Excited state second hyperpolarizability

[pandey28]

Hi,

I want to calculate the cubic response (second hyperpolarizability) of CO2, but on an excited state instead of the ground state. It seems that Dalton does its calculations with respect to a reference state, which is usually the ground state. Is there a way I can set an excited state as the reference state, to get the second hyperpolarizability on the excited state?

Thanks

[magnus]

You can get excited-state polarizabilities from the double residue of the cubic response function but not hyperpolarizabilities.

[kennethruud]

CO2 is small enough that you may consider also doing an MCSCF calculation, selecting the excited state of interest as the reference state. You can then get the second hyperpolarizability by performing a MCSCF cubic response calculation.

[magnus]

Yes, of course. Didn't consider MCSCF

[pandey28]

@kennethruud: How exactly do I "select the excited state of interest as the reference"?

[kennethruud]

In the
**WAVE FUNCTION
....
*CONFIGURATION
.SYMMETRY
2 <- Symmetry of the excited state
.STATE
2 <- Second state (i.e. first excited state) of symmetry 2.

See Dalton 2018 manual pages 294-299.

Kenneth

[pandey28]

Thank you @kennethruud for the detailed explanation. However, when I try to specify the excited state to be calculated, I get an "illegal keyword" error. My .dal file is as follows:

Code: Select all

**DALTON INPUT               <- must start all input files
.RUN RESPONSE                <- run integrals, wave function and response
**INTEGRALS 
.DIPLEN.                          <- dipole length integrals for the chosen basis	
**WAVE FUNCTIONS          <- wave function input
.HF
.MP2                                <- starting orbital for MCSCF
.MCSCF
*SCF INPUT                       <- HF input
.DOUBLY OCCUPIED
2 1 1 0 2 1 1 0
*CONFIGURATION INPUT
.SYMMETRY
1                                      <- symmetry of the excited state
.STATE
2                                      <- second (first excited) state of symmetry 1
.SPIN MULTIPLICITY
1
.INACTIVE
3 0 0 0 0 0 0 0                    <- 1s orbitals on all atoms are inactive
.CAS SPACE
3 2 2 0 3 1 1 0                    <- irrep. ordering: Ag B3u B2u B1g B1u B2g B3g Au
.ELECTRONS
16                                      <- no. of valence (2s & 2p) electrons in CO2
**RESPONSE
*CUBIC
.DIPLEN
**END OF DALTON INPUT

The error I get is:

Keyword .STATE not recognized for *CONFIG

[kennethruud]

My error, .STATE should be under *OPTIMIZATION, i.e.

....
*OPTIMIZATION
.STATE
2 <- second (first excited) state of symmetry 1
*CONFIGURATION INPUT
.SYMMETRY
1 <- symmetry of the excited state
.SPIN MULTIPLICITY
1
......

[taylor]

I would be surprised if you need the STATE keyword, given that you are running with symmetry, because I am fairly certain that the first excited state of CO₂ is a different symmetry to the ground state (I think perhaps a Pi_u state). This would then be the lowest state in symmetry 2 or 3. In that case, however, there is the possibility of Renner-Teller distortion of a degenerate electronic state of a linear molecule, and it is most likely that at the equilibrium geometry the molecule will be bent. Even if it is not (unlike the Jahn-Teller effect, where the symmetry is always lowered for a degenerate state of a nonlinear polyatomic molecule, the Renner-Teller effect may produce a linear equilibrium geometry) and the molecule remains linear in the excited state, you will have to deal with the issue of the electric field perturbation lifting the degeneracy of the electronic state, which will complicate analyzing the results of the response calculation (assuming you are interested in all components of the hyperpolarizability tensor).

Best regards
Pete