Vibration-rotation Spectra Research Articles

A calculation of the rovibronic energies and spectrum of the B̃A11 electronic state of SiH2

The B1A1 electronic state of silylene (SiH2) is the second excited singlet state of the molecule and, like the analogous c state of methylene (CH2), it is quasilinear with symmetry 1sigmag+ at linearity. This state dissociates to Si(1D) + H2(1sigmag+). At equilibrium, the B state of SiH2 has an energy that we calculate to be 0.71 eV above that of the dissociation products. However, there is a barrier to dissociation that allows quasibound rovibrational levels to occur, and some have been observed recently [Y. Muramoto et al., J. Chem. Phys. 122, 154302 (2005)]. Starting with our analytical ab initio potential-energy surface, we adjusted it in a fitting to the experimental term values in order to determine the optimum potential-energy function in the bound region. This potential has a C2v equilibrium structure with a SiH bond length of 1.459 angstroms and a bond angle of 165.4 degrees; the barrier to linearity is only 129 cm(-1). Using the optimized potential-energy surface we calculate B-state term values, and using our calculated y and z dipole moment surfaces, we simulate the rotation-vibration spectrum of the state in order to assist in the detection of the matrix isolation spectrum.

Calculating the vibration–rotation spectrum of water

The spectrum of water is ubiquitous and therefore the demand for a reliable theoretical model for it remains pressing. The treatment of nuclear motion using methods based on the variational principle has led to a major advance in the development of the model but places great emphasis on the accurate treatment of the underlying potential energy surface. Progress in constructing high-accuracy potentials both ab initio and by fitting to spectroscopic data is discussed.

Rotational-vibrational transitions of interstitial HD in Si

The ir spectrum of interstitial HD in Si provides unique insight into the rotational motion of interstitial ${\mathrm{H}}_{2}$ because the rotational-vibrational transitions for the heteronuclear HD molecule are subject to less restrictive selection rules. ir lines for transitions between rotational-vibrational states of the interstitial HD molecule with rotational quantum numbers $J=0$, 1, and 2 have been observed. The assignment of the rotational-vibrational spectrum of interstitial HD, with additional transitions that occur for HD but not for ${\mathrm{H}}_{2}$ or ${\mathrm{D}}_{2}$, is confirmed by uniaxial stress results.

Analysis of Pure Rotational and Vibration-rotational Spectra of NaCl X1Σ+and Quantum-chemical Calculation of Related Molecular Properties

We fitted published frequency and wave number data for pure rotational and vibration-rotational spectra, respectively, of 23Na35Cl and 23Na37Cl to derive parameters related to potential energy and to the rotational g factor. For comparison with these experimental data we undertook quantum-chemical computation of adiabatic corrections, rotational and vibrational g factors, electric dipolar moment and its derivative as a function of internuclear distance in a range near Re as a test of an algebraic approach to spectral analysis; experimental, 0.0287 ± 0.0014, and calculated, 0.02149, values of gr at Re are in moderate agreement. The combined results are discussed from a point of view of computational spectrometry.

Microwave spectroscopy of ternary and quaternary van der Waals clusters

The study of weakly bound complexes and clusters promises to provide a bridge between the properties of isolated molecules and those of dense phases. We describe briefly the method of pulsed nozzle Fourier transform microwave spectroscopy, which we use in our laboratory to study rotational and low-lying van der Waals vibrational spectra of weakly bound complexes and clusters. Systematic studies of three different classes of clusters are described: (i) mixed rare gas dimers, trimers, and tetramers, where the transition dipole moment is entirely provided by the weak van der Waals interactions; (ii) (rare gas)1,2,3–ammonia clusters where the internal motions of the ammonia subunit are affected by the rare gas atom solvation; (iii) (helium)1,2,3–molecule clusters, which provide a basis for the study of larger helium atoms containing clusters. We also discuss the effect of three-body non-additive contributions on spectroscopic parameters, such as dipole moments, rotational constants, and nuclear quadrupole coupling constants.

Dipole moment and rovibrational intensities in the electronic ground state of NH3: Bridging the gap between ab initio theory and spectroscopic experiment

We report theoretical values for the transition moments of an extensive set of vibrational bands in the electronic ground state of (14)NH(3). For selected bands, we have further made detailed simulations of the rotational structure. The calculations are carried out by means of recently developed computational procedures for describing the nuclear motion and are based on a high-level ab initio potential energy surface, and high-level dipole moment surfaces, for the electronic ground state of NH(3). The reported theoretical intensity values are compared to, and found to agree very well with, corresponding experimental results. It is believed that the computational method, in conjunction with high-quality ab initio potential energy and dipole moment surfaces, can simulate rotation-vibration spectra of XY(3) pyramidal molecules prior to observation with sufficient accuracy to facilitate the observation of these spectra. By degrading the accuracy of selected elements of the calculations, we have also investigated the influence of customary approximations on the computed intensity values.

Rotation–vibration motion of pyramidal XY3 molecules described in the Eckart frame: Theory and application to NH3

We present a new model for the rotation-vibration motion of pyramidal XY3 molecules, based on the Hougen–Bunker–Johns approach. Inversion is treated as a large-amplitude motion, while the small-amplitude vibrations are described by linearized stretching and bending coordinates. The rotation–vibration Schrödinger equation is solved variationally. We report three applications of the model to 14NH3 using an analytic potential function derived from high-level ab initio calculations. These applications address the J = 0 vibrational energies up to 6100 cm, the J≤2 energies for the vibrational ground state and the ν2, ν4, and 2ν2 excited vibrational states, and the J≤7 energies for the vibrational state. We demonstrate that also for four-atomic molecules, theoretical calculations of rotation–vibration energies can be helpful in the interpretation and assignment of experimental, high-resolution rotation–vibration spectra. Our approach incorporates an optimum inherent separation of different types of nuclear motion and thus remains applicable for rotation–vibration states with higher J values where alternative variational treatments are no longer feasible.

Pulsed supersonic expansions of CF 2 studied by diode laser spectroscopy

The vibration–rotation spectrum of the ν 3 band of CF 2 radical has been recorded in a supersonic expansion by tunable diode laser absorption spectroscopy near 1114 cm −1. The radical was prepared by pulse pyrolysis of hexafluoropropylene oxide, which decomposes at relatively low temperatures. The rotational temperature of CF 2 has been evaluated to be 260 ± 15 K for a heating nozzle temperature of 1225 K. The average absolute number density of the radical at the nozzle exit in the jet has been obtained, and the efficiency of precursor conversion into CF 2 is shown to be nearly unity at 1225 K.

The vibrational g-factor of dihydrogen from theoretical calculation and analysis of vibration-rotational spectra

We present the first results from quantum-chemical calculation of a vibrational g-factor; the calculations were performed at the level of full configuration interaction using a basis set of aug-cc-pVQZ quality. The theoretical results are consistent with experimental results from analysis of pure rotational and vibration-rotational spectra of dihydrogen in six isotopic variants, in which calculated results for either the rotational g-factor or adiabatic corrections are employed to constrain fits of coefficients of radial functions from wave numbers of transitions. When fits are constrained with data for the rotational g-factor, we reproduce also the radial dependence of adiabatic corrections relative to their value at equilibrium internuclear separation.

Global Least-Squares Analysis of the IR Rotation–Vibration Spectrum of HCl

The study of the IR rotation–vibration spectrum is a mainstay of the undergraduate laboratory curriculum in spectroscopy. Typical spectra consist of the fundamental and overtone bands for H35Cl and H37Cl (and sometimes D35Cl and D37Cl). These can be analyzed by least-squares fitting (i) one vibrational level at a time (using the method of combination differences), (ii) one band at a time, (iii) one isotopomer at a time, and (iv) both bands of both (or all) isotopomers simultaneously. The last two approaches involve the simultaneous fitting of two or more similar data sets and yield statistically optimal results. Procedures for doing such fits are illustrated for the data presentation and analysis program KaleidaGraph, with emphasis on the use of the program’s Macro Library for defining components of complex-fit models. Such methods greatly enhance operator efficiency and make global analysis truly feasible for students, as the only effort required of the user is (i) importing or entering the data and (ii)...

Line strengths and transition dipole moment of the ν2 fundamental band of the methyl radical

The line strengths of nine Q-branch lines in the nu(2) fundamental band of the methyl radical in its ground electronic state have been measured by diode laser absorption spectroscopy. The vibration-rotation spectrum of methyl was recorded in a microwave discharge in ditertiary butyl peroxide heavily diluted in argon. The absolute concentration of the radical was determined by measuring its kinetic decay when the discharge was extinguished. The translational, rotational, and vibrational temperatures, also required to relate the line strengths to the transition dipole moment, were determined from relative integrated line intensities and from the Doppler widths of the lines after allowing for instrumental factors. The line strengths of the nine Q-branch lines were used to derive a more accurate value of the transition dipole moment of this band, mu(2)=0.215(25) D. Improved accuracy over earlier measurements of mu(2) (derived from line strengths of single lines) was obtained by integrating over the complete line profile instead of measuring the peak absorption and assuming a Doppler linewidth to deduce the concentration. In addition, a more precise value for the rate constant for methyl radical recombination than available earlier was employed. The new value of mu(2) is in very good agreement with high-quality ab initio calculations. Furthermore, the ratio of the transition dipole moments of the nu(2) and nu(3) fundamental bands in the gas phase is now in highly satisfactory agreement with the ratio determined for the condensed phase.

Infrared and near infrared emission spectra of SbH and SbD

The X 3Σ − ground state vibration–rotation spectrum of SbH and the near infrared spectra of the b 1Σ +– X 3Σ − transitions of SbH and SbD have been measured at high resolution by Fourier transform spectroscopy. The SbH and SbD radicals were generated in a tube furnace with a D.C. discharge of a flowing mixture of argon, hydrogen (or deuterium), and antimony vapor. In the infrared region, the 1–0 and 2–1 bands of the three components (0 +, 1 e , and 1 f ) as well as the 0 + component of the 3–2 band were observed for 121SbH and 123SbH. In the near infrared region, the 0–0, 1–1, and 2–2 bands of the b 1Σ +– X 3Σ − system of both SbH and SbD as well as the 3–3 band of SbD were observed. Except for a few lines, the antimony isotopic shift was not resolved for these electronic spectra. The present data set was combined with the available ground state data on SbD and a 1Δ data for SbH and SbD from previous work, and a least-squares fit was performed for each of the four isotopologues: 121SbH, 123SbH, 121SbD, and 123SbD. Improved spectroscopic constants were obtained for the observed vibrational levels of the X 3Σ −, a 1Δ, and b 1Σ + states of these four isotopologues. In addition, all the above data were also fitted simultaneously to a multi-isotopologue Dunham model, which yielded Dunham constants and Born–Oppenheimer breakdown parameters for these three electronic states. Interestingly, we found that Born–Oppenheimer breakdown corrections were also required for some of the spin–spin and spin–rotation parameters of the X 3Σ − state.

DVR3D: a program suite for the calculation of rotation–vibration spectra of triatomic molecules

The DVR3D program suite calculates energy levels, wavefunctions, and where appropriate dipole transition moments, for rotating and vibrating triatomic molecules. Potential energy and, where necessary, dipole surfaces must be provided. Expectation values of geometrically defined functions can be calculated, a feature which is particularly useful for fitting potential energy surfaces. The programs use an exact (within the Born–Oppenheimer approximation) Hamiltonian and offer a choice of Jacobi or Radau internal coordinates and several body-fixed axes. Rotationally excited states are treated using an efficient two-step algorithm. The programs uses a Discrete Variable Representation (DVR) based on Gauss–Jacobi and Gauss–Laguerre quadrature for all 3 internal coordinates and thus yields a fully point-wise representation of the wavefunctions. The vibrational step uses successive diagonalisation and truncation which is implemented for a number of possible coordinate orderings. The rotational, expectation value and transition dipole programs exploit the savings offered by performing integrals on a DVR grid. The new version has been rewritten in FORTRAN 90 to exploit the dynamic array allocations and the algorithm for dipole and spectra calculations have been substantially improved. New modules allow the z-axis to be embedded perpendicular to the plane of the molecule and for the calculation of expectation values. Program summary Title of the program: DVR3D suite Catalogue number: ADTI Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTI Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Programming language: Fortran 90 No. of lines in distributed program, including test data, etc.: 61 574 No. of bytes in distributed program, including test data, etc.: 972 404 Distribution format: tar.gz New version summary Title of program: DVR3DRJZ Catalogue number: ADTB Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADTB Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Reference in CPC to previous version: 86 (1995) 175 Catalogue identifier of previous version: ADAK Authors of previous version: J. Tennyson, J.R. Henderson and N.G. Fulton Does the new version supersede the original program?: DVR3DRJZ supersedes DVR3DRJ Computer: PC running Linux Installation: desktop Other machines on which program tested: Compaq running True64 Unix; SGI Origin 2000, Sunfire V750 and V880 systems running SunOS, IBM p690 Regatta running AIX Programming language used in the new version: Fortran 90 Memory required to execute: case dependent No. of lines in distributed program, including test data, etc.: 4203 No. of bytes in distributed program, including test data, etc.: 30 087 Has code been vectorised or parallelised?: The code has been extensively vectorised. A parallel version of the code, PDVR3D has been developed [1], contact the first author for details Additional keywords: perpendicular embedding Distribution format: gz Nature of physical problem: DVR3DRJZ calculates the bound vibrational or Coriolis decoupled rotational–vibrational states of a triatomic system in body-fixed Jacobi (scattering) or Radau coordinates [2] Method of solution: All coordinates are treated in a discrete variable representation (DVR). The angular coordinate uses a DVR based on (associated) Legendre polynomials and the radial coordinates utilise a DVR based on either Morse oscillator-like or spherical oscillator functions. Intermediate diagonalisation and truncation is performed on the hierarchical expression of the Hamiltonian operator to yield the final secular problem. DVR3DRJ provides the vibrational wavefunctions necessary for ROTLEV3, ROLEV3B or ROTLEV3Z to calculate rotationally excited states, DIPOLE3 to calculate rotational–vibrational transition strengths and XPECT3 to compute expectation values Restrictions on the complexity of the problem: (1) The size of the final Hamiltonian matrix that can practically be diagonalised. (2) The order of integration in the radial coordinates that can be dealt with within the machine exponent range. Some adjustment in the code may be necessary when large order Gauss–Laguerre quadrature is used Typical running time: Case dependent but usually dominated by the final (3D) matrix diagonalisation. The test runs take minutes on a fast PC Unusual features of the program: A user supplied subroutine containing the potential energy as an analytic function is a program requirement

Infrared spectra of carbon monoxide–hydrogen sulfide van der Waals complexes in the C–O stretching region

The CO-stretching vibration–rotation spectra of CO–H 2S, CO–D 2S, and CO–HDS complexes have been studied in the 2150 cm −1 region using a supersonic slit-jet expansion and a tunable diode laser spectrometer. The spectra were analyzed with the help of very recent microwave pure rotational studies of the same complexes. Two bands were assigned for each of the symmetric hydrogen sulfide isotopes, corresponding to the two nuclear spin modifications, para and ortho. The band origins were blue shifted, relative to the free CO molecule, by about 3.8 cm −1 for CO–H 2S and 4.3 cm −1 for CO–D 2S. These are considerably smaller shifts than exhibited by the related CO–water complexes, indicating that the intermolecular forces in CO–H 2S are weaker and more isotropic.

Direct potential fit analysis of the X1sigma+ ground state of CO.

A collection of 21,559 highly precise spectroscopic line positions from pure rotational and vibration-rotational spectra for seven isotopomers of carbon monoxide in the X1sigma+ ground electronic state has been employed in direct least-squares fits of the rovibrational Hamiltonian operator obtained from Watson's work [J. Mol. Spectrosc. 80, 411 (1980)] and that obtained by Herman and Ogilvie [Adv. Chem. Phys 103, 187 (1998)]. Fully analytical models are used for the various functions, including the Born-Oppenheimer internuclear potential function, and an account is taken of breakdown of the Born-Oppenheimer approximation. The resulting representations are more compact than currently available traditional Ukl/deltakl extended Dunham descriptions, and they generate quantum-mechanical eigenvalues that reproduce reliably the spectroscopic line positions to within the associated measurement uncertainties. Rayleigh-Schrodinger perturbation theory has been used to calculate highly accurate rotational and centrifugal distortion constants Bupsilon-Oupsilon for nine isotopomers of carbon monoxide. These constants are just as successful at reconstructing the observed spectroscopic information as the quantum-mechanical eigenvalues of the fitted Hamiltonian operators.

Diode laser spectroscopy of the fundamental bands of [formula omitted], [formula omitted], [formula omitted], [formula omitted] free radicals in the ground 2Σ + electronic state

Rotationally resolved spectra of the fundamental band of the CN free radical in four isotopic forms have been measured using tunable diode laser absorption spectroscopy. The source of the radical was a microwave discharge in a mixture of isotopically selected methane and nitrogen diluted with argon. The lines were measured to an accuracy of 5×10 −4 cm −1 and fitted to the formula for the vibration rotation spectrum of a diatomic molecule, including quartic distortion constants. The band origins of each of the isotopomers from the five parameter fits were found to be 12 C 14 N : 2042.42115(38) cm −1, 13 C 14 N : 2000.08479(23) cm −1, 12 C 15 N : 2011.25594(25) cm −1, 13 C 15 N : 1968.22093(33) cm −1 with one standard deviation from the fit given in parenthesis. Some of the lines showed a resolved splitting due to the spin rotation interaction. This was averaged for fitting purposes. The average equilibrium internuclear distance derived from the v=0 and 1 rotational constants of the four isotopomers is 1.171800(6) Å which is in good agreement with the value determined from microwave spectroscopy.

The vibration–rotation spectrum of 12C 2HD: new overtone bands and global vibrational analysis

Two new bands, 2 ν 1+ ν 2+ ν 3+2 ν 5 and 5 ν 3 with origin at 12220.692 and 12496.158 cm −1, respectively, were identified on new FT-ICLAS spectra of 12C 2HD and rotationally analyzed. The rotational analysis of two known bands, with origin at 12038.538 and 12234.872 cm −1 was extended. Another band, 2 ν 1+2 ν 5 with origin at 7843.6622 cm −1, was identified for the first time and rotationally analyzed, from a high pressure conventional FT spectrum. Some 115 known vibrational state energies in the molecule, extending up to the visible range, were used to produce updated vibrational constants. Both a straightforward Dunham model and a global model accounting for a single anharmonic resonance, K 1/255, were used. The results are discussed.

Absorption spectroscopy in solid hydrogen: challenges to experimentalists and theorists

Hydrogen is the most abundant molecule in the universe, and over the years has provided a fundamental testing ground for both theory and experiment. By symmetry, isolated H 2 molecules do not have allowed dipole rotational or vibration-rotational spectra. However, when they interact in the gas, liquid, or solid, there are induced dipoles that can interact with radiation. In the solid because of the large lattice constant, these dipoles arise primarily from the long-range induction by multipole moments of one molecule with the polarizability in its neighbors. By analyzing the intensities, one is able to obtain experimental values for not only the quadrupole moment, but also for higher-order moments as well. In the present paper, we review only a very limited part of the extensive research that has been carried out; namely, that of solid H 2 , although extensive experimental and theoretical results for other phases and for other isotopes exist. Solid H 2 is a quantum crystal, in which the individual molecules undergo almost free rotation and vibration in the hcp lattice. This simplifies the identification of the observed transitions based on their frequencies calculated from well-known gaseous spectroscopic constants. Although high-resolution studies have revealed subtle effects such as crystal-field splittings, interferences between the allowed and induced dipoles in HD, structure of the phonon density of states, triple transitions, etc. we limit ourselves to only the zero-phonon single and double transitions in para -hydrogen, or for an isolated ortho -hydrogen molecule in a para -hydrogen environment. We review the extensive literature over the last four decades, and present comparisons between theory and experiment. From this analysis, we can draw a number of conclusions about the accuracy and consistency of the experimental data and the need for improvements in theory.

Absorption spectroscopy in solid hydrogen: challenges to experimentalists and theorists

Hydrogen is the most abundant molecule in the universe, and over the years has provided a fundamental testing ground for both theory and experiment. By symmetry, isolated H 2 molecules do not have allowed dipole rotational or vibration-rotational spectra. However, when they interact in the gas, liquid, or solid, there are induced dipoles that can interact with radiation. In the solid because of the large lattice constant, these dipoles arise primarily from the long-range induction by multipole moments of one molecule with the polarizability in its neighbors. By analyzing the intensities, one is able to obtain experimental values for not only the quadrupole moment, but also for higher-order moments as well. In the present paper, we review only a very limited part of the extensive research that has been carried out; namely, that of solid H 2, although extensive experimental and theoretical results for other phases and for other isotopes exist. Solid H 2 is a quantum crystal, in which the individual molecules undergo almost free rotation and vibration in the hcp lattice. This simplifies the identification of the observed transitions based on their frequencies calculated from well-known gaseous spectroscopic constants. Although high-resolution studies have revealed subtle effects such as crystal-field splittings, interferences between the allowed and induced dipoles in HD, structure of the phonon density of states, triple transitions, etc. we limit ourselves to only the zero-phonon single and double transitions in para-hydrogen, or for an isolated ortho-hydrogen molecule in a para-hydrogen environment. We review the extensive literature over the last four decades, and present comparisons between theory and experiment. From this analysis, we can draw a number of conclusions about the accuracy and consistency of the experimental data and the need for improvements in theory.

Can ortho-para transitions for water be observed?

The spectrum of water can be considered as the juxtaposition of the spectra of two molecules, with different total nuclear spin: ortho-H2O, and para-H2O. No transitions have ever been observed between the two different nuclear-spin isotopomers. The interconversion time is unknown and it is widely assumed that interconversion is forbidden without some other intervention. However, weak nuclear spin-rotation interaction occurs and can drive ortho to para transitions. Ab initio calculations show that the hyperfine nuclear spin-rotational coupling constants are about 30 kHz. These constants are used to explore the whole vibration-rotation spectrum with special emphasis on the coupling between nearby levels. Predictions are made for different spectral regions where the strongest transitions between ortho and para levels of water could be experimentally observed.