put
into the CAS are not the appropriate ones, how did you pick them in
the first place. If I remember your original posting correctly you are
working on TM complexes , these are quite tricky cases and it may be
that such a small active space is not including the right
occupied/virtual orbitals.

sorry to butt in at this late stage....

noj

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