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.     

Effect of Coulomb interactions on the vibronic couplings in C60(-)

Vibronic couplings in C(60)(-) anion are discussed on the basis of the concept of the vibronic coupling density (VCD) [T. Sato, K. Tokunaga, and K. Tanaka, J. Chem. Phys. 124, 024314 (2006); K. Tokunaga, T. Sato, and K. Tanaka, J. Chem. Phys. 124, 154303 (2006); and T. Sato, K. Tokunaga, and K. Tanaka, J. Phys. Chem. A 112, 758 (2008)]. The VCD analysis clearly reveals that the coupling to the bending h(g)(2) mode is weaker than the coupling to the stretching h(g)(7) and h(g)(8) modes. For the vibronic couplings with the stretching modes, polarizations of the electron density difference on the bonds play a crucial role in the vibronic couplings. Such a polarized electron density difference appears as a result of the Coulomb interactions between the electrons in the lowest unoccupied molecular orbital and relevant doubly-occupied orbitals.     

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.     

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.     

13C n.m.r. spectra of 2-substituted pyrimidines

¹³C n.m.r. chemical shifts and carbon-proton coupling constants of 2-substituted pyrimidines are reported. The carbon chemical shifts are correlated with π-electron densities. Substituents which cause deshielding at the directly bound carbon (e.g. NH₂, OCH₃ and F) exert a more powerful effect in the benzene series than in the pyridine or pyrimidine series. The carbon-proton coupling constants do not correlate with the electronegativity of the substituents. Carbon-proton coupling constants and proton-proton coupling constants over the same number of bonds do not obey the Karabatsos relationship. The changes in the carbon-proton coupling constants in 2(1H)-pyrimidinone and 2(1H)-pyrimidinethione which accompany anion and cation formation are reported.     

Vibronic interaction in metalloporphyrin pi-anion radicals

The vibronic (vibrational-electronic) interactions in the pi-anion radicals of the metalloporphyrins (M=Cr, Mn, Fe, Co, Ni, Cu, and Zn), which show delocalized D4h structures in the neutral states, are discussed using B3LYP density-functional-theory calculations. The B1g and B2g modes of vibration can remove the degenerate 2Eg state of the pi-anion radicals in the D4h symmetric structures to lead to rectangular and diamond D2h distortions, respectively. Calculated vibronic coupling constants demonstrate that the B1g modes of vibration better couple with the degenerate electronic state, leading to the rectangular D2h distortion. In particular, the B1g modes of nu10 and nu11, which have dominant contributions from Calpha-Cm and Cbeta-Cbeta stretching, give large vibronic coupling constants in the pi-anion radicals. The vibronic coupling constant can be viewed as the Jahn-Teller distortion force, and therefore these C-C stretching B1g modes will play a central role in the Jahn-Teller effect of the pi-anion radicals of the metalloporphyrins.     

Spectroscopic and computational studies on the rearrangement of ionized [1.1.1]propellane and some of its valence isomers: the key role of vibronic coupling

The [1.1.1]propellane radical cation 1(?+), generated by radiolytic oxidation of the parent compound in argon and Freon matrices at low temperatures, undergoes a spontaneous rearrangement to form the distonic 1,1-dimethyleneallene (or 2-vinylideneallyl) radical cation 3(?+) consisting of an allyl radical substituted at the 2-position by a vinyl cation. In similar matrix studies, it is found that the isomeric dimethylenecyclopropane radical cation 2(?+) also rearranges to 3(?+). The unusual molecular and electronic structure of 3(?+) has been established by the results of ESR, UV-vis, and IR spectroscopic measurements in conjunction with detailed theoretical calculations. Also of particular interest is an NIR photoinduced reaction by which 3(?+) is cleanly converted to the vinylidenecyclopropane radical cation 4(?+), a process that can be represented in terms of a single electron transfer from the allyl radical to the vinyl cation followed by allyl cation cyclization. The specificity of this photochemical reaction provides additional strong chemical evidence for the structure of 3(?+). Theoretical calculations reveal the decisive role of vibronic coupling in shaping the potential energy surfaces on which the observed ring-opening reactions take place. Thus vibronic interaction in 1(?+) mixes the (2)A(1)' ground state, characterized by its "non-bonding" 3a(1)' SOMO, with the (2)E' first excited state resulting in the destabilization of a lateral C-C bond and the initial formation of the methylenebicyclobutyl radical cation 5(?+). The further rearrangement of 5(?+) to 3(?+) occurs via 2(?+) and proceeds through two additional lateral C-C bond cleavages characterized by transition states of extremely low energy, thereby explaining the absence of identifiable intermediates along the reaction pathway. In these consecutive ring-opening rearrangements, the "non-bonding" bridgehead C-C bond in 1(?+) is conserved and ultimately transformed into a normal bond characterized by a shorter C-C bond length. This work provides strong support for the Heilbronner-Wiberg interpretation of the vibrational structure in the photoelectron spectrum of 1 in terms of vibronic coupling.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

Solute-solvent intermolecular vibronic coupling as manifested by the molecular near-field effect in resonance hyper-Raman scattering

Vibronic coupling within the excited electronic manifold of the solute all-trans-β-carotene through the vibrational motions of the solvent cyclohexane is shown to manifest as the "molecular near-field effect," in which the solvent hyper-Raman bands are subject to marked intensity enhancements under the presence of all-trans-β-carotene. The resonance hyper-Raman excitation profiles of the enhanced solvent bands exhibit similar peaks to those of the solute bands in the wavenumber region of 21,700-25,000 cm(-1) (10,850-12,500 cm(-1) in the hyper-Raman exciting wavenumber), where the solute all-trans-β-carotene shows a strong absorption assigned to the 1A(g) → 1B(u) transition. This fact indicates that the solvent hyper-Raman bands gain their intensities through resonances with the electronic states of the solute. The observed excitation profiles are quantitatively analyzed and are successfully accounted for by an extended vibronic theory of resonance hyper-Raman scattering that incorporates the vibronic coupling within the excited electronic manifold of all-trans-β-carotene through the vibrational motions of cyclohexane. It is shown that the major resonance arises from the B-term (vibronic) coupling between the first excited vibrational level (v = 1) of the 1B(u) state and the ground vibrational level (v = 0) of a nearby A(g) state through ungerade vibrational modes of both the solute and the solvent molecules. The inversion symmetry of the solute all-trans-β-carotene is preserved, suggesting the weak perturbative nature of the solute-solvent interaction in the molecular near-field effect. The present study introduces a new concept, "intermolecular vibronic coupling," which may provide an experimentally accessible∕theoretically tractable model for understanding weak solute-solvent interactions in liquid.     

Vibronic states in single molecules: C60 and C70 on ultrathin Al2O3 films

Vibronic states are observed in single C(60) and C(70) molecules by scanning tunneling microscopy. When single fullerene molecules are adsorbed on a thin layer of Al(2)O(3) grown on a NiAl(110) substrate, equally spaced features are observed in the differential conductance (dI/dV), which are clearly resolved in d(2)I/dV(2) spectra. These features are attributed to the vibronic states of the molecule. The vibronic progressions are sensitive to the molecular orientations and can have different spacings in different electronic bands of the same molecule. For C(60,) these vibronic states are associated with the intramolecular A(g) and H(g) vibrational modes. Vibronic states are not resolved in molecules adsorbed on the metal surface. However, inelastic electron tunneling spectroscopy exhibits a vibrational mode at 64 meV for C(60) and 61 meV for C(70) adsorbed on NiAl(110).     

Strong vibronic coupling effects in ionization spectra: The “mystery band” of butatriene

A theory of vibronic coupling in molecules is presented and applied to butatriene. The energies and coupling constants which enter the calculation are computed using ab initio Hartree—Fock and many-body methods. The influence of the energy splitting and the coupling constants on the calculated spectrum is discussed. It is definitely shown that the “mystery band” in the photoelectron spectrum of butatriene arises from the vibronic coupling between the electronic states ²B_3g and ²B_3u. To reproduce the experimental observations it is essential to include in the calculation both totally and non-totally symmetric vibrational modes.     

Vibronic coupling in the superoxide anion: the vibrational dependence of the photoelectron angular distribution

We present a comprehensive photoelectron imaging study of the O(2)(X (3)Σ(g)(-),v(')=0-6)←O(2)(-)(X (2)Π(g),v(")=0) and O(2)(a?(1)Δ(g),v(')=0-4)←O(2)(-)(X (2)Π(g),v(")=0) photodetachment bands at wavelengths between 900 and 455 nm, examining the effect of vibronic coupling on the photoelectron angular distribution (PAD). This work extends the v(')=1-4 data for detachment into the ground electronic state, presented in a recent communication [R. Mabbs, F. Mbaiwa, J. Wei, M. Van Duzor, S. T. Gibson, S. J. Cavanagh, and B. R. Lewis, Phys. Rev. A 82, 011401(R) (2010)]. Measured vibronic intensities are compared to Franck-Condon predictions and used as supporting evidence of vibronic coupling. The results are analyzed within the context of the one-electron, zero core contribution (ZCC) model [R. M. Stehman and S. B. Woo, Phys. Rev. A 23, 2866 (1981)]. For both bands, the photoelectron anisotropy parameter variation with electron kinetic energy, β(E), displays the characteristics of photodetachment from a d-like orbital, consistent with the π(g)(?) 2p highest occupied molecular orbital of O(2)(-). However, differences exist between the β(E) trends for detachment into different vibrational levels of the X (3)Σ(g)(-) and a?(1)Δ(g) electronic states of O(2). The ZCC model invokes vibrational channel specific "detachment orbitals" and attributes this behavior to coupling of the electronic and nuclear motion in the parent anion. The spatial extent of the model detachment orbital is dependent on the final state of O(2): the higher the neutral vibrational excitation, the larger the electron binding energy. Although vibronic coupling is ignored in most theoretical treatments of PADs in the direct photodetachment of molecular anions, the present findings clearly show that it can be important. These results represent a benchmark data set for a relatively simple system, upon which to base rigorous tests of more sophisticated models.     

Vibronic induced one- and two-photon absorption in a charge-transfer stilbene derivate

Both the electronic and the vibronic contributions to one- and two-photon absorption of a D-pi-D charge-transfer molecule (4-dimethylamino-4'-methyl-trans stilbene) are studied by means of density functional response theory combined with a linear coupling model. Vibronic profiles of the first four excited states are fully explored. The dominating vibrational modes for both Franck-Condon and Herzberg-Teller contributions are identified. The Franck-Condon contribution dominates the spectra of first, second, and fourth excited states. The Herzberg-Teller contribution is on the other hand of comparable size for the third excited state, where its inclusion leads to a blueshift with respect to the vertical transition. A similar vibronic coupling behavior is found for both one- and two-photon absorptions.     

Substituent effects on the vibronic coupling for the phenoxyl/phenol self-exchange reaction

The impact of substituents on the vibronic coupling for the phenoxyl/phenol self-exchange reaction, which occurs by a proton-coupled electron transfer mechanism, is investigated. The vibronic couplings are calculated with a grid-based nonadiabatic method and a nuclear-electronic orbital nonorthogonal configuration interaction method. The quantitative agreement between these two methods for the unsubstituted phenoxyl/phenol system and the qualitative agreement in the predicted trends for the substituted phenoxyl/phenol systems provides a level of validation for both methods. Analysis of the results indicates that electron-donating groups enhance the vibronic coupling, while electron-withdrawing groups attenuate the vibronic coupling. Thus, if all other aspects of the reaction are the same, then electron-donating groups will increase the rate, while electron-withdrawing groups will decrease the rate. Correlations between the vibronic coupling and physical properties of the phenol are also analyzed. Negative Hammett constants correspond to higher vibronic couplings, while positive Hammett constants correspond to similar or slightly lower vibronic couplings relative to the unsubstituted phenoxyl/phenol system. In addition, lower bond dissociation enthalpies, ionization potentials, and redox potentials, as well as higher pKa values, tend to correspond to higher vibronic couplings relative to the unsubstituted phenoxyl/phenol system. The observed trends enable the prediction of the impact of general substituents on the vibronic coupling, and hence the rate, for the phenoxyl/phenol self-exchange reaction. The fundamental physical insights obtained from these studies are applicable to other proton-coupled electron transfer systems.     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

Vibronic coupling in charge transfer complexes. II

Vibronic coupling in excited charge transfer states of crystalline donor—acceptor complexes is reconsidered in relationship to recent electromodulation experiments for anthracene—PMDA. It is demonstrated that vibronic coupling, both linear and quadratic, may substantially affect the electric field dependence of the eigenstates, which may explain, at least semiquantitatively, the observed behaviour. Some consequences for experimental determination of dipole moments by means of electromodulation spectroscopy are pointed out.     

Electronic Substitution Effect on the Ground and Excited State Properties of Indole Chromophore: A Computational Study**

Indole, being the main chromophore of amino acid tryptophan and several other biologically relevant molecules like serotonin, melatonin, has prompted considerable theoretical and experimental interest. The current work focuses on the investigation of substitution effect on the ground and excited electronic states of indole using computational quantum chemistry. Having three close-lying excited electronic states, the vibronic coupling effect becomes extremely important yet challenging for the photophysics and photochemistry of indole. Here, we have evaluated the performance of time-dependent density functional theory against available experimental and ab initio results from the literature. The electronic effects on the excited states of indole and indole derivatives e. g. tryptophan, serotonin and melatonin are reported. A bathochromic shift has been observed in the absorption spectrum for the L_a state. The absorption wavelength increases in the order of indole<tryptophan <serotonin <melatonin. While the contribution of the in-plane small adjacent groups increases the electron density of the indole ring, the out-of-plane long substituent groups have minor effect. The absorption spectra calculated including the vibronic coupling are in good agreement with experiments. These results can be used to estimate the error in photophysical observables of indole derivatives calculated considering indole as a prototypical system.     

An ab initio study of the hyperfine structure in the X2 Pi electronic state of CCCH

The results of an ab initio study of the magnetic hyperfine structure in the X (2)Pi electronic state of CCCH are reported. The potential surfaces for two components of the X (2)Pi electronic state were computed by means of an extensive configuration interaction approach. The electronically averaged hyperfine coupling constants of H and (13)C for (12)C (12)C (12)CH, (13)C (12)C (12)CH, (12)C (13)C (12)CH, and (12)C (12)C (13)CH are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with the help of a variational approach which takes into account the Renner-Teller effect and spin-orbit coupling. The model Hamiltonian is expressed in terms of the normal bending coordinates. It is found that, due to the generally strong geometry dependence of the hyperfine coupling constants, it is necessary to carry out the vibronic averaging of the corresponding functions in order to obtain the values which can be compared to the results of the measurements. The results of the present study help to reliably interpret the experimental data previously published. They also predict the yet unobserved hyperfine structure in excited vibronic states.     

Unusual electron charge density in carboxylic acid. 17O quadrupole coupling in cis-cyclobutane-1,2-dicarboxylic acid

The (17)O NQR frequencies have been measured in cis-cyclobutane-1,2-dicarboxylic acid and the quadrupole coupling tensors have been determined at various temperatures. Two O···H oxygen positions and two O-H oxygen positions are observed, showing the presence of two different types of O-H···O hydrogen bonds in the unit cell. The quadrupole coupling constants at the O-H oxygen positions are approximately 30% lower than the lowest quadrupole coupling constants experimentally observed at the C-O-H positions in other carboxylic acids with either ordered or disordered hydrogen bonds. The O-H distances have been calculated from the (17)O-(1)H dipole-dipole interaction at the O-H oxygen positions. The obtained values are longer than the O-H distances usually found in O-H···O hydrogen bonds with comparable O···O distance, in agreement with the proposed proton exchange O-H···O ? O···H-O, which partially averages the dipole-dipole interaction. The energy difference of the two proton configurations, O-H···O and O···H-O, is calculated from the O-H distances determined by NQR. The temperature dependence of the (17)O quadrupole coupling tensors at the (17)O···H-O oxygen positions is analyzed in the model of proton exchange and the energy differences of the two proton configurations obtained by this analysis agree with the values obtained from the O-H distances. The quadrupole coupling tensors are analyzed in a model based on the Townes and Dailey model. The model shows that the population of an oxygen lone pair orbital is at this oxygen position reduced from 2 to approximately 1.3. The electron electric charge is most probably transferred to the oxygen σ and π electron orbitals. This may be associated with the structure of the cyclobutane ring, where the X-ray data show the presence of two unusually short C-C bonds.     

Symmetry forbidden vibronic spectra and internal conversion in benzene

The spectra of symmetry-forbidden transitions and internal conversion were investigated in the present work. Temperature dependence was taken into account for the spectra simulation. The vibronic coupling, essential in the two processes, was calculated based on the Herzberg-Teller theory within the Born-Oppenheimer approximation. The approach was employed for the symmetry-forbidden absorption/fluorescence, and internal conversion between 1(1)A(1g) and 1(1)B(2u) states in benzene. Vibrational frequencies, normal coordinates, electronic transition dipole moments, and non-adiabatic coupling matrix elements were obtained by ab initio quantum chemical methods. The main peaks, along with the weak peaks, were in good agreement with the observed ones. The rate constant of the 1(1)A(1g)← 1(1)B(2u) internal conversion was estimated within the order of 10(3) s(-1). This could be regarded as the lower limit (about 4.8 × 10(3) s(-1)) of the internal conversion. It is stressed that the distortion effect was taken into account both in the symmetry-forbidden absorption/fluorescence, and the rate constants of internal conversion in the present work. The distortion effects complicate the spectra and increase the rate constants of internal conversion.