Vibronic reduction of Heisenberg and double exchange in multielectron mixed-valency clusters

Vibronic reduction is considered for Coulomb interaction between centers for Heisenberg and double exchange in multielectron mixed-valency d²-d³ clusters. A simplified multimode vibration model indicates how effects arise via vibrations from the correlation interaction between electron shells. Vibronic reduction in double exchange can alter the magnetic parameters for the cluster's ground state.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 2, pp. 114–121, March–April, 1992.     

Magnetic moments of bare and benzene-capped cobalt clusters

Magnetic moments of bare cobalt clusters Co(n) (n=7-32) and benzene-capped cobalt clusters Co(n)(bz)(m) have been measured at temperatures ranging from 54 to 150 K using a molecular beam deflection method. It was observed that Co(12-32) produced at temperatures greater than approximately 100 K display high-field-seeking behavior at all temperatures in the range investigated, indicating that they are superparamagnetic species. At temperatures below approximately 100 K, the field-on beam profiles of Co(7-11) and some larger clusters displayed substantial symmetric broadening, indicating that some fraction of the clusters in the beam were no longer superparamagnetic, but rather were in a blocked (locked-moment) state. In the superparamagnetic regime (T=150 K) Co(n) clusters in the n=7-32 size range were found to possess per-atom moments ranging from 1.96+/-0.04 micro(b)(Co(24)) to 2.53+/-0.04 micro(b)(Co(16)), significantly above the bulk value of 1.72 micro(b). Locked-moment isomers were found to display moments of approximately 1 micro(b) per atom. Cobalt clusters containing a layer of adsorbed benzene molecules were found to possess significantly lower moments per cobalt atom than the corresponding bare cobalt clusters.     

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.     

Effects of the dipole moments behavior on a vibronic coupling model for the four‐wave mixing signal

In the present work, we have studied modifications in the transition and permanent dipole moments of states in a coupled basis (including vibronic coupling) due to variations in the transition dipole moment between the uncoupled states, m₁₂, as a function of the parameter δ = ₀/ω₀ (relative aperture) of the potential‐energy curves of the states involved. Modifications in the slopes of the transition and permanent dipole moments of the coupled states and changes in the magnitude of maximal intensity of the four‐wave mixing (FWM) signal are observed due to variations in these parameters. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Magnetic properties of Mn(III)−Mn(IV) mixed-valence dimers in a dynamic vibronic model

For Mn(III)−Mn(IV) mixed-valence dimers, a dynamic pseudo-Jahn-Teller vibronic problem is solved. Temperature dependences of the magnetic moment of the clusters are calculated with inclusion of Heisenberg and double exchange as well as vibronic coupling. Conditions for antiferromagnetic, intermediate, and ferromagnetic ground spin-vibronic states and the accompanying low-temperature limits of magnetic moments are determined. State University, Moldova Republic. Valencia University, Spain. Institute of Chemistry, Academy of Sciences, Moldova Republic. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 4, pp. 28–34, July–August, 1994. Translated by L. Smolina     

Some aspects of vibronic coupling in circular dichroism

After a review of the quantum mechanical formulation of vibrational-electronic coupling, the adiabatic approximations for ordinary absorption dipole strength and circular dichroic absorption rotatory strength are presented and interpreted. The expressions include the effect of two vibrational quantum changes coupled to electronic excitation in addition to the more familiar concept of coupling by a one quantum change. A polarizability theory of vibronically coupled rotatory strength is presented which is comparable to the polarizability theory of rotatory strength without regard to vibration.     

Hydrogen bond-induced vibronic mode mixing in benzoic acid dimer: a laser-induced fluorescence study

Laser-induced dispersed fluorescence spectra of benzoic acid dimer in the cold environment of supersonic jet expansion have been reinvestigated with improved spectral resolution of measurements. The spectra are analyzed with the aid of the normal mode vibrations of the dimer calculated by the ab initio quantum chemistry method at the DFT/B3LYP/6-311+G(*) (*) level of theory. The analysis reveals that the low-frequency intermolecular hydrogen bond modes are mixed extensively with the carboxyl as well as aromatic ring vibrations upon electronic excitation. The mode mixing is manifested as the complete loss of mirror symmetry relation between the fluorescence excitation and dispersed fluorescence spectra of the S(1) origin, and appearance of large number of cross-sequence transitions when the DF spectra are measured by exciting the low-energy vibrations near the S(1) origin. The cross-sequence bands are found in all the cases to be the combinations of two nontotally symmetric fundamentals consisting of one of the intermolecular hydrogen bond modes and the other from the aromatic ring and carboxyl group vibrations. The implications of this mode mixing on the excited state dynamics of the dimer are discussed.     

Jahn-Teller effect in Rydberg series: a multi-state vibronic coupling problem

Two simple limiting cases of Jahn-Teller (JT) coupling in Rydberg states of polyatomic molecules are considered, namely(i) JT coupling in Rydberg orbitals as well as in the ionization continuum (nondegenerate ion core, degenerate Rydberg series) and(ii) JT coupling in the ion core (degenerate ion core, nondegenerate Rydberg series). For both models simple and efficient algorithms for the computation of spectra (dynamical JT effect) are developed. The orbital JT effect is shown to represent a novel type of multi-state vibronic coupling, giving rise to interesting spectroscopic phenomena, among them resonant inter-Rydberg perturbations and JT induced autoionization. Particular attention is paid to the demonstration of the characteristic spectroscopic signatures of the two types of JT coupling in Rydberg states.     

Intermolecular vibronic coupling and energy transfer in a flat molecular aggregate

Summary The migration of excitation within a small flat molecular aggregate composed of identical molecules is described using a Davidov-like model and a mechanism of excitation transfer of Förster type. We consider in this model the changes that take place in the equilibrium position of each molecule upon excitation and construct energy surfaces that describe paths, that is, conditions for excitation localization and transfer that govern, in first-order, the motion of excitation within the aggregate.Presented in part at XVIII Jornadas Chilenas de Química, Santiago, 1989     

On vibronic coupling in nonradiative transitions of polyatomic molecules

The vibronic coupling between quasidegenerate adiabatic Born—Oppenheimer states has been calculated by going beyond the Condon approximation. A simplified model in which accepting modes are distorted (non-totally symmetric) and of the same frequency, has been considered. The decay rate obtained with this approach is one order of magnitude larger than in the Condon scheme and seems to be practically independent of the symmetry of the accepting modes.     

Selectivity of vibronic coupling in complex molecules with benzene fragments

This paper deals with the mechanisms of localization of Franck-Condon vibronic coupling of πσ^*- or πlπ^*-orbital type in a few vibrational modes, (LVM) in excited electronic states of polyatomic molecules. The analysis of vibronic coupling uses highly symmetric basis sets (for representing MO structures and normal coordinates ξ_R) as well as simplified models that relate the shift Δ_R of the electron potential minima along the normal coordinates to the MO structure and to ξ_R in the form of analytical expressions. The modes that are active in LVM are determined from the experimental luminescence spectra. These ideas about approximately high local symmetry of vibronic coupling in benzene fragments as well as the estimates of Δ_R depending on variations in the MO structure explain the experimental results. L. Ya. Karpov Physicochemical Scientific Research Institute. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 286–291, March–April, 1995. Translated by L. Smolina     

On the vibronic coupling approximation: a generally applicable approach for determining fully quadratic quasidiabatic coupled electronic state Hamiltonians

In this report we introduce an iterative procedure for constructing a quasidiabatic Hamiltonian representing N(state)-coupled electronic states in the vicinity of an arbitrary point in N(int)-dimensional nuclear coordinate space. The Hamiltonian, which is designed to compute vibronic spectra employing the multimode vibronic coupling approximation, includes all linear terms which are determined exactly using analytic gradient techniques. In addition, all [N(state)][N(int)] quadratic terms, where [n]=n(n+1)/2, are determined from energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. The use of energy gradient and derivative coupling information enables the large number of second order parameters to be determined employing ab initio data computed at a limited number of points (N(int) being minimal) and assures a maximal degree of quasidiabaticity. Numerical examples are given in which quasidiabatic Hamiltonians centered around three points on the C(3)H(3)N(2) potential energy surface (the minimum energy point on the ground state surface and the minimum energy points on the two- and three-state seams of conical intersection) were computed and compared. A method to modify the conical intersection based Hamiltonians to better describe the region of the ground state minimum is introduced, yielding improved agreement with ab initio results, particularly in the case of the Hamiltonian defined at the two-state minimum energy crossing.     

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.     

Modeling properties of the HF dimer in argon clusters

We compare geometry configurations, vibrational properties, and electronic structures of (HF)₂ in a free state and inside argon atom shells Ar_n. For the first stage, molecular dynamics calculations for the (HF)₂ · Ar₆₂ heterocluster are performed with the help of model potentials HF(SINGLE BOND)HF, Ar(SINGLE BOND)Ar, and Ar(SINGLE BOND)HF. Then, ab initio quantum chemistry analysis is carried out for the smaller systems (HF)₂ · Ar₁₅ and (HF)₂ · Ar₆ when keeping the argon atoms closest to the trapped dimer. We conclude that the hydrogen-bonded complex (HF)₂ gains some extra stability inside the argon shells, originating primarily from a decrease of intermolecular distance R_FF. Electronic structure calculations are in accord with the changes in dynamical properties, namely, a noticeable increase in the vibrational frequency assigned to the F(SINGLE BOND)F stretching mode (+25 cm⁻¹) and decrease in rms deviations for the corresponding coordinate δ_FF. In addition to these changes, the argon atoms of the nearest solvent shell donate a small fraction of electron charge which is spent for an increase of population of the antibonding orbital σ^* of the free monomer unit and shift orbital energies primarily of the lone-pair fluorine species. These shifts are greater than the changes due to geometry alterations and the possible inaccuracies of the calculation scheme. © 1997 John Wiley & Sons, Inc.     

Magnetic deflection of neutral metal clusters in a beam

A new apparatus for measuring the magnetic properties of metal clusters has been constructed. The technique involves the conventional Stern-Gerlach deflection scheme together with modern pulsed laser vaporization source technology and time of flight mass spectrometry. High field seeking monodirectional deflections have been measured for cobalt clusters containing between 40 and 400 atoms. The measured magnetic moments per atom are found to be lower than the known values for the bulk. Special attention has been given to velocity measurements of the metal clusters and the carrier gas atoms in the beam. The residence time of the particles in the source cavity has been measured.     

Spectroscopic effects of first-order relativistic vibronic coupling in linear triatomic molecules

It has recently been shown that there exists, in addition to the well-known nonrelativistic Renner-Teller coupling, a linear (that is, of the first order in the bending distortion) vibronic-coupling mechanism of relativistic (that is, spin-orbit) origin in 2II electronic states of linear molecules [L. V. Poluyanov and W. Domcke, Chem. Phys. 301, 111 (2004)]. The generic aspects of the relativistic linear vibronic-coupling mechanism have been analyzed in the present work by numerical calculations of the vibronic spectrum for appropriate models. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations for the X 2II states of a series of triatomic radicals and radical cations. It is shown for the example of GeCH that the relativistic linear vibronic-coupling mechanism provides a quantitative explanation of the pronounced perturbations in the vibronic spectrum of the X 2II state of GeCH, which previously have been termed "Sears resonances" [S.-G. He, H. Li, T. C. Smith, D. J. Clouthier, and A. J. Merer, J. Chem. Phys. 119, 10115 (2003)]. The X 2II vibronic spectra of the series BS2, CS2+, OCS+, and OBS illustrate the interplay of nonrelativistic and relativistic vibronic-coupling mechanisms in Renner-Teller systems.     

The dynamical crystal field model of selective vibronic coupling in d-d spectra

Summary The dynamic crystal field operators, corresponding to the normal point-charge displacements in an octahedral complex are analyzed in detail. The strict equivalence of absolute versus relative coordinate treatments is established. The resulting formalism is applied to the intensity distribution in the vibronic side bands of the sharp line luminescence spectra ofd ³ complexes. Thereby special attention is given to the role of spin-orbit coupling and to the elastic properties of the molecular force field. Using the closure procedure, the relative intensities of the side bands may be expressed in terms of a single dynamic crystal field parameter. These expressions provide a simple rationalization of the observed vibronic selection rules, entirely within the framework of dynamic crystal field theory.     

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled pi shell

The vibronic and spin-orbit-induced interactions among the (3)Sigma(-), (1)Delta, and (1)Sigma(+) electronic states arising from a half-filled pi orbital of a linear triatomic molecule are considered, employing the microscopic (Breit-Pauli) spin-orbit coupling operator. The 6 x 6 Hamiltonian matrix is derived in a diabatic spin-orbital electronic basis set, including terms up to fourth order in the expansion of the molecular Hamiltonian in the bending normal coordinate about the linear geometry. The symmetry properties of the Hamiltonian are analyzed. Aside from the nonrelativistic fourth-order Renner-Teller vibronic coupling within the (1)Delta state and the second-order nonrelativistic vibronic coupling between the (1)Sigma(+) and (1)Delta states, there exist zeroth-order, first-order, as well as third-order vibronic coupling terms of spin-orbit origin. The latter are absent when the phenomenological expression for the spin-orbit coupling operator is used instead of the microscopic form. The effects of the nonrelativistic and spin-orbit-induced vibronic coupling mechanisms on the (3)Sigma(-), (1)Delta, and (1)Sigma(+) adiabatic potential energy surfaces as well as on the spin-vibronic energy levels are discussed for selected parameter values.