# C-DFT-CI including localized excited state

Dear colleagues,

I would like to know if it is possible to perform a calculation using Constrained DFT-CI including localized excited states. I am thinking of two interacting monomers (M) forming a dimer structure and I would like to have a CI scheme like this:

|S_1S_0> |S_0S_1> |M+M-> |M-M+>

Thank you very much in advance.

F

I think that a Q-Chem sample job `cdft/restart-cdftci.in` does exactly that for the water molecule:

``````\$comment
Water near a conical intersection.
We include two neutral states (H_2 as a triplet and O as a triplet)
and two ionic states (OH^- and H^+) to describe the surfaces of interest.
Using the core guess for the neutral states causes the SCF to
converge an order of magnitude faster.
\$end

\$molecule
0 1
O1
H2   O1 1.455465
H3   O1 1.455465        H2  179
\$end

\$rem
symmetry off
sym_ignore = true
method = b3lyp
basis = cc-pvdz
unrestricted = true
scf_convergence = 8
max_scf_cycles = 200
scf_guess = core
xc_grid = 100000302
cdftci = true
cdftci_print = 2
cdftci_stop = 2
cdft_thresh = 6
cdftci_prom_guess = 2
incdft = 1
\$end

\$cdft
0.0
1. 1 1
2.0
1. 1 1 s
0.0
1. 2 3
-2.0
1. 2 3 s
----------
0.0
1. 1 1
-2.0
1. 1 1 s
0.0
1. 2 3
2.0
1. 2 3 s
----------
1.0
1. 1 2
0.
1. 1 2 s
-1.0
1. 3 3
0.
1. 3 3 s
----------
1.0
1. 1 1
1. 3 3
0.
1. 1 1 s
1. 3 3 s
-1.0
1. 2 2
0.
1. 2 2 s
\$end

@@@

\$comment
The same system as above (the cdft block must be the same!)
but here the SAD guess works well.
\$end

\$molecule
\$end

\$rem
symmetry off
sym_ignore = true
method = b3lyp
basis = cc-pvdz
unrestricted = true
scf_convergence = 8
max_scf_cycles = 200
xc_grid = 100000302
cdftci = true
cdftci_print = 2
cdftci_restart = 2
cdft_thresh = 6
incdft = 1
\$end

\$cdft
0.0
1. 1 1
2.0
1. 1 1 s
0.0
1. 2 3
-2.0
1. 2 3 s
----------
0.0
1. 1 1
-2.0
1. 1 1 s
0.0
1. 2 3
2.0
1. 2 3 s
----------
1.0
1. 1 2
0.
1. 1 2 s
-1.0
1. 3 3
0.
1. 3 3 s
----------
1.0
1. 1 1
1. 3 3
0.
1. 1 1 s
1. 3 3 s
-1.0
1. 2 2
0.
1. 2 2 s
\$end
``````

Deaf Evgeny,

thank you very much for your reply. Forgive me because I have not understood correctly the example you kindly give me. I assume those triplet states that are involved in the water system represent the localized excited states. If I am right, it would be almost impossible to include localized excited states with pi* character because it is not a straightforward manner to constraint the electron (spin) in a particular region of the molecule.

Cheers

F

Oh, I see what you mean, I missed the localized excited state part. CDFT is not able to form localized excited states directly because it only deals with charge / spin localization. So unless the localized excited state is dominated by charge or spin separation, CDFT will probably not be helpful.

You might look into the ab initio Frenkel-Davydov exciton model (AIFDEM). Here, you form direct-product basis states and then perform a nonorthogonal CI in that basis. For a dimer, that might mean matrix elements like <S0 S1 | H | S1 S0>, where either molecule #1 is excited (in the ket) or #2 is excited (in the bra). For AIFDEM, you don’t generate these monomer with constrained DFT but rather via standard monomer-based CIS or TDDFT, and you can include S2, S3, … for additional variational flexibility. There is also an option for ionized basis states |CA> (C=cation, A=anion). This is in the manual, recent example here: https://pubs.acs.org/doi/10.1021/acs.jpcc.0c07932