Calculation of the vibronic structure of the X2Pi photoelectron spectra of XCN, X=F, Cl, and Br

The vibronic structure of the photoelectron spectra of the X (2)Pi state of XCN(+) (X=F, Cl, and Br) has been calculated, assuming that the X (2)Pi state can be considered as an isolated electronic state. The Renner-Teller coupling of the two components of the (2)Pi state via the degenerate bending mode as well as spin-orbit coupling effects are taken into account. The two stretching modes are treated within the so-called linear vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While spin-orbit effects are small in FCN(+), the large spin-orbit splitting of the X (2)Pi state of the BrCN(+) leads to a complete quenching of the Renner-Teller effect. The X (2)Pi state of the ClCN(+) is shown to be of particular interest: here the resonance condition for linear-relativistic Renner-Teller coupling is approximately fulfilled. This coupling mechanism leads to a significant intensity transfer to vibronic levels with odd quanta of the bending mode. The calculated spectrum indicates that this novel relativistic vibronic-coupling effect should be observable in high-resolution (electron energy resolution of the order of a few meV) photoelectron spectra of ClCN.     

Renner-Teller and spin-orbit vibronic coupling effects in linear triatomic molecules with a half-filled pi shell

The vibronic and spin-orbit-induced interactions among the (3)Sigma(-), (1)Delta, and (1)Sigma(+) electronic states arising from a half-filled pi orbital of a linear triatomic molecule are considered, employing the microscopic (Breit-Pauli) spin-orbit coupling operator. The 6 x 6 Hamiltonian matrix is derived in a diabatic spin-orbital electronic basis set, including terms up to fourth order in the expansion of the molecular Hamiltonian in the bending normal coordinate about the linear geometry. The symmetry properties of the Hamiltonian are analyzed. Aside from the nonrelativistic fourth-order Renner-Teller vibronic coupling within the (1)Delta state and the second-order nonrelativistic vibronic coupling between the (1)Sigma(+) and (1)Delta states, there exist zeroth-order, first-order, as well as third-order vibronic coupling terms of spin-orbit origin. The latter are absent when the phenomenological expression for the spin-orbit coupling operator is used instead of the microscopic form. The effects of the nonrelativistic and spin-orbit-induced vibronic coupling mechanisms on the (3)Sigma(-), (1)Delta, and (1)Sigma(+) adiabatic potential energy surfaces as well as on the spin-vibronic energy levels are discussed for selected parameter values.     

Spectroscopic effects of first-order relativistic vibronic coupling in linear triatomic molecules

It has recently been shown that there exists, in addition to the well-known nonrelativistic Renner-Teller coupling, a linear (that is, of the first order in the bending distortion) vibronic-coupling mechanism of relativistic (that is, spin-orbit) origin in 2II electronic states of linear molecules [L. V. Poluyanov and W. Domcke, Chem. Phys. 301, 111 (2004)]. The generic aspects of the relativistic linear vibronic-coupling mechanism have been analyzed in the present work by numerical calculations of the vibronic spectrum for appropriate models. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations for the X 2II states of a series of triatomic radicals and radical cations. It is shown for the example of GeCH that the relativistic linear vibronic-coupling mechanism provides a quantitative explanation of the pronounced perturbations in the vibronic spectrum of the X 2II state of GeCH, which previously have been termed "Sears resonances" [S.-G. He, H. Li, T. C. Smith, D. J. Clouthier, and A. J. Merer, J. Chem. Phys. 119, 10115 (2003)]. The X 2II vibronic spectra of the series BS2, CS2+, OCS+, and OBS illustrate the interplay of nonrelativistic and relativistic vibronic-coupling mechanisms in Renner-Teller systems.     

Theoretical investigation of the vibronic spectrum in the X(2)Pi(u) electronic state of C(6)(+)

In this study we employ the recently developed model for handling the Renner-Teller effect in Pi electronic states of six-atomic molecules with linear equilibrium geometry to calculate the vibronic spectrum in the X(2)Pi(u) electronic state of the C(6)(+) ion. The applied model Hamiltonian excludes the stretching vibrations and end-over-end rotations. On the other hand, it considers the interplay between the vibronic and spin-orbit couplings. The parameters determining the shape of the bending potential energy surfaces are computed by means of a Density functional theory, and the spin-orbit coupling constant by the Multireference CI program using state-averaged complete active space self-consistent field (SA-CASSCF) wavefunctions. The results of the present study are expected to motivate and help future experimental investigations on C(6)(+).     

Is the HCCS radical linear in the excited state?

The A (2)Pi-X (2)Pi 415 nm band system of the linear HCCS radical has been known since 1978, but the vibronic structure in this complex spectrum, which has both spin-orbit and Renner-Teller complications, has never been satisfactorily assigned, despite serious experimental and theoretical efforts. In a further attempt to understand the spectrum, we have studied the laser-induced fluorescence spectra of jet-cooled HCCS and DCCS, produced from thiophene precursors using the discharge jet technique. The 0(0) (0) bands of HCCS and DCCS have been rotationally analyzed, providing precise ground and excited state spin-orbit splittings. The energy levels of the v(')=0 (2)Pi(3/2) component of DCCS are found to be perturbed by a very low-lying (2)Sigma vibronic level, indicating that the HCC bending mode Renner-Teller effect is much larger than predicted by ab initio calculations with a linear excited state geometry. With this observation, the vibronic bands in the spectra of both isotopomers have been consistently assigned for the first time. Model calculations show that the large Renner-Teller effect and substantially different HCCS and DCCS excited state zero-point spin-orbit splittings can be explained with the assumption of a quasilinear excited state geometry.     

Renner-Teller vibronic analysis for a tetra-atomic molecule. I. The effective Hamiltonian and matrix elements

The effective vibronic Hamiltonian for a linear tetra-atomic molecule in a Pi state has been investigated. In addition to the usual vibrational and Renner-Teller coupling terms, the bending mode anharmonicity, spin-orbit coupling, and Fermi resonance interactions have been added to the model. Terms in the Hamiltonian up to the fourth order are given explicitly for molecules of C(infinityupsilon) symmetry and simplifications for symmetric D(infinityh) molecules are discussed. The matrix elements for the HCCS free radical have been obtained and are used to analyze the observed ground-state levels of HCCS and DCCS in a companion paper. The Sears resonance vibronic interaction that couples levels with the selection rules DeltaK=+/-1, DeltaSigma=-/+1, and DeltaP=0 has also been studied and the matrix elements derived. The determinable combinations of signs for the major parameters in the model are discussed.     

Renner-Teller effect in C2H2+(X2Pi u) studied by rotationally resolved zero kinetic energy photoelectron spectroscopy

The Renner-Teller effect in C(2)H(2)(+)(X(2)Pi(u)) has been studied by using zero kinetic energy (ZEKE) photoelectron spectroscopy and coherent extreme ultraviolet (XUV) radiation. The rotationally resolved vibronic spectra have been recorded for energies up to 2000 cm(-1) above the ground vibrational state. The C triple bond C symmetric stretching (upsilon(2)), the CCH trans bending (upsilon(4)), and the CCH cis bending (upsilon(5)) vibrational excitations have been observed. The assigned vibronic bands are 4(1)(1)(kappa(2)Sigma(u)(+))(hot band), 4(1)(0)(mu/kappa(2)Sigma (u)(-/+)), 5(1)(0)(mu/kappa(2)Sigma (g)(+/-)), and 4(2)(0)(mu(2)Pi(u)), 4(2)(0)(kappa(2)Pi(u)), 4(1)(0)5(1)(0) (mu(2)Pi(g)), 0(0)(0)(X(2)Pi(u)), and 2(1)(0)(X(2)Pi(u)). The Renner-Teller parameters, the harmonic frequencies, the spin-orbit coupling constants, and the rotational constants for the corresponding vibronic bands have been determined by fitting the spectra with energy eigenvalues from the Hamiltonian that considers simultaneously Renner-Teller coupling, vibrational energies, rotational energies, and spin-orbit coupling interaction.     

Calculation of the vibronic structure of the photodetachment spectra of CCCl- and CCBr-

The vibronic structure of the closely spaced and strongly coupled X 2Sigma+ and A 2Pi states in the photodetachment spectra of CCCl- and CCBr- has been calculated by considering Sigma-Pi vibronic coupling together with spin-orbit coupling. The stretching modes are treated within the so-called linear-vibronic-coupling model. The vibronic and spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations. While the nonrelativistic vibronic-coupling parameters are of approximately equal strength in CCCl and CCBr, the vibronic-coupling parameters of spin-orbit origin are found to be larger in the latter. The calculated photodetachment spectra of both systems are shown to exhibit a complicated vibronic structure due to strong Sigma-Pi vibronic coupling. The spectral envelopes of the calculated photodetachment spectra exhibit a double-hump reminiscent of strongly coupled Exe Jahn-Teller systems.     

Experimental and ab initio study of a new D 1Deltag state of the C3 radical

We report here the first observation of the D (1)Delta(g) state of the C(3) radical, which provides the first comprehensively analyzed example of the dynamic Renner-Teller splitting in Delta symmetry. Two color double resonance spectroscopy via the A (1)Pi(u) state was employed to experimentally probe an extensive range of vibronic levels in this D (1)Delta(g) state, covering all three modes of vibration of C(3). The analysis was supported by ab initio potential energy surface calculations on the C(3) radical to outline the lowest eight singlet electronic states. Two methods were used to analyze the Renner-Teller effect. The first method is an empirical Hamiltonian based on normal modes, using harmonic oscillator functions as a basis, with Renner-Teller and other terms added as required, which allows conventional vibrational parameters to be determined. The second is a much larger program that uses the exact kinetic energy operator for a triatomic molecule to calculate vibronic energy levels directly from the Renner-Teller pair of potential energy surfaces. Both methods give a good fit to the experimental results, with only a small adjustment to the ab initio surfaces required for the latter. One of the overall conclusions is that the Renner-Teller effect is rather smaller in the D (1)Delta(g) state than in the A (1)Pi(u) state.     

An ab initio study of the hyperfine structure in the X2 Pi electronic state of CCCH

The results of an ab initio study of the magnetic hyperfine structure in the X (2)Pi electronic state of CCCH are reported. The potential surfaces for two components of the X (2)Pi electronic state were computed by means of an extensive configuration interaction approach. The electronically averaged hyperfine coupling constants of H and (13)C for (12)C (12)C (12)CH, (13)C (12)C (12)CH, (12)C (13)C (12)CH, and (12)C (12)C (13)CH are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with the help of a variational approach which takes into account the Renner-Teller effect and spin-orbit coupling. The model Hamiltonian is expressed in terms of the normal bending coordinates. It is found that, due to the generally strong geometry dependence of the hyperfine coupling constants, it is necessary to carry out the vibronic averaging of the corresponding functions in order to obtain the values which can be compared to the results of the measurements. The results of the present study help to reliably interpret the experimental data previously published. They also predict the yet unobserved hyperfine structure in excited vibronic states.     

A dispersed fluorescence and ab initio investigation of the X2B1 and A2A1 electronic states of the PH2 molecule

In this work, the X2B1 and A2A1 electronic states of the phosphino (PH2) free radical have been studied by dispersed fluorescence and ab initio methods. PH2 molecules were produced in a molecular free-jet apparatus by laser vaporizing a silicon rod in the presence of phosphine (PH3) gas diluted in helium. The laser-induced fluorescence, from the excited A2A1 electronic state down to the ground electronic state, was dispersed and analyzed. Ten (upsilon1upsilon2upsilon3) vibrationally excited levels of the ground electronic state, with upsilon1 < or = 2, upsilon2 < or = 6, and upsilon3 = 0, have been observed. Ab initio potential-energy surfaces for the X2B1 and A2A1 electronic states have been calculated at 210 points. These two states correlate with a 2Pi(u) state at linearity and they interact by the Renner-Teller coupling and spin-orbit coupling. Using the ab initio potential-energy surfaces with our RENNER computer program system, the vibronic structure and relative intensities of the A2A1 --> X2B1 emission band system have been calculated in order to corroborate the experimental assignments.     

Low-lying bending vibronic bands of the MgNC A 2Pi-X 2Sigma+ transition

We have generated MgNC in supersonic free jet expansions and measured the laser induced fluorescence excitation spectra of the Mg-N-C bending vibronic bands of the A 2Pi-X 2Sigma+ transition. In addition to the two vibronic bands, 2(0) (1), kappa 2Sigma(+)- and 2(0) (2), kappa 2Pi-2Sigma+, reported previously, the 2(0) (2), mu 2Pi1/2-(2)Sigma+ vibronic subband was found just above the 2(0) (1) band. The most remarkable feature of this subband is unexpected rotational structure of the A (020) mu 2Pi1/2 level, showing the splitting of the e and f sublevels. On the basis of the fact that the A (020) mu 2Pi1/2 level lies very close to the A (010) kappa2Sigma+ level, the ef splitting is ascribed to P-type doubling which is induced by Coriolis interaction between these two bending vibronic levels. Introducing the Coriolis coupling terms arising from the G-uncoupling operator, -J+/-G22-/+, and the spin-Coriolis interaction, S+/-G22-/+, into the rotational Hamiltonian, this unexpected rotational structure has been analyzed. This P-type doubling would be one of the rare examples exhibiting the Coriolis interaction between two bending vibronic levels with Deltav2=+/-1 and Deltal=-/+1. Through the molecular constants of the A (010) kappa 2Sigma+, (020) kappa 2Pi, and mu 2Pi1/2 levels, the Renner-Teller vibronic structure of the nu2 bending mode in the A 2Pi state has been characterized. The observed vibronic bands analyzed in this study show some anomalies in the band intensities. Based on the information of the nu2 bending vibronic structure derived from the present analyses, we discuss the intensity anomalies.     

The molecular structure and a Renner-Teller analysis of the ground and first excited electronic states of the jet-cooled CS2 + molecular ion

The A 2Pi(u) - X 2Pi(g) electronic band system of the jet-cooled CS2 + ion has been studied by laser-induced fluorescence and wavelength-resolved emission techniques. The ions were produced in a pulsed electric discharge jet using a precursor mixture of carbon disulfide vapor in high-pressure argon. Rotational analysis of the high-resolution spectrum of the 2Pi32 component of the 0(0) 0 band gave linear-molecule molecular structures of r0" = 1.5554(10) A and r0' = 1.6172(12) A. Renner-Teller analyses of the vibronic structure in the spectra showed that the ground-state spin-orbit splitting (A = -447.0 cm(-1)) is much larger than that of the excited state (A = -177.5 cm(-1)), but that the Renner-Teller parameters are of similar magnitude and that a strong nu1 - 2nu2 Fermi resonance occurs in both states. Previous analyses of the vibronic structure in the ground and excited states of the ion from pulsed field-ionization-photoelectron data are shown to be substantially correct.     

A time-dependent wave packet study of the vibronic and spin-orbit interactions in the dynamics of Cl((2)P)+H(2)-->HCl(X (1)Sigma(g) (+))+H((2)S) reaction

We investigate the vibronic and spin-orbit (SO) coupling effects in the state-selected dynamics of the title reaction with the aid of a time-dependent wave packet approach. The ab initio potential energy surfaces of Capecchi and Werner [Science 296, 715 (2002)] have been employed for this purpose. Collinear approach of the Cl((2)P) atom to the H(2) molecule splits the degeneracy of the (2)P state and gives rise to (2)Sigma and (2)Pi electronic states. These two surfaces form a conical intersection at this geometry. These states transform as 1 (2)A('), 1 (2)A("), and 2 (2)A('), respectively, at the nonlinear configurations of the nuclei. In addition, the SO interaction due to Cl atom further splits these states into (2)Sigma(1/2), (2)Pi(3/2), and (2)Pi(1/2) components at the linear geometry. The ground-state reagent Cl((2)P(3/2))+H(2) correlates with (2)Sigma(1/2) and (2)Pi(3/2), where as the SO excited reagent Cl(*)((2)P(1/2))+H(2) correlates with (2)Pi(1/2) at the linear geometry. In order to elucidate the impact of the vibronic and SO coupling effects on the initial state-selected reactivity of these electronic states we carry out quantum scattering calculations based on a flux operator formalism and a time-dependent wave packet approach. In this work, total reaction probabilities and the time dependence of electronic population of the system by initiating the reaction on each of the above electronic states are presented. The role of conical intersection alone on the reaction dynamics is investigated with a coupled two-state model and for the total angular momentum J=0 (neglecting the electronic orbital angular momentum) both in a diabatic as well as in the adiabatic electronic representation. The SO interaction is then included and the dynamics is studied with a coupled three-state model comprising six diabatic surfaces for the total angular momentum J=0.5 neglecting the Coriolis Coupling terms of the Hamiltonian. Companion calculations are carried out for the uncoupled adiabatic and diabatic surfaces in order to explicitly reveal the impact of two different surface coupling mechanisms in the dynamics of this prototypical reaction.     

A theoretical study of the fine and hyperfine interactions in the NCO and CNO radicals

The geometries, the harmonic vibrational frequencies, and the Renner-Teller parameter have been reported for the NCO(+)(X (3)Sigma(-)), NCO(X (2)Pi,A (2)Sigma(+),B (2)Pi,2 (2)Sigma(+)), NCO(-)(X (1)Sigma(+)), CNO(+)(X), CNO(X (2)Pi,A (2)Sigma(+),B (2)Pi,2 (2)Sigma(+)), and CNO(-)(X (1)Sigma(+)) systems at the full valence-complete active space self-consistent-field (fv-CASSCF) level of theory. The (2)Pi electronic states of the NCO and CNO radicals have two distinct real vibrational frequencies for the bending modes and these states are subject to the type A Renner-Teller effect. The total energy of CNO(+) without zero point energy correction of the linear geometry is approximately 31 cm(-1) higher than the bent geometry at the fv-CASSCF level and the inversion barrier vanishes after the zero point energy correction; therefore, the ground state of the CNO(+) may possess a quasilinear geometry. The spin-orbit coupling constants estimated using atomic mean field Hamiltonian at the fv-CASSCF level of theory are in better agreement with the experimental values. The excitation energies, the electron affinity, and the ionization potential have been computed at the complete active space second order perturbation theory (CASPT2) and the multireference singles and doubles configuration (MRSD-CI) levels of theory. The computed values of the electric hyperfine coupling constants for the (14)N atom in the ground state of the NCO radical agree well with the experimental data. The magnetic hyperfine coupling constants (HFCC's) have been estimated employing the configuration selected MRSD-CI and the multireference singles configuration interaction (MRS-CI) methods using iterative natural orbitals (ino) as one particle basis. Sufficiently accurate value of the isotropic contribution to the HFCC's can be obtained using an MRS-CI-ino procedure.     

An ab initio calculation of the anisotropic hyperfine coupling constants in the low-lying vibronic levels of the X 2Pi electronic state of CCCH

The results of ab initio calculations of the vibronically averaged components of the anisotropic magnetic hyperfine tensor in the low-lying vibronic species of the X (2)Pi electronic state of CCCH and CCCD are reported. The electronically averaged hyperfine coupling constants for hydrogen and (13)C in (12)C (12)C (12)CH, (13)C (12)C (12)CH, (12)C (13)C (12)CH, (12)C (12)C (13)CH, and (12)C (12)C (12)CD are obtained as functions of two bending vibrational modes by the density functional theory method. The vibronic wave functions are calculated with help of a variational approach which takes into account the Renner-Teller effect and spin-orbit coupling. The results of the present study help to reliably interpret the experimental data previously published and predict the yet unobserved hyperfine structure in excited vibronic states of CCCH and CCCD.     

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).     

Experimental and theoretical investigation of the dispersed fluorescence spectroscopy of HC4S

A high-resolution single vibronic level emission study from the A (2)Pi(32) state of the HC(4)S radical is reported. Ground state density functional theory frequencies have been used to assign ground state vibronic levels involving three stretching modes nu(2), nu(3), and nu(5) in the region of 0-3250 cm(-1), while the frequency of nu(4) remains speculative. Tentative assignments are given for the complicated structures arising from Renner-Teller and spin-orbit interactions within the bending energy levels. From analysis of the dispersed emission spectra, Fermi resonances involving pairs of bands have been identified in the A (2)Pi(32)<--X (2)Pi(32) laser induced fluorescence spectrum.     

Characterization of C4H in the A2Π and X2Σ+ states by double resonance four-wave mixing

The B(2)Π-X(2)Σ(+) electronic spectrum of C(4)H has been studied by degenerate and double resonance four-wave mixing. The technique identifies vibrational levels in the X(2)Σ(+) ground state. Its sensitivity and unique characteristics permit detection of new levels. The A(2)Π state lying 222 cm(-1) above the X(2)Σ ground state is also observed, confirming the analysis from anion photoelectron spectroscopy but with improved accuracy. Vibrational level determination in the A(2)Π electronic manifold up to 700 cm(-1) above v = 0 is made. A Renner-Teller analysis is carried out for the two lowest bending modes v(6) and v(7) in the A(2)Π state by diagonalization of the effective Hamiltonian matrix. The Renner-Teller parameters ∈(6), ∈(7), and ∈(67), the vibrations ω(6) and ω(7) and the spin-orbit coupling constant A(so) are determined.