On quantifying the vibronic interaction between electronic states

An accurate estimation of the interstate vibronic coupling strength is of particular relevance for the treatment of nonadiabatic dynamics. This is not a trivial task because direct interactions between electronic states have to be separated from intrinsic frequency shifts. Surprisingly, this issue has not been discussed in detail in the literature so far. An analysis of the error dependence is given for two formulas derived from linear vibronic coupling theory. The difficulty in estimating the interstate coupling parameters is shown to originate from the initially unknown contribution of the diagonal quadratic coupling coefficients to the total vibronic coupling. An interpretation of the error analysis including a numerical case study is followed by a more general discussion of the different mechanisms that can shape adiabatic electronic potential energy functions. Qualitative criteria are formulated for the differentiation between interstate and intrastate vibronic coupling effects based on electronic structure information. These ideas are then applied to investigate vibronic coupling problems in pyrazine as well as trans- and cis-hexatriene.     

A new spin-specific mechanism of attractive vibronic interaction

An interesting new type of spin-specific vibronic coupling is found. The non-adiabatic coupling induces an effective attractive interaction which softens the orginal repulsive interaction between a pair of electrons. The relation with the Cooper pair of superconducting electrons is discussed.     

On the floating basis set model for studying the vibronic interaction in polyatomic molecules

The floating basis set model by Johnson and Weigang is reinvestigated using a general picture of the molecular hamiltonian. It is found that Johnson and Weigang, though considering explicitly that electrons move with the nuclei, ignored a contribution to the electronic wavefunction from the coupling of the vibrational and electronic motions of the electrons. The vibrational wavefunctions and energies of the molecule are also modified.     

Effects of the vibronic interaction on anisotropy of ESR parameters for three-coordinate complexes of univalent nickel

Vibronic interaction effects on anisotropy of ESR parameters for three-coordinate complexes of univalent nickel have been investigated. Analytical expressions in the first order of the perturbation theory were obtained for wave functions of the ground and excited doubly degenerate states having taken into account vibronic and spin-orbital interactions. Based on the assumption that the vibronic interaction prevails over spin-orbital, there were obtained the expressions for main components of the g-tensor and isotropic HFS constants with ligand cores which are consistent with experimental data for three-coordinate complexes of the composition [Ni(PPh₃)₃]BF₄ and [Ni(PCy₃)₃]BF₄.     

Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n) = n(-2beta/nu)[phi0 + phi1n(1/nu)(T-T(c)) + O(n(2/nu)(T-T(c))2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature T(c) = 1.784 J/k(B) and critical exponents 2beta/nu approximately 0.668 and nu approximately 1.0. The self-diffusion constant and the chain dimensions (R2) and (S2) do not obey such a scaling law.     

Studies of the vibronic interaction between Eu3+ ions and glass-forming units in oxide glasses

Vibronic spectra involving intramolecular vibrations of glass-forming units have been measured for the f–f transitions of Eu³⁺ ions doped into sodium germanate and sodium silicate glasses. It is shown, from the analysis of relative intensities of these spectra, that the interaction of the Eu³⁺ ion with the vibrations of the surrounding forming units of oxide glasses is well described by the electric multipole–multipole interaction.     

Vibronic coupling in cyclopentadienyl radical: a method for calculation of vibronic coupling constant and vibronic coupling density analysis

A method of calculation of vibronic or electron-phonon coupling constant is presented for a Jahn-Teller molecule, cyclopentadienyl radical. It is pointed out that symmetry breaking at degenerate point and violation of Hellmann-Feynman theorem occur in the calculations based on a single Slater determinant. In order to overcome these difficulties, the electronic wave functions are calculated using generalized restricted Hartree-Fock and complete active space self-consistent-field method and the couplings are computed as matrix elements of the electronic operator of the vibronic coupling. Our result agrees well with the experimental and theoretical values. A concept of vibronic coupling density is proposed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. It illustrates the local properties of the coupling and enables us to control the interaction. It could open a way to the engineering of vibronic interactions.     

Ab initio CI study and vibronic analysis of the photoelectron spectra of formaldoxime

The photoelectron spectrum of formaldoximie, CH₂NOH, has been re-investigated with higher resolution and interpreted by, means of ab initio SCF Cl calculations. Calculations have confirmed that the states increase in energy as π₁ < n₁ < π₂ < n₂ and have shown the existence of a shake-up peak at ≈15 eV. The calculation of Franck-Condon factors allowed the interpretation of the observed vibrational structure.     

Some comments on vibronic intensities of naphthalene fluorescence spectra from single vibronic levels

It is shown that some features of intensity distribution among certain vibronic transitions in naphthalene molecule can be understood, when one takes into account adiabatic and nonadiabatic interaction between S₁(¹B_3u), S₂(^tB_2u), and S₃(^IB_3u) electronic states. the vibronic activity of the $\text{6}\text{?}$(b_1g) mode in naphthalene-d₈ can be explained in terms of an anharmonic coupling with the $\text{7}\text{?}$(b_1g) mode. The theoretical analysis suggests reinterpretation of some vibronic transitions.     

Calculation of the vibronic spectra of adenine

The vibrational structure of the absorption spectra of the first two π-π* singlet transitions of adenine is calculated in the Franck-Condon approximation including Herzberg-Teller interactions. The effect of excitation-induced changes in molecular angles on the intensities of the vibrational components is estimated. Structural models of the adenine molecule in the excited states are constructed. The theoretical and absorption spectra of the first π-π* transition are compared. The results of the electronic structure calculations of adenine by different CNDO/S methods are discussed. Translated fromZhumal Struktumoi Khimii, Vol. 38, No. 2, pp. 334–344, March–April, 1997.     

Estimation of the contribution of vibronic interaction to the isotope effect on the nuclear magnetic shielding constant of a hydrogen bridge

A nonadiabatic correction to the H/D isotope effect on the constant of electronic magnetic shielding of a nucleus was estimated within the framework of the first-order perturbation theory. The procedure consists in the ab initio calculation of frequencies and relative intensities in the vibronic spectrum for H and D forms of a molecule taking into account only the transitions allowed in the magnetic-dipole approximation. With the elementary assumptions (case of Herzberg vibronic interaction), the semiquantitative estimation of adiabatic (geometrical) and nonadiabatic contributions to the H/D isotope effect on the ¹⁵N shielding constant of a complex with the HF-pyridine hydrogen bond was carried out. These two contributions to the isotope effect are comparable in the order of magnitude, at least for unsaturated molecules with low-lying excited electronic states. A correct solution to the problem requires ab initio calculation that is not based on the Born-Oppenheimer approximation.     

Semicalassical vibronic model for the Creutz-Taube ion

Institute of Chemistry, Academy of Sciences of the Moldavian SSR. Translated from Zhurnal Strukturnoi Khimii, Vol. 32, No 1, pp. 44–48, January–February, 1991.     

On the calculation of vibronic coupling matrix elements

The non-diagonal matrix elements in the adiabatic Born-Oppenheimer approximation are considered. The effect of the Q-dependence of the electronic energy denominator is calculated explicitly for an arbitrary initial and final state. It is shown that the inclusion of this effect does not change the relative values of the coupling matrix elements for different initial vibronic states.     

Reaction mechanism in the mechanochemical synthesis of dibenzophenazine: application of vibronic coupling density analysis

The reaction mechanism for mechanochemical synthesis of dibenzophenazine was theoretically investigated in terms of the vibronic coupling density, which describes the interactions between electrons and nuclear motions. The concept theoretically indicates experimentally observed reactive sites that cannot be explained by the conventional frontier orbital theory. The results of vibronic coupling density analysis suggested the difference between reaction mechanisms under thermal and mechanochemical conditions.     

A method to reduce the size of the vibronic basis employed in the simulation of spectra using the multimode vibronic coupling approximation

In the time-independent multimode approach for the determination of vibronic spectra involving strongly coupled electronic states, the equilibrium geometry and normal modes of the reference or precursor state are usually employed as the basis for the multimode expansion. This basis, while easily constructed, is generally ill-suited for determining the eigenstates of the observed species. Employing a more computationally effective basis requires the evaluation of Franck-Condon overlap integrals. Using established generalized Hermite polynomial generating function formalisms, an algorithm is developed that can efficiently determine the enormous requisite number of these overlap integrals. It is found that this flexibility in the choice of multimode basis can significantly reduce the size of the basis needed to obtain converged spectral simulations. The previously reported spectrum of the ethoxy (C(2)H(5)O) radical serves as an example of the efficacy of the new technique.     

Finite-size effects in simulations of nucleation

We investigate the importance of finite-size effects in simulations of nucleation processes. Most molecular dynamics simulations of first order phase transitions, such as vapor-liquid nucleation, are performed in the canonical NVT ensemble where, owing to the fixed total number of molecules N, the growth of the new phase causes the depletion of the metastable phase. This effect may lead to significant errors in the simulation and even to the impossibility of observing nucleation in a small finite system. We present a theory to estimate the system size beyond which these finite-size effects are expected to be negligible. This optimization saves valuable calculation time and can extend the range of supersaturations and rates attainable by simulations by several orders of magnitude. Our results are applicable to diverse situations, such as crystallization, capillary condensation, or the melting of nanoclusters.