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.     

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.     

Complex dynamics at conical intersections: vibronic spectra and ultrafast decay of electronically excited trifluoroacetonitrile radical cation

An ab initio quantum dynamical study is performed here to examine the complex nuclear motion underlying the first two photoelectron bands of trifluoroacetonitrile. The highly overlapping structures of the latter are found to originate from transitions to the five lowest electronic states (viz., X(2)E, A(2)A1, B(2)A2, C(2)A1, and D(2)E) of the trifluoroacetonitrile radical cation. The Jahn-Teller (JT) instability of the doubly degenerate X and, D and their pseudo-Jahn-Teller (PJT) interactions with the nondegenerate A, B, and C electronic states along the degenerate vibrational modes lead to multiple multidimensional conical intersections and complex nuclear trajectories through them. It is found that the JT splitting is very weak in the X and relatively stronger in the D state. However, the PJT couplings play the pivotal role in the detailed shape of the vibronic bands of the radical cation. Ultrafast nonradiative decay of electronically excited radical cation has been examined. The findings of this paper are compared with the experimental data and are also discussed in relation to those observed for the methyl cyanide radical cation.     

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.     

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.     

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.     

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.     

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.     

Theoretical study of the electronic nonadiabatic transitions in the photoelectron spectroscopy of F2O

The photoelectron spectrum of F2O pertaining to ionizations to the ground (X2B1) and low-lying excited electronic states (A2B2, B2A1, and C2A2) of F2O+ is investigated theoretically. The near equilibrium potential energy surfaces of the ground electronic state (X2B1) of F2O and the mentioned ground and excited electronic states of F2O+ reported by Wang et al. ( J. Chem. Phys. 2001, 114, 10682) for the C2v configuration are extended for the Cs geometry assuming a harmonic vibration along the asymmetric stretching mode. The vibronic interactions between the A2B2 and B2A1 electronic states of F2O+ are treated within a linear coupling approach, and the strength of the vibronic coupling parameter is calculated by an ab initio method. The nuclear dynamics is simulated by both time-independent quantum mechanical and time-dependent wave packet approaches. Although the first photoelectron band exhibits resolved vibrational progression along the symmetric stretching mode, the second one is highly overlapping. The latter is attributed to the nonadiabatic interactions among the energetically close A2B2, B2A1, and C2A2 electronic states of F2O+. The theoretical findings are in good accord with the available experimental results.     

Intermolecular interaction in an open-shell pi-bound cationic complex: IR spectrum and coupled cluster calculations for C2H2+-Ar

The intermolecular potential energy surface (PES) of Ar interacting with the acetylene cation in its (2)Pi(u) ground electronic state is characterized by infrared photodissociation (IRPD) spectroscopy and quantum chemical calculations. In agreement with the theoretical predictions, the rovibrational analysis of the IRPD spectrum of C(2)H(2) (+)-Ar recorded in the vicinity of the antisymmetric CH stretching fundamental (nu(3)) is consistent with a vibrationally averaged T-shaped structure and a ground-state center-of-mass separation of R(c.m.) = 2.86 +/- 0.09 A. The nu(3) band experiences a blueshift of 16.7 cm(-1) upon complexation, indicating that vibrational excitation slightly reduces the interaction strength. The two-dimensional intermolecular PES of C(2)H(2) (+)-Ar, obtained from coupled cluster calculations with a large basis set, features strong angular-radial coupling and supports in addition to a global pi-bound minimum also two shallow side wells with linear H-bound geometries. Bound state rovibrational energy level calculations are carried out for rotational angular momentum J = 0-10 (both parities) employing a discrete variable representation-distributed Gaussian basis method. Effective spectroscopic constants are determined for the vibrational ground state by fitting the calculated rotational energies to the standard Watson A-type Hamiltonian for a slightly asymmetric prolate top.     

Imaging the state-specific vibrational predissociation of the C2H2-NH3 hydrogen-bonded dimer

The state-to-state vibrational predissociation (VP) dynamics of the hydrogen-bonded ammonia-acetylene dimer were studied following excitation in the asymmetric CH stretch. Velocity map imaging (VMI) and resonance-enhanced multiphoton ionization (REMPI) were used to determine pair-correlated product energy distributions. Following vibrational excitation of the asymmetric CH stretch fundamental, ammonia fragments were detected by 2 + 1 REMPI via the B1E' <-- X1A1' and C'1A1' <-- X1A1' transitions. The fragments' center-of-mass (c.m.) translational energy distributions were determined from images of selected rotational levels of ammonia with one or two quanta in the symmetric bend (nu2 umbrella mode) and were converted to rotational-state distributions of the acetylene co-fragment. The latter is always generated with one or two quanta of bending excitation. All the distributions could be fit well when using a dimer dissociation energy of D0 = 900 +/- 10 cm(-1). Only channels with maximum translational energy <150 cm(-1) are observed. The rotational excitation in the ammonia fragments is modest and can be fit by temperatures of 150 +/- 50 and 50 +/- 20 K for 1nu2 and 2nu2, respectively. The rotational distributions in the acetylene co-fragment pair-correlated with specific rovibrational states of ammonia appear statistical as well. The vibrational-state distributions, however, show distinct state specificity among channels with low translational energy release. The predominant channel is NH3(1nu2) + C2H2(2nu4 or 1nu4 + 1nu5), where nu4 and nu5 are the trans- and cis-bend vibrations of acetylene, respectively. A second observed channel, with much lower population, is NH3(2nu2) + C2H2(1nu4). No products are generated in which the ammonia is in the vibrational ground state or the asymmetric bend (1nu4) state, nor is acetylene ever generated in the ground vibrational state or with CC stretch excitation. The angular momentum (AM) model of McCaffery and Marsh is used to estimate impact parameters in the internal collisions that give rise to the observed rotational distributions. These calculations show that dissociation takes place from bent geometries, which can also explain the propensity to excite fragment bending levels. The low recoil velocities associated with the observed channels facilitate energy exchange in the exit channel, which results in statistical-like fragment rotational distributions.     

Nonadiabatic quantum dynamics of Br2 in solid Ar: A four-dimensional study of the B to C state predissociation

Quantum dynamics simulations are performed for a diatomics-in-molecules based model of Br₂ in solid Ar which incorporates four nuclear degrees of freedom and four electronic states. The nuclear motions comprise two large amplitude coordinates describing the Br₂ bond distance and an effective symmetry-preserving matrix mode. Two symmetry-lowering harmonic modes are added in the spirit of linear vibronic coupling theory. Initiating the dynamics on the B state by means of an ultrafast laser pulse, nonadiabatic transitions to the two degenerate C states are monitored and the effect of vibrational preexcitation in the electronic ground state is investigated.     

Time-dependent pump-probe spectra of NeBr2

Time- and frequency-resolved pump-probe measurements on NeBr2 have been performed to better characterize its fragmentation dynamics on the B electronic state for vibrational levels in the energy region of the transition from direct vibrational predissociation to intramolecular vibrational relaxation dynamics. Above nu'=20 of the Br2 stretching mode, it was observed that the dependence of lifetime on the vibrational quantum number deviates from the energy-gap law by leveling off in the range of 10 psE transitions of the complex. These transitions are shifted 20 cm(-1) to lower energy from the free Br2 resonances, indicating an E state Ne-Br2 bond energy of 82 cm(-1). Measurements of NeBr2 vibrational predissociation via the delta nu=-2 channel were also performed for nu'=27, 28, and 29. The closing of the delta nu=-1 channel leads to an increase in the lifetimes of these vibrational levels. A new Nd:yttrium aluminum garnet pumped dual optical parametric oscillator/optical parametric amplifier system is described that allows us to conveniently record time-delayed pump-probe spectra with 2-cm(-1) spectral resolution and 15-ps time resolution.     

Mode-specific tunneling dynamics in the ground electronic state of tropolone

The mode specificity of proton-transfer dynamics in the ground electronic state (X (1)A(1)) of tropolone has been explored at near-rotational resolution by implementing a fully coherent variant of stimulated emission pumping within the framework of two-color resonant four-wave mixing spectroscopy. Three low-lying (E(vib) approximately 550-750 cm(-1)) vibrational features, assigned to nu(30)(a(1)), nu(32)(b(2)), and nu(31)nu(38)(a(1)), have been interrogated under ambient, bulk-gas conditions, with term energies determined for the symmetric and antisymmetric (tunneling) components of each enabling the attendant tunneling-induced bifurcations of 1.070(9), 0.61(3), and 0.07(2) cm(-1) to be extracted. The dependence of tunneling rate (or hydron migration efficiency) on vibrational motion is discussed in terms of corresponding atomic displacements and permutation-inversion symmetries for the tropolone skeleton.     

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.     

Time-dependent quantum wave-packet description of the 1pi sigma* photochemistry of phenol

The photoinduced hydrogen elimination reaction in phenol via the conical intersections of the dissociative 1pi sigma* state with the 1pi pi* state and the electronic ground state has been investigated by time-dependent quantum wave-packet calculations. A model including three intersecting electronic potential-energy surfaces (S0, 1pi sigma*, and 1pi pi*) and two nuclear degrees of freedom (OH stretching and OH torsion) has been constructed on the basis of accurate ab initio multireference electronic-structure data. The electronic population transfer processes at the conical intersections, the branching ratio between the two dissociation channels, and their dependence on the initial vibrational levels have been investigated by photoexciting phenol from different vibrational levels of its ground electronic state. The nonadiabatic transitions between the excited states and the ground state occur on a time scale of a few tens of femtoseconds if the 1pi pi*-1pi sigma* conical intersection is directly accessible, which requires the excitation of at least one quantum of the OH stretching mode in the 1pi pi* state. It is shown that the node structure, which is imposed on the nuclear wave packet by the initial preparation as well as by the transition through the first conical intersection (1pi pi*-1pi sigma*), has a profound effect on the nonadiabatic dynamics at the second conical intersection (1pi sigma*-S0). These findings suggest that laser control of the photodissociation of phenol via IR mode-specific excitation of vibrational levels in the electronic ground state should be possible.     

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.     

State-to-state reaction dynamics of CH3I photodissociation at 304 nm

The detailed reaction dynamics of CH(3)I photodissociation at 304 nm were studied by using high-resolution long time-delayed core-sampling photofragment translation spectroscopy. The vibrational state distributions of the photofragment, i.e., CH(3), are directly resolved due to the high kinetic resolution of this experiment for the first time. CH(3) radicals produced from I((3)Q(0+)), I((1)Q(1) <--( 3)Q(0+)), and I((3)Q(1)) channels are populated in different vibrational state distributions. The I((3)Q(0+)) and I((3)Q(1)) channels show only progressions in the nu2'(a2") umbrella bending mode, and the I((1)Q(1) <-- (3)Q(0+)) channel shows both progression in the nu2' umbrella bending mode and a small amount of excitation in the nu1'(a1') C-H stretching mode. The photodissociation processes from the vibrational hot band of CH(3)I (upsilon3 = 1, upsilon3 = 2) were also detected, primarily because of the absorption probability from the vibrational excited states, i.e., hot bands are relatively enhanced. Photofragments from the hot bands of CH(3)I show a cold vibrational distribution compared to that from the vibrational ground state of CH(3)I. The I* quantum yield and the curve crossing possibility were also studied for the ground vibrational state of CH(3)I. The potential energy at the curve crossing point was calculated to be 32 790 cm(-1) by using the one-dimensional Landau-Zener model.