Jahn-Teller Coupling Constants Research Articles

Photoelectron spectroscopic study of the E ⊗ e Jahn–Teller effect in the presence of a tunable spin–orbit interaction. II. Rovibronic analysis of the 2E ground state of CH3CI+

The PFI-ZEKE photoelectron spectrum of the CH3Cl+ E ← CH3Cl transition was recorded in the range 90900–93400 cm−1 following single-photon excitation from the ground state. The spectrum consists of well-resolved spin-vibronic bands, some of which with partially resolved rotational structure, and provides new information on the combined effects of the Jahn–Teller and spin–orbit interaction in the E ground state of CH3Cl+. The analysis of its spin-rovibronic structure reveals a weak linear Jahn–Teller effect along the H3C–Cl bending e mode (ν6) and enabled the derivation of Jahn–Teller coupling constants along ν6, rotational constants, and spin–orbit interaction parameters for the E ground state of CH3Cl+. The Jahn–Teller effect is dynamical in the ground state of CH3Cl+ and the photoelectron spectrum does not provide evidence for a reduction of the molecular symmetry to Cs symmetry. Weak rotational satellite bands were observed in transitions to several excited vibrational levels of CH3Cl+ and interpreted in terms of the spin-rovibronic photoionization selection rule derived in the analysis of the photoelectron spectrum of CH3I (M. Grütter, J. M. Michaud and F. Merkt, J. Chem. Phys. 134, 054308 (2011)). Compared to the ground state of HCl+ ( cm−1), the spin–orbit splitting is strongly reduced to cm−1. The reduction is primarily attributed to an electronic effect and, to a lesser extent, to the quenching of the spin–orbit interaction by the Jahn–Teller effect .

Experimental investigation of the Jahn-Teller effect in the ground and excited electronic states of the tropyl radical. Part II. Vibrational analysis of the ÃE3″2-X̃E2″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+.

Conical intersections: A perspective on the computation of spectroscopic Jahn–Teller parameters and the degenerate ‘intersection space’

We present a perspective on the computation and interpretation of force constants at points of symmetry-induced (Jahn-Teller) conical intersection. Our method is based upon the projection of the 'branching space' from the full (3N - 6)-dimensional Hessian for each component of a degenerate electronic state. For Jahn-Teller active molecules, this has the effect of removing the linear Jahn-Teller coupling from all but the interstate coupling and gradient difference vectors. The quadratic coupling constants are determined by the splitting of the harmonic vibrational frequencies within degenerate vibrational normal coordinates of the 'intersection space'. The potential energy surface topology along these normal modes is analogous to the Renner-Teller effect occurring in orbitally degenerate linear molecules. Our methodology gives a straightforward theoretical analysis of the various Jahn-Teller intersections and allows the determination of the seam curvature. Thus, we are in a position to compute the various Jahn-Teller coupling constants, in a particular coordinate system, and in addition to determine the nature of the high-symmetry Jahn-Teller geometry (i.e., minimum or saddle-point on the seam). We illustrate these concepts with various examples of different Jahn-Teller conical intersections in some small molecules.

Calculation of the Jahn-Teller effect in benzene cation: Application to spectral analysis

Ab initio calculations have been performed for the cations of benzene, C6H6, and its fluorinated analogs, C6F6 and C6H3F3. Calculated molecular parameters characterizing the Jahn-Teller potential energy surface (PES) are very consistent with those derived from the spectra of C6F6+ and C6H3F3+. However the calculated Jahn-Teller stabilization energy for the benzene cation is roughly three times greater than that previously reported experimentally. With the aid of the calculated values, a more complete analysis of the available spectral data for C6H6+ and C6D6+ is performed, with an emphasis on the data from ZEKE experiments and IR spectra of the Ar⋅C6H6+, Ne⋅C6H6+, and Ar⋅C6D6+ complexes. The comprehensive analysis reveals Jahn-Teller activity in 3 e2g modes for C6(H/D)6+ and provides values for their vibrational frequencies, linear and quadratic Jahn-Teller coupling constants, as well as quadratic coupling constants for several other degenerate modes. These new molecular parameters are generally in good agreement with the corresponding values derived from the ab initio calculations and produce a total Jahn-Teller stabilization energy in good agreement with the computed value.

Pseudo Jahn–Teller origin of formaldehyde molecular geometry in excited states

The pseudo Jahn–Teller effect is employed to explain the origin of the out-of-plane displacement of the oxygen atom (bending of the C–O group) in the excited singlet 1A2 and triplet 3A2 electronic states of formaldehyde which is planar in the ground state. The ground state, the excited 1A2 and 3A2 states, and several higher excited 1B2 and 3B2 states formed by one-electron MO excitations are calculated in a single-transition approximation and by including configuration interaction with single and double excitations using the GAMESS program. With these data the corresponding pseudo Jahn–Teller coupling constants and the contribution of the B2 states to the instability of the A2 states with respect to the oxygen out-of-plane displacements is estimated, and an explanation of both the larger instability of the triplet state as compared with the singlet state and the elongation of the C–O bond in the bent states is obtained.

Multiple surface intersections and strong nonadiabatic coupling effects between the D̃ 2E 1 u and Ẽ 2B 2 u states of C 6H 6+

The multimode vibronic interactions between the D̃ 2E 1 u and Ẽ 2B 2 u excited states of the benzene radical cation are investigated theoretically. In first order of the nuclear displacements the four Jahn–Teller active (e 2 g ) vibrational modes can couple the two electronic states. Ab initio Green's function calculations including electron correlation effects have been carried out to determine the pertinent inter-state coupling constants as well as the Jahn-Teller coupling constants for the D̃ 2E 1 u state. After a slight readjustment of some of the parameters the diffuse shape of the corresponding photoelectron bands is well reproduced by theory. Ensuing wave-packet dynamical calculations reveal a Ẽ → D̃ electronic population decay (internal conversion process) on a timescale of several fs. The importance of this ultrafast population decay for the fragmentation dynamics of electronically excited C 6H 6 + is pointed out.

Self-trapped hydrogen states in metals determined from quantum mechanical calculations using potentials based on ab initio data: I. Hydrogen isotopes in Pd

Ab initio pseudopotential calculations for H in Pd are used in order to construct an auxiliary short-ranged host-lattice-particle potential which well reproduces the large number of available ab initio data. This potential (instead of an empirical potential as employed in previous treatments) is used in a quantum mechanical calculation of hydrogen as well as of mu + and pi + states in Pd, which takes into account the dependence of the lattice relaxation on particle mass and particle state. These calculations allow us to determine Jahn-Teller coupling constants of excited states and the dependence of lattice displacements on the isotopic mass. It is found that coupling to lattice modes with E-symmetry is dominant. The effect of lattice relaxation on the total energy difference if hydrogen is localized at tetrahedral or octahedral sites and on the excitation energies as measured by inelastic neutron scattering experiments is also discussed.

Point-charge model for vibronic coupling constants of metal atom trimers

A simple point charge model is proposed for estimating the relative size of Jahn-Teller (JT) and pseudo Jahn-Teller (PJT) coupling constants in metal trimers with a single ‘active’ valence electron. Applied to the B-system of the two-photon ionization spectrum of Na3 it correctly reproduces the unexpected relative smallness of the linear JT coupling in the final electronic state. General implications for the nuclear dynamics in metal trimers and possible extensions of the approach are discussed.

Peierls instabilities in one-dimensional systems with Jahn-Teller-active monomers

A one-dimensional system is investigated which consists of monomers with Jahn-Teller-active vibrational coordinates. Peierls distortions in the ground states of the half- and quarter-filled systems are studied as a function of the electron-lattice and Jahn-Teller coupling constants. For both degrees of filling and for all the values of the coupling constants the band structure of the ground state is doubly degenerate. The interrelation is discussed between the present system and systems where the active internal degrees of freedom are not of the Jahn-Teller type.

The role of the Jahn-Teller effect and of the intermediate ligand field in the optical spectra of Cr3+-doped GaP and GaAs

The Jahn-Teller coupling constants for the ground state (4T1) and first excited state (4T2) of Cr3+-doped GaP and GaAs were evaluated by the angular overlap model. The calculation could provide quantitative justification for the recent proposal of Dunn and Bates (1987) according to which the Jahn-Teller effect is responsible for the differences observed in the optical spectra of these systems. The importance of configuration mixing in the ground state is discussed.

State mixing and the preferred jahn-teller coupling in cubic fx systems

The effect of the inclusion of state mixing is examined for the calculation of the Jahn-Teller coupling constants of the two Γ 8 states of f 1 systems in O h symmetry, both ML 6 and ML 8 species being considered. For the values of the spin-orbit coupling constants and ligand-field splitting parameters usually encountered, the results differ significantly from the strong-field limit values, but only slightly from those of the weak-field limit. For ML 6 systems the available estimates for the e λ and ∂ e λ ∂R parameters of the angular overlap model, together with the appropriate force-constant ratios, predict dominant coupling to the ϵ g mode for the Γ 8( 2 F 5 2 : 2 T 2u) level, whilst coupling to the τ 2g mode should prevail for the Γ 8( 2 F 7 2 : 2 T 1u) state. For ML 8 species the calculations similarly lead to the expectation of predominant τ 2g(δ) coupling for Γ 8( 2 F 5 2 : 2 T 1u), with prevailing ϵ g coupling for Γ 8 ( 2 F 7 2 : 2 T 2u). The results suggest the general adequacy of the weak-field limit results for cubic f x systems and, as an example, the T 1 and T 2 states for 3 H 4 of f 2, O h ML 6, systems are thus briefly treated.

Jahn–Teller stabilization energies for ZnS:Mn and ZnSe:Mn excited states obtained by the angular overlap model

Linear Jahn–Teller coupling constants are obtained by the angular overlap model. A comparison with the data published recently [Parrot et al., J. Chem. Phys. 87, 1463 (1987)] is made in order to demonstrate the considerable improvement in the calculated Jahn–Teller coefficients when the parameters of the angular overlap model are extracted from a spectral analysis of the systems under consideration.

Angular overlap model for the Jahn–Teller coupling constants in the orbital triplet states of d5 ions: Case of Mn2+ in ZnS and ZnSe

A theoretical determination of the Jahn–Teller coupling constants of d5 ions in tetrahedral clusters is performed in the framework of the angular overlap model and the quasimolecular approximation. It is shown that the angular model correctly predicts the trend of the preponderant coupling of the 4T1(G) and 4T2(G) levels of Mn2+ in MnS4 and MnSe4 to the E-vibrational effective mode. Finally, the limitations of this model are discussed. In particular, it is shown that more elaborated covalent models are needed to interpret the Jahn–Teller coupling coefficients of the 4E and 4A1 levels of d5 configurations and to determine the influence of the crystal on the clusters.

Jahn-Teller activity in eight-coordinate O h f x systems

The angular overlap model is used for the calculation of the Jahn-Teller coupling constants for O h, MX 8, f x systems in the ( LSJM J ) basis. For the 5f 1 anion, [UF 8] 3−, the Γ 8 ground state is predicted to show substantial Jahn-Teller activity for coupling to the τ 2g bending mode, with E JT comparable to ω, a result consistent with the available magnetic susceptibility data.

Calculations of Jahn-Teller coupling constants in the weak-field basis via the angular overlap model: a simple operator equivalent technique

Within the framework of the angular overlap model the matrix elements of the linear Jahn-Teller operator may easily be calculated in the weak-field basis in terms of simple operator equivalents. The method is applied to the calculation of the 〈 M J |∂ V/∂ Q| M j 〉 matrix elements for the | LSJMj〉 ground states of t x species ( x = 1) − 13) in ) * symmetry.

Rcenter in KCl. II. Line-shape calculation of theR2band

The optical-absorption properties of the $R$ center in KCl are investigated theoretically. The single-phonon-sideband line shapes associated with the creation of ${A}_{1}$- and $E$-symmetry phonons are simulated for the ${R}_{2}$ band, where self-consistent-field molecular-orbital point-ion-model wave functions are employed. The electron-lattice interaction is treated in two approximations: a Ritter and Markham approach appropriate to relatively diffuse wave functions, and a Green's-function approach appropriate to relatively compact wave functions. The Green's-function method admits a treatment of perturbed-lattice dynamics although such an extension is not possible in the Ritter and Markham approach. The Green's-function method appropriate to the perfect-lattice spectrum gives results which most closely agree with experiment. The calculated line shapes, Huang-Rhys factors, and effective Jahn-Teller coupling constants and frequencies are presented.

Trap depth in Tl +-like phosphors: Deduction of Jahn-Teller coupling constants

The relationship between trap-depth and Stokes shift in impurities with the sp electronic configuration is generalized and explained. A new simple method is developed to estimate the Jahn-Teller coupling constants from spectroscopic and trap-depth data.

Low temperature luminescence spectra of the d 10s 2 complexes Cs 2MX 6 (M = Se, Te and X = Cl, Br). The Jahn—Teller effect in the Γ −4( 3T 1u) excited state

The emission spectra of the title compounds in microcrystalline form have been measured at 10 K. The extensive vibrational progression in the e g mode is indicative of a tetragonal Jahn—Teller distortion in the Γ − 4( 3T 1u) excited state. The vibronic coupling of a threefold electronic state with a doubly degenerate e g mode (T—e coupling), linear in the nuclear coordinates, has been reinvestigated considering spin—orbit coupling up to second order perturbation on energy levels which result from an a 1 1gt 1 1u electron configuration. For an estimation of Jahn—Teller coupling constants, the intensity distributions in the progressions were compared with the theoretical line shape functions which were obtained from a model which also permits the determination of potential energy minima and vibrational fundamentals of the excited state. The unusually large increase in the e g vibrational frequency compared to the ground state is due to Jahn-Teller forces which distort the potential surface, yielding steeper excited state energy curves.

Angular-overlap calculation of the Jahn-Teller stabilization energies for f-orbital degeneracies

The angular-overlap model is applied to the calculation of the linear Jahn-Teller coupling constants for f-orbital degeneracies. The MX/sub 6/, O/sub h/, chromophore is treated as representative of the highest symmetry commonly occurring in the lanthanide and actinide series, and it is shown that, even when spin-orbit effects are taken into account, 5f orbital degeneracies may lead to significant Jahn-Teller stabilization energies. The operation of this effect for F/sup 1/ GAMMA/sub 8/ states is considered. 2 tables.

Jahn-Teller coupling constants evaluated by the angular overlap model

It is shown how the characteristic features of the angular overlap model allow a straightforward evaluation of the Jahn-Teller coupling constants. Moreover, differently from the crystal field or more general molecular orbital approaches, the expressions we have obtained contain a very limited number of parameters and have the advantage of the transferability from one chromophore MXq to another MXp of different symmetry. In the present communication an outline of the method is given and some applications to inorganic complexes and to biological molecules containing transition metal ions are presented.