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 and pseudo-Jahn-Teller effects in the anion photoelectron spectroscopy of B3 cluster

The photodetachment spectroscopy of B3- anion is theoretically studied with the aid of a quantum dynamical approach. The theoretical results are compared with the available experimental photoelectron spectra of B3-. Both B3- and B3 possess D(3h) symmetry at the equilibrium configuration of their electronic ground state. Distortion of B3 along its degenerate vibrational mode nu2 splits the degeneracy of its excited C2E' electronic manifold and exhibits (E [symbol: see text] e)-Jahn-Teller (JT) activity. The components of the JT split potential energy surface form conical intersections, and they can also undergo pseudo-Jahn-Teller (PJT) crossings with the X2A1' electronic ground state of B3 via the degenerate nu2 vibrational mode. The impact of the JT and PJT interactions on the nuclear dynamics of B3 in its X2A1'-C2E' electronic states is examined here by establishing a diabatic model Hamiltonian. The parameters of the electronic part of this Hamiltonian are calculated by performing electronic structure calculations and the nuclear dynamics on it is simulated by solving quantum eigenvalue equation. The theoretical results are in good accord with the experimental data.     

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.     

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.     

Photophysics of fluorinated benzene. III. Hexafluorobenzene

A theoretical study of the photoabsorption spectroscopy of hexafluorobenzene (HFBz) is presented in this paper. The chemical effect due to fluorine atom substitution on the electronic structure of benzene (Bz) saturates in HFBz. State- of-the-art quantum chemistry calculations are carried out to establish potential energy surfaces and coupling surfaces of five energetically low-lying electronic (two of them are orbitally degenerate) states of HFBz. Coupling of these electronic states caused by the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type of interactions are examined. The impact of these couplings on the nuclear dynamics of the participating electronic states is thoroughly investigated by quantum mechanical methods and the results are compared with those observed in the experiments. The complex structure of the S(1) ← S(0) absorption band is found to originate from a very strong nonadiabatic coupling of the S(2) (of πσ* origin) and S(1) (of ππ* origin) state. While S(2) state is orbitally degenerate and JT active, the S(1) state is nondegenerate. These states form energetically low-lying conical intersections (CIs) in HFBz. These CIs are found to be the mechanistic bottleneck of the observed low quantum yield of fluorescence emission, non overlapping absorption, and emission bands of HFBz and contribute to the spectral width. Justification is also provided for the observed two peaks in the second absorption (the unassigned "c band") band of HFBz. The peaks observed in the third, fourth, and fifth absorption bands are also identified and assigned.     

Vibronic interactions in the photodetachment spectroscopy of phenide anion

Photodetachment spectroscopy of phenide anion C6H5- is theoretically studied with the aid of electronic structure calculations and quantum dynamical simulations of nuclear motion. The theoretical results are compared with the available experimental data. The vibronic structure of the first, second, and third photoelectron bands associated with the ground X 2A1 and low-lying excited A 2B1 and B 2A2 electronic states of the phenyl radical C6H5 is examined at length. While the X state of the radical is energetically well separated and its interaction is found to be rather weak with the rest, the A and B electronic states are found to be only approximately 0.57 eV apart in energy at the vertical configuration. Low-energy conical intersections between the latter two states are discovered and their impact on the nuclear dynamics underlying the second and third photoelectron bands is delineated. The nuclear dynamics in the X state solely proceeds through the adiabatic path and the theoretically calculated vibrational level structure of this state compares well with the experimental result. Two Condon active totally symmetric (a1) vibrational modes of ring deformation type form the most dominant progression in the first photoelectron band. The existing ambiguity in the assignment of these two vibrational modes is resolved here. The A-B conical intersections drive the nuclear dynamics via nonadiabatic paths, and as a result the second and third photoelectron bands overlap and particularly the third band due to the B state of C6H5 becomes highly diffused and structureless. Experimental photodetachment spectroscopy results are not available for these bands. However, the second band has been detected in electronic absorption spectroscopy measurements. The present theoretical results are compared with these absorption spectroscopy data to establish the nonadiabatic interactions between the A and B electronic states of C6H5.     

Higher order (A+E) multiply sign in circle e pseudo-Jahn-Teller coupling

The pseudo-Jahn-Teller (PJT) coupling of a nondegenerate state A with a twofold degenerate state E by a degenerate vibrational mode e is studied for a general system with a C(3) main rotational axis. The PJT coupling terms up to sixth order are derived by symmetry considerations for this general (A+E) multiply sign in circle e case. The obtained expression for the 3 x 3 diabatic potential energy matrix is found to be closely related to the expression recently developed for the higher order Jahn-Teller case [A. Viel and W. Eisfeld, J. Chem. Phys. 120, 4603 (2004)]. The dynamical PJT coupling, which can arise for states of appropriate symmetry if one of the vibrational modes induces a change of the nuclear point group between D(3h), C(3v), C(3h), and C(3), is discussed. The effect of the higher order PJT coupling is tested by a two-dimensional model study based on the e bending mode of NH(3)(+). The models are analyzed by fitting the two-dimensional potential energy surfaces. The significance of the higher order terms on the nonadiabatic dynamics is demonstrated by quantum wave packet propagations.     

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.     

On the (Emultiply sign in circlee)-Jahn-Teller conical intersections in the 3p(E') and 3d(E") Rydberg electronic states of triatomic hydrogen

The static and dynamic aspects of the Jahn-Teller (JT) interactions in the 3p(E') and 3d(E") Rydberg electronic states of H3 are analyzed theoretically. The static aspects are discussed based on recent ab initio quantum chemistry results, and the dynamic aspects are examined in terms of the vibronic spectra and nonradiative decay behavior of these states. The adiabatic potential-energy surfaces of these degenerate electronic states are derived from extensive ab initio calculations. The calculated adiabatic potential-energy surfaces are diabatized following our earlier study on this system in its 2p(E') ground electronic state. The nuclear dynamics on the resulting conically intersecting manifold of electronic states is studied by a time-dependent wave-packet approach. Calculations are performed both for the uncoupled and coupled state situations in order to understand the importance of nonadiabatic interactions due to the JT conical intersections in these excited Rydberg electronic states.     

The Jahn-Teller effect in the triply degenerate electronic state of methane radical cation

A quantum dynamics study is performed to examine the complex nuclear motion underlying the first photoelectron band of methane. The broad and highly overlapping structures of the latter are found to originate from transitions to the ground electronic state, X(2)T(2), of the methane radical cation. Ab initio calculations have also been carried out to establish the potential energy surfaces for the triply degenerate electronic manifold of CH(4)(+). A suitable diabatic vibronic Hamiltonian has been devised and the nonadiabatic effects due to Jahn-Teller conical intersections on the vibronic dynamics investigated in detail. The theoretical results show fair accord with experiment.     

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.     

Pseudo Jahn-Teller origin of cis-trans and other conformational changes. The role of double bonds

Based on the pseudo Jahn-Teller effect (PJTE) theory, an approach is developed to rationalize and predict the conformations and conformational changes in molecular systems with a common pattern, a double bond. It is shown that starting with the high-symmetry geometry of the environment (in many cases D(2d)), the double bond descends from an e(2) electronic configuration (e is a twofold degenerate MO) which produces a variety of PJT distortions, the main of which is the rotational (b(1)) transformation D(2d) → D(2h) accompanied by the formation of the double bond. Further PJT interactions with higher energy E-states may trigger additional distortions which in D(2h) symmetry are classified as in-plane (e(i)) cis and trans, and out-of-plane (e(o)) chair and boat. The realization of these conformations depends on the positions of the excited E-states and the PJTE parameter values. The two emerging PJTE problems, ((3)A(2) + (3)E(1) + (3)E(2)) ? (e(i) + e(o)) and ((1)A(1) + (1)B(1) + (1)B(2) + (1)E(1) + (1)E(2)) ? (b(1) + e(i) + e(o)), are formulated in the matrix form and provide a general picture of the ground and excited adiabatic potential energy surfaces. Following this scheme in combination with ab initio calculations, the possible conformations and conformational transitions are analyzed for several specific systems including (in increasing complexity) N(2)H(2), C(2)H(4), N(2)(NH(2))(2) and N(2)(C(6)H(5))(2) (azobenzene). The family of molecular systems with a double bond is vast, but the importance of the PJT approach developed here is also in its general validity as it can be applied to any other systems.     

On the vibronic level structure in the NO3 radical. I. The ground electronic state

The model Hamiltonian approach of Koppel et al. [Adv. Chem. Phys. 57, 59 (1984)] is used to analyze the electronic spectroscopy of the nitrate radical (NO3). Simulations of negative ion photodetachment of NO3-, the X 2A2'<--B 2E' dispersed fluorescence spectrum of NO3, and the B 2E'<--X 2A2' absorption spectrum are all in qualitative agreement with experiment, indicating that the model Hamiltonian contains most or all of the essential physics that govern the strongly coupled X 2A2' and B 2E' electronic states of the radical. All 14 bands seen in the dispersed fluorescence spectrum below 2600 cm-1 are assigned based on the simulations, filling in a few gaps left by previous work, and 7 additional bands below 4000 cm-1 are tentatively assigned. The assignment is predicated on the assumption that the nu3 level of NO3 is near 1000 cm-1 rather than 1492 cm-1 as is presently believed. Support for this reassignment (which associates the 1492 cm-1 band with the nu1+nu4 level) comes from both the model Hamiltonian spectrum and a Fourier-transform infrared feature at 2585 cm-1 that is consistent with the large and positive cross anharmonicity between nu1 and nu4 needed for the alternative 1492 cm-1 assignment. An apparent systematic deficiency exists in the treatment of the model Hamiltonian for levels involving nu4. A discussion of the correlation between energy levels in the rigid D3h and C2v limits is illustrative, and provides insight into just how hard it is to treat the degenerate bending coordinate (q4) of NO3 accurately.     

Jahn–Teller Effects in Molecular Cations Studied by Photoelectron Spectroscopy and Group Theory

The traditional “ball‐and‐stick” concept of molecular structure fails when the motion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn–Teller (JT) effect which is very common in open‐shell molecular systems, such as radicals or ions. The JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise symmetric system. Its implications on the dynamics of molecules still represent unsolved problems in many cases. Herein we review recent progress in understanding the dynamic structure of molecular cations that have a high permutational symmetry by using rotationally resolved photoelectron spectroscopy and group theory. Specifically, we show how the pseudo‐Jahn–Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization. The fundamental physical mechanisms underlying the vaguely defined concept of “antiaromaticity” are thereby elucidated. Our investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the JT effect has been discovered and is predicted to exist in all JT systems in which the minima on the potential‐energy surface are separated by substantial barriers.     

Toward the observation of quartet states of the ozone radical cation: insights from coupled cluster theory

Since the discovery of ozone depletion, the doublet electronic states of the ozone radical cation have received much attention in experimental and theoretical investigations, while the low-lying quartet states have not. In the present research, viable pathways to the quartet states from the lowest three triplet states of ozone, (3)A(2), (3)B(2), and (3)B(1), and excitations from the (2)A(1) and (2)B(2) states of the ozone radical cation have been studied in detail. The potential energy surfaces, structural optimizations, and vibrational frequencies for several states of ozone and its radical cation have been thoroughly investigated using the complete active space self-consistent field, unrestricted coupled cluster theory from a restricted open-shell Hartree-Fock reference including all single and double excitations (UCCSD), UCCSD method with the effects of connected triple excitations included perturbatively, and unrestricted coupled cluster including all single, double, and triple excitations with the effects of connected quadruple excitations included perturbatively. These methods used Dunning's correlation-consistent polarized core-valence basis sets, cc-pCVXZ (X = D, T, Q, and 5). The most feasible pathways (symmetry and spin allowed transitions) to the quartet states are (4)A(1)<--(3)A(2), (4)A(2)<--(3)A(2), (4)A(1)<--(3)B(2), (4)A(2)<--(3)B(1), (4)B(2)<--(3)B(1), (4)A(2)<--(1)A(1), (4)B(2)<--(1)A(1), and (4)A(1)<--(1)A(1) with vertical ionization potentials of 12.46, 12.85, 12.82, 12.46, 12.65, 13.43, 13.93, and 14.90 eV, respectively.     

Computational investigation of the Jahn-Teller effect in the ground and excited electronic states of the tropyl radical. Part I. Theoretical calculation of spectroscopically observable parameters

Theoretical calculations are performed for the X2E"2 and A 2E"3 states of the cycloheptatrienyl (tropyl) radical C7H7. An important goal of these calculations is to predict and to guide the analysis of the experimentally observed A 2E"3-X 2E"2 electronic spectrum. Vibrational frequencies of the tropyl radical at the conical intersection and stationary points of its X and A state Jahn-Teller distorted potential energy surfaces are given. Spectroscopically obtainable parameters describing the Jahn-Teller effect are calculated for the X and A electronic states. Additionally, the stabilization energies for the X and A states are computed at the CASSCF(7,7) and EOMEA-CCSD levels of theory using various basis sets.     

Theoretical study of photodetachment processes of anionic boron clusters. I. Structure

Photo-induced electron detachment spectroscopy of anionic boron clusters, B(4)(-) and B(5)(-), is theoretically investigated by performing electronic structure calculations and nuclear dynamics simulations. While the electronic potential energy surfaces (X(1)A(g), ?(3)B(2u), b(3)B(1u), ?(1)B(2u), c(3)B(2g), and B(1)B(2g) of neutral B(4) and X(2)B(2), ?(2)A(1), B(2)B(2), C(2)A(1), D(2)B(1), and E(2)A(1) of neutral B(5)) and their coupling surfaces are constructed in this paper, the details of the nuclear dynamics on these electronic states are presented in Paper II. Electronic structure calculations are carried out at the complete active space self-consistent field-multi-reference configuration interaction level of theory employing the correlation consistent polarized valance triple zeta basis set. Using the calculated electronic structure data suitable vibronic Hamiltonians are constructed utilizing a diabatic electronic basis and displacement coordinates of the normal vibrational modes. The theoretical results are discussed in relation to those recorded in recent experiments.     

A laser spectroscopic study of the X2pi(g), A2pi(u), and B2sigma+ states of BS2: Renner-Teller, spin-orbit, and K-resonance effects

The lowest-lying vibronic levels of the X, A, and B states of BS2 have been investigated at high resolution using a combination of room-temperature absorption and supersonic jet data. In both cases, the BS2 radical was prepared in an electric discharge using a precursor gas mixture of BCl3,CS2, and either helium or argon. Extensive absorption spectra were obtained for the 0(0)0 and 2(1)1 bands of the A2pi(u)-X2pi(g) electronic transition in the visible. The A-X 2(1)1 and B2sigma(u)(+)-X2pi(g) 2(1) bands of jet-cooled BS2 were also studied with laser-induced fluorescence techniques. By fitting the 0(0) bands of both electronic transitions simultaneously, we were able to precisely determine the spin-orbit splittings in both the A and X states. Similarly, the 21 bands were fitted in a merged analysis in order to determine the relative separations of the vibronic components of the ground and first excited state bending levels as accurately as possible. Due to a large spin-orbit splitting and small Renner-Teller interaction, the A state bending level shows small but definite K-resonance effects, which were fitted using a full matrix for the four components of upsilon2' = 1. The resulting parameters were used along with previously published data to refine the Renner-Teller analyses in both the A2pi(u), and X2pi(g) electronic states. Where possible, the fitted constants and observed boron isotope splittings have been shown to be in accord with theoretical estimates of their sign and magnitude.     

Relativistic Jahn-Teller effects in the photoelectron spectra of tetrahedral P4, As4, Sb4, and Bi4

The group-V tetrahedral cluster cations P(4)(+), As(4)(+), Sb(4)(+), and Bi(4)(+) are known to exhibit exceptionally strong Jahn-Teller (JT) effects of electrostatic origin in their (2)E ground states and (2)T(2) excited states. It has been predicted that there exist, in addition, JT couplings of relativistic origin (arising from the spin-orbit (SO) operator) in (2)E and (2)T(2) states of tetrahedral systems, which should become relevant for the heavier elements. In the present work, the JT and SO couplings in the group-V tetramer cations have been analyzed with ab initio relativistic electronic structure calculations. The vibronic line spectra and the band shapes of the photoelectron spectra were simulated with time-dependent quantum wave-packet methods. The results provide insight into the interplay of electrostatic and relativistic JT couplings and SO splittings in the complex photoelectron spectra of these systems.