Effective Rotational Constants Research Articles

OCS in small para-hydrogen clusters: Energetics and structure with N=1–8 complexed hydrogen molecules

We determine the structure and energetics of complexes of the linear OCS molecule with small numbers of para-hydrogen molecules, N=1–8, using zero temperature quantum Monte Carlo methods. Ground state calculations are carried out with importance-sampled rigid body diffusion Monte Carlo and excited state calculations with the projection operator imaginary time spectral evolution methodology. The ground states are found to be highly structured, with a gradual build up of two axial rings as N increases to 8. Analysis of the azimuthal density correlations around the OCS molecule shows that these rings are quite delocalized for small N values, but become strongly localized for N⩾5. Excited state calculations are made for a range of total cluster angular momentum values and the rotational energy levels fitted to obtain effective rotational and distortion constants of the complexed OCS molecule as a function of cluster size N. Detailed analysis of these spectroscopic constants indicates that the complexes of OCS with para-hydrogen have an unusually rich variation in dynamical behavior, with sizes N=1–2 showing near rigid behavior, sizes N=3–4 showing extremely floppy behavior, and the larger sizes N=5–8 showing more rigid behavior again. The large values of the distortion constant D obtained for N=3–4 are rationalized in terms of the coupling between the OCS rotations and the “breathing” mode of the first, partially filled ring of para-hydrogen molecules.

Rotational spectrum of CoF in the X[formula omitted] electronic ground state

The rotational spectrum of the CoF radical in the X 3 Φ 4 state was observed by employing a source modulation microwave spectrometer. The CoF radical was generated in a free space cell by a dc glow discharge in CF 4 and He. The cobalt atoms were supplied by the sputtering reaction from cobalt powder placed over a lower surface of the cylindrical electrodes. The transitions with J=11–10 to 17–16 were measured in the region between 250 and 400 GHz. The effective rotational, centrifugal distortion, and hyperfine constants were obtained by a least-squares analysis.

Photoassociation of ultracold K atoms: Observation of high lying levels of the 1g∼1 1Πg molecular state of K2

Very high-lying vibrational levels of the 1g∼1 1Πg electronic state of K2 have been observed in a photoassociation experiment using an ion detection scheme. The photoassociation measurements have been treated together with laser induced fluorescence data recorded by Fourier transform spectrometry to construct a pointwise potential curve for this electronic state. Several vibrational levels were observed by both techniques, so the dissocation energy can be deduced without extrapolation, from the sum of binding energies measured in photoassociation and vibrational energies established with respect to the potential minimum (defined by the fluorescence data), giving De=1290.292±0.002 cm−1 (1 standard deviation). The potential curve reproduces over 2000 term values (up to v=138) with a root mean square error of 0.0025 cm−1. Nevertheless, small differences are found between the rotational constants generated from the potential curve and the effective rotational constants deduced from binding energy measurements at very high v. The smoothness of the outermost part of the pointwise potential energy curve has been investigated through fits to a Hund’s case (c) asymptotic model.

High resolution FTIR spectroscopy of 1,1,1,2-tetrafluoroethane: [formula omitted

High resolution FTIR spectra of 1,1,1,2-tetrafluoromethane (R134a) were recorded using both an enclosive flow cell and a supersonic jet expansion. The temperature in the collisionally cooled enclosive flow was approximately 150 K, whilst in the jet a rotational temperature of 65 K was achieved. A rovibrational analysis was performed for ν 6 , an a / b hybrid band at 1104.5 cm - 1 . Least squares fits were used to derive effective rotational and centrifugal distortion constants for ν 6 using a total of 799 assigned transitions with quantum numbers up to K a = 21 and J = 32 . A second fit is presented considering the Coriolis interactions with two dark state combination bands perturbing the rotational structure of the fundamental, fitting a total of 1118 lines and with quantum numbers up to K a = 21 and J = 42 .

The S1state geometry of phenol determined by simultaneous Franck–Condon and rotational constants fits

We describe a program for Franck–Condon simulations of dispersed fluorescence spectra obtained from excitation of single vibronic fundamental, overtone and combination levels. The S1 state geometry of phenol has been determined by a simultaneous fit of the geometry to the vibronic intensities and effective rotational constants in the harmonic limit based on ab initio force constants.

Rovibrational energy levels of the LiOLi molecule from dispersed fluorescence and stimulated emission pumping studies

Dispersed fluorescence (DF) and stimulated emission pumping (SEP) experiments have been carried out on the jet-cooled 7Li16O7Li molecule. Rotationally resolved SEP bands to υ2l(l=0,2) vibrational angular momentum levels show that LiOLi is a linear molecule. The DF experiments have resulted in the measurement of 54 (υ1,υ2l,0) levels of the X̃ 1Σg+ ground state, up to 6000 cm−1. The energy levels determined experimentally are amazingly close to those calculated very recently for a high-level ab initio LiOLi(X̃ 1Σg+) potential surface. The DF vibrational level energies are analyzed and discussed in terms of a global fit to an 11-term power series. From the SEP experiments, effective rotational constants Bυ1,υ2l,0 for several of these vibrational levels [including σg+(l=0) and δg(l=2) vibrational angular momentum states for (υ1,υ2l⩾2(even),υ3=0) levels] have also been determined. The bond distance R0 is estimated to be 1.611±0.003 Å from an extrapolation of Bυ1,0,0 values. Finally, the unusual “Li+O−2Li+” ionic bonding and the low ω2=112 cm−1 bending frequency for LiOLi(X̃ 1Σg+) are briefly discussed.

Hyperfine Interactions in HSiCl

The J = 1−0 transitions of the microwave spectra of H28Si35Cl, H28Si37Cl, H29Si35Cl, and H30Si35Cl were measured at 14−15 GHz. The effective rotational constants are obtained, and the chlorine nuclear quadrupole coupling constants and nuclear spin-rotation constants of the four isotopomers are determined for the first time. These constants are compared with their values obtained from ab initio calculations.

Laser induced fluorescence spectroscopy of the HC 6S radical

New vibronic bands were observed in the 17 000–17 600 cm −1 region by laser induced fluorescence (LIF) spectroscopy in the discharged products of a mixture of C 2H 2 and CS 2 in a supersonic jet. The effective rotational constants and the position of the vibronic band origin have been determined to be B″ eff =0.01910(2) cm −1, B ′ eff =0.01891(2) cm −1 , and T 0=16961.5161(5) cm −1 , respectively. The spectral carrier of the bands has been confirmed to be the HC 6S radical from the chemical behavior of the products and the determined rotational constant.

High-Resolution Visible Laser Spectroscopy of Cobalt Monochloride

The electronic spectrum of cobalt monochloride has been investigated from 415 to 725 nm using a laser-ablation/molecular-beam laser-induced fluorescence spectrometer. Two separate electronic systems with origins near 483.3 and 470.3 nm were observed. Data have been recorded for these two transitions at both low and high resolution. These transitions are now characterized as the [20.7]3Φ4−X3Φ4 and [21.3]3Φ4−X3Φ4 transitions. A low-resolution vibrational analysis and a high-resolution rotational analysis have been carried out for each system, resulting in accurate values for the ground and excited state vibrational spacings and effective rotational constants. In addition, the magnetic hyperfine structure resulting from the spin of the Co nucleus was resolved and the hyperfine constants were determined. Comparison of the CoCl spectrum with that of CoH and CoF has allowed the ground state electron configuration of (core)(10σ)2(4π)4(1δ)3(5π)3(11σ)2 to be determined. The hyperfine constants support the electron promotion 11σ→12σ for the observed transitions.

Laser induced fluorescence spectroscopy of the HC 4S and DC 4S radicals

Vibronic band systems for the HC 4S and DC 4S radicals were observed in supersonic jets for the first time by laser induced fluorescence (LIF) spectroscopy. The rotational structures of the bands were resolved by high-resolution scans. It was found that all the observed bands are 2Π 3/2– 2Π 3/2 transitions. Band origins and effective rotational constants of the origin bands are determined to be T 0=19 980.687(1) and B ′ eff =0.046580(4) cm −1 for HC 4S, T 0=20 034.8748(9) and B eff ′=0.044294(3) cm −1 for DC 4S. Ab initio calculations were carried out to interpret the vibronic transitions.

Electronic spectroscopy in He droplets

Recent experiments on the electronic spectroscopy of atoms, clusters, and organic molecules embedded in helium nanodroplets are reviewed. Electronic transitions imply a larger degree of distortion of the helium environment as compared to vibrational and rotational excitations. Thus new phenomena arise such as the appearance of side bands in the spectra, which are due to the excitation of helium collective vibrations, large changes of the effective molecular rotational constants and even the expulsion of an atom (or molecule) from the cluster upon excitation. These features make it possible to probe the helium environment and its interactions with molecular chromophores on the atomic scale. Real-time studies of the manifestations of superfluidity and of chemical processes in the droplets via femtosecond excitation techniques, provide a new perspective to this field. The considerable amount of data available so far shows the large potential of helium droplets for isolation and spectroscopy of large molecules and clusters. The low temperature and the high spectral resolution achievable because of the relative homogeneity of this medium, are instrumental for separating solvation effects that are obscured by the presence of much larger fluctuations in more classical environments. Hence, electronic and geometrical structures of even large entities become accessible.

Quantum structure and rotational dynamics of HCN in helium clusters

We present diffusion Monte Carlo calculations of ground states and rotationally excited states of HCN Hen4, using our recently developed algorithm for importance sampled rigid body diffusion Monte Carlo [Viel et al., Comput. Phys. Commun. (in press, 2001)] within the mixed frame implementation. Excited states are studied with both fixed node approximations, and the Projection Operator Imaginary Time Spectral Evolution (POITSE) method that allows nodal constraints to be circumvented. Improvements in the POITSE algorithm allow excited states of clusters with up to 80 degrees of freedom to be determined here. The results presented here show that the rotational dynamics of the HCN molecule in He4 clusters are very different from the behavior of heavier molecules such as SF6. Detailed analysis of ground state densities shows that the lighter HCN molecule induces negligible adiabatic following of the helium density as a result of its rotational motion. The excited state calculations show that for small numbers of He4 atoms the nodal structure does not correspond to that of a freely rotating molecule. Nevertheless, the POITSE calculations indicate that there is some admixture of this nodal structure in the low-lying rotational excitations. It is found that a relatively large number of He4 atoms are required to achieve saturation of the effective rotational constant at the experimental value, in contradistinction to the small numbers of atoms required to saturate the rotational constant for heavier molecules such as SF6 and OCS.

Submillimeter-Wave Spectroscopy of TiCl in the Ground Electronic State

The submillimeter-wave rotational transitions of TiCl in the ground state were observed using a double-modulation technique. TiCl was generated in a DC-discharge of a mixture of TiCl4 vapor (less than 1 mTorr) and Ar buffer gas (80 mTorr) at a current of 200 mA. The 4Φ3/2, 4Φ5/2, 4Φ7/2, and 4Φ9/2 spin components of Ti35Cl (v=0, 1, 2) and Ti37Cl (v=0) were detected. The data were analyzed using effective rotational constants for each spin component as well as with the usual N2 reduced Hamiltonian. Recent Fourier transform and laser data were included in our fits and we confirm that the ground state of TiCl is a 4Φr electronic state.

Ab Initio Study on the Equilibrium Structure and CCN Bending Energy Levels of Cyanofulminate (NCCNO)

The molecular parameters of cyanofulminate, NCCNO, have been determined in large-scale ab initio calculations using the coupled-cluster method, CCSD(T), and basis sets of double- through quadruple-ζ quality. The equilibrium structure of the molecule was found to be linear, with a strongly anharmonic potential energy function of the CCN bending motion (ν7 mode). The rotation−bending energy levels were then calculated using a semirigid-bender Hamiltonian. The vibrational energy levels and effective rotational constants determined for various ν7 states were found to be in good agreement with the experimental data.

Fourier transform millimeter-wave spectroscopy of chlorocarbene (HCCl)

The 101–000 and 202–101 rotational transitions of HC35Cl and HC37Cl in the X̃ 1A′ ground vibronic state have been observed with a Fourier transform millimeter-wave spectrometer. The HCCl molecule is produced by discharging a gaseous sample of CH2Cl2 diluted in Ar with a pulsed discharge nozzle. The effective rotational constant (B+C)/2, the centrifugal distortion constant ΔJ, the nuclear quadrupole interaction constants, and the nuclear-spin rotation interaction constant are determined for each isotopic species. The nuclear-spin rotation interaction is found to make a significant contribution to the hyperfine structure of this molecule, which originates from the relatively low-lying electronic excited state. The nuclear quadrupole interaction tensor is highly asymmetric, indicating a significant π character of the C–Cl bond. This can be interpreted in terms of the backdonation of π electrons from the chlorine atom to the carbon atom.

Microwave Spectrum of the FCO Radical in the 2A′ Electronic Ground State

The 101–000, 202–101, and 303–202 rotational transitions of the FCO radical are observed at 22.3, 44.5, and 66.8 GHz, respectively, using a Fourier transform millimeter-wave spectrometer with a pulsed discharge nozzle. The FCO radical is produced by discharging F2CO diluted in the Ar buffer gas. Twelve fine and hyperfine components for the three transitions are observed, and the effective rotational constant, the centrifugal distortion constant, the spin–rotation constant with its centrifugal correction term, and three hyperfine constants are determined. Furthermore, the vibrational satellites for the v1=1, v2=1, v3=1, and v3=2 states are also observed in the 22.3 GHz region. From the dipolar interaction constants, the principal axis of the dipolar interaction tensor is estimated and is discussed in relation to the distribution of the unpaired electron.

Rotation in liquid He4 Lessons from a highly simplified model

This paper presents an analysis of a model problem, consisting of two interacting rigid rings, for the rotation of molecules in liquid He4. Due to Bose symmetry, the excitation of the rotor corresponding to a ring of N helium atoms is restricted to states with integer multiples of N quanta of angular momentum. This minimal model shares many of the same features of the rotational spectra that have been observed for molecules in nanodroplets of ≈103–104 helium atoms. In particular, this model predicts, for the first time, the very large enhancements of the centrifugal distortion constants that have been observed experimentally. It also illustrates the different effects of increasing rotational velocity by increases in the angular momentum quantum number or by increasing the rotational constant of the molecular rotor. It is found that a fixed node, diffusion Monte Carlo and a hydrodynamic model provide upper and lower bounds respectively on the size of the effective rotational constant of the molecular rotor when coupled to the helium.

Spectra of jet-cooled SO232 and SO234 in systems ã 3B1 and b̃ 3A2–X̃ 1A1: Rotational structure of perturbed b̃ 3A2

Spectra of ã 3B1(ν1ν2ν3)=(110) and (200)–X̃ 1A1(000) of SO232 and SO234 are obtained in a supersonic jet at a resolution 0.015 cm−1. The rotational structures are analyzed for both isotopic species to obtain precise rotational and spin constants. Two new bands at 27 032.222(1) and 27 515.41(1) cm−1 arising from vibronic interaction separately with vibrational state (110) and (200) of ã 3B1 are assigned to transitions to b̃ 3A2(011) and (101). The rotational structure of b̃ 3A2 is observed and analyzed for the first time. The two vibrational states are analyzed to yield effective rotational constants A=1.4348(3), 1.89(3), B=0.3610(3), 0.412(3), and C=0.2689(3), 0.239(3) cm−1, respectively. Then the difference ν1−ν2 of vibrational frequency of b̃ 3A2 is obtained to be 483.19 cm−1. Because of interaction to b̃ 3A2(011) the observed spacing of K stack and spin constants α and β for ã 3B1(110) are smaller whereas the state ã 3B1(200) is relatively unaffected and only spin constants vary significantly.

Application of the Symmetric Top Approximation to Spectroscopy of High-Temperature Water Vapor

A new model for calculating the energies of pure rotational levels of water vapor molecules treated as a symmetric top is suggested for large values of the quantum number Ka ≥ J/2 >> 1. The effective rotational constants of model representation (using the Pade form) of the ground vibrational state of the H2O molecule are determined. The results of calculations of the rotational line intensities and positions of line centers for the suggested model are preliminarily tested with the help of the information system HOTGAS. The contribution of transitions between high rotational states to the water vapor absorption at temperatures between 1000 and 10000 K is estimated for the 8–12 μm wavelength range.

Intermolecular potential-energy surface for the Ar–SH(2Πi) complex studied by Fourier-transform microwave spectroscopy

Rotational spectra of the Ar–SH(2Πi) radical complex and its deuterated species have been studied using a Fourier-transform microwave spectrometer. The complexes are produced in a supersonic free jet using a pulsed discharge of H2S or D2S diluted in Ar. R-branch transitions in the lower spin component (Ω=3/2) for the linear Πi2 radical were observed for J″=1.5–7.5 in the 8–26 GHz region, in which the parity doublings and hyperfine splittings associated with the H/D nuclei have been observed. Effective rotational constants for Ar–SH and Ar–SD are determined to be 1569.660(3) and 1567.723(4) MHz, respectively, using an effective Π2 Hamiltonian including hyperfine terms. An effective centrifugal distortion constant, D, has been determined to be negative. A two-dimensional intermolecular potential energy surface for the Ar–SH(2Πi) complex has been derived from a least-squares fitting of the observed rotational transitions, where several parameters are constrained to the values from an ab initio calculation at the RCCSD(T)/aug-cc-pVQZ level. The average potential turned out to be fairly isotropic with two shallow minima corresponding to the linear Ar⋯SH and Ar⋯HS configurations, among which the former is 7.2 cm−1 more stable than the latter. The determined equilibrium distance between Ar and the SH center-of-mass is 3.791 Å at the Ar⋯SH global minimum configuration. The vibrational ground state is located above the barrier of only about 20 cm−1 between the two minima, and its wave function is widely spread along the bending coordinate. The negative sign of the effective D constant is well explained by the enhancement of the probability at the linear Ar⋯SH configuration by the centrifugal force, which results in a decrease of the vibrationally averaged Ar–SH intermolecular distance.