Experimental study of the NaK 3 3Pi double minimum state

We have used the Doppler-free, perturbation-facilitated optical-optical double-resonance technique to investigate the vibrational, rotational, and hyperfine structure of the 3 (3)Pi double minimum state of NaK. Since this electronic state arises from an avoided crossing with the nearby 4 (3)Pi state, we observe striking patterns in the data that provide a sensitive probe of the electronic wave function in the various regions of the double well potential. A single-mode cw dye laser excites 2(A) (1)Sigma(+)(v(A),J) approximately 1(b) (3)Pi(Omega=0)(v(b),J) mixed singlet-triplet "window" levels from thermally populated rovibrational ground state levels, 1(X) (1)Sigma(+)(v(X),J+/-1). Further excitation by a single-mode cw Ti:sapphire laser selects various 3 (3)Pi(0)(v(Pi),J(Pi)) rovibrational levels, which are detected by observing direct 3 (3)Pi(0)-->1(a) (3)Sigma(+) fluorescence in the green spectral region. Using the inverse perturbation approximation method, we have determined a 3 (3)Pi(0) potential curve that reproduces the measured energies to approximately 0.24 cm(-1). In addition, the hyperfine and spin-orbit constants, b(F) and A(v), have been determined for each region of the potential curve.     

The K2 2(3)Pi(g) state: new observations and analysis

Totally 3045 transitions into the 2(3)Pi(g) v = 0-42, J = 0-103, Omega = 0, 1, 2 rovibrational levels have been observed by infrared-infrared double resonance fluorescence excitation and two-photon spectroscopy. Molecular constants including the spin-orbit interaction parameters are obtained. Although the K2 2(3)Pi(g) state dissociates to the 4s + 3d atomic limit, it is strongly mixed with the 3P ionic states in the range of the potential well. This mixing results in a relatively large equilibrium internuclear distance Re = 5.254 A and a larger spin-orbit constant A0 approximately 14.17 cm(-1) than that of the atomic limit -2.33 cm(-1). Strong perturbations of the 2(3)Pi(g) levels observed are attributed to the spin-orbit coupling with the 4(1)Sigma(g)+ state.     

Theoretical spectroscopy of the calcium dimer in the A 1Sigma(u)+, c3Pi(u), and a3Sigma(u)+ manifolds: an ab initio nonadiabatic treatment

Nonadiabatic theory of molecular spectra of diatomic molecules is presented. It is shown that in the fully nonadiabatic framework, the rovibrational wave functions describing the nuclear motions in diatomic molecules can be obtained from a system of coupled differential equations. The rovibrational wave functions corresponding to various electronic states are coupled through the relativistic spin-orbit coupling interaction and through different radial and angular coupling terms, while the transition intensities can be written in terms of the ground state rovibrational wave function and bound rovibrational wave functions of all excited electronic states that are electric dipole connected with the ground state. This theory was applied in the nearly exact nonadiabatic calculations of energy levels, line positions, and intensities of the calcium dimer in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states. The excited state potentials were computed using a combination of the linear response theory within the coupled-cluster singles and doubles framework for the core-core and core-valence electronic correlations and of the full configuration interaction for the valence-valence correlation, and corrected for the one-electron relativistic terms resulting from the first-order many-electron Breit theory. The electric transition dipole moment governing the A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) transitions was obtained as the first residue of the frequency-dependent polarization propagator computed with the coupled-cluster method restricted to single and double excitations, while the spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction wave functions restricted to single and double excitations. Our theoretical results explain semiquantitatively all the features of the observed Ca(2) spectrum in the A (1)Sigma(u) (+)(1 (1)S+1 (1)D), c (3)Pi(u)(1 (3)P+1 (1)S), and a (3)Sigma(u) (+)(1 (3)P+1 (1)S) manifolds of states.     

Laser induced amplified spontaneous emission from the B2Pi, L2Pi, and I2Sigma+ valence states of NO

Amplified spontaneous emission (ASE) from single rovibrational levels of valence (non-Rydberg) states of NO molecules has been investigated. The B2Pi (v=24 and 25), L2Pi (v=5 and 6), and I2Sigma+ (v=6) levels have been populated through laser optical-optical double resonance excitation via the Rydberg A2Sigma+ state. Term values for the 2Pi states have been determined with an accuracy of +/-0.03 cm(-1). Analyses of rotationally resolved dispersed ASE spectra in the near infrared region have shown that all the lower states belonged to the Rydberg states. The valence approximately Rydberg coupling in the upper manifolds has driven ASE systems from the valence to the Rydberg levels where they benefit from the strong intensities of inter-Rydberg transitions with Deltav=0. The experimentally predicted valence approximately Rydberg interactions have been compared with theoretical treatments.     

Direct deperturbation analysis of the A 2Pi approximately B 2Sigma+ complex of 7,6LiAr isotopomers

Direct deperturbation analysis of the highly accurate experimental rovibronic term values of the A (2)Pi approximately B (2)Sigma(+) complex of LiAr [R. Bruhl and D. Zimmermann, J. Chem. Phys. 114, 3035 (2001)] has been performed in the framework of inverted close-coupling approach implicitly adjusted to the unified treatment of the overall A approximately B coupling effect without reducing the rovibrational dimensionality. The nonlinear fitting procedure was supported by the ab initio calculations on the spin-orbit and angular coupling matrix elements between the lowest X (2)Sigma(+), A (2)Pi, and B (2)Sigma(+) states. The analytical grid mapping based on the reduced variable representation of the radial coordinate r was used to improve the efficiency of the solution of the close-coupling radial equations near the dissociation limit. The mutual A approximately X perturbation effect on the A (2)Pi term values and spin-rotation splitting of the ground state were evaluated for both (7,6)LiAr isotopomers. The resulting empirical potential-energy curves for the adiabatic A (2)Pi and B (2)Sigma(+) states, along with the refined r-dependent nonadiabatic matrix elements, reproduce the total rovibronic structure of the (7)LiAr complex with the standard deviation of 0.003 cm(-1). The mass invariance of the deperturbed electronic parameters was confirmed by the calculation of the rovibronic term values of the (6)LiAr isotopomer which coincided with their experimental counterparts within 0.004 cm(-1).     

The NaK 1(b) 3Pi(Omega=0) state hyperfine structure and the 1(b) 3Pi(Omega=0) approximately 2(A) 1Sigma+ spin-orbit interaction

We have measured the hyperfine structure of mutually perturbing rovibrational levels of the 1(b) 3Pi0 and 2(A) 1Sigma+ states of the NaK molecule, using the perturbation-facilitated optical-optical double resonance method with copropagating lasers. The unperturbed 1(b) 3Pi0 levels are split into four hyperfine components by the Fermi contact interaction bFIS. Mixing between the 1(b) 3Pi0 and 2(A) 1Sigma+ levels imparts hyperfine structure to the nominally singlet component of the perturbed levels and reduces the hyperfine splitting of the nominally triplet component. Theoretical analysis relates these observations to the hyperfine splitting that each 1(b) 3Pi0 level would have if it were not perturbed by a 2(A) 1Sigma+ level. Using this analysis, we demonstrate that significant hyperfine splitting arises because the 1(b) 3Pi0 state cannot be described as pure Hund's case (a). We determine bF for the 1(b) 3Pi0 levels and also a more accurate value for the magnitude of the singlet-triplet spin-orbit coupling HSO=[1(b) 3Pi0(vb,J)(H(SO))2(A) 1Sigma+(vA,J). Using the known spectroscopic constants of the 1(b) 3Pi state, we obtain bF=0.009 89+/-0.000 27 cm(-1). The values of (H(SO)) are found to be between 2 and 3 cm(-1), depending on vb, vA, and J. Dividing (H(SO)) by calculated vibrational overlap integrals, and taking account of the 1(b) 3Pi(Omega) rotational mixing, we can determine the magnitude of the electronic part H(el) of H(SO). Our results yield (H(el))=(16.33+/-0.15) cm(-1), consistent with our previous determinations using different techniques.     

Photodissociation spectroscopy of stored CH+ and CD+ ions: analysis of the b 3Sigma(-)-a 3Pi system

We have measured the photodissociation spectrum of CH(+) and CD(+) molecular ions, stored as fast (MeV) ion beams in the heavy-ion storage ring TSR. Several b (3)Sigma(-)-a (3)Pi bands were observed as strong resonances because a large fraction of the ions in the metastable a (3)Pi(v=0) state were pumped to b (3)Sigma(-) levels and predissociated via the c (3)Sigma(+) state into C(+) and H(D) fragments. From a rotational analysis of the 2-0, 3-0, and 4-0 bands in CH(+) and the 3-0 and 4-0 bands in CD(+), we derive spectroscopic constants for these levels and also revise a previous analysis of the 0-0 and 1-0 bands in CH(+). Combining all data delivers new, significantly adjusted equilibrium constants for the b (3)Sigma(-) and a (3)Pi electronic states. Apart from the spectroscopic analysis, we estimate the predissociation rates of the upper b (3)Sigma(-) vibrational levels in CH(+) and compare them to a model. For the initial rovibrational distribution of the stored metastable CH(+) molecules, the data indicate a faster vibrational cooling than derived before, and rotational cooling at a rate similar to the X (1)Sigma(+) ground state. New aspects of the spin-forbidden a (3)Pi-X (1)Sigma(+) radiative decay are discussed. Finally, we predict b (3)Sigma(-)-a (3)Pi absorption and a (3)Pi-X (1)Sigma(+) emission lines through which CH(+) in the metastable a (3)Pi(v=0) state might be detectable in astrophysical environments.     

Observation and calculation of the Cs2 2 3Delta(1g) and b 3Pi(0u) states

The Cs(2) 2 (3)Delta(1g) and b (3)Pi(0u) states have been observed by infrared-infrared double resonance spectroscopy for the first time. 221 2 (3)Delta(1g)<--A (1)Sigma(u) (+)<--X (1)Sigma(g) (+) double resonance lines have been assigned to transitions into the 2 (3)Delta(1g) v=6-13 vibrational levels. Resolved fluorescence into the b (3)Pi(0u) v(')=0-48 levels has been recorded. Molecular constants and potential energy curves are determined by the global fit of the entire set of the experimental data. Theoretical potential energy curves of the 2 (3)Delta(g) and b (3)Pi(u) states have been determined in the framework of the pseudopotential method and are compared with the experimental results.     

Identification and analysis of the perturbed c3Pi(v=1)-X 1Sigma+ and k 3Pi(v=5)-X 1Sigma+ absorption bands of carbon monoxide

Two new red-degraded bands in the room-temperature vacuum-ultraviolet absorption spectrum of carbon monoxide have been identified in the 94,000-94,500 cm(-1) energy region and analyzed. One of the bands at approximately 94,225 cm(-1) (106.1 nm) has three observable bandheads and is partially overlapped with the strong C 1Sigma+-X 1Sigma+ (1-0) transition at lower energy. It is assigned to the c 3Pi-X 1Sigma+ (1-0) transition. The other band at approximately 94,437 cm(-1) (105.9 nm) with one clear bandhead is assigned to the k 3Pi-X 1Sigma+ (5-0) transition. A strong homogeneous perturbation was found to exist between the two upper states that strongly influences the line positions and shapes of these bands. A rotational deperturbation analysis was performed and molecular rotational constants for both upper states were determined. These deperturbed molecular constants are entirely consistent with the expected values for the k 3Pi valence and c 3Pi Rydberg states. The Hamiltonian interaction term between these two states is found to be separable into vibrational and electronic factors and the electronic factor is determined to be H(e)=323+/-40 cm(-1). A discrepancy in the literature regarding the location of the c 3Pi (v=1) state is identified and discussed.     

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.     

Extremely narrow peaks in predissociation of sodium dimer due to rovibronic coupling

In sodium dimer the 2 (3)Pi(g), 3 (3)Pi(g), and 4 (3)Sigma(g) (+) electronic states are coupled; the coupling of the two (3)Pi(g) states is due to vibrational motion while the nonadiabatic interaction between the (3)Sigma(g) (+) and the (3)Pi(g) states-in particular, the 3 (3)Pi(g) state-is mediated by rotational interaction. The resulting vibronic problem is studied in some detail. The bound vibrational states of the 3 (3)Pi(g) and 4 (3)Pi(g) (+) states lie in the dissociation continuum of the 2 (3)Pi(g) state and become resonances due to the prevailing nonadiabatic coupling. The resonances are calculated using the complex scaling method and the available ab initio adiabatic potential energy curves. It is demonstrated that the resonances associated with rotational nonadiabatic coupling are narrower by several orders of magnitude than those that emerge from the vibrational nonadiabatic coupling. The predissociation cross section is computed and compared with experiment.     

Spectroscopic constants and potential energy curves of yttrium carbide (YC)

The potential energy curves of the low-lying electronic states of yttrium carbide (YC) and its cation are calculated at the complete active space self-consistent field and the multireference single and double excitation configuration interaction (MRSDCI) levels of theory. Fifteen low-lying electronic states of YC with different spin and spatial symmetries were identified. The X (4)Sigma- state prevails as the ground state of YC, and a low-lying excited A (4)Pi state is found to be 1661 cm(-1) higher at the MRSDCI level. The computations of the authors support the assignment of the observed spectra to a B (4)Delta(Omega=72)<--A (4)Pi(Omega=52) transition with a reinterpretation that the A (4)Pi state is appreciably populated under the experimental conditions as it is less than 2000 cm(-1) of the X (4)Sigma- ground state, and the previously suggested (4)Pi ground state is reassigned to the first low-lying excited state of YC. The potential energy curves of YC+ confirm a previous prediction by Seivers et al. [J. Chem. Phys. 105, 6322 (1996)] that the ground state of YC+ is formed through a second pathway at higher energies. The calculated ionization energy of YC is 6.00 eV, while the adiabatic electron affinity is 0.95 eV at the MRSDCI level. The computed ionization energy of YC and dissociation energy of YC+ confirm the revised experimental estimates provided by Seivers et al. although direct experimental measurements yielded results with greater errors due to uncertainty in collisional cross sections for YC+ formation.     

The radiative lifetime of metastable CO (a 3Pi, v=0)

We present a combined experimental and theoretical study on the radiative lifetime of CO in the a (3)Pi(1,2), v=0 state. CO molecules in a beam are prepared in selected rotational levels of this metastable state, Stark-decelerated, and electrostatically trapped. From the phosphorescence decay in the trap, the radiative lifetime is measured to be 2.63+/-0.03 ms for the a (3)Pi(1), v=0, J=1 level. From the spin-orbit coupling between the a (3)Pi and the A (1)Pi states a 20% longer radiative lifetime of 3.16 ms is calculated for this level. It is concluded that coupling to other (1)Pi states contributes to the observed phosphorescence rate of metastable CO.     

Theoretical study on the electronic states of NaLi

Configuration interaction calculations have been carried out on electronic states of the NaLi molecule and the cation NaLi(+). Potential energy curves are presented for the lowest nine (1)Sigma(+), seven (1)Pi, four (1)Delta, eight (3)Sigma(+), seven (3)Pi, and four (3)Delta states of NaLi as well as for the lowest ten (2)Sigma(+), six (2)Pi, and two (2)Delta states of NaLi(+). The results of the present many-electron configuration interaction calculations on the cation are in support of previous core-polarization effective potential calculations. The present calculations on the NaLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously as well as an investigation of nonadiabatic effects leading to spectral perturbations. Furthermore, ab initio potential energy curves of the neutral and the ground state of the cation are employed to determine quantum defect that may be employed to generate potential energy curves for nd and (n+1)p (for n>3) Rydberg states of NaLi. The present results on the 3 (1)Pi and 4 (1)Pi states are in good agreement with recent experimental work, whereas on the basis of theoretical data, the recently observed state 5 (1)Pi is better described as 6 (1)Pi.     

The spin-orbit and rotational constants for the N2 C" 5Pi(ui) (v = 3) state

The spin-orbit (A = -16.4 cm(-1)) and rotational (B = 1.017 cm(-1)) constants for the N2 C" 5Pi(ui)(v = 3) level are determined by a fit to rotational lines in the C" 5Pi(u)-A' 5Sigma(g)+(3-1) band that terminate in J'Omega' = 3(3), 4(3), 3(2), and 4(2) levels of the C" state. The C"-state spin-orbit constant is consistent with semi-empirical estimates, based on spin-orbit constants observed in several other electronic states of N2 and the atomic spin-orbit coupling constant, zeta(N 2p). The C"-A' bands exhibit the unusual feature of oppositely degraded sub-band heads, Omega' = 3 (red) and Omega' = 1, 0, and -1 (blue). The unusually wide range of B(Omega)eff values, from 0.85 cm(-1) (Omega = 3) to 1.28 cm(-1) (Omega = -1) for C" 5Pi(v = 3) should be diagnostically useful for Omega'-assignments. The C" 5Pi(v = 3) level lies 14257.17 and 90599 cm(-1) above A' 5Sigma(g)+(v = 1) and X 1Sigma(g)+(v = 0), respectively, and Re(C" 5Pi) = 1.50 A.     

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.     

Ab initio calculations and vibrational energy level fits for the lower singlet potential-energy surfaces of C3

Ab initio multireference configuration interaction potential energy surfaces are computed for the eight lowest singlet surfaces of C(3). These reveal several important features, including several conical intersections in linear, nonlinear, and equilateral triangle geometries. These intersections are important because, particularly for the excited A (1)Pi(u) state, reasonable ab initio results could only be obtained by including nearby, near degenerate, (1)Sigma(u) (-) and (1)Delta(u) states that cross the A (1)Pi(u) state around 4500 cm(-1) above the equilibrium geometry, and a (1)Pi(g) state whose potential in turn crosses the other states about 2000 cm(-1) further up. These states are probably responsible for the complexity of the shorter wavelength UV absorption spectrum of C(3). The computed potential energy surface for the ground, X (1)Sigma(g) (+), state and for the lowest two excited singlet surfaces (which both correlate with the A (1)Pi(u) state in a collinear geometry) are fitted to analytic functional forms. Vibrational energy levels are calculated for both states, taking account of the Renner-Teller coupling in the excited A (1)Pi(u) state. The potential parameters for both states are then least-squares fitted to experimental data. The ground-state fit covers a range of approximately 8500 cm(-1) above the lowest level, and reproduces 100 observed vibrational levels with an average error of 2.8 cm(-1). The A (1)Pi(u) state surfaces cover a range of 3250 cm(-1) above the zero-point level, and reproduce the 44 observed levels in this range with an average error of 2.8 cm(-1).     

Rovibrational energy transfer in the 4nu CH manifold of acetylene viewed by IR-UV double resonance spectroscopy. 2. Perturbed states with J = 17 and 18

Collision-induced state-to-state molecular energy transfer between rovibrational states in the 12,700 cm(-1) 4nu(CH) manifold of the electronic ground state X of acetylene (C(2)H(2)) is monitored by time-resolved infrared-ultraviolet double resonance (IR-UV DR) spectroscopy. Rotational J-states associated with the (nu(1) + 3nu(3)) or (1 0 3 0 0)(0) vibrational combination level, initially prepared by an IR pulse, are probed at approximately 299, approximately 296, or approximately 323 nm with UV laser-induced fluorescence via the Alpha electronic state. The rovibrational J-states of interest belong to a congested manifold that is affected by anharmonic, l-resonance, and Coriolis couplings, yielding complex intramolecular dynamics. Consequently, collision-induced rovibrational satellites observed by IR-UV DR comprise not only regular even-DeltaJ features but also supposedly forbidden odd-DeltaJ features. A preceding paper (J. Phys. Chem. A 2003, 107, 10759) focused on low-J-value rovibrational levels of the 4nu(CH) manifold (particularly those with J = 0 and J = 1) whereas this paper examines locally perturbed states at higher values of J (particularly J = 17 and 18, which display anomalous doublet structure in IR-absorption spectra). Three complementary forms of IR-UV DR experiments (IR-scanned, UV-scanned, and kinetic) are used to address the extent to which intramolecular perturbations influence the efficiency of J-resolved collision-induced energy transfer with both even and odd DeltaJ.     

Extensive ab initio study of the valence and low-lying Rydberg states of BBr including spin-orbit coupling

The electronic states of the BBr molecule, including 12 valence states and 12 low-lying Rydberg states, have been studied at the theoretical level of MR-CISD+Q with all-electron aug-cc-pVQZ basis sets and Douglas-Kroll [Ann. Phys. (N.Y.) 82, 89 (1974)] scalar relativistic correction. The spin-orbit coupling effect in the valence states was calculated by the state interaction approach with the full Breit-Pauli Hamiltonian. This is the first multireference ab initio study of the excited electronic states of BBr. Potential energy curves of all states were plotted with the help of the avoided crossing rule between electronic states of the same symmetry. The structural properties of these states were analyzed. Computational results reproduced most experimental data well. The transition properties of the a (3)Pi(0(+) ), a (3)Pi(1), and A (1)Pi(1) states to the ground state X (1)Sigma(0(+) ) (+) transitions were obtained, including the transition dipole moments, the Franck-Condon factors, and the radiative lifetimes. The evaluated radiative lifetime of the a (3)Pi(0(+) ), and a (3)Pi(1) states are near 1 ms, much longer than that of the A (1)Pi(1) state.     

Optogalvanic spectroscopy of the C"5Pi ui-A' 5Sigma+g electronic system of N2

We have recorded spectra involving the 3-1, 4-2, 2-0, and 2-2 bands of the C" 5Pi(ui)-A' (5)Sigma+(g) electronic system of N(2) using optogalvanic detection in a discharge through a supersonic jet expansion of argon mixed with a trace of nitrogen gas. The spectra have an effective rotational temperature of about 45 K. They involve all five spin-orbit components of the C" 5Pi(ui) state, which has allowed for precise determination of the spin-orbit coupling in this state. Analysis of the C" 5Pi(ui) state Lambda-doubling shows that it is caused primarily by a first-order spin-spin effect rather than by interaction with Sigma(u) (+/-) states. Our results allow us to assign lines in the 4-2 and 2-0 bands observed in a fluorescence depletion experiment conducted over ten years ago [Ch. Ottinger and A. F. Vilesov, J. Chem. Phys. 103, 9929 (1995)], and to comment on the suggestion that perturbations to the C (3)Pi(u) v=1 level of N(2) arise from interactions with the C" 5Pi(ui) state.