Quadratic Vibronic Coupling Research Articles

The phonon and energy splitting in the D3d minima for the T1u×hg Jahn-Teller system

In C60 molecules, the lowest unoccupied molecular orbital has T1u symmetry. The orbital is easily occupied by an electron through molecular inner excitation or doping and becomes an active Jahn-Teller (JT) electronic state. The T1u-hg- JT system is formed by the coupling of such an electronic state to a five-fold degenerate hg mode. The linear vibronic coupling in the system forms a trough on the adiabatic potential surface of the system, but D5d and D3d minima will be warped while considering the quadratic vibronic coupling. Phonon states in minima will have anisotropic effects and the vibrational frequencies should be different in different directions. This phenomenon will further affect the energy distribution, phonon overlap and tunneling effect in the system. The anisotropic effect is carefully studied in detail for D3d-minima. The energies and vibrational frequencies are calculated using unitary shift transformation, pick-Pryce method, scale transformation and energy minimization procedure. The energy gap and the variation of perturbation energy in minima are obtained in this paper and the same physical quantities in trough are derived through changing the values of the quadratic coupling constants.

Mode mixing via resonance Raman excitation profiles

In the case of linear+quadratic vibronic coupling with an arbitrary number of configurational coordinates, the exact equation for the resonance Raman amplitude has been derived via the absorption Fourier transform. There are some actual cases when this equation has simple solutions: change of vibrational frequency at the electronic transition without mode mixing, mixing of two modes, mixing of modes with close frequency. The corresponding transform relations between Raman amplitudes (→excitation profiles) and the absorption are given, which allow to determine the mixing parameters, vibrational frequencies as well as the linear vibronic coupling parameters.

All mode dynamics at the conical intersection of an octa-atomic molecule: Multi-configuration time-dependent Hartree (MCTDH) investigation on the butatriene cation

The ground state and the first excited electronic states of the octa-atomic butatriene cation (C4H4+) exhibit a multidimensional conical intersection. This intersection is energetically low lying and is located in the vicinity of the Franck–Condon region of the neutral molecule’s ground state. The conical intersection thus dominates the nuclear dynamics in ionization processes of this molecule. This is a particularly interesting example of vibronic coupling, introducing what appears to be a new, structured band into the energy spectrum. In this work, the potential energy surfaces and their intersection are investigated by ab initio methods. A diabatic model Hamiltonian including all possible linear, quadratic and bilinear vibronic coupling terms is introduced, with coupling constants determined by a fit to the ab initio data. The nuclear dynamics of all 18 vibrational modes is then evaluated by propagating the wave packet using the multi-configuration time-dependent Hartree method. Finally, the photoelectron spectrum of butatriene is computed and compared with the experimental one.

Two-dimensional vibrational spectroscopy. VII. Investigation of the vibronic and vibrational couplings by using novel triply resonant two-dimensional vibrational spectroscopies

A single vibrational coherence state can be created by using either vibrationally resonant infrared field-matter interactions or Raman transitions induced by the electronically off-resonant fields. Then, the two-dimensional (2D) vibrational coherence created by two such interactions can be probed by using electronically off-resonant optical pulse via scattering by the 2D transient grating. However, due to the off-resonant field-matter interactions during the probing process, the signal intensity is likely to be small. Thus, in this paper, the cases when the 2D transient grating is probed by electronically resonant optical pulse are theoretically considered and the associated nonlinear response functions are investigated. It turns out that these novel 2D vibrational spectroscopic methods utilizing an electronically resonant probe pulse can be used to study both the linear and quadratic vibronic coupling strengths of molecules in either isotropic or anisotropic condensed phases, in addition to the vibrational anharmonicity and nonlinearity of the coordinate dependencies of the dipole moment, polarizability, and hyperpolarizability.

Multiple lines of conical intersections and nondegenerate ground state in T⊗t2 Jahn–Teller systems

We have investigated the T⊗t2 Jahn–Teller problem with linear and quadratic vibronic coupling including a fourth-order term. First, numerical calculations of the lowest vibronic states were carried out by direct diagonalization of the Hamiltonian. The results show that the energy level of the ground vibronic state, which is triply degenerate T for small quadratic coupling g values, intersects the next A level with increasing g, thus realizing the nondegenerate ground state at sufficiently large g values. This result reverses the long-standing belief that the ground vibronic state for the T⊗t2 system has the same degeneracy and symmetry T as the initial electronic state. To explain these results in terms of Berry phase requirements and conical intersections, the adiabatic potential energy surface of the system is analyzed, and the relationships among the type and number of minima, conical intersections, and relevant tunneling paths are revealed. Depending on the vibronic coupling parameter values, there are four trigonal minima and six orthorhombic saddle points, which become minima at large g values, plus ten lines of conical intersections on the lowest potential energy surface. The barriers between the minima are significantly increased near the lines of conical intersections where the Born–Huang terms diverge. For small enough quadratic coupling, only four lines of conical intersections that originate from the highest symmetry point and proceed along the four trigonal directions are significant in determining the Berry phase, and the triply degenerate ground T state is obtained. By increasing the quadratic coupling parameter, the remaining six lines of conical intersections approach the point of highest symmetry, thus allowing for alternative tunneling paths and Berry phases which lead to the nondegenerate A ground state. This explanation of the origin of the nondegenerate ground state for some range of values of the vibronic coupling parameters is strengthened by model calculations of tunneling splitting.

Cooperative jahn-teller coupling in the manganites

The cooperative Jahn-Teller coupling between the Mn e(g) electrons and the oxygen octahedral distortions in LaMnO3 is studied using ab initio density-functional calculations and tight-binding models. The linear and quadratic vibronic coupling parameters are calculated using density-functional methods. It is shown that the cooperative Jahn-Teller coupling, primarily due to the interoctahedral electron hopping (band structure term), leads to the ordering of the octahedral distortion and simultaneously to orbital ordering. The coupling results in a two-minima adiabatic potential surface in the solid, instead of the three-minima "Mexican-hat" surface for the isolated octahedron.

Symmetry vibronic wavefunction basis set and Hamiltonian representation for XY 3Z molecules near a doubly degenerate Jahn-Teller electronic state in the C 3v point group

Methodology based on the crude adiabatic approximation is presented for the complete linear and quadratic vibronic coupling of a degenerate E electronic state to the 3e 1 and 3e vibrational modes in the case of XY 3Z molecules with C 3v symmetry. First we present a method for building a symmetry adapted vibronic wavefunction basis set which block diagonalizes the Hamiltonian representation. Secondly we report the representation of the electronic Hamiltonian in the crude adiabatic approximation for XY 3Z molecules with C 3v symmetry. Computer codes developed for solving the vibronic coupling are also briefly reviewed. Finally some results are given with reasonable force constants and different choices of coupling constants for the limited dynamic Jahn-Teller E⊗e coupling.

Resonance Raman activity in odd quanta of the trans bending vibration of acetylene: Strong vibronic coupling in the X̃ to à and X̃ to B̃ transitions

Resonance Raman spectra of acetylene with excitation at 204 and 178 nm in the region X̃→Ã( 1Σ g→ 1Σ − u in D ∞h) and X̃→B̃( 1Σ + g→ 1Δ u in D ∞h) transitions exhibit very strong activity in both even and odd quanta of the π g( v 4) trans bending vibration. Enhancement of the two-quantum even overtone is expected from linear vibronic activity in these forbidden transitions resulting in quadratic (C-term) Raman activitiy. The higher even quanta overtone activity is consistent with strongly bent excited states or nonlinear vibronic coupling. The induction of intensity in the odd overtones of this non-totally symmetric vibrational mode, however, requires mixed linear and quadratic vibronic coupling involving two different allowed excitations (to states of 1Π u and 1Σ + u symmetry).

Homogeneous lineshapes and shifts of the b 1∑ + ← X 3∑ − transition in matrix-isolated NH: comparison with quadratic coupling theory

The lack of linear electron-phonon coupling in the b 1∑ + ← X 3∑ − transition of matrix-isolated NH in rare gases gives rise to narrow rotational lines without phonon sidebands. Asymmetric homogeneous broadening and a systematic shift to higher frequencies of the QP (0) ZPL in solid Kr has been studied systematically in the range 5–40 K. An improved version of a recently proposed non-perturbative theory of quadratic vibronic coupling is presented, and applied to the experimental result. Assuming coupling to a single low-frequency pseudolocal mode of 10 cm −1, and a state-to-state frequency change of 1.5 cm −1, excellent agreement between observed and calculated T-dependent lineshapes has been obtained. In particular, the increasing asymmetry of the line, which is purely Lorentzian at low temperature, is reproduced quantitatively.

Topological phase in molecular bound states: Application to the E⊗e system

We extend recent works of Berry, Simon, and others on the evolution of adiabatic wave functions in parameter spaces with nontrivial global geometry, to show the interesting ways in which wave functions can acquire nonintegrable phase (commonly termed Berry’s phase, geometric phase, or topological phase) upon transport along paths in the parameter space. We emphasize the case of arbitrary paths on the Born–Oppenheimer potential energy surfaces (the parameter space of the electronic states in an isolated molecule) of the linear plus quadratic E⊗e Jahn–Teller system. It is found that these surfaces are degenerate not only at the origin but also at three other, equivalent points, which lie on a radius ρ=2k/g. Here k and g are the linear and quadratic vibronic coupling constants, respectively. This radius is then shown to mark a sharp transition between Jahn–Teller behavior, characterized by half-odd-integral vibronic angular momentum, and Renner–Teller behavior, which has integral angular momentum. Finally, we examine the conditions necessary for adiabatic evolution in the E⊗e system, and the observable consequences of the geometric phase.

Vibrational relaxation and hot luminescence in impurity centres with a strong vibronic coupling

The results of theoretical and experimental study of vibrational relaxation processes in impurity centres with a strong electron-phonon interaction are presented. General expressions are obtained which describe the temporal evolution of the configurational-coordinate distribution function and the envelope of the emission spectrum consisting of ordinary and hot luminescence. The problem is solved exactly in the harmonic approximation with allowance made for both linear and quadratic vibronic coupling providing a small number of actual configurational coordinates. The hot luminescence bands in KI-Tl positioned at 3.1 and 2.25 eV are detected. The computations show that in Tl+ centres the main portion of the excess vibrational energy relaxes in a time shorter than the mean period of vibrations ( approximately=0.5 ps) and, therefore, the observed spectral features are caused by the first classical turning point in the configurational-coordinate relaxation law. Thus, the centres under study serve as an example of ultrafast relaxing systems. Other weak spectral features are related with the complicated structure of adiabatic potential surfaces in the excited state and are interpreted as a barrier and post-tunnel hot luminescence.

Anomalies of transverse dielectric susceptibility in DyVO 4 and DyAsO 4 Jahn-Teller crystals, caused by quadratic vibronic coupling

The transverse dielectric susceptibility χ ⊥ in DyVO 4 and DyAsO 4 crystals is examined theoretically. The terms of quadratic vibronic coupling, which contain as the optical E u modes so the soft acoustic branch or the electron order parameter, are taken into account. Such coupling is shown to lead to anomaly of χ ⊥ near the temperature of Jahn-Teller structural phase transition. From the experimental data the constants of the quadratic vibronic coupling are appreciated.

Effect of quadratic interactions on the resonance raman scattering of T × t 2 jahn-teller systems

Raman excitation profiles and depolarization dispersion curves are calculated for T × t 2 Jahn-Teller systems that are subject to quadratic vibronic (Renner-Teller) coupling as well as frequency changes of the active vibrational mode.

The assignment of the benzene first-ionization rydberg spectrum via J-T splittings involving linearly inactive modes

In this paper we report the first identification of a Jahn-Teller (J-T) splitting (≈ 160 cm −1) arising via quadratic vibronic coupling in a mode which is non-active in the linear J-T coupling. This splitting has been detected in the hot-band structure of the out-of-plane mode v 20(e 2u) in the Rydberg spectrum of benzene converging to the first ionization limit. This observation enables us to resolve the long-standing controversy with respect to the assignment of the relevant Rydberg spectrum.

Resonance Raman profile with consideration for quadratic vibronic coupling

A relation is found between the first-order Raman profile and the absorption spectrum of a scattering centre with regard to the quadratic vibronic coupling in a zero-temperature case. Two non-degenerate electronic states of the centre are considered, the adiabatic and Condon approximations are used, and the vibrations of the centre are assumed to be harmonic.