PFI-ZEKE photoelectron spectra of the methane cation and the dynamic Jahn-Teller effect

High resolution pulsed-field-ionization (PFI) zero-kinetic-energy (ZEKE) photoelectron spectroscopy has been used to record the photoelectron spectra of CH4, CDH3, CD2H2 and CD4. The observed extensive progression of rotationally resolved transitions between 100,800 cm-1 and 104,100 cm-1 reveals for the first time the complex energy level structure of the methane cation. The high resolution enabled the determination of accurate values for the adiabatic ionization potentials of the different isotopomers. Based on a simple one-dimensional model for the pseudorotation in the different isotopomers, progress has been made towards the understanding of the Jahn-Teller effect at low energies. The static Jahn-Teller distortion in the ion could be determined directly from the vibrationless photoelectron transition in CD2H2. The analysis of the rotational structure in this spectrum with a rigid rotor model leads to an approximate experimental C2v structure. The dynamics of the other methane isotopomers near the adiabatic ionization potentials is dominated by large amplitude vibrational motions between equivalent structures. The corresponding ground state tunneling motions takes place on a picosecond time scale.     

A valence bond analysis of electronic degeneracies in Jahn-Teller systems: low-lying states of the cyclopentadienyl radical and cation

The lowest doublet electronic state of the cyclopentadienyl radical (CPDR) and the lowest singlet state of the cyclopentadienyl cation (CPDC) are distorted from the highly symmetric D(5h) structure due to the Jahn-Teller effect. A valence bond analysis based on the phase-change rule of Longuet-Higgins reveals that in both cases the distortion is due to the first-order Jahn-Teller effect. It is shown that, while for the radical an isolated Jahn-Teller degeneracy is expected, in the case of the cation the main Jahn-Teller degeneracy is accompanied by five satellite degeneracies. The method offers a chemically oriented way for identifying the distortive coordinates.     

Exploring the Jahn-Teller and pseudo-Jahn-Teller conical intersections in the ethane radical cation

We report a theoretical account on the static and dynamic aspects of the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) interactions in the ground and first excited electronic states of the ethane radical cation. The findings are compared with the experimental photoionization spectrum of ethane. The present theoretical approach is based on a model diabatic Hamiltonian and with the parameters derived from ab initio calculations. The optimized geometry of ethane in its electronic ground state (1A1g) revealed an equilibrium staggered conformation belonging to the D3d symmetry point group. At the vertical configuration, the ethane radical cation belongs to this symmetry point group. The ground and low-lying electronic states of this radical cation are of 2Eg, 2A1g, 2Eu, and 2A2u symmetries. Elementary symmetry selection rule suggests that the degenerate electronic states of the radical cation are prone to the JT distortion when perturbed along the degenerate vibrational modes of eg symmetry. The 2A1g state is estimated to be approximately 0.345 eV above the 2Eg state and approximately 2.405 eV below the 2Eu state at the vertical configuration. The symmetry selection rule also suggests PJT crossings of the 2A1g and the 2Eg electronic states of the radical cation along the vibrational modes of eg symmetry and such crossings appear to be energetically favorable also. The irregular vibrational progressions, with numerous shoulders and small peaks, observed below 12.55 eV in the experimental recording are manifestations of the dynamic (E x e)-JT effect. Our findings revealed that the PJT activity of the degenerate vibrational modes is particularly strong in the 2Eg-2A1g electronic manifold which leads to a broad and diffuse structure of the observed photoelectron band.     

One-photon mass-analyzed threshold ionization spectroscopy of 1,3,5-trifluorobenzene: the Jahn-Teller effect and vibrational analysis for the molecular cation in the ground electronic state

One-photon mass-analyzed threshold ionization spectrum of 1,3,5-trifluorobenzene was obtained by using vacuum ultraviolet radiation generated by four-wave difference frequency mixing in Kr. The Jahn-Teller parameters for the e' modes (nu(8)-nu(14)) of 1,3,5-C(6)H(3)F(3)(+) in the ground electronic state needed for spectral analysis were taken from the density functional theory results initially and were upgraded through fits to the experimental results. Excellent agreement was achieved between the experimental and calculated Jahn-Teller energy levels. Assignments of the Jahn-Teller inactive modes were accomplished by referring to the calculated frequencies and the selection rule. The ionization energy of 1,3,5-trifluorobenzene determined from the position of the 0-0 band was 9.6359+/-0.0006 eV.     

Vibrational and electronic study of the methyl viologen radical cation MV+. in the solid state

A complete vibrational analysis (IR, Raman) of the methyl viologen radical cation MV^+., generated either via thermolysis from the solid MV²⁺(Cl⁻)₂ salt, or via chemical reduction from the dictation intercalated in the layered CdPS₃ compound, is reported fpr different isotopic derivatives. The results are discussed with respect to the conformation and the electronic configuration of the radical species, (MV^+.) and (MV^+.)₂.     

Density functional calculations on Jahn-Teller effect of tetrachloromethane cation

Density functional (DF) calculations of the tetrachloromethane cation and its most important competitive process, the formation of CCl⁺₃, were carried out to explain the possible stability of CCl⁺₄. From results obtained with B-LYP and B-P86 methods, it is possible to produce a slight Jahn-Teller (JT) effect for a C_s planar structure of the cation type CCl₂(SINGLE BOND)Cl(SINGLE BOND)Cl⁺ compatible with the experimental data obtained by electron-spin resonance spectroscopy. A complex of C_3v structure CCl⁺₃(SINGLE BOND)Cl which is similar to the previous one found in CF⁺₄ appears when symmetry-broken wave functions are used in HF-LYP and HF-P86 methods. Depending of the DF method employed, either one of the minima [C_s (planar) and C_3v] is the most stable and competes with the dissociation of the molecular ion to give CCl⁺₃. The JT stabilization energy is smaller when the JT active coordinates are considered. © 1997 John Wiley & Sons, Inc.     

Theoretical study of the static Jahn-Teller effect—I. Two-mode vibronic coupling in octahedral halocomplexes with doubly degenerate electronic states

A two-mode E_g-(a_1g+e_g) vibronic coupling is analyzed for octahedral systems. Analytic formula for the adiabatic potential surface (APS) is obtained considering quadratic vibronic terms and anharmonicities of normal vibrations as well. Potential constants, viz. five elastic force constants and three vibronic constants, are evaluated from the numerical map of the APS applying the non-linear regression analysis. Numerical values are obtained for hexahalocomplexes on the CNDO/INDO level of total energy calculations.     

The Jahn-Teller effect in solid state chemistry of transition metal compounds

The general features of the local and cooperative Jahn-Teller effect of dⁿ cations with E_g ground states in octahedral coordination and simple model structures are discussed. Examples of different cooperative Jahn-Teller ordering patterns and of phase transitions from static to partially dynamic and finally fully dynamic Jahn-Teller determined structures are given. While in general a tetragonally elongated coordination of the Jahn-Teller ions is favored, the compressed configuration may be stabilized under certain conditions also. It is demonstrated by some examples that the extent of the Jahn-Teller distortion depends on the symmetry and connection pattern of the polyhedra in the host lattice structure. Finally it is shown that the crossover between high- and low-spin configurations of d⁷ cations is strongly influenced by the additional Jahn-Teller stabilization of the low-spin ²E_g state.     

Jahn-Teller effect in the cyclopentadienyl radical: an example of three mode coupling

The cyclopentadienyl radical C₅H₅· vibronic wavefunctions and energy levels are calculated and used to discuss the vibrational structure of the allowed ²A″₂ ←²E″₁ electronic transition in C₅H₅ and allowed A←E transitions in similar systems in which Jahn-Teller coupling occurs through two or three vibrational modes. As has been pointed out by Alpert and Silbey, the vibrational pattern predicted for single mode coupling is markedly distorted. With larger coupling parameters than those used by Alpert and Silbey, in an E ← A transition (e.g., the benzene Rydberg states) progressions in the individual coupling vibrations cannot be distinguished. In an A ← E transition (e.g., C₅H₅·), the higher progression members lose intensity and combination levels in the coupling vibrations appear. In both cases, a complex pattern of 1-1 hot band splittings results. Comparison is made with the experimental C₅H₅· spectrum, and assignments are suggested for three of the observed A″₂ state frequencies.     

DFT-based studies on the Jahn-Teller effect in 3d hexacyanometalates with orbitally degenerate ground states

The topology of the ground-state potential energy surface of M(CN)(6) with orbitally degenerate (2)T(2g) (M = Ti(III) (t(2g)(1)), Fe(III) and Mn(II) (both low-spin t(2g)(5))) and (3)T(1g) ground states (M = V(III) (t(2g)(2)), Mn(III) and Cr(II) (both low-spin t(2g)(4))) has been studied with linear and quadratic Jahn-Teller coupling models in the five-dimensional space of the epsilon(g) and tau(2g) octahedral vibrations (Tg[symbol: see text](epsilon(g)+tau(2g)) Jahn-Teller coupling problem (T(g) = (2)T(2g), (3)T(1g))). A procedure is proposed to give access to all vibronic coupling parameters from geometry optimization with density functional theory (DFT) and the energies of a restricted number of Slater determinants, derived from electron replacements within the t(2g)(1,5) or t(2g)(2,4) ground-state electronic configurations. The results show that coupling to the tau(2g) bending mode is dominant and leads to a stabilization of D(3d) structures (absolute minima on the ground-state potential energy surface) for all complexes considered, except for [Ti(CN)(6)](3-), where the minimum is of D(4h) symmetry. The Jahn-Teller stabilization energies for the D3d minima are found to increase in the order of increasing CN-M pi back-donation (Ti(III) < V(III) < Mn(III) < Fe(III) < Mn(II) < Cr(II)). With the angular overlap model and bonding parameters derived from angular distortions, which correspond to the stable D(3d) minima, the effect of configuration interaction and spin-orbit coupling on the ground-state potential energy surface is explored. This approach is used to correlate Jahn-Teller distortion parameters with structures from X-ray diffraction data. Jahn-Teller coupling to trigonal modes is also used to reinterpret the anisotropy of magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-), and the (3)T(1g) ground-state splitting of [Mn(CN)(6)](3-), deduced from near-IR spectra. The implications of the pseudo Jahn-Teller coupling due to t(2g)-e(g) orbital mixing via the trigonal modes (tau(2g)) and the effect of the dynamic Jahn-Teller coupling on the magnetic susceptibilities and g tensors of [Fe(CN)(6)](3-) are also addressed.     

Bimolecular hole transfer from the trimethoxybenzene radical cation in the excited state

Bimolecular hole transfer quenching of the 1,3,5-trimethoxybenzene radical cation (TMB*+) in the excited state (TMB*+*) by hole quenchers (Q) such as biphenyl (Bp), naphthalene (Np), anisole (An), and benzene (Bz) with higher oxidation potentials than that of TMB was directly observed during the two-color two-laser flash photolysis at room temperature. From the linear relationships between the inverse of the transient absorption changes of TMB*+ during the second 532-nm laser excitation versus the inverse of the concentration of Q, the rate constant of the hole transfer from TMB*+* to Q was estimated to be (8.5 +/- 0.4) x 10(10), (1.4 +/- 0.7) x 10(11), (1.3 +/- 0.6) x 10(11), and (6.4 +/- 0.3) x 10(10) M(-1)s(-1) for Bp, An, Np, and Bz, respectively, in acetonitrile based on the lifetime of TMB*+*. The estimated rate constants are larger than the diffusion-controlled rate constant in acetonitrile. Short lifetime, high energy, and high oxidation potential of TMB*+* cause the lifetime-dependent quenching process or static quenching process as the major process during the quenching of TMB*+* by Q as indicated by the Ware's theoretical model. The subsequent hole transfer from Q*+ to TMB, giving TMB*+, was found to occur at the diffusion-controlled rate for Bp and An as Q. For Q such as Np and Bz, the dimerization of Q*+ with Q to give dimer radical cation (Q2*+) occurred competitively with the hole transfer from Q*+ to TMB.     

Vibronic dynamics in the low-lying coupled electronic states of methyl cyanide radical cation

Static and dynamic aspects of the Jahn–Teller (JT) and pseudo-Jahn–Teller (PJT) interactions between the ground and first excited electronic states of the methyl cyanide radical cation are theoretically investigated here. The latter involves construction of a theoretical model by ab initio computation of electronic potential energy surfaces and their coupling surfaces and simulation of the nuclear dynamics employing time-independent and time-dependent quantum mechanical methods. The present system represents yet another example belonging to the (E + A)  e JT–PJT family, with common JT and PJT active degenerate (e) vibrational modes. The theoretical results are found to be in very good accord with the recent experimental data revealing that the JT interactions are particularly weak in the ground electronic manifold of methyl cyanide radical cation, On the other hand, the PJT interactions of this ground electronic manifold with the first excited electronic state of the radical cation are stronger which cause an increase of the spectral line density. The effect of deuteration on the JT–PJT dynamics of the methyl cyanide radical cation is also discussed.     

Multimode Jahn-Teller and pseudo-Jahn-Teller interactions in the cyclopropane radical cation: complex vibronic spectra and nonradiative decay dynamics

The complex vibronic spectra and the nonradiative decay dynamics of the cyclopropane radical cation (CP+) are simulated theoretically with the aid of a time-dependent wave packet propagation approach using the multireference time-dependent Hartree scheme. The theoretical results are compared with the experimental photoelectron spectrum of cyclopropane. The ground and first excited electronic states of CP+ are of X2E' and A2E' type, respectively. Each of these degenerate electronic states undergoes Jahn-Teller (JT) splitting when the radical cation is distorted along the degenerate vibrational modes of e' symmetry. The JT split components of these two electronic states can also undergo pseudo-Jahn-Teller (PJT)-type crossings via the vibrational modes of e', a1' and a2' symmetries. These lead to the possibility of multiple multidimensional conical intersections and highly nonadiabatic nuclear motions in these coupled manifolds of electronic states. In a previous publication [J. Phys. Chem. A 2004, 108, 2256], we investigated the JT interactions alone in the X2E' ground electronic manifold of CP+. In the present work, the JT interactions in the A2E' electronic manifold are treated, and our previous work is extended by considering the coupling between the X2E' and A2E' electronic states of CP+. The nuclear dynamics in this coupled manifold of two JT split doubly degenerate electronic states is simulated by considering fourteen active and most relevant vibrational degrees of freedom. The vibronic level spectra and the ultrafast nonradiative decay of the excited cationic states are examined and are related to the highly complex entanglement of electronic and nuclear degrees of freedom in this prototypical molecular system.     

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.     

Conical and glancing Jahn-Teller intersections in the cyclic trinitrogen cation

The ground and electronically excited states of cyclic N(3) (+) are characterized at the equilibrium D(3h) geometry and along the Jahn-Teller distortions. Lowest excited states are derived from single excitations from the doubly degenerate highest occupied molecular orbitals (HOMOs) to the doubly degenerate lowest unoccupied molecular orbitals (LUMOs), which give rise to two exactly and two nearly degenerate states. The interaction of two degenerate states with two other states eliminates linear terms and results in a glancing rather than conical Jahn-Teller intersection. HOMO-2-->LUMOs excitations give rise to two regular Jahn-Teller states. Optimized structures, vertical and adiabatic excitation energies, frequencies, and ionization potential (IP) are presented. IP is estimated to be 10.595 eV, in agreement with recent experiments.     

Transitory forms of carotenoids: triplet state and radical cation

Abstract— Reactions between toluidine blue (a thiazine dye) and carotenoids (β-carotene and zeaxanthine) were studied by flash photolysis, in ethanolic solutions. Two types of reactions were evidenced:

• 1 a triplet-triplet energy transfer from the triplet state of monoprotonated toluidine blue to the carotenoid whose triplet state decays rapidly (t_1/2= 5μsec).
• 2 an electron transfer from the carotenoid to the mono- and bi-protonated triplet states of toluidine blue. This produces a radical-cation of the carotenoid (Car⁺) which decays slowly (t_1/2? 200 μsec) and has a strong absorption band around 900 nm.

     

PMR study of the degenerate electron transfer between 1,2,3-trimethyl-2-phenylbenzimidazoline and its cation radical

The degenerate electron transfer (electron exchange) between 1,2,3-trimethyl-2-phenylbenzimidazoline and the perchlorate of its radical cation has been studied by PMR in deuteriated aceonitrile. We have determined rate constants and activation parameters for this process, and also some hyperfine interaction (HFI) constants for the cation radical, inaccessible by ESR measurements.Translated from Teoreticheskie i Éksperimental'naya Khimiya, Vol. 26, No. 6, pp. 658–663, November–December, 1990.     

A simultaneous eigen valued expression to model the three coupled electronic states with triply and doubly degenerate seams together II

In part I a novel and yet complicated mathematical model to predict the presence of triply degenerate seam was presented and was illustrated its efficiency using some physical models. Here in this part, a discussion on the the model's ability to account for the triple degeneracy found in the potential energy surface is presented in addition to a discussion on the derivatives and its discontinuities and infiniteness at a specific point. Analytical evaluation of derivatives is possible in principle but in practice, numerical approximation to the exact derivatives is the only way out to solve this problem. Two examples (one being physical and the other being chemically realistic) are taken to the probe the above mentioned properties of the proposed simultaneous model. Integration of model function gives finite values everywhere irrespective of the point of degeneracy being present or not. This is just opposite to derivative evaluation.