4Pa021

Vibronic computation and modelingin significant chemical problems
Fanica Cimpoesu and Kimihiko Hirao
Department of Applied Chemistry, School of Engineering
University of Tokyo, Tokyo, Japan 113-8656

The vibronic interactions have multiple impacts in various chemical and physical phenomena,1(supraconductivity, charge density and magnetism in mixed valence systems including theorbital ordering problems in manganites, stereochemistry and spectroscopy of various molecularspecies). The molecular dynamics and potential energy surface problems (topology, adiabaticity
vs. non-adiabaticity) are also genuine vibronic topics. Such an extended relevance of the vibronic
keyword faces also a certain fragmentation of the paradigm within rather disjointed areas of use,
the methodologies ranging from semiempirical approaches to the state of the art ab initio
calculations in certain restricted problems. The actual work follows the red line of our systematicinterest in the coherent unification of the formal vibronic-type Hamiltonian models with the abinitio calculation apparatus. In a very general sense, the vibronic interactions are comprised in
the force constants of a given normal coordinate under a form expressible as
occ virt

K v = 2∑∑ u ni(1) ⋅ Vin(1) where the u are coefficients related to the response ofi

MO basis ton

coordinate perturbation and V, the vibronic constants, have effective mono-electronic meaning
whose concrete construction depends on the method of electronic structure calculation.2, 3
occupiedvirtualorbitals
vibronic orbital

vibronic orbitals

vibroniccontributions

O rbital
assym etrization-0.1379(m d yne /Å)-0.0815(m d yne /Å)Figure 1. The vibronic orbitals for delocalized to localized mixed valence states inhypothetical molecule [Al2Cl6]2-.

The general strategy is to connect vibronic formal definitions with analytical derivative andresponse theory techniques. Within the sketched frame, a new definition, the vibronic orbitals,was elaborated. Their obtaining concern the simultaneous diagonalization of the following
unocc

occ

matrices µ ij = ∑ (u (1) ⋅V (1) + u (1) ⋅V (1)) (i, j -occupied orbitals) and ν mn = ∑ (u (1) ⋅ V (1) + u (1) ⋅V (1))
ninnjnjniniimimini(m,n -virtual orbitals). The vibronic orbitals are designed as the functions most sensitive to themolecular geometry changes, whose transition density products offer the best partition ofelectron density flows during a distortion. An application is illustrated in fig.1 for the charge
density disproportionation in the hypothetical molecule [Al2Cl6]2- taken as simple“academic” model for the vibronic treatment of the mixed valence.
Bab

Baa

1

1

4

JaBabb

Bbbb

Jba

Ja

Ja

3

BaaadαBab

JaaBabJb

BbbBabb2Jb

3BabJbBaa

Baa

Jd2BabaJ

Ja

BabBabJbBab
Bbb
BaaJa

Bbb

JaJb

BabBabHˆ = −2∑ ( J ij + 1 / 2) Sˆi ⋅ Sˆ j + 8∑∑ Bij , kl ( Sˆi ⋅ Sˆ j )( Sˆk ⋅ Sˆl )j <i

j <i l < kScheme 1. Generalized spin Hamiltonian used to fit potential energy surfaces ofrepresented systems and their corresponding parameter definitions.

A series of particular applications was worked imbricating, in a new formalism, thespin-coupling and vibronic effective Hamiltonian models for sake of meaningful fit of potential
energy surface data. In this way, treating the H3 molecule, a particular description of theprototypical reaction coordinate and of the Jahn-Teller effect at the conical intersection was done.
The same method comparatively applied to C4H4 and C6H6 allowed new analysis of π-distortions
as key for antiaromaticity vs. aromaticity features. A general strategy, of setting vibronic-type
Hamiltonians in order to rationalize the reaction coordinate data is proposed, proving the utilityof vibronic paradigm in chemical reactivity problems.
References
I. B. Bersuker, Chem. Revs., 101, 1067 (2001)
L. F. Chibotaru and F. Cimpoesu, Int. J. Quant. Chem., 65, 37 (1997)
3 F. Cimpoesu and K. Hirao, Adv. in Quant. Chem., (2003) in press
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