Long-range correction effects on the evaluation of first ... - TDDFT.org

LC <strong>effects</strong> on the evaluation of β
of high intrinsic
hyperpolarizability molecules.
Cláudia Cardoso, Universidade de Coimbra

F, external
Study the nonlinear
optical response of
organic molecules
Study of the molecules
with high intrinsic
hyperpolarizability
applied field
Technological Applications:
signal processing,
optical data storage,
etc.
, first
hyperpolarizability

How to compare different
molecules?
●
two molecules with the same β but different
number of π electrons are not intrinsically
equivalent.
●
quantum sum rules impose limits on the first
and second hyperpolarizabilities.

fundamental limit:
N: effective
number of
polarizable
electrons
M. G. Kuzyk, Phys. Rev. Lett. 85, 1218 (2000)
Intrinsic
Hyperpolarizability:

e- acceptor
group
e- donor
group
<strong>Long</strong> pi bridge
Optimization of...
●
●
the electron-donating/withdrawing strengths of
the terminal donor and acceptor groups
conjugation path

1
4
2
5
3
6
7

Experimental Results
The best molecules are ones that
are long with many undulations in
the potential energy function,
which allows the electron densities
of the eigenstates to be well
separated.
OPTICS LETTERS Vol. 32, 59 2007
Recipe
● increased length
● linear chain
● mimic the optimal undulation
● make use of aromatic moieties with a
wide <strong>range</strong> of stabilization energies

Calculation
Method
●
Geometries optimization
●
β : Finite field calculation
● Semi-empirical calculations :
●
TDDFT absorption spectra
●
PM6 Hamiltonian (COSMO)
DFT / TDDFT:
B3LYP / 6-311G(d,p)+
LC-BLYP/ 6-311G(d,p)+
Solvent <strong>effects</strong>: PCM
●
●
Aim:
Reproduce the exp. values
Understand the role of the
different conjugation paths

Gas-phase calculations underestimate β
Calculations do
not reproduce
increase for
MOL6 and MOL7
(au)
1.2E+5
9.0E+4
6.0E+4
exp
PM6
DFT
DFT:
1,2,4 OK!
3.0E+4
0.0E+0
0 1 2 3 4 5 6 7 8
molecules

Solvent <strong>effects</strong> improve (some) results
PM6:
Solvent improves
trend
Mols 6, 7 not
well reproduced
(au)
2.0E+5
1.5E+5
1.0E+5
exp
PM6
DFT
DFT/B3LYP:
1,2,4 KO!
5.0E+4
0.0E+0
0 1 2 3 4 5 6 7 8
molecules

Molecules under study
1
4
2

DFT B3LYP
2.0E+5
1.5E+5
exp
vac
dmso
(au)
1.0E+5
5.0E+4
0.0E+0
0 31 52 63 47 5 16 27 48 9
molecules

Wrong geometry?
mol2
Increasing the
torsion angle:
Fast energy
increase
Low decrease
9E+4
6E+4
B3LYP+solv.
exp
Azobenzene:
“(...) the energetic difference
between the planar and twisted
forms is either zero or totally
negligible at room temperature.”
L. Briquet et al, Chem. Phys. Lett.,
417, 2006, 190
(au)
3E+4
0E+0
0 10 20 30 40 50 60 70 80
Torsion angle (º)

Orbitals:
HOMO
mol4
mol7

Orbitals:
LUMO
mol4
mol7

<strong>Long</strong> Range
<strong>correction</strong>s
<strong>Long</strong> molecules
– Sekino et al. J. Chem.
Phys. 126, 014107 2007
Strong e-
donors/acceptors
The β ratio of BLYP and
HF increases
monotonically
– J. Phys. Chem. A, Vol.
113, No. 6, 2009 Loboda
et al.

<strong>Long</strong> <strong>range</strong> <strong>correction</strong>s
●
DFT and HF exchange contributions are
partitioned at the operator level.
●
The electron repulsion operator, 1/ r12, is
partitioned using the error function
●
nonlocal HF part becomes larger for greater
distances.
GAMESS | Y.Tawada et al J.Chem.Phys. 120, 8425 (2004)

LC improves calculated β
2.0E+5
1.5E+5
exp
LC-BLYP
B3LYP
Large
difference
for molecules
1, 2, 4
(au)
1.0E+5
5.0E+4
Still problems
with mol 2...
and 7
0.0E+0
0 31 52 63 47 5 61 72 84
9
molecules

Different
conformers
ΔE = 0.16 eV
2E+5
mol2
(au)
1E+5
5E+4
exp
LC
0E+0
0 1 2 3 4 5 6 7 8
ΔE = 0.09 eV

Mols 6 and 7 are isoelectronic but
the additional Cl atom in molecule
6, induces a twist in the conjugation
path, resulting in a decreased
hyperpolarizability.
x
mol7
mol6

B3LYP + solvent:
Huge effect on
mols 1, 2, 4
2.0E+5
1.5E+5
1.0E+5
exp
B3LYP –
vac
B3LYP –
dmso
LC/BLYP –
dmso
2E+5
2E+5
1E+5
5E+4
mol4
mol7
0E+0
5.0E+4
-5E+4
0.0E+0
0 1 2 3 4
-1E+5
PM6 B3LYP LC PM6 B3LYP LC
Gas phase
DMSO

Solvent and LC:
Same effect on
mol 4 and 7
0
LC:
B3LYP LC-BLYP
B3LYP+solv LC-BLYP+solv
opens the gap
B3LYP LC-BLYP
B3Lyp+solv LC-BLYP+solv
-0.1
Solvent:
closes the
gap
E (Hartree)
-0.2
-0.3
HOMO-1
HOMO
LUMO
LUMO+1
mol4
mol7
-0.4

LC solvent
Have opposite
<strong>effects</strong>
LC effect
larger for mol4
LC+solvent
Coincides with
B3LYP-vac

3
8
6
E01 (eV)
2
1
B3LYP
LC-BLYP
Transition dipole
4
2
B3LYP
LC-BLYP
0
0 1 2 3 4 5 6 7 8
molecules
Two level model:
2.0E+5
1.5E+5
1.0E+5
0
0 1 2 3 4 5 6 7 8
B3LYP
LC-BLYP
exp
molecules
5.0E+4
0.0E+0
0 1 2 3 4 5 6 7 8
molecules

Conclusions
●
●
LC BLYP + solvent reproduce exp.
Two sets of molecules
1. Mols 1,2,4: Azo-benzene
2. Mols 3, 5, 6, 7
● LC important for group 1
●
●
Solvent and LC have opposite <strong>effects</strong>
transitions dipoles and excitation energies
follow hyperpolarizability trends