Orbital Vibronic Constants Research Articles

Proton-lattice coupling and vibronic effects in KDP-family thermodynamics

Based on the vibronic theory of heteroligand complexes a new model Hamiltonian is proposed for the ferroelectrics of KDP (KH2PO4) family. In local representation three items of this Hamiltonian describe the H-bond protons, the potential energy of lattice's oscillators and the coupling of these two subsystems respectively. In Ising form, convenient for numerical calculations, the Hamiltonian offered includes explicitly the characteristics of the electronic structure as well as the orbital vibronic constants of the AO4 tetrahedra. The Ising version of theory is then applied to numerical studying of some questions for KDP thermodynamics.

A comparative study of the pseudo Jahn–Teller instability of linear molecules Ag 3 and I 3 and their positive and negative ions

In confirmation of the general idea of pseudo Jahn–Teller origin of instability of high-symmetry configurations of polyatomic systems that determines their geometry, a series of six molecules, Ag 3 n and I 3 n, n=−1,0,+1, were investigated. The electronic structure of the ground state of all the six molecules in the linear configuration was calculated by the extended-Hückel method with atomic charge and electron configuration self-consistency, while the excited state energy levels and wavefunctions were estimated in the single transition approximation. Then, the orbital vibronic constants, bare force constants and the vibronic contribution of the appropriate excited states to the instability of the linear configuration were evaluated. The obtained results show that in both series, silver and iodine, the curvature of the adiabatic potential of the linear configuration, in the direction of the bending distortions, decreases from the negative ions to the neutral atoms to the positive ions and becomes negative in the latter two cases, thus explaining the origin of the experimentally observed geometries. The numerical data give a detailed insight into: (1) the origin of the linear→bent distortions as being due to the additional covalency created by the σ–π overlap in the bent configuration; (2) the specific excited states that contribute to this process of geometry formation; and (3) the difference between the silver and iodine series.

Extended Hückel Orbital Forces and the Jahn‐Teller Distortions in Molecules

AbstractLinear orbital vibronic constants are calculated within the Extended Hückel formalism and used to evaluate the forces acting on the atoms along the symmetry coordinates, in a planar arrangement of four identical atoms. It is shown, from the magnitude and direction of the forces, that the high‐symmetry square planar arrangement is unstable and distorts to lower symmetry.

Vibronic instability of molecular configurations in the Hartree–Fock–Roothaan approximation

The traditional description of pseudo-Jahn–Teller molecular configuration instability based on Bader's formula for the curvature of the adiabatic potential is reconsidered in order to make it consistent with straightforward calculations of the ground-state energy surface within Hartree–Fock–Roothaan approximation. The proposed approach employs floating molecular orbitals constructed by “frozen LCAO” coefficients (computed in the reference geometry) and floating atomic orbitals, which allows one to exclude the vibronic mixing with the excited states irrelevant from chemical point of view. The relaxation (vibronic) contribution to the instability, expressed in terms of one-electron quantities, involves two sets of orbital vibronic constants. These are, respectively, defined as matrix element derivatives of correct and “frozen LCAO” Fock operators between occupied and unoccupied molecular orbitals. The canonical form of the relaxation contribution can be achieved when the vibronic interaction is presented as a mixing between the ground electronic state and the excited states calculated within the random-phase approximation © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 37–48, 1997

Molecular dynamic structure and dimerization of polyacetylene

The vibronic interaction in an (A)2N chain (e.g., polyacetylene) has been studied within the Huckel framework. A Huckel framework scheme for calculating the parameters of molecular dynamic structure, i.e., the linear and quadratic orbital vibronic constants (OVCs), has been presented. Selection rules for the OVCs in this scheme have been obtained and discussed by using graph theory and group theory, under various boundary conditions. A Huckel noncoupling rule has been concluded and discussed. The dimerization of polyacetylene has then been discussed based on the molecular dynamic structure. It has been shown that for a finite undoped (A)2N chain the occupied orbital energy en at the unified configuration has a negative slope in direction of Q2n. As a result, there exists a net Hellmann–Feynman force leading to dimerization. When the chain length goes to infinity, the slopes and forces tend to zero. However, a significant negative curvature in potential surface may occur in the direction of Q2n, due to the two-phonon coupling of the π-electrons, which could also induce the dimerization. These can be interpreted as the results of the hidden C4N+2 symmetry and the imaginary degeneracy in an (A)2N chain, according to the graph theory for molecular orbitals. Thus, the dimerization of an (A)2N chain actually destroys its hidden symmetry of C4N+2 and reduces its imaginary degeneracy.

Vibronic constants of internal valence orbitals in diatomic molecules

A correlation is established between the spectroscopic values of the orbital vibronic constants (OVC) for the upper molecular orbitals MO and the contributions of these MO to the resonance energy, which has been used to determine the OVC for the inner valence MO 3sigma for the molecules CO, BF, CN, NO, N2, and O2. A relationship has been derived for the OVC as a function of the difference in atomic electronegativities and of the number of valance electrons. An increase in the electronegativities and of the number of valence electrons. An increase in the electronegativity in a series of isoelectronic molecules has the largest effects on the OVC for the 4sigma and 2 * MO. An increase in the number of electrons caused the internal MO 3sigma to expand considerably, and the same occurs with the 1 orbital, but there is virtually no effect on the bonding character of the 4sigma and 5sigma MO.

Mutual vibronic influence of weakly coordinated molecular systems in chemical reactions and catalysis

A new approach to the problem of mutual influence of weakly interacting molecular systems, important to the investigation of origin and mechanism of chemical reactions (especially with catalyst participation), is reported. The influence of one system upon the other is approximately characterized by changes in molecular orbital (MO) population numbers — orbital charge transfers Δ q i — which through the vibronic coupling result in distorting forces F α (linear vibronic effect) and force constant changes Δ K α, (second order vibronic effect). Both effects — distorting and softening (or hardening) — lead to a change in the activation energy Δ D α of processes involving nuclear displacements in certain direction of the subsystem under consideration. Approximate formulae for F α′ Δ K α and Δ D α as functions of Δ q i and orbital vibronic constants are obtained. As an example a model reaction of nitrogen fixation under catalyst vibronic influence is considered. Some simple formulae and numerical estimates for the reduction of the activation energy are derived.