Vibronic Coupling Constants Research Articles

Vibronic coupling density and related concepts

Vibronic coupling density is derived from a general point of view as a one-electron property density. Related concepts as well as their applications are presented. Linear and nonlinear vibronic coupling density and related concepts, orbital vibronic coupling density, reduced vibronic coupling density, atomic vibronic coupling constant, and effective vibronic coupling density, illustrate the origin of vibronic couplings and enable us to design novel functional molecules or to elucidate chemical reactions. Transition dipole moment density is defined as an example of the one-electron property density. Vibronic coupling density and transition dipole moment density open a way to design light-emitting molecules with high efficiency.

Pseudo Jahn–Teller Effect and Natural Bond Orbital Analysis of Structural Properties of Tetrahydridodimetallenes M2H4, (M = Si, Ge, and Sn)

The structural properties of ethene (1) and tetrahydridodimetallenes M(2)H(4) [M = Si (2), Ge (3), and Sn (4)] have been examined by means of CCSD(T)/Def2-TZVPP, MP4(SDTQ)/Def2-TZVPP, and B3LYP/Def2-TZVPP levels of theory and natural bond orbital analysis (NBO) interpretations. The results obtained showed the expected planar ground state structure for compound 1 (D(2h) symmetry) but trans-bent ground state structures for compounds 2-4 (C(2h) symmetry). The distortions of the high-symmetry configurations of compounds 2-4 are due to the pseudo Jahn-Teller effect (PJTE), which is the only source of instability of high-symmetry configurations in nondegenerate states. The distortions are due to the mixing of the ground A(g) and excited B(2g) states [i.e., HOMO(B(3u)) → LUMO + 3(B(1u)) for compound 1, HOMO(B(3u)) → LUMO + 2(B(1u)) for compound 2, and HOMO(B(3u)) → LUMO + 1(B(1u)) for compounds 3 and 4]. Importantly, the higher-lying B(1g), B(2u), and B(2g) states are not involved in the PJT interactions. The energy gaps between reference states (Δ) in the undistorted configurations decrease from compound 1 to compound 4, and the PJT stabilization energies increase. Therefore, the primary force constant of the ground state in the Q((b2g)) direction (K(0)) decreases from compound 1 to compound 4. This fact can be justified by the valence isoelectronic systems of these compounds (having similar vibronic coupling constants, F). For the purpose of more chemical transparency, the NBO results were analyzed, and their relation to the PJT interactions has been revealed. The NBO analysis showed that stabilization energy associated with π(M-H) (b(u)) → σ*(M═M) (b(u)) electron delocalization (i.e., the mixing of the distorted b(u) molecular orbitals along the b(2g) bending distortions) increases from compound 1 to compound 4. Also, by using the hybridized orbitals obtained, an n parameter is defined. The NBO results revealed that the n values in the mean hybrid orbitals (sp(n)) increase from compound 1 to 4. The correlations between the PJT stabilization energies, bond orders, n values, π(M-M) → σ*(M═M) electron delocalizations, and structural parameters of compounds 1-4 have been investigated.

Vibronic coupling density analysis for the chain-length dependence of reorganization energies in oligofluorenes: a comparative study with oligothiophenes

The vibronic coupling constants and reorganization energies of oligofluorenes OF(n) (n = 1-6) are calculated for their cationic states (hole transport). Those of oligothiophenes OT(2n) (n = 1-6) are also calculated for comparison. The vibronic coupling constants of OF(n) are smaller than those of OT(2n), and decrease with increasing n. For the elucidation of the small vibronic couplings of the oligofluorenes, the calculated vibronic coupling constants are analyzed on the basis of the concept of vibronic coupling density. The vibronic coupling density of OF(n) becomes small in the middle of the chain with increasing n because of the reduction in the electron-density difference between the neutral and cationic states. It is found that orbital relaxation plays a crucial role in the distribution of the electron-density difference. From the fragment molecular orbital analyses, the large orbital relaxation in OF(n) is found to originate from the small transfer integral between the fragment molecular orbitals. These findings led to a design principle for a carrier-transporting oligomer/polymer with small vibronic couplings, or small reorganization energy, as follows: the orbital interaction between the monomers should be small from the view of vibronic couplings.

General treatment of the multimode Jahn–Teller effect: study of fullerenecations

A general model for the analysis of the Adiabatic Potential Energy Surfaces (APES) of the molecules that are subject to the multimode Jahn-Teller effect is presented. The method utilizes the information obtained by DFT calculations on a distorted stationary point on the APES. The essence of the model is to express the distortion along a model minimal energy path called Intrinsic Distortion Path (IDP), projecting the geometry of the system on the normal modes of the either high-symmetry (HS) or low symmetry (LS) nuclear configuration. This allows us to determine the significance of all of the involved normal modes along a relevant particular path of distortion, and the direct calculation of the vibronic coupling constants. The IDP analysis is illustrated by the discussion of the multimode H ⊗ (g + 2h) JT effect in fullerene cations (C(60)(+)) giving a deep insight into the origin and the mechanism of vibronic coupling in fullerene based molecules.

Bending Of Adsorbed FCN And FNC Molecules Induced By The Renner-Teller Effect

Abstract It is shown that the bending of FCN and FNC molecules adsorbed on Si (100) - (2 × 1) surface, is due to the Renner-Teller effect induced by the orbital charge transfers by adsorption. From ab initio calculations of free FCN and FNC and the molecules adsorbed on the model Si9H12 cluster, the orbital charge transfers to and from the molecules were calculated, the vibronic coupling constants were estimated, and the curvature K of the adiabatic potentials for the bending coordinate of adsorbed molecules was evaluated. Calculations show that for both side-on adsorbed species, as well as for end-on adsorbed FNC molecule K<0 that leads to their bending. For the end-on adsorbed FCN K>0, and this molecule remains linear

Chemical Reactivity in Nucleophilic Cycloaddition to C70: Vibronic Coupling Density and Vibronic Coupling Constants as Reactivity Indices

The chemical reactivity in nucleophilic cycloaddition to C70 is investigated on the basis of vibronic (electron-vibration) coupling density and vibronic coupling constants. Because the e1″ LUMOs of C70 are doubly degenerate and delocalized throughout the molecule, it is difficult to predict the regioselectivity by frontier orbital theory. It is found that vibronic coupling density analysis for the effective mode as a reaction mode illustrates the idea of a functional group embedded in the reactive sites. Furthermore, the vibronic coupling constants for localized stretching vibrational modes enable us to estimate the quantitative reactivity. These calculated results agree well with the experimental findings. The principle of chemical reactivity proposed by Parr and Yang is modified as follows: the preferred direction is the one for which the initial vibronic coupling density for a reaction mode of the isolated reactant is a minimum.

Isotopic Substitution as a Strategy to Control Non-Adiabatic Dynamics in Photoelectrochemical Cells: Surface Complexes between TiO2 and Dicyanomethylene Compounds

We investigate the effect of deuteration on geminate recombination in photoelectrochemical cells operating by interfacial charge transfer absorption bands. The trend in recombination in surface complexes of tetracyanoethylene (TCNE), 7,7,8,8-tetracyanoquinodimethane (TCNQ), and 11,11,12,12-tetracyanonaphtho-2,6-quinodimethane (TCNAQ) with TiO2 is treated as internal conversion (IC) in the model compounds TCNX–O–Ti(OH)3-. The deuteration of TCNQ and TCNAQ significantly modifies the spectrum of vibronic coupling constants for many vibrational modes, but affects little the modes with the strongest contribution to IC. As a result, the overall effect on recombination/internal conversion is expected to be limited, slightly increasing its rate. We also consider the influence on the recombination of vibrational modes of the Ti(OH)3 moiety which only crudely models the oxide surface. We conclude that even as the model is sensitive to the motions of Ti(OH)3, the predicted trend in recombination in the series TCNE–TCNQ–TCNAQ holds under different treatments of Ti(OH)3 modes.

Electronic Spectra of Cycl[3.3.2]azine and Related Compounds: Solvent Effect on Vibronic Couplings

Quantitative ab initio calculations are presented for the ultraviolet-visible peaks of cycl[3.2.2]azine and its mono- and dibenzannulated polycyclic compounds at the multistate CASPT2 (MS-CASPT2) level of theory, with 11 nm deviation from the experimental S0 → S1 absorption. The electrophilic substitution reactions of cycl[3.2.2]azine, benzo[a]/[g]annulated cycl[3.2.2]azines, and 6-dimethylamino[2.2.3]cyclazine-1-carboxylates with 3-cyano-4-methylthiomaleimide gave the corresponding functionalized cycl[3.2.2]azine derivatives, which exhibited the absorption maxima around 510-630 nm. The first intense peaks were investigated by means of time-dependent density functional theory (TD-DFT). These peaks were systematically underevaluated by ∼50 nm, within the acceptable accuracies of TD-DFT. Furthermore, we calculated vibronic coupling constants of the electronic excited states of cycl[3.2.2]azine and simulated absorption spectra both in vacuo and in ethanol. The solvent effect is found to enhance oscillator strengths and vibronic couplings. This is because the solvent effect gives rise to changes in the electron density difference on the phenyl ring, and in turn, the intensified overlap between the electron density difference and the potential derivative in the phenyl ring leads to enhanced vibronic couplings in ethanol.

Dynamic Jahn–Teller effect for V2+ in MgO single crystal

In this paper we studied the dynamic Jahn–Teller effect in the excited state 4T2g of the V2+ ions doped in MgO crystal, in octahedral coordination. Calculation of the fine structure of the energy levels in the frame of crystal field theory, estimation of the vibronic coupling constants and the Jahn–Teller stabilization energy are presented. The dynamic Jahn–Teller effect in the lowest excited 4T2g state of the V2+ ions is considered using the Ham effect and analysis of the displacements of ligands, due to the combined effect of the a1g and eg normal modes of the obtained octahedral cluster.

Critical reinvestigation of vibronic couplings in picene from view of vibronic coupling density analysis

Vibronic coupling constants in the monoanionic, trianionic, and excited states of picene are evaluated from the total energy gradients using the density functional theory. Employing the calculated vibronic coupling constants in the excited state of the neutral molecule, electron energy loss spectrum (EELS) is simulated to be compared with the experimental spectrum. The calculated vibronic coupling constants are analyzed in terms of the vibronic coupling density which enables us to analyze vibronic couplings based on the relation between the electronic and vibrational structures. The vibronic coupling constants reported by Kato et al. [J. Chem. Phys. 116, 3420 (2002) and Phys. Rev. Lett. 107, 077001 (2011)] are critically discussed based on the vibronic coupling density analysis.

The theory of surface-enhanced Raman scattering

By considering the molecule and metal to form a conjoined system, we derive an expression for the observed Raman spectrum in surface-enhanced Raman scattering. The metal levels are considered to consist of a continuum with levels filled up to the Fermi level, and empty above, while the molecule has discrete levels filled up to the highest occupied orbital, and empty above that. It is presumed that the Fermi level of the metal lies between the highest filled and the lowest unfilled level of the molecule. The molecule levels are then coupled to the metal continuum both in the filled and unfilled levels, and using the solutions to this problem provided by Fano, we derive an expression for the transition amplitude between the ground stationary state and some excited stationary state of the molecule-metal system. It is shown that three resonances contribute to the overall enhancement; namely, the surface plasmon resonance, the molecular resonances, as well as charge-transfer resonances between the molecule and metal. Furthermore, these resonances are linked by terms in the numerator, which result in SERS selection rules. These linked resonances cannot be separated, accounting for many of the observed SERS phenomena. The molecule-metal coupling is interpreted in terms of a deformation potential which is compared to the Herzberg-Teller vibronic coupling constant. We show that one term in the sum involves coupling between the surface plasmon transition dipole and the molecular transition dipole. They are coupled through the deformation potential connecting to charge-transfer states. Another term is shown to involve coupling between the charge-transfer transition and the molecular transition dipoles. These are coupled by the deformation potential connecting to plasmon resonance states. By applying the selection rules to the cases of dimer and trimer nanoparticles we show that the SERS spectrum can vary considerably with excitation wavelength, depending on which plasmon and/or charge-transfer resonance is excited.

Theoretical design for carrier-transporting molecules in view of vibronic couplings

Vibronic coupling constants (VCC) in aromatic diboranes are calculated. For a carrier-transporting molecule, vibronic couplings should be small. Vibronic couplings, or reorganization energy, can be controlled by applying the vibronic coupling density (VCD) analysis. To suppress vibronic couplings, electron density difference should be localized not on bonds but on atoms. Aromatic diboranes as electron-transporting molecules are designed based on this design principle. Introducing the protecting groups that prevent the boron atoms in the diborane from being attacked suppresses the vibronic couplings. Based on the nonequilibrium Green's function (NEGF) theory, energy dissipations through a single molecule are also calculated.

Quantum Chemistry Study on Internal Conversion of Diphenyldibenzofulvene in Solid Phase

We investigate the nonradiative decay process of diphenyldibenzofulvene (DPDBF) in solid phase by using the quantum chemistry methods. To carry out the nonradiative rate constant calculation, we construct a solid phase model based on the ONIOM method. The geometry of the DPDBF molecule is optimized for the ground state by DFT and the first excited state by TD-DFT, and the corresponding vibrational frequencies and normal coordinates are computed. Under displaced-distorted harmonic oscillator potential approximation, Huang-Rhys factors are obtained. Vibronic coupling constants are calculated as a function of the normal mode based on Domcke's scheme. We find that vibronic coupling constants of 12 modes with large reorganization energies are of similar order, and if this result is still valid for other modes, the internal conversion rate would be determined by high frequency modes because they have a significant nuclear factor that is related to Franck-Condon overlap intergrals. We also find that geometrical changes are suppressed due to the stacking effect, which yields small Huang-Rhys values in the solid phase.

Ab initioquantum dynamical study of the multi-state nonadiabatic photodissociation of pyrrole

There has been a substantial amount of theoretical investigations on the photodynamics of pyrrole, often relying on surface hopping techniques or, if fully quantal, confining the study to the lowest two or three singlet states. In this study we extend ab initio based quantum dynamical investigations to cover simultaneously the lowest five singlet states, two π-σ∗ and two π-π∗ excited states. The underlying potential energy surfaces are obtained from large-scale MRCI ab initio computations. These are used to extract linear and quadratic vibronic coupling constants employing the corresponding coupling models. For the N-H stretching mode Q(24) an anharmonic treatment is necessary and also adopted. The results reveal a sub-picosecond internal conversion from the S(4) (π-π∗) state, corresponding to the strongly dipole-allowed transition, to the S(1) and S(2) (π-σ∗) states and, hence, to the ground state of pyrrole. The significance of the various vibrational modes and coupling terms is assessed. Results are also presented for the dissociation probabilities on the three lowest electronic states.

Optical investigations of intermolecular electronic interactions and “free” charge carriers in quasi-two-dimensional organic conductors and superconductors of the group κ-(BEDT-TTF)2Cu[N(CN)2]Br x Cl1 − x

The reflectance spectra and optical conductivity spectra of quasi-two-dimensional organic conductor crystals of the group of compounds κ-(BEDT-TTF)2Cu[N(CN)2]Br x Cl1 − x with x = 0, 0.40, 0.73, 0.85, and 0.90 in the spectral region from 6 meV to 0.74 eV at temperatures T = 90-20 K have been quantitatively analyzed in the framework of a combined semiempirical model including the cluster (tetramer) theory for strongly correlated electrons coupling with intramolecular vibrations and the Drude theory of free electrons with the aim of studying intermolecular electronic interactions and their influence on the formation of the ground state in these crystals. It has been established that the parameters characterizing the charge transfer between molecules in dimers and tetramers and the vibronic coupling constants are almost identical for the compounds under investigation. A large value of the effective Coulomb repulsion (U/t = 1.3–1.5) indicates that strong electron correlations occur in the compounds both with a metal-insulator phase transition (x = 0, 0.40) and with a metal-superconductor phase transition (x = 0.85, 0.90). The conclusion has been drawn that, at x = 0, electron correlations favor an antiferromagnetic spin ordering and a metal-insulator phase transition, whereas for superconductors (x = 0.85, 0.90), the metal-insulator phase transition is hindered as a result of the structural disorder due to the difference in orientations of the terminal CH2 groups of the BEDT-TTF molecule. It has been shown that quasi-free charge carriers interact with electrons localized on the clusters and do not interact with intramolecular vibrations. It has been noted that the oscillator strength of the observed electronic transitions in the initial metallic band (N eff = 0.38–0.31 per dimer) is considerably less than the corresponding value for free (noninteracting) charge carriers (N = 1). This suggests that the Coulomb correlations and vibronic coupling play a decisive role in the kinetic phenomena observed in the molecular conductors and superconductors under investigation.

Jahn–Teller, pseudo Jahn–Teller, and Renner–Teller effects in systems with fractional charges

It is shown that modeling a part of a molecular system by means of fractional charges is very useful in many situations when its interaction with the rest of the systems is relatively weak as, for instance, in some coordination systems, mixed-valence compounds, molecular adsorption on surfaces, early stages of interactions in chemical reactions, etc. The structural changes in such subsystems can be described by means of orbital charge transfers (OCT) that change the intramolecular vibronic coupling leading to instabilities and distortions of the Jahn–Teller effect (JTE), pseudo JTE (PJTE), and Renner–Teller effect (RTE). A molecular orbital theory of these effects in systems with fractional charges involving orbital vibronic coupling constants and orbital force constants is worked out in the approximation of small OCT. The efficiency of the theory is demonstrated by means of ab initio calculations revealing the vibronic coupling constants and distortions of coordinated molecules in coordination systems and showing how the JTE, PJTE, and RTE allow one to predict and rationalize experimental data. The PJTE instability in coordinated systems with fractional charges is analyzed by considering three coordination compounds, [M(N 2H 2)(dmpe) 2] with M = Fe, Ru (dmpe = Me 2PCH 2CH 2PMe 2), and [(N 2H 2)Ru 2DPB(Im) 2] (DPB = diporphyrinato-biphenylene tetraanion, Im = imidazole), in which the η 2-coordinated N 2H 2 molecule distorts from a trans-planar to a nonplanar (C 2) shape due to OCT to and from its frontier orbitals. As an example of the induced JTE in coordinated molecules the [(triphos)RhH(η 1: η 2-P 4)] complex is considered, and it is shown that the white phosphorus (P 4) distortion from tetrahedron to butterfly geometry by coordination is due to the OCT to its excited degenerate t 1 orbital. The RTE effect in coordinated systems is demonstrated by the distortion of the acetylene molecule from its linear configuration to the non-linear cis-form by its coordination in Y-η 2-C 2H 2 and Pd-η 2-C 2H 2 systems.

Cation Ordering in Natural and Synthetic (Cu1–xZnx)2CO3(OH)2 and (Cu1–xZnx)5(CO3)2(OH)6

In the present paper we report combined experimental and theoretical studies of the UV-vis-NIR spectra of the mineral compounds malachite, rosasite, and aurichalcite and of the precursor compounds for Cu/ZnO catalysts. For the copper species in the minerals the crystal field splitting and the vibronic coupling constants are estimated using the exchange charge model of the crystal field accounting for the exchange and covalence effects. On this basis the transitions responsible for the formation of the optical bands arising from the copper centers in minerals are determined and the profiles of the absorption bands corresponding to these centers are calculated. The profiles of the absorption bands calculated as a sum of bands of their respective Cu species are in quite good agreement with the experimental data. In agreement with crystal chemical considerations, the Zn ions were found to be preferentially located on the more regular, i.e., less distorted, octahedral sites in zincian malachite and rosasite, suggesting a high degree of metal ordering in these phases. This concept also applies for the mineral aurichalcite, but not for synthetic aurichalcite, which seems to exhibit a lower degree of metal ordering. The catalyst precursor was found to be a mixture of zincian malachite and a minor amount of aurichalcite. The best fit of the optical spectrum is obtained assuming a mixture of contributions from malachite (0% Zn) and rosasite (38% Zn of [Zn + Cu]), which is probably due to the intermediate Zn content of the precursor (30%).

Redox Properties of Manganese-Containing Zirconia Solid Solution Catalysts Analyzed by In Situ UV–Vis Spectroscopy and Crystal Field Theory

The optical absorption spectra of manganese-promoted sulfated zirconia, a highly active alkane isomerization catalyst, were found to be characterized by oxygen-to-manganese charge-transfer transitions at 300-320 nm and d-d transitions of manganese ions at 580 and 680 nm. The latter were attributed to Mn(4+) and Mn(3+) ions, which are known to be incorporated in the zirconia lattice. The oxygen surroundings of these ions were modeled assuming a substitutional solid solution. The crystal field splittings, vibronic coupling constants, and oscillator strengths of the manganese ions were calculated on the basis of a cluster model that considers the manganese center as a complex with the adjacent ions of the lattice as ligands. The ratio of Mn(3+) to Mn(4+) ions was determined using the spectra and the model, and the relative concentrations of Mn(2+), Mn(3+), and Mn(4+) ions were determined with the help of the average valence known from X-ray absorption data in the literature. The redox behavior of manganese-promoted sulfated zirconia in oxidizing and inert atmosphere was elucidated at temperatures ranging from 323 to 773 K.

Vibronic interactions in hole-transporting molecules: An interplay with electron–hole interactions

Vibronic coupling constants of hole-transporting molecules, TPF and CBP, are estimated. Despite the planar structure of TPF, the calculated vibronic coupling constants are close to those of nonplanar TPD. The origin of the vibronic couplings in TPF is investigated employing the vibronic coupling density analysis. Based on a Hubbard Hamiltonian, electron–hole interactions are found to be crucial in the vibronic couplings. A large difference of on-site Coulomb interactions, or electron–hole interactions gives rise to a localization of the electron-density difference on a site which can lead to small vibronic couplings.

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.