Vibronic coupling and symmetry breaking in core electron ionization

It is shown that for highly symmetric molecules the ionization of a core electron leads quite generally to a lowering of the symmetry. The breaking of the symmetry is a consequence of the vibronic coupling between nearly degenerate core orbitals of different symmetry. The vibronic coupling leads to strong excitation of non-totally symmetric vibrational modes in addition to the usually observed excitation of totally symmetric modes. As an example, the vibrational structure of the Ols line of the CO₂ molecule is computed on the one-particle level.     

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.     

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.     

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.     

Quasibound continuum states in SiF4 (D2A1) photoionization: photoelectron-vibrational coupling

The authors report a fully vibrationally resolved photoelectron spectroscopy investigation of a nonplanar molecule studied over a range of excitation energies. Experimental results for all four fundamental vibrational modes are presented. In each case significant non-Franck-Condon effects are seen. The vibrational branching ratio for the totally symmetric mode nu1+ is found to be strongly affected by resonant excitation in the SiF4+ (D2A1) photoionization channel. This is shown to be the result of two distinct shape resonances, which for the first time have been both confirmed by theoretical calculations. Vibrationally resolved Schwinger photoionization calculations are used to understand the vibronic coupling for the photoelectrons, both using ab initio and harmonic vibrational wave functions.     

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.     

Treatment of the multimode Jahn-Teller problem in small aromatic radicals

The family of the Jahn-Teller (JT) active hydrocarbon rings, C(n)H(n) (n = 5-7), was analyzed by the means of multideterminantal density functional theory (DFT) approach. The multimode problem was addressed using the intrinsic distortion path (IDP) method, in which the JT distortion is expressed as a linear combination of all totally symmetric normal modes in the low symmetry minimum energy conformation. Partitioning of the stabilization energy into the various physically meaningful terms arising from Kohn-Sham DFT has been performed to get further chemical insight into the coupling of the nuclear movements and the electron distribution.     

Zero-point fluctuations in naphthalene and their effect on charge transport parameters

We calculate the effect of vibronic coupling on the charge transport parameters in crystalline naphthalene, between 0 and 400 K. We find that nuclear fluctuations can cause large changes in both the energy of a charge on a molecule and on the electronic coupling between molecules. As a result, nuclear fluctuations cause wide distributions of both energies and couplings. We show that these distributions have a small temperature dependence and that, even at high temperatures, vibronic coupling is dominated by the effect of zero-point fluctuations. Because of the importance of zero-point fluctuations, we find that the distributions of energies and couplings have substantial width, even at 0 K. Furthermore, vibronic coupling with high energy modes may be significant, even though these modes are never thermally activated. Our results have implications for the temperature dependence of charge mobilities in organic semiconductors.     

Vibronic coupling calculation of the pre-resonance Raman intensities of naphthalene

The relative enhancement of the Raman intensities in the pre-resonance region has been computed for naphthalene, using the vibronic coupling expansion proposed by Albrecht. The relevant vibronic and transition moments have been computed in the CNDO/S approximation, while the normal coordinates of naphthalene have been evaluated using a MINDO/3 program. The experimental pattern of intensities is reproduced in a satisfactory way both for b_3g and a_g vibrations. The most important states and the main vibronic terms in the expansion are individuated and discussed with respect to the vibronic borrowing present in the Fluorescence spectrum of naphthalene.     

Photon-driven charge transfer and Herzberg-Teller vibronic coupling mechanism in surface-enhanced Raman scattering of p-aminothiophenol adsorbed on coinage metal surfaces: a density functional theory study

The chemical enhancement effects in surface-enhanced Raman scattering of p-aminothiophenol (PATP, it is also called p-mercaptoaniline or p-aminobenzenthiol) adsorbed on coinage metal surfaces with single thiol end or trapped into metal-molecule-metal junctions with both thiol and amino groups have been studied by density functional theory (DFT). We focus on the influence of photon-driven charge transfer (PDCT) and chemical bonding interaction (ground-state charge transfer) on the intensity enhancement and frequency shift in the surface Raman spectra of PATP. For comparison, the electronic structures and transitions of free PATP are studied first. The simulated pre-resonance UV Raman spectra illustrate that b(2) modes can be selectively enhanced via vibronic coupling. The fundamentals of all the b(2) modes in the frequency range of 1000 to 1650 cm(-1) are assigned in detail. For PATP adsorbed on coinage metals, the time-dependent-DFT calculations indicate that the low-lying CT excited state arises from the π bonding orbital of molecule to the antibonding s orbital of metallic clusters. Our results further show that the PDCT resonance-like Raman scattering mechanism enhances the totally symmetric vibrational modes and the NH(2) wagging vibration. Finally, the effect of chemical bonding interaction is also investigated. The amino group binding to metals gives a characteristic band of the NH(2) wagging mode with the large blueshift frequency and an intense Raman signal.     

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.     

Nuclear dynamics for a three-state Jahn-Teller model system

We report wavepacket dynamics on a model system with a three-state conical intersection. Quantum wavepacket dynamics using the multiconfigurational time-dependent Hartree method have been carried out for the T ? (e + t(2)) Jahn-Teller problem, using a Jahn-Teller vibronic model Hamiltonian. The effects of the magnitude of the coupling parameters and of the initial position of the wavepacket on the dynamics around the three-state conical intersection have been considered. It was found that the effect of the coupling strength is not dramatic for the population transfer in most cases, but the details of the dynamics and the involvement of the different modes are affected by it.     

Fluorescence spectrum of the benzyl radical in methylcyclohexane at 4.2 K

The fluorescence spectrum of the benzyl radical (BR) is characterized by participation of many totally symmetric vibrational modes with less intensity activeness. To make this point more clear, the fluorescence spectra of the benzyl radical and its deuterated compounds in methylcyclohexane (MCH) have been observed at 4.2 K and detailed vibrational analysis has been carried out. Two non-totally symmetric modes such as nu6b and nu8b play a role of Herzberg-Teller type vibronic coupling together with one totally symmetric mode nu6a. There are only a few progression bands with very weak intensity. These are nu12, nu1 and nu(phi-CH2) vibrational modes.     

Experimental investigation of the Jahn-Teller effect in the ground and excited electronic states of the tropyl radical. Part II. Vibrational analysis of the A 2E"3-X 2E"2 electronic transition

Laser-induced fluorescence (LIF) and laser-excited dispersed fluorescence (LEDF) spectra of the cycloheptatrienyl (tropyl) radical C7H7 have been observed under supersonic jet-cooling conditions. Assignment of the LIF excitation spectrum yields detailed information about the A-state vibronic structure. The LEDF emission was collected by pumping different vibronic bands of the A 2E"3<--X 2E"2 electronic spectrum. Analysis of the LEDF spectra yields valuable information about the vibronic levels of the X 2E"2 state. The X- and A-state vibronic structures characterize the Jahn-Teller distortion of the respective potential energy surfaces. A thorough analysis reveals observable Jahn-Teller activity in three of the four e'3 modes for the X 2E"2 state and two of the three e'1 modes for the A 2E"3 state and provides values for their deperturbed vibrational frequencies as well as linear Jahn-Teller coupling constants. The molecular parameters characterizing the Jahn-Teller interaction in the X and A states of C7H7 are compared to theoretical results and to those previously obtained for C5H5 and C6H6+.     

Allene and pentatetraene cations as models for intramolecular charge transfer: vibronic coupling Hamiltonian and conical intersections

We consider the vibronic coupling effects involving cationic states with degenerate components that can be represented as charge localized at either end of the short cumulene molecules allene and pentatetraene. Our aim is to simulate dynamically the charge transfer process when one component is artificially depopulated. We model the Jahn-Teller vibronic interaction within these states as well as their pseudo-Jahn-Teller coupling with some neighboring states. For the manifold of these states, we have calculated cross sections of the ab initio adiabatic potential energy surfaces along all nuclear degrees of freedom, including points at large distances from the equilibrium to increase the physical significance of our model. Ab initio calculations for the cationic states of allene and pentatetraene were based on the fourth-order M?ller-Plesset method and the outer valence Green's function method. In some cases we had to go beyond this method and use the more involved third-order algebraic diagrammatic construction method to include intersections with satellite states. The parameters for a five-state, all-mode diabatic vibronic coupling model Hamiltonian were least-square fitted to these potentials. The coupling parameters for the diabatic model Hamiltonian are such that, in comparison to allene, an enhanced preference for indirect charge transfer is predicted for pentatetraene.     

Structure and bonding of the vanadium(III) hexa-aqua cation. 2. Manifestation of dynamical Jahn-Teller coupling in axially distorted vanadium(III) complexes

Ground-state spin-Hamiltonian parameters, magnetic data, and electronic Raman spectra of hexacoordinate vanadium(III) complexes are calculated with consideration to the ((3)A (3)E) e vibronic interaction and compared to experimental data. It is shown that the zero-field-splitting of the (3)A(g) (S(6)) ground term may be reduced significantly by the dynamical Jahn-Teller effect, particularly when the pi-anisotropy of the metal-ligand bonding interaction is significant, and the energy of the Jahn-Teller active vibration is comparable to the diagonal axial field. The dynamical Jahn-Teller effect may also give rise to a significant enhancement in the Raman intensity of overtones and higher harmonics of Jahn-Teller active vibrations, when the energies of these transitions fall in the proximity of intra-(3)T(1g) (O(h)) electronic Raman transitions. A simple method of conducting vibronic coupling calculations is described, employing ligand field matrices generated by angular overlap model calculations, which may in principle be applied to any transition metal complex.     

Spectroscopy of the free phenalenyl radical

After benzene and naphthalene, the smallest polycyclic aromatic hydrocarbon bearing six-membered rings is the threefold-symmetric phenalenyl radical. Despite the fact that it is so fundamental, its electronic spectroscopy has not been rigorously scrutinized, in spite of growing interest in graphene fragments for molecular electronic applications. Here we used complementary laser spectroscopic techniques to probe the jet-cooled phenalenyl radical in vacuo. Its spectrum reveals the interplay between four electronic states that exhibit Jahn-Teller and pseudo-Jahn-Teller vibronic coupling. The coupling mechanism has been elucidated by the application of various ab initio quantum-chemical techniques.     

Calculation of the vibronic structure of the photodetachment spectra of CCCl- and CCBr-

The vibronic structure of the closely spaced and strongly coupled X 2Sigma+ and A 2Pi states in the photodetachment spectra of CCCl- and CCBr- has been calculated by considering Sigma-Pi vibronic coupling together with spin-orbit coupling. The stretching modes are treated within the so-called linear-vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While the nonrelativistic vibronic-coupling parameters are of approximately equal strength in CCCl and CCBr, the vibronic-coupling parameters of spin-orbit origin are found to be larger in the latter. The calculated photodetachment spectra of both systems are shown to exhibit a complicated vibronic structure due to strong Sigma-Pi vibronic coupling. The spectral envelopes of the calculated photodetachment spectra exhibit a double-hump reminiscent of strongly coupled Exe Jahn-Teller systems.     

The Jahn-Teller effect in the lower electronic states of benzene cation. III. The ground-state vibrations of C6H6+ and C6D6+

New mass analyzed threshold ionization (MATI) spectra of the molecules C(6)H(6) (+) and C(6)D(6) (+) have been collected using tunable vacuum ultraviolet (VUV) single photon excitation from the neutral ground state and also using two-photon excitation through the 6(1) vibration of the (1)B(2u) S(1) state. Emphasis was placed on obtaining accurate relative intensities of the vibrational lines in order to use this information in the vibronic analysis. The MATI spectra collected from VUV (S(0) originating state), triplet (T(1)), and resonant two photon (S(1)) excitation schemes were compared with Jahn-Teller calculations employing the classical model of Longuet-Higgins and Moffitt to obtain the Jahn-Teller coupling parameters of 3 of the 4 linearly active modes (e(2g) modes 6-9 in Wilson's notation). Franck-Condon factors, including the effects of geometry changes, were calculated from the vibronic wave functions and used to identify the lines in the various spectra. It is found that most of the lines with substantial intensity can be understood using only the modes 1, 6, 8, and 9. Weaker peaks are due to various non-e(2g) modes, but these do not derive intensity through Jahn-Teller coupling. When the effects of geometry change were included, simulations of the spectra from the calculated vibrational energies and intensities were close to the experimental spectra. This verifies the applicability of the model to the understanding of the vibrational structure of this type of molecule, but some variations indicate directions for further improvement of the model.     

Spectroscopy of the A(1B2)-X(1A1) transition of jet-cooled fluorobenzene: laser-induced fluorescence, dispersed fluorescence, and pathological Fermi resonances

A detailed study of the S1((1)B2)-S0((1)A1) electronic transition of jet-cooled fluorobenzene has been carried out using laser-induced fluorescence and dispersed fluorescence (DF) spectroscopies. Analysis of over 40 single vibronic level DF spectra resulted in the assignment of 16 fundamental frequencies in the excited electronic state. Progressions in totally symmetric modes, particularly in the ring-breathing mode nu9, feature in both types of fluorescence spectrum. There is also significant activity in non-totally-symmetric modes, with activity in Franck-Condon (FC)-allowed overtones, FC-forbidden combinations induced by Duschinsky mixing, and symmetry-forbidden transitions induced by the same Herzberg-Teller vibronic coupling mechanism that induces the benzene S1-S0 transition. Fermi resonances (FRs) are extensive throughout the spectrum, especially in the important FC-active a1 modes. A consequence of these extensive FRs is that several important previous assignments are shown to be incorrect and have been reassigned here. Ab initio and density functional theory calculations have also been performed to support the experimental assignments.