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.     

Spin-orbit vibronic coupling in 3Pi states of linear triatomic molecules

The Renner-Teller vibronic-coupling problem of a 3Pi electronic state of a linear molecule is analyzed with the inclusion of the spin-orbit coupling of the 3Pi electronic state, employing the microscopic (Breit-Pauli) spin-orbit coupling operator for the two unpaired electrons. The 6x6 Hamiltonian matrix in a diabatic spin-electronic basis is obtained by an expansion of the molecular Hamiltonian in powers of the bending amplitude. The symmetry properties of the Hamiltonian with respect to the time-reversal operator and the relativistic vibronic angular momentum operator are analyzed. It is shown that there exists a linear vibronic-coupling term of spin-orbit origin, which has not been considered so far in the Renner-Teller theory of 3Pi electronic states. While two of the six adiabatic electronic wave functions do not exhibit a geometric phase, the other four carry nontrivial topological phases which depend on the radius of the integration contour. The spectroscopic effects of the linear spin-orbit vibronic-coupling mechanism have been analyzed by numerical calculations of the vibronic spectrum for selected model examples.     

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.     

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)(+).     

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.     

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.     

In search of the germanium halomethylidyne (Ge=C-X; X=F,Cl,Br) free radicals: Ab initio studies of their spectroscopic signatures

A variety of ab initio methods have been used to calculate the X (2)Pi and A (2)Sigma(+) state spectroscopic parameters of the GeCX (X=F,Cl,Br) free radicals. The theoretical methods and basis sets were tested on GeCH, for which extensive experimental data are available, and found to give predictions sufficiently reliable to guide experimental searches for spectra. In all cases, the linear Ge=C-X species was found to be the global minimum on the potential energy surface, with the bent X-Ge=C ((2)A(')) isomer as a local minimum much higher (62-36 kcal/mol) in energy. In both the ground and excited states, the GeC moiety is very similar to that of GeCH, with a double bond in the lower state and a triple bond in the excited state, indicating that halogenation does not radically perturb the energetics or structure of germanium methylidyne. Ground state GeCX radicals have suitable rotational constants for microwave studies, although they suffer from only modest dipole moments. Matrix infrared experiments are most likely to detect the nu(1) fundamentals in the 1450-1100 cm(-1) region or the nu(3) fundamentals at the transition between the mid- and far-infrared regions. We have used the ab initio values for the Renner-Teller parameter, the average bending frequency, and the spin-orbit coupling constant to calculate the ground state energy levels, which will be helpful in the interpretation of A-X single vibronic level emission spectra, if they can be observed. The electronic absorption spectra of the (2)Pi(32) spin component of the 0(0) (0) bands of all three radicals have been calculated assuming typical jet-expansion conditions and should be useful in future laser-induced fluorescence, resonance enhanced multiphoton ionization, or cavity ringdown searches for the electronic band systems.     

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.     

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.     

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.     

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.     

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.     

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.     

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).     

An ab initio study of the vibronic, spin-orbit, and magnetic hyperfine structure in the X2Pi electronic state of NCO

In the present study we give the results of the ab initio calculations on the vibronic, spin-orbit, and magnetic hyperfine structure in the X (2)Pi electronic state of the NCO radical. The calculations of the potential surfaces and the electronic mean values of the hyperfine coupling constants are carried out by means of the density functional theory approach (B3LYP functional combined with an atomic orbital basis set suitable for calculations of the hyperfine structure). The vibronic levels, spin-orbit splitting, and the vibronic mean values of the components of the hyperfine tensor in the vibronic species are calculated using a variational method. The results of the calculations are in good agreement with the available experimental data.     

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.     

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.     

The Jahn-Teller effect in CH(3)CN(+) (X(2)E) and CD(3)CN(+) (X(2)E) studied by zero kinetic energy photoelectron spectroscopy

The Jahn-Teller effect in CH(3)CN(+) (X(2)E) and CD(3)CN(+) (X(2)E) has been found experimentally by zero kinetic energy (ZEKE) photoelectron spectroscopy using coherent extreme ultraviolet (XUV) radiation. The vibronic bands of CH(3)CN(+) (X(2)E) and CD(3)CN(+) (X(2)E) at about 4500 cm(-1) above the ground states have been recorded. The spectra consist mainly of the Jahn-Teller active C-C[triple bond]N bending (v(8)), the CN stretching (v(2)), the CH(3) (CD(3)) deforming (v(6)), and the C-C stretching (v(4)) vibronic excitations. The Jahn-Teller active vibronic bands (v(8)) have been assigned with a harmonic model including linear and quadratic Jahn-Teller coupling terms, taking into account only the single mode vibronic excitation. The ionization potentials of CH(3)CN and CD(3)CN have also been determined, and their values are 12.2040(+/-0.001) and 12.2286(+/-0.001) eV, respectively.