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Solntsev Pasha
solntsev@univ.kiev.ua

I am trying to model 1st and 2nd excited state of a molecule. From experiments are known, excited state is double degenerated (E - orbitals). Also, it is known from experiment and from a theoretical study either TD-DFT or CIS that first excited state forms by HOMO->LUMO transition, while 2nd excited state  forms HOMO-1->LUMO transition. From TD-DFT and CIS we have 2 excitation (double degenerated LUMO) HOMO->LUMO (1st excited state) and two transition HOMO-1->LUMO.

My goal is to calculate excitation energies and to study excited state. So i am using XMCQDPT approach.

I did CASSCF(4,4)/6-311G(d,p) calculations with 6 states (ntrack=5) and different wstate(1) array value. First excited state corresponds to ground state (only biggest coefficients are printed):
STATE #    1  ENERGY =   -1727.128479778

     CSF      COEF    OCCUPANCY (IGNORING CORE)

       1    0.964072  2200

.................
       4   -0.151002  2002

.................
       9    0.137168  1111

.................
      15   -0.150937  2020

.................

Second excited state has following configuration and corresponds to excitation from HOMO->LUMO. However, component from HOMO-1->LUMO also significantly contribute to formation of the second.
STATE #    2  ENERGY =   -1726.991351175

     CSF      COEF    OCCUPANCY (IGNORING CORE)

....................
       2    0.942511  2101

....................
       8    0.261968  1210

....................
      13    0.136427  1012

....................
Third excited state has following configuration, very similar to the 2nd:
STATE #    3  ENERGY =   -1726.991351174

     CSF      COEF    OCCUPANCY (IGNORING CORE)

.......................
       3    0.261719  1201
.......................        

       7   -0.942700  2110
......................        

      10    0.129259  2011

.....................
      18   -0.137203  1021

....................

The states from 4th don't have single excitation configuration with big coefficients and they have not been presented here. I believe they are not important for our case.

Afterward, i ran XMCQDPT using
$xmcqdpt kstate(1)=1,1,1,1,0,0                                                

avecoe(1)=1,1,1,1,1,-0                                                        

wstate(1)=1,1,1,1,1,-0  $end    
$gugdm2 wstate(1)=1,1,1,1,1,0 $end

In $DRT group=c1.

I used different value for wstate(1) and wstate(1)=1,1,1,1,1,-0 works better. I don't know why.

After XMCQDPT run i got

*** MC-XQDPT2 ENERGIES ***

-----------------------------------------------------------------------

  STATE                       1ST ORDER                       2ND ORDER

    1     E(MCSCF)=    -1727.1284797779     E(MP2)=    -1731.6455874427

    2     E(MCSCF)=    -1726.9913511748     E(MP2)=    -1731.6292601411

    3     E(MCSCF)=    -1726.9913511741     E(MP2)=    -1731.5827124526

    4     E(MCSCF)=    -1726.9163689912     E(MP2)=    -1730.2704096821

EIGENVECTORS OF THE EFFECTIVE HAMILTONIAN



                     1          2          3          4



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



   1             0.990372   0.120637   0.025590   0.062892

   2             0.107653  -0.972246   0.185035   0.094396

   3             0.044631  -0.178233  -0.982213   0.038706

   4            -0.074714   0.091749   0.019079   0.992792

EIGENVALUES OF THE NON-SYMMETRIC EFFECTIVE HAMILTONIAN



    1    -1731.63989383779100000000 + I *        0.00000000000000000000

    2    -1731.62858390071600000000 + I *        0.00000000000000000000

    3    -1731.58269032210300000000 + I *        0.00000000000000000000

    4    -1730.27680165785000000000 + I *        0.00000000000000000000

OVERLAP NORM MATRIX OF NON-ORTHOGONAL EIGENVECTORS



            1           2           3           4



   1    1.0000000   0.1024935   0.0001352   0.1266622

   2    0.1024935   1.0000000   0.0001875   0.0617847

   3    0.0001352   0.0001875   1.0000000   0.0086499

   4    0.1266622   0.0617847   0.0086499   1.0000000
   
From "EIGENVECTORS OF THE EFFECTIVE HAMILTONIAN" i can say we very close to correct results. But i don't know what to do next.

From experiment, first excited state has absorption at 565 nm (~17700 cm^-1).

Also, i have a question. That is a difference between
$xmcqdpt kstate(1)=1,1,1,0,0,0                                                

avecoe(1)=1,1,1,-0                                                        

wstate(1)=1,1,1,-0  $end    

and

$xmcqdpt kstate(1)=1,1,1,1,0,0                                                

avecoe(1)=1,1,1,-0                                                        

wstate(1)=1,1,1,-0  $end    

For 4th state in kstate array weight is 0.

Below you will find complete input file instructions:

$SYSTEM MWORDS=50 kdiag=0 fastf=.t. nojac=100 timlim=9999999 $END              

$CONTRL RUNTYP=energy wide=.t. inttyp=hondo mplevl=2 icut=11 itol=30 d5=.t. coord=unique exetyp=run maxit=120  $end                

$contrl  fstint=.t.  gencon=.t. $END
$trans cuttrf=1d-13 dirtrf=.t. altpar=.t. mode=112 $end
$smp call64=.t. $end                                                

$drt  group=c1 fors=.t. nmcc=108 ndoc=2 nalp=0 nval=2   $end
$mcscf cistep=guga soscf=.t. fors=.t. acurcy=1d-7 engtol=1d-12 maxit=200 ntrack=5 $end            
$GUGEM pack2=.t. dirci=.t.  $end
$xmcqdpt kstate(1)=1,1,1,1,0,0 avecoe(1)=1,1,1,1,1,-0  wstate(1)=1,1,1,1,1,-0  $end
$mcqfit $end
$gugdia nstate=6 itermx=150   $end  
$gugdm iroot=1  $end  
$gugdm2 wstate(1)=1,1,1,1,1,0 $end
$CONTRL SCFTYP=mcscf $END  
$CONTRL ICHARG=0  MULT=1 $END  
$BASIS gbasis=n311 ngauss=6 ndfunc=1 npfunc=1 $END
$guess guess=moread  norb=688    norder=0 $end  
$moorth nostf=1 nozero=1 syms=1 symden=1 symvec=1  $end

$SCF DIRSCF=.TRUE. FDIFF=.f. soscf=.f. diis=.t. nconv=6 $END
$DATA
......................

Thank you very much for willing to help me.

Best, Pavel.