Jahn-Teller effect in van der Waals complexes; Ar-C6H6 + and Ar-C6D6 +

The two asymptotically degenerate potential energy surfaces of argon interacting with the X (2)E(1g) ground state benzene(+) cation were calculated ab initio from the interaction energy of the neutral Ar-benzene complex given by Koch et al. [J. Chem. Phys. 111, 198 (1999)] and the difference of the geometry-dependent ionization energies of the complex and the benzene monomer computed by the outer valence Green's function method. Coinciding minima in the two potential surfaces of the ionic complex occur for Ar on the C(6v) symmetry axis of benzene(+) (the z axis) at z(e)=3.506 A. The binding energy D(e) of 520 cm(-1) is only 34% larger than the value for the neutral Ar-benzene complex. The higher one of the two surfaces is similar in shape to the neutral Ar-benzene potential, the lower potential is much flatter in the (x,y) bend direction. Nonadiabatic (Jahn-Teller) coupling was taken into account by transformation of the two adiabatic potentials to a two-by-two matrix of diabatic potentials. This transformation is based on the assumption that the adiabatic states of the Ar-benzene(+) complex geometrically follow the Ar atom. Ab initio calculations of the nonadiabatic coupling matrix element between the adiabatic states with the two-state-averaged CAS-SCF(5,6) method confirmed the validity of this assumption. The bound vibronic states of both Ar-C(6)H(6) (+) and Ar-C(6)D(6) (+) were computed with this two-state diabatic model in a basis of three-dimensional harmonic oscillator functions for the van der Waals modes. The binding energy D(0)=480 cm(-1) of the perdeuterated complex agrees well with the experimental upper bound of 485 cm(-1). The ground and excited vibronic levels and wave functions were used, with a simple model dipole function, to generate a theoretical far-infrared spectrum. Strong absorption lines were found at 10.1 cm(-1) (bend) and 47.9 cm(-1) (stretch) that agree well with measurements. The unusually low bend frequency is related to the flatness of the lower adiabatic potential in the (x,y) direction. The van der Waals bend mode of e(1) symmetry is quadratically Jahn-Teller active and shows a large splitting, with vibronic levels of A(1), E(2), and A(2) symmetry at 1.3, 10.1, and 50.2 cm(-1). The level at 1.3 cm(-1) leads to a strong absorption line as well, which could not be measured because it is too close to the monomer line. The level at 50.2 cm(-1) gives rise to weaker absorption. Several other weak lines in the frequency range of 10 to 60 cm(-1) were found.     

The effect of the torsional and stretching vibrations of C2H6 on the H + C2H6 --> H2 + C2H5 reaction

We present a three-dimensional quantum scattering model to treat reactions of the type H + C2H6 --> H2 + C2H5. The model allows the torsional and the stretching degrees of freedom to be treated explicitly. Zero-point energies of the remaining modes are taken into account in electronic structure calculations. An analytical potential-energy surface was developed from a minimal number of ab initio geometry evaluations using the CCSD(T,full)/cc-pVTZ//MP2(full)/cc-pVTZ level of theory. The reaction is endothermic by 1.5 kcal mol(-1) and exhibits a vibrationally adiabatic barrier of 12.0 kcal mol(-1). The results show that the torsional mode influences reactivity when coupled with the vibrational C-H stretching mode. We also found that ethyl radical products are formed internally excited in the torsional mode.     

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.     

The role of the excited electronic states in the C+ + H2O reaction

The electronic excited states of the [COH2]+ system have been studied in order to establish their role in the dynamics of the C+ + H2O-->[COH]+ +H reaction, which is a prototypical ion-molecule reaction. The most relevant minima and saddle points of the lowest excited state have been determined and energy profiles for the lowest excited doublet and quartet electronic states have been computed along the fragmentation and isomerization coordinates. Also, nonadiabatic coupling strengths between the ground and the first excited state have been computed where they can be large. Our analysis suggests that the first excited state could play an important role in the generation of the formyl isomer, which has been detected in crossed beam experiments [D. M. Sonnenfroh et al., J. Chem. Phys. 83, 3985 (1985)], but could not be explained in quasiclassical trajectory computations [Y. Ishikawa et al., Chem. Phys. Lett. 370, 490 (2003); J. R. Flores, J. Chem. Phys. 125, 164309 (2006)].     

C6H and C6D: electronic spectra and Renner-Teller analysis

Rotationally resolved spectra of the B(2)Π - X(2)Π 0(0)(0) electronic origin bands and 11(1)(1) μ(2)Σ-μ(2)Σ vibronic hot band transitions of both C(6)H and C(6)D have been recorded in direct absorption by cavity ring-down spectroscopy through a supersonically expanding planar plasma. For both origin and hot bands accurate spectroscopic parameters are derived from a precise rotational analysis. The origin band measurements extend earlier work and the 11(1)(1) μ(2)Σ-μ(2)Σ vibronic hot bands are discussed here for the first time. The Renner-Teller effect for the lowest bending mode ν(11) is analyzed, yielding the Renner parameters ε(11), vibrational frequencies ω(11), and the true spin-orbit coupling constants A(SO) for both (2)Π electronic states. From the Renner-Teller analysis and spectral intensity measurements as a function of plasma jet temperature, the excitation energy of the lowest-lying 11(1) μ(2)Σ vibronic state of C(6)H is determined to be (11.0 ± 0.8) cm(-1).     

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.     

The C4H7+ cation. A theoretical investigation

The potential energy surface of the C4H7+ cation has been investigated with ab initio quantum chemical theory. Extended basis set calculations, including electronic correlation, show that cyclobutyl and cyclopropylcarbinyl cation are equally stable isomers. The saddle point connecting these isomers lies 0.6 kcal/mol above the minima. The global C4H7+ minimum corresponds to the 1-methylallyl cation, which is 9.0 kcal/mol more stable than the cyclobutyl and the cyclopropylcarbinyl cation and 9.5 kcal/mol below the 2-methylallyl cation. These results are in excellent agreement with experimental data.     

Assignment on the X,A, B,C, and D states of the C6H5Br+ cation based on high‐level calculations

Geometries, frequencies, and energies of the 1²B₁, 1²A₂, 1²B₂, 2²B₁, 2²B₂, and 1²A₁, of the C₆H₅Br⁺ ion were calculated by using CASSCF and CASPT2 methods in conjunction with an ANO‐RCC basis. The CASPT2//CASSCF adiabatic excitation energies and CASPT2 relative energies for the six states are in good agreement with experiment. The X, A, B, C, and D electronic states of the C₆H₅Br⁺ ion were assigned to be X²B₁, A²A₂, B²B₂, C²B₁, and D²B₂ based on the CASSCF and CASPT2 calculations. The assignment on the D state of the C₆H₅Br⁺ ion is different from the previously published works. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Gas phase hydration and deprotonation of the cyclic C3H3+ cation. Solvation by acetonitrile, and comparison with the benzene radical cation

The binding energies of the first 5 H2O molecules to c-C3H3+ were determined by equilibrium measurements. The measured binding energies of the hydrated clusters of 9-12 kcal/mol are typical of carbon-based CH+...X hydrogen bonds. The ion solvation with the more polar CH3CN molecules results in stronger bonds consistent with the increased ion-dipole interaction. Ab initio calculations show that the lowest energy isomer of the c-C3H3+(H2O)4 cluster consists of a cyclic water tetramer interacting with the c-C3H3+ ion, which suggests the presence of orientational restraint of the water molecules consistent with the observed large entropy loss. The c-C3H3+ ion is deprotonated by 3 or more H2O molecules, driven energetically by the association of the solvent molecules to form strongly hydrogen bonded (H2O)nH+ clusters. The kinetics of the associative proton transfer (APT) reaction C3H3+ + nH2O --> (H2O)nH+ + C3H2* exhibits an unusually steep negative temperature coefficient of k = cT(-63+/-4) (or activation energy of -37 +/- 1 kcal mol(-1)). The behavior of the C3H3+/water system is exactly analogous to the benzene+*/water system, suggesting that the mechanism, kinetics and large negative temperature coefficients may be general to multibody APT reactions. These reactions can become fast at low temperatures, allowing ionized polycyclic aromatics to initiate ice formation in cold astrochemical environments.     

3Sigma- -X 3Sigma- electronic transition of linear C6H+ and C8H+ in neon matrixes

The electronic absorption spectra of linear C6H+ and C8H+ were recorded in 6 K neon matrixes following mass selective deposition. The (1) 3Sigma- -X 3Sigma- electronic transition is identified with the origin band at 515.8 and 628.4 nm for l-C6H+ and l-C8H+, respectively. One strong (near 267 nm) and several weaker electronic transitions of l-C8H+ have also been observed in the UV. The results of ab initio calculations carried out for linear and cyclic C6H+ are consistent with the assignment.     

Ab initio calculation of electronic states of the ions H4+ and H5+

Electronic state calculations for the ions H₄⁺ (with symmetries D ₄ and C _2v) and H (with symmetries D ₅ and D _2d) are made using the valence-bond method. All the configurations obtained from the given set of 1s-functions of Slater type are taken into account. Space functions are used throughout the computation (“spin-free quantum chemistry”). Preliminary quasidiagonalization of the secular equation is implemented by the construction of the multiplet eigenfunctions ^2S+1Γ^(α) from the initial variational functions. The results of the calculations are as follows: the ion H is unstable, the ion H is stable with equilibrium nuclear conformation of symmetry D _2d and with the energy of dissociation into H and H₂ near 4 eV.     

OOCO+ cation I: characterization of its isomers and lowest electronic states

Accurate ab initio calculations are performed in order to investigate the stable isomers of OOCO+ and its electronic states at both the molecular and asymptotic regions. These calculations are done using large basis sets and configuration interaction methods. Our theoretical computations predict the presence of four stable forms: A global minimum where a weakly bound charge transfer complex (OOOC+) may be found. Few tenths of cm(-1) above in energy, the OOCO+ very weakly bound isomer is predicted. At 1.75 eV above OOCO+, a strongly bound centrosymmetric isomer (c-CO3+) is located. For energies >8 eV, a third isomer of C(2v) symmetry is found where one oxygen is in the center. The one-dimensional potential energy surface cuts of these electronic states reveal the existence of shallow potential wells for OOCO+ and OOOC+ and of deep potential wells for the two other forms, where electronically excited molecules can be formed at least transiently. Finally, the electronic states of each isomer should interact by spin-orbit, vibronic, Renner-Teller, and Jahn-Teller couplings in competition with isomerization processes converting one form to another.     

Dissociation of benzene dication [C6H6]2+: exploring the potential energy surface

The singlet potential energy surface for the dissociation of benzene dication has been explored, and its three major dissociation channels have been studied: C6H6(2+) --> C3H3(+) + C3H3(+), C4H3(+) + C2H3(+), and C5H3(+) + CH3(+). The calculated energetics suggest that the products will be formed with considerable translational energy because of the Coulomb repulsion between the charged fragments. The calculated energy release in the three channels shows a qualitative agreement with the experimentally observed kinetic energy release. The formation of certain intermediates is found to be common to the three dissociation channels.     

The C2H 3 + cation and its interaction with HF

The structure and stability of classical and bridged C₂H ₃ ⁺ is reinvestigated. The SCF and CEPA-PNO computations performed with flexibles andp basis sets including twod-sets on carbon confirm our previous results. We find the protonated acetylene structure to be more stable than the vinyl cation by 3.5–4 kcal/mol. The energy barrier for the interconversion of these two structures is at most a few tenths of a kcal/mol. The equilibrium SCF geometries of Weberet al. [15] are affected insignificantly by further optimization at the CEPA-PNO level. Several structures for the interaction of C₂H ₃ ⁺ with HF have been investigated at the SCF level. With our largest basis set which includes a complete set of polarization functions we find a remarkable levelling of the stabilities of most of the structures. In these cases the stabilization energy ΔE ranges from −10 to −13 kcal/mol.     

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.     

The benzoyl cation: The participation of isolated electronic excited states in the dissociation of molecular ions of the form [C6H5COX]+˙

The heat of formation of the benzoyl cation generated from [C₆H₅COX]⁺˙ is found to depend on X, while the heat of formation of the phenyl ion produced therefrom is, with one exception, independent of X. The excess energy of the benzoyl cation can be accounted for by an electronic excited state of the ion in the mass spectra of benzoic acid, benzaldehyde, benzamide, methyl benzoate and possibly benzophenone; the benzoyl cation is not excited in the mass spectra of acetophenone and benzoyl chloride.     

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.     

Jahn-Teller effect in CH3D+ and CD3H+: conformational isomerism, tunneling-rotation structure, and the location of conical intersections

High-resolution pulsed-field-ionization zero-kinetic-energy photoelectron spectra of CH(3)D and CD(3)H have been recorded at rotational resolution from the adiabatic ionization energy up to 600 cm(-1) of internal energy of the respective cations. The spectra are characterized by the effects of a large-amplitude pseudorotational motion exchanging the equivalent nuclei in each molecule. With increasing internal energy, a transition from the tunneling regime with splittings of the order of 1-10 cm(-1) to the free pseudorotation regime is observed. A theoretical model that treats the simultaneous rotational and pseudorotational motions and incorporates the effects of the geometric phase has been developed. The model provides the appropriate rovibronic symmetries in the C(3v)(M) molecular symmetry group and reaches a near-quantitative agreement with the experimental data. The complete group-theoretical analysis of the rovibronic problem is also given. The analysis of the spectra has revealed the existence of two different isomers for both CH(3)D(+) and CD(3)H(+), which differ in the bond length between the carbon atom and the unique ligand atom. All isomers are subject to a fast pseudorotational motion between three equivalent minima with a period of 3-5 ps in CH(3)D(+) and 18-28 ps in CD(3)H(+). The analysis has also provided the ordering of the tunneling sublevels for each isomer, which enables the location of the twofold conical intersections on the potential energy surface that could not be determined from experiments on CH(4) (+).     

Extensive theoretical studies on the low-lying electronic states of indium monochloride cation, InCl+

The global potential energy curves for the 14 low-lying doublet and quartet Lambda-S states of InCl+ are calculated at the scalar relativistic MR-CISD+Q (multireference configuration interaction with single and double excitations, and Davidson's correction) level of theory. Spin-orbit coupling is accounted for via the state interaction approach with the full Breit-Pauli Hamiltonian, which leads to 30 Omega states. The computed spectroscopic constants of nine bound Lambda-S states and 17 bound Omega states are in good agreement with the available experimental data. The transition dipole moments and Franck-Condon factors of selected transitions are also calculated, from which the corresponding radiative lifetimes are derived.     

X, A, B, C, and D states of the C6H5F+ ion studied using multiconfiguration wave functions

Electronic states of the C6H5F+ ion have been studied within C2v symmetry by using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with an atomic natural orbital basis. Vertical excitation energies (Tv) and relative energies (Tv') at the ground-state geometry of the C6H5F molecule were calculated for 12 states. For the five lowest-lying states, 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, geometries and vibrational frequencies were calculated at the CASSCF level, and adiabatic excitation energies (T0) and potential energy curves (PEC) for F-loss dissociations were calculated at the CASPT2//CASSCF level. On the basis of the CASPT2 T0 calculations, we assign the X, A, B, C, and D states of the ion to 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, respectively, which supports the suggested assignment of the B state to (2)(2)B1 by Anand et al. based on their experiments. Our CASPT2 Tv and Tv' calculations and our MRCI T0, Tv, and Tv' calculations all indicate that the 2(2)B1 state of C6H5F+ lies below 1(2)B2. By checking the relative energies of the asymptote products and checking the fragmental geometries and the charge and spin density populations in the asymptote products along the CASPT2//CASSCF PECs, we conclude that the 1(2)B1, 1(2)B2, and 1(2)A1 states of C6H5F+ correlate with C6H5+ (1(1)A1) + F (2P) (the first dissociation limit). The energy increases monotonically along the 1(2)B1 PEC, and there are barriers and minima along the 1(2)B2 and 1(2)A1 PECs. The predicted appearance potential value for C6H5+ (1(1)A1) is very close to the average of the experimental values. Our CASPT2//CASSCF PEC calculations have led to the conclusion that the 1(2)A2 state of C6H5F+ correlates with the third dissociation limit of C6H5+ (1(1)A2) + F (2P), and a preliminary discussion is presented.