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.     

Photostability of electronically excited polyacenes: a case study of vibronic coupling in the naphthalene radical cation

Novel issues of electronic nonadiabatic coupling in the excited state dynamics of prototypical naphthalene radical cation of polycyclic aromatic hydrocarbon of the polyacene family are theoretically investigated. A benchmark ab initio quantum dynamical study is performed and its complex vibronic spectra and nonradiative decay are examined. The findings are in very good accord with the experiment, unambiguously establishing the crucial role of intricate electron-nuclear coupling in the photoinduced dynamical processes of this system.     

Structural and spectroscopic effects of vibronic coupling in the C2F radical

The lowest three (1²A^′,2²A^′,1²A^′′) potential energy surfaces of the C₂F radical have been studied at the ab initio level, using Multi Reference Configuration Interaction techniques. For linear geometries, the three surfaces correlate with a ²Π and a ²Σ⁺ state, which are very close in energy. Only the X²A^′ ground state was found to be bent, with R_CC=1.271 Å; R_CF=1.276 Å; CCF=165°, and a barrier to linearity of 275 cm⁻¹. The spin–rovibronic energy levels up to J=7/2 have been calculated using a recently developed method [Carter et al., Mol. Phys. 98 (2000) 1967]. Almost all of the resulting levels arise from a strong mixture of two out of three electronic states and their assignment is intrinsically ambiguous. A partial characterization, based on the shape of the vibronic wavefunctions, has been made.     

Ionized bicyclo[2.2.2]oct-2-ene: a twisted olefinic radical cation showing vibronic coupling

The bicyclo[2.2.2]oct-2-ene radical cation (1(.+)) exhibits matrix ESR spectra that have two very different types of gamma-exo hydrogens (those hydrogens formally in a W-plan with the alkene pi bond), a(2H) about 16.9 G and a(2H) about 1.9 G, instead of the four equivalent hydrogens as would be the case in an untwisted C(2v) structure. Moreover, deuterium substitution showed that the vinyl ESR splitting is not resolved (and under about 3.5 G); this is also a result of the twist. Enantiomerization of the C(2) structures is rapid on the ESR timescale above 110 K (barrier estimated at 2.0 kcalmol(-1)). Density functional theory calculations estimate the twist angle at the double bond to be 11-12 degrees and the barrier as 1.2-2.0 kcalmol(-1). Single-configuration restricted Hartree-Fock (RHF) calculations at all levels that were tried give untwisted C(2v) structures for 1(.+), while RHF calculations that include configuration interactions (CI) demonstrate that this system undergoes twisting because of a pseudo Jahn-Teller effect (PJTE). Significantly, twisting does not occur until the sigma-orbital of the predicted symmetry is included in the CI active space. UHF calculations at all levels that include electron correlation (even semiempirical) predict twisting at the alkene pi bond because they allow the filled alpha and the beta hole of the SOMO to have different geometries. The 2,3-dimethylbicyclo[2.2.2]oct-2-ene radical cation (2(.+)) is twisted significantly less than 1(.+), but has a similar temperature for maximum line broadening. Neither the 2,3-dioxabicyclo[2.2.2]octane radical cation (3(.+)) nor its 2,3-dimethyl-2,3-diaza analogue (5(.+)) shows any evidence of twisting. Calculations show that the orbital energy gap between the SOMO and PJTE-active orbitals for 3(.+) is too large for significant PJTE stabilization to occur.     

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.     

Near Resonance vibronic coupling. Isoquinoline

The interaction spectrum is considered resulting from the near-resonance coupling of a small number of vibronic levels of two different electronic states. In the simple model proposed, the interactions between the near-resonance states are first explicitly considered and then the off-resonance interactions are treated by perturbation theory. The model is applied to the isoquinoline spectrum and it is shown that for isoquinoline the latter interactions may be safely ignored. Good agreement is achieved between the theoretical and experimental spectra, and many puzzling features, such as the irregular nature of the sequence structure and the ambiguous isotope effects are readily explained. The lowest excited singlet state is the nπ*, and it is located within about 1000 cm^?1 of the first excited ¹ππ*. Two vibronic levels of the ¹nπ* state, corresponding to single quanta of the out-of-plane vibrations, are in near-resonance with the vibrationless ¹ππ* level.     

Photoelectron studies on vibronic coupling in pyrazine

Ionization pathways from the S(1) and T(1) states of pyrazine are investigated using one- and two-photon ionization of the excited state by both resonance enhanced multiphoton ionization photoelectron spectroscopy and zero electron kinetic energy pulsed field ionization techniques. For the triplet manifold, we show that two-photon ionization of T(1) is enhanced by a vibronically induced resonance for which we determine the inducing mode and the nature of the intermediate state, as well as the (3)3s(n(-1)) Rydberg state. For the singlet manifold, we identify the mode responsible for the vibronically induced intensity of a 3p Rydberg state that was previously found to greatly perturb the 1+2(') photoelectron spectrum of S(1) by a resonance at the two-photon level.     

Electronic transitions and vibronic coupling in neptunyl compounds

The low-lying electronic transitions of the neptunyl (NpO(2)(2+)) ion are characterized as either charge transfer (CT) or intra- 5f. Comparison of these classes of electronic transitions reveals significantly different photophysical properties, especially in vibronic coupling. An empirical model developed for analyses of uranyl CT vibronic transitions is used here to simulate the absorption (excitation) spectra of neptunyl in two compounds of different chemical compositions and structural symmetries. Analyses reveal that CT vibronic coupling in neptunyl has the same characteristics as that in typical uranyl analogues. The primary profile of the CT spectra is similar for neptunyl respectively with respect to chloride- and oxide-neptunium bonding interactions. On the other hand, vibronic coupling to the CT transitions is significantly different from that of f-f transitions, even within a given neptunyl compound. Electronic energy levels, vibronic coupling strength, and frequencies of various vibration modes were evaluated for transitions to the excited states of different origins in the region from 8000 cm(-1) to 21000 cm(-1) for two neptunyl compounds.     

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.     

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.     

Vibronic coupling in naphthalene anion: vibronic coupling density analysis for totally symmetric vibrational modes

Vibronic coupling, or electron-phonon coupling, of naphthalene is calculated. A method of vibronic coupling density analysis, which has been proposed for the vibronic coupling of the Jahn-Teller active modes in a Jahn-Teller molecule, is extended for totally symmetric vibrational modes of a molecule including a non-Jahn-Teller molecule. Contrary to non-totally-symmetric modes, orbital relaxation upon a charge transfer plays a crucial role in the vibronic coupling calculation for the totally symmetric modes. The method is applied for the ground state of the naphthalene anion to compare with that of the benzene anion. The relationship between the vibronic coupling density and a nuclear Fukui function is also discussed.     

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.     

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.     

The formyloxyl radical: electrophilicity,C–H bond activation and anti-Markovnikov selectivity in the oxidation of aliphatic alkenes

In the past the formyloxyl radical, HC(O)O˙, had only been rarely experimentally observed, and those studies were theoretical-spectroscopic in the context of electronic structure. The absence of a convenient method for the preparation of the formyloxyl radical has precluded investigations into its reactivity towards organic substrates. Very recently, we discovered that HC(O)O˙ is formed in the anodic electrochemical oxidation of formic acid/lithium formate. Using a [Co^IIIW₁₂O₄₀]⁵⁻ polyanion catalyst, this led to the formation of phenyl formate from benzene. Here, we present our studies into the reactivity of electrochemically in situ generated HC(O)O˙ with organic substrates. Reactions with benzene and a selection of substituted derivatives showed that HC(O)O˙ is mildly electrophilic according to both experimentally and computationally derived Hammett linear free energy relationships. The reactions of HC(O)O˙ with terminal alkenes significantly favor anti-Markovnikov oxidations yielding the corresponding aldehyde as the major product as well as further oxidation products. Analysis of plausible reaction pathways using 1-hexene as a representative substrate favored the likelihood of hydrogen abstraction from the allylic C–H bond forming a hexallyl radical followed by strongly preferred further attack of a second HC(O)O˙ radical at the C1 position. Further oxidation products are surmised to be mostly a result of two consecutive addition reactions of HC(O)O˙ to the C C double bond. An outer-sphere electron transfer between the formyloxyl radical donor and the [Co^IIIW₁₂O₄₀]⁵⁻ polyanion acceptor forming a donor–acceptor [D⁺–A⁻] complex is proposed to induce the observed anti-Markovnikov selectivity. Finally, the overall reactivity of HC(O)O˙ towards hydrogen abstraction was evaluated using additional substrates. Alkanes were only slightly reactive, while the reactions of alkylarenes showed that aromatic substitution on the ring competes with C–H bond activation at the benzylic position. C–H bonds with bond dissociation energies (BDE) ≤ 85 kcal mol⁻¹ are easily attacked by HC(O)O˙ and reactivity appears to be significant for C–H bonds with a BDE of up to 90 kcal mol⁻¹. In summary, this research identifies the reactivity of HC(O)O˙ towards radical electrophilic substitution of arenes, anti-Markovnikov type oxidation of terminal alkenes, and indirectly defines the activity of HC(O)O˙ towards C–H bond activation.

The formyloxyl radical, formed electrochemically, is electrophilic, yields anti-Markovnikov oxidation products from alkenes, and is effective for C–H bond activation.     

Enhanced two-photon absorption of novel four-branched chromophore via vibronic coupling

A novel four-branched chromophore TOZ-4 with starburst linker was synthesized and showed two-photon absorption cross-section (δ) as large as 5254 GM, which was principally resulted from vibronic coupling enhancement.     

Vibronic coupling in benzene cation and anion: vibronic coupling and frontier electron density in Jahn-Teller molecules

Vibronic coupling constants of Jahn-Teller molecules, benzene radical cation and anion, are computed as matrix elements of the electronic part of the vibronic coupling operator using the electronic wave functions calculated by generalized restricted Hartree-Fock and state-averaged complete active space self-consistent-field methods. The calculated vibronic coupling constants for benzene cation agree well with the experimental and theoretical values. Vibronic coupling density analysis, which illustrates the local properties of the coupling, is performed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. This analysis reveals that the couplings of the e2g2 and e2g3 modes in which the large displacements locate on C-C bonds are strong in the cation. On the other hand, they are greatly weakened in the anion because of the decrease of electron density in the region of the C-C bonds, which originates from the antibonding nature of the singly occupied molecular orbital of the anion. However, the difference of the electronic structure has a little influence on the vibronic coupling of the e2g4 mode. These results indicate that the vibronic coupling depends not only on the direction of the nuclear displacement but also on the frontier electron density.