Vibronic energies and spectra of molecular dimers

We consider three distinct methods of calculating the vibronic levels and absorption spectra of molecular dimers coupled by dipole-dipole interactions. The first method is direct diagonalization of the vibronic Hamiltonian in a basis of monomer eigenstates. The second method is to use creation and annihilation operators leading in harmonic approximation to the Jaynes-Cummings Hamiltonian. The adiabatic approximation to this problem provides insight into spectral behavior in the weak and strong coupling limits. The third method, which serves as a check on the accuracy of the previous methods, is a numerically exact solution of the time-dependent Schrodinger equation. Using these methods, dimer spectra are calculated for three separate dye molecules and show good agreement with measured spectra.     

Magnetic moments of multielectron mixed-valency dimer clusters in a dynamic intermediate vibronic coupling approach

The vibronic aspect of the Jahn-Teller effect is considered for multielectron mixed-valency dimer clusters. A basic intermediate-coupling set is used in the numerical diagonalization of the vibronic Hamiltonian. The temperature dependence of the vibronic magnetic moment is derived for symmetrical and distorted mixed-valency dimer clusters. Strong vibronic interaction can suppress double exchange and lead to an antiferromagnetic ground state for the cluster. Distortions that eliminate the inversion center localize the surplus electron and suppress the ferromagnetic effect caused by double exchange.Chemical Institute, Moldovian Academy of Sciences. Moldovian State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 2, pp. 11–19, March–April, 1993.     

The E x e dynamic Jahn-Teller problem: a new insight from the strong coupling limit

Correct boundary conditions for the E x e dynamic Jahn-Teller problem are considered explicitly for the first time to obtain approximate analytical solutions in the strong coupling limit. Numerical solutions for the decoupled equations using the finite difference method are also presented. The numerical solutions for the decoupled equations exhibit avoided crossings in the weak coupling region, which explains the oscillating behavior of the solutions obtained by Longuet-Higgins et al. for the coupled equations. The obtained analytical energy expressions show improved agreement with the numerical calculations as compared with the previous treatment in which the potentials were assumed to be harmonic. We demonstrate that the pseudorotational energy j(2)/(2g(2)), where g is the dimensionless vibronic coupling constant, and j total angular momentum: j=+/-1/2,+/-3/2,..., in the conventional strong coupling expression for the vibronic levels of the lower sheet is exact. Non-Hermitian first-order perturbation theory gives the energy which is correct up to 1/g(4). The asymptotic behavior of the wave function at the origin does not influence the corrected energy up to order of 1/g(4). At the same time the treatment of the upper sheet with correct boundary conditions gives solutions which are entirely different from the corresponding Slonczewski's solutions. Besides, the correct boundary conditions enable us to evaluate the nonadiabatic coupling between the lower and upper potential sheets. The energy correction due to the nonadiabatic coupling is estimated to be of order 1/g(6).     

Jahn-Teller effect in tetraclusters of transition metals,taking into account vibronic coupling with E-vibrations

Conclusion From the results obtained it follows that the shape of the surface for the lower sheet of the adiabatic potential for the cluster in the E vibration space is similar to the surface for the E-e problem both in the linear and in the quadratic cases. Taking into account the extra modes of the E vibration which were discarded in this treatment does not qualitatively change the shape of the adiabatic potential surface (the number of minima and saddle points), which is a consequence of its symmetry [4]. The deformation pattern of the cluster corresponding to movement of the system along the bottom of the channel of one of the lower sheets is analogous to the case of the E-e problem for an octahedral and tetrahedral environment of a Jahn-Teller ion [10]. The average values of the pseudospin operators in the vibronic ground states are the same for all centers, which is evidence (taking into account the equality of the Jahn-Teller distortions at all centers) for ferrodistortion ordering of all the distortions, both in the linear and in the quadratic cases. If each vibronic center has spin s=1/2, all vibronic levels of the cluster have additional 16-fold spin degeneracy. Taking into account the effect of spin-orbit coupling on the shape of the adiabatic potential using perturbation theory shows that removal of spin degeneracy for the lower sheet does not occur, that the adiabatic potential does not change its shape but rather is only reduced in energy by , where is the spin-orbit coupling constant.The high orbital degeneracy of sheets 2, 3, 4 (Fig. 2a, b) is not removed by taking into account the quadratic vibronic coupling and is accidental. The indicated orbital and spin accidental degeneracy of the sheets is removed by taking into account the intercenter interaction.Translated from Teoreticheskaya i Éksperimental' naya Khimiya, Vol. 20, No. 1, pp. 1–9, January–February, 1984.     

Molecular design for high-spin molecules in view of vibronic couplings

A high-spin ground state is possible if a molecule has degenerate or pseudo-degenerate frontier orbitals. Since strong vibronic couplings, or electron-vibration interactions give rise to reduce the degeneracy or pseudo degeneracy, a lower-spin state is the ground state in such a molecule. Therefore small vibronic couplings are desirable for designing molecules with a high-spin ground state. Vibronic coupling constants of derivatives of m-phenylene diamine are evaluated. The calculated results are analyzed based on vibronic coupling density which enables us to control the vibronic coupling constants. Based on the vibronic coupling density analysis, we succeed in recovering the high-spin ground state from the closed-shell singlet ground state of a methoxy derivative of m-phenylene diamine by introducing an appropriate substituent.     

Polarization and polarizability in extended one-dimensional organic materials

The modern theory of polarization in extended insulators is applied to one-dimensional models for conjugated polymers and charge transfer salts. Closed expressions for the dependence of the polarization on the site and bond energy alternations are presented for uncorrelated models, and results from exact real-space diagonalization are obtained for correlated models. Changes in polarization induced by lattice phonons or molecular vibrations are directly related to the intensity of infrared bands in the far and mid-IR, respectively. We model intensities by introducing linear electron-vibration coupling and show that coupling to delocalized electrons generates a combination band consisting of a lattice phonon and a molecular vibration. The displaced dipole operator is defined on a real-space basis allowing for the finite field calculation of linear polarizability in finite size systems with periodic boundary conditions. Size-consistency arguments are used to demonstrate that the resulting polarizability becomes exact in the thermodynamic limit, and numerical calculations demonstrate that this approach leads to reliable results that converge rapidly to the thermodynamic limit.     

Vibronic absorption spectrum of the ethylene dimer

Vibronic coupling theory is used to construct the vibronic absorption spectrum of the ethylene dimer. It is shown that in this case an extended four-parameter form of the vibronic Hamiltonian should be considered. In addition to the commonly used three vibronic parameters, the difference between the ground and excited state force constants of the monomer is taken into account. Numerical calculations were performed for the dimer geometry resembling that of norbornadiene. Some comments on the interpretation of the absorption spectrum of norbornadiene are made.     

Information theoretic indices for characterization of chemical structures. By Danail Bonchev Wiley,New York, 1983

Wilson, Jankowski, and Paldus have recently applied nondegenerate many-body perturbation theory (MBPT ) to simple models, in which the degree of quasidegeneracy could be varied continuously, and concluded that the nondegenerate theory was applicable even near degeneracy. The error in their results changes, however, considerably with geometry, leading to an incorrect potential surface. An extension of their calculations shows convergence even at exact degeneracy (square planar H₄). It is shown here that the apparently good convergence is due to the suppression of the large (infinite at exact degeneracy) component of the perturbation energy in low order by the way the Hamiltonian is partitioned. This component will, however, resurface at higher orders, leading to slow convergence or even divergence. The low-order sum of the perturbation series is not very meaningful, depends strongly on details of the zero-order Hamiltonian, and yields, in general, incorrect potential surfaces. Multireference MBPT eliminates these problems.     

Bath-induced correlations and relaxation of vibronic dimers

We consider a vibronic dimer bilinearly coupled through its two vibrational monomer modes to two harmonic reservoirs and study, both analytically and numerically, how correlations of the reservoir-induced fluctuations affect dimer relaxation. For reservoirs with fully correlated fluctuations, we derive an exact quantum master equation for the density matrix of the symmetric vibronic dimer. We demonstrate that reservoirs with fully correlated or anticorrelated fluctuations do not allow for complete vibrational relaxation of the dimer due to the existence of decoherence-free subspaces. For reservoirs with partially correlated fluctuations, we establish the existence of three different mechanisms of vibrational relaxation. Weak inter-monomer couplings, as well as predominantly correlated or anticorrelated fluctuations, render two of these mechanisms relatively inefficient, leading to slow decays of the populations and coherences of the dimer density matrix. The analytical results are illustrated and substantiated by numerical studies of the relaxation behavior of photoexcited dimers.     

Dimeres composes de molecules dont l'excitation electronique entraine un deplacement de la configuration nucleaire d'equilibre accompagne d'un changement de constante de force

We have studied the validity of the traditional model of a dimer that has been treated exactly by Merrifield and Fulton and Gouterman, solving the vibronic coupled equations by a numerical method. This model takes into account the modification of the nuclear equilibrium configuration, but it neglects the variation of the force constant when the monomer is electronically excited from the fundamental to a given excited state (the corresponding electronic potentials are both considered as harmonic). We have shown by inspection of the absorption and fluorescence spectra calculated by solving the vibronic equation exactly that the variation force constant cannot be neglected, even if it is weak, particularly in the weak coupling region. The weak, intermediate and strong coupling criteria have been deduced, for the model studied, by examination of the dimeric electronic potential surfaces for different cases of intermolecular interactions.     

Inelastic electron tunneling spectroscopy and vibrational coupling

We discuss the relationship between the inelastic electron tunneling spectroscopy (IETS) and vibronic coupling constant within the Green's function formalism at a level of perturbation theory approximation. We also compare our results with experimental measurements. Our results can provide insights into the mechanism of active vibronic modes for IETS.     

Davydov splitting of Herzberg—Teller-induced vibronic transitions

Based on a simple dimer model of vibronic coupling it is demonstrated that, contrary to the conventional notion, the Davydov splitting of the fundamental vibronic transition in non-totally symmetric vibrations, induced by the Herzberg—Teller mechanism, does not need to be very small.     

Synthesis, molecular structure, and EPR analysis of the three-coordinate Ni(I) complex [Ni(PPh3)3][BF4

The compound [Ni(PPh(3))(3)][BF(4)] x BF(3) x OEt(2) was isolated in crystalline form from the olefin oligomerization catalyst system Ni(PPh(3))(4)/BF(3) x OEt(2) and structurally characterized by X-ray diffraction. The influence of vibronic coupling on the EPR parameters of three-coordinate metal complexes with a 3d(9) electronic configuration was investigated within the framework of ligand field theory. Analytical expressions for g-tensor components and isotropic hyperfine coupling constants with ligand nuclei were obtained using first-order perturbation theory. It has been shown that the account of the vibronic interaction in the excited state predicts the existence of three-axial anisotropy of the g-tensor even at the level of first-order perturbation theory; two axes of the g-tensor located in a plane of three-coordinate structure can rotate about the main z axis when a compound is distorted by motion of ligands. It has been shown that in three points of the potential energy surface minimum, for which linear and quadric constants of the vibronic interactions have an identical signs, the HFS isotropic constant from one ligand is larger than HFS constants from the other two; for different vibronic constant signs the ratio between HFS constants varies on opposite. This theoretical researches are in the quality consent with experimental data for a three-coordinate Ni(I) and Cu(II) flat complexes.     

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.     

Theoretical development of a Gaussian potential function in the description of the radial portion of isotropic bending vibrations

Analysis of a Gaussian potential function suitable for modeling degenerate bending vibrations in weakly bound molecular complexes is presented. Approximate eigenvalues and eigenvectors are obtained by application of perturbation theory. Comparison to the “exact” eigenvalues obtained via a numerical solution shows that the first- and higher-order perturbation corrections are consistent with variational principles.     

Beyond exciton theory: a time-dependent DFT and Franck-Condon study of perylene diimide and its chromophoric dimer

The diimide perylene motif exhibits a dramatic intensity reversal between the 0 --> 0 and 0 --> 1 vibronic bands upon pi-pi stacking; this distinct spectral property has previously been used to measure folding dynamics in covalently bound oligomers and synthetic biological hybrid foldamers. It is also used as a tool to assess organization of the pi-stacking, indicating the presence of H- or J-aggregation. The zeroth-order exciton model, often used to describe the optical properties of chromophoric aggregates, is solely a transition dipole coupling scheme, which ignores the explicit electronic structure of the system as well as vibrational coupling to the electronic transition. We have therefore examined the optical properties of gas-phase perylene tetracarboxylic diimide (PTCDI) and its chromophoric dimer as a function of conformation to relate the excited-state distributions predicted by exciton theory with that of time-dependent density functional theory (TDDFT). Using ground- and excited-state geometries, the Franck-Condon (FC) factors for the lowest energy molecular nature electronic transition have been calculated and the origin of the intensity reversal of 0 --> 0 and 0 --> 1 vibronic bands has been proposed.     

The phosphorescence of benzene obtained byab initio and semi-empirical calculations

Summary Radiative decay and phosphorescence of triplet stare benzene is doubly -orbital and spin- forbidden and is only activated through vibronic coupling among the manifold of triplet states. For this reason the determination of lifetime and transition moments for the decay of triplet benzene has posed a considerable challenge to both theory and experiment. In the present work we have addressed the triplet benzene problem at several levels of theory; by truncated perturbation theory and semiempirical, CNDO/S-CI, calculations; by complete sum-over-state calculations as implemented in recentab initio multiconfiguration quadratic response (MCQR) theory; and by direct MCQR calculations of vibronic phosphorescence. The vibronic coupling is in the two former cases treated by the Herzberg-Teller (H-T) perturbation theory, involving four main mechanisms for the phosphorescent decay of triplet benzene. The results and interpretations given by these approaches as well as their merits and limitations are presented and discussed in some detail. Our calculations indicate that the phosphorescent decay of the³ B _1u state takes place predominantly through vibronic coupling along thee _2g mode. We obtain a phosphorescence that is almost completely out-of-plane polarized, which is in line with more recent measurements by the microwave-induced delayed phosphorescence technique, and could reproduce quite well the intensity ratios for different vibronic bands obtained in that experiment. The final triplet state lifetime is the result of a delicate sum of contributions from several vibronic degenerate and non-degenerate modes. The direct vibronic phosphorescence calculations predict a long lifetime, about one minute — 68 seconds for the best wavefunction — and seem to focus on a doubling of the assumed, albeit not established, best experimental value for the radiative lifetime of triplet benzene; 30 seconds.Dedicated to Inga Fischer-Hjalmars on her 75th birthday     

Ab initio surface hopping excited-state molecular dynamics approach on the basis of spin–orbit coupled states: An application to the A-band photodissociation of CH3I

Ab initio molecular dynamics approach has been extended to multi-state dynamics on the basis of the spin–orbit coupled electronic states that are obtained through diagonalization of the spin–orbit coupling matrix with the multi-state second-order multireference perturbation theory energies in diagonal elements and the spin–orbit coupling terms at the state-averaged complete active space self-consistent field level in off-diagonal elements. Nonadiabatic transitions over the spin–orbit coupled states were taken into account explicitly by a surface hopping scheme with utilizing the nonadiabatic coupling terms calculated by numerical differentiation of the spin–orbit coupled wavefunctions and analytical nonadiabatic coupling terms. The present method was applied to the A-band photodissociation of methyl iodide, CH₃I + hv → CH₃ + I (²P_3/2)/I* (²P_1/2), for which a pioneering theoretical work was reported by Amatatsu, Yabushita, and Morokuma. The present results reproduced well the experimental branching ratio and energy distributions in the dissociative products. © 2018 Wiley Periodicals, Inc.     

Analysis of pseudo jahn–teller distortion based on natural bond orbital theory: Case study for silicene

Ground state (GS) instability of nondegenerate molecules in high symmetric structures is understood through Pseudo Jahn–Teller mixing of the electronic states through the vibronic coupling. The general approach involves setting up of a Pseudo Jahn–Teller (PJT) problem wherein one or more symmetry allowed excited states couple to the GS to create vibrational instability along a normal mode. This faces two major complications namely (1) estimating the adiabatic potential energy surfaces for the excited states which are often difficult to describe in case the excited states have charge-transfer or multi-excitonic (ME) character and (2) finding out how many such excited states (all satisfying the symmetry requirements for vibronic coupling) of increasing energies need to be coupled with the GS for a particular PJT problem. An analogous alternative approach presented here for the well-known case of symmetry breaking of planar (D_6h) hexasilabenzene (Si₆H₆) to the buckled (D_3d) structure involves identifying the second-order donor–acceptor, hyperconjugative interactions (E²_{i → j}) that stabilize the distorted structure. Following the recent work of Nori-Shargh and Weinhold, one observes that the orbitals involved in the vibronic coupling between the S₀/S_n states and those for the donor (filled)–acceptor (empty) interactions are identical. In fact, deletion of any particular pair of E²_{i → j} interaction creates vibrational instability in the buckled structure and as a corollary, deleting it for the planar structure removes its instability. The one-to-one correlation between the natural bond orbital theory and PJT theory assists in an intuitive identification of the relevant (few) excited states from a manifold of computed ones that cause symmetry breaking by vibronic coupling. © 2019 Wiley Periodicals, Inc.