Linear Polyatomic Molecules Research Articles

Vibrational excitation and relaxation of five polyatomic molecules in an electrical discharge

Vibrational excitation and relaxation of five linear polyatomic molecules, OCS, OC3S, HC3N, HC5N, and SiC2S, have been studied by Fourier transform microwave spectroscopy in a supersonic expansion after the application of a low-current dc electric discharge. For each chain, the populations in bending and stretching modes have been characterized as a function of the applied discharge current; for stable OCS and HC3N, vibrational populations were studied as well in the absence of a discharge. With no discharge present the derived vibrational temperatures are slightly below T, the temperature of the gas before the supersonic expansion (i.e., 300 K). In the presence of the discharge, vibrational excitation occurs via inelastic collisions with the electrons and the vibrational temperatures rise as the applied current increases. Global vibrational relaxation is governed by rapid vibration-vibration (VV) energy transfer and slow vibration-translation (VT) energy transfer. The latter process is rate-determining and depends primarily on the wave number of the vibration. Vibrational modes with wave numbers near and below kT/hc (where T = 300 K and kT/hc-210 cm(-1)) are efficiently cooled by VT transfer because a sufficient number of collisions occur in the initial stages of the supersonic expansion. Vibrational modes with wave numbers around 450 cm(-l) appear to be inefficiently cooled in the molecular beam; at these energies VV and VT rates are probably comparable. For high-frequency vibrations, VV energy transfer dominates. For the longer chains OC3S and HC5N, higher-lying modes are generally not detectable and vibrational temperatures of most lower-lying modes were found to be lower than those of OCS and HC3N, suggesting that as the size of the molecules increases, intermode VV transfer becomes more efficient, plausibly due to the higher density of vibrational levels. New high resolution spectroscopic data have been obtained for several vibrationally excited states of OC3S, HC3N, and HC5N. Rotational lines of the 13C and 15N isotopic species of HC5N have been measured, yielding improved rotational and centrifugal distortion constants; 14N nitrogen quadrupole coupling constants for the isotopic species of HC5N with 13C have been determined for the first time.

An Atomic Charge−Charge Flux−Dipole Flux Atom-in-Molecule Decomposition for Molecular Dipole-Moment Derivatives and Infrared Fundamental Intensities

The molecular dipole moment and its derivatives are determined from atomic charges, atomic dipoles, and their fluxes obtained from AIM formalism and calculated at the MP2(FC)/6-311++G(3d,3p) level for 16 molecules: 6 diatomic hydrides, CO, HCN, OCS, CO2, CS2, C2H2, C2N2, H2O, H2CO, and CH4. Root-mean-square (rms) errors of 0.052 D and 0.019 e are found for the dipole moments and their derivatives calculated using AIM parameters when compared with those obtained directly from the MP2(FC)/6-311++G(3d,3p) calculations and 0.097 D and 0.049 e when compared to the experimental values. The major deviations occur for the NaH, HF, and H2O molecules. Parallel polar tensor elements for the diatomic and linear polyatomic molecules, except H2, HF, LiH, and NaH, have values resulting from cancellations of substantial contributions from atomic charge fluxes and atomic dipole fluxes. These fluxes have a large negative correlation coefficient, -0.97. IR fundamental intensity sums for CO, HCN, OCS, CO2, CS2, C2H2, C2N2, H2CO, and CH4 calculated using AIM charges, charge fluxes, and atomic dipole fluxes have rms errors of 14.9 km mol(-1) when compared with sums calculated directly from the molecular wave function and 36.2 km mol(-1) relative to experimental values. The classical model proposed here to calculate dipole-moment derivatives is compared with the charge-charge flux-overlap model long used by spectroscopists for interpreting IR vibrational intensities. The utility of the AIM atomic charges and dipoles was illustrated by calculating the forces exerted on molecules by a charged particle. AIM quantities were able to reproduce forces due to a +0.1 e particle over a 3-8-A separation range for the CO and HF molecules in collinear and perpendicular arrangements. These results show that IR intensities do contain information relevant to the study of intermolecular interactions.

Observation and rovibrational analysis of the intermolecular HCl libration band ν16 of HCN–HCl, DCN–HCl and H13CN–HCl

The high-resolution far-infrared absorption spectrum of the intermolecular HC1 libration band upsilon6(1) (upsilonB) of the gaseous molecular complex H12CN-HCl and the two isotopically substituted species H13CN-HCl and D12CN-HCl is recorded by means of static gas-phase Fourier transform far-infrared spectroscopy at 205 K using an electron storage ring source. The rotational structure of the upsilon6(1) band has the typical appearance of a perpendicular type band of a linear polyatomic molecule. The structure is analyzed using a standard semi-rigid linear molecule model including l-type doubling to yield the band origin upsilon0, together with values for the upper state rotational constant B', the upper state quartic centrifugal distortion constant D'j and the value for the l-type doubling constant q6. The values for the ground-state spectroscopic constants B" and D"j for D12CN-H35Cl and H13CN-H35Cl are determined for the first time by ground state combination difference analyses. A number of upsilon6(1) + upsilon7(1) - upsilon7(1) and upsilon6(1) + 2upsilon7(2) - 2upsilon7(2) hot bands are observed in the spectra and the sum of the anharmonicity constants X(6,7) + g(6,7) is estimated. The observed decrease of the rotational constant B together with the simultaneous increase of the quartic centrifugal distortion constant Dj upon excitation of the HCl libration mode indicate that the hydrogen bond in the molecular complex is significantly destabilized upon intermolecular vibrational excitation. The calculated harmonic force constants for the intermolecular hydrogen bond stretching vibration upsilon(sigma) for the ground state and the excited HCl libration state indicate that the excitation of the HCl libration mode destabilizes the intermolecular interaction between HCN and HCl by almost 20%. The hydrogen bond is elongated by 0.030 A upon excitation of the upsilon6(1) mode.

Peculiarities of atom–quasidiatom collision complex formation: classical trajectory study

General peculiarities in the formation of quasibound complexes (QC) in collisions of an atom with a rigid diatomic or linear polyatomic molecule are studied using the method of classical trajectories. The CO2–Ar system is taken as an example. Statistical distributions of parameters characterizing either the formation of QC or those appropriate to rotational relaxation cross-sections are simulated and analyzed. Various factors are examined as far as their role in the formation of the QC is concerned: (1) the complexity of a trajectory approach (exact classical, planar, coplanar); (2) the selection of intermolecular potential energy surface (ab initio Parker–Snow–Pack potential; empirical Berreby–Dayan potential); (3) the departure of the initial CO2 rotational distribution from equilibrium. The cross-sections and bimolecular thermal rates for QC formation are obtained using the modified Sorbie–Murrell model. The use of derived analytical expressions makes the computations of QC fractions in CO2–Ar collisions easier both in equilibrium and in rotational non-equilibrium conditions.

Observation and Rovibrational Analysis of the Intermolecular HCl Libration Band in OC−HCl. Modeling of the Intermolecular Potential Energy Surface

The high-resolution far-infrared spectrum of the intermolecular HC1 libration band v(4)(1) of the OC-H(35)C1 heterodimer is recorded in the gas phase by means of Fourier transform IR spectroscopy in a static multipass absorption cell at 137 K using a synchrotron radiation source. This is the first direct observation of an intermolecular vibration band of the OC-HC1 dimer in the gas phase. The rotational structure of the band has the typical appearance of a perpendicular band of a linear polyatomic molecule. The structure is analyzed to yield the band origin nu(0) = 201.20464(27) cm(-1) together with values for the upper state rotational constant, the upper state quartic and sextic centrifugal distortion constants, and the l-type doubling constant. The determined values for the rotational constant and the centrifugal distortion constants are used to obtain a Morse potential for the stretching of the intermolecular distance. The results are compared to the results from quantum-chemical calculations. (Less)

Algebraic force-field Hamiltonian expansion approach to linear polyatomic molecules

The algebraic force-field Hamiltonian expansion recently proposed for vibrations of bent triatomic molecules [T. Sako, K. Yamanouchi, and F. Iachello, Chem. Phys. Lett. 299, 35 (1999)] is extended to linear polyatomic molecules by introducing operators constructed from the unitary algebra U(3). A comparison with the conventional force-field method is made by fitting the experimental vibrational-level energies of CO2. The results show that the algebraic Hamiltonian in local coordinates reproduces the level-energies with a smaller root-mean-square deviation and much faster convergence.

A Statistical Mechanical Perspective on the Temperature Dependence of the Isosteric Heat of Adsorption and Adsorbed Phase Heat Capacity

Statistical mechanical concepts were applied to analyze the temperature dependence of the isosteric heat of adsorption and, consequently, the difference between the adsorbed and gas phase heat capacities for monatomic, diatomic, and linear and nonlinear polyatomic molecules. Expressions were developed at the two extremes of localized and mobile adsorption. Also, the effects of the molecular size and shape on the isosteric heats of adsorption and the dependence on temperature were analyzed. The temperature dependence of the isosteric heat of adsorption was always important, especially for localized adsorption, heavily adsorbed molecules, or relatively low temperatures. At relatively high temperatures, the temperature dependence of the isosteric heat of adsorption became linear with a fixed slope, regardless of the molecular size (for both localized and mobile adsorption) and molecular shape (for mobile adsorption). Depending on the type of molecule and/or temperature, the difference between the adsorbed and gas phase heat capacity could be either negative or positive; and in some cases, significant deviations were exhibited mostly at industrially relevant conditions.

Rovibrational Spectrum of C15NC15N in the Region of the Stretching Modes ν1and ν2

The high-resolution gas-phase Fourier transform infrared spectrum of the doubly15N substituted isocyanogen C15NC15N has been measured in the spectral region 1670–2450 cm−1with an unapodized resolution of 0.0033 cm−1. The spectrum includes the band systems of the C≡N stretching modes ν1and ν2around 2272 and 2023 cm−1as well as the uppermost component of a Fermi triad involving 4ν4, 2ν4+ ν3, and 2ν3around 1940 cm−1. The two remaining components of this Fermi resonance triad are too weak to be seen under the given experimental conditions. Constants of a power series inJ(J+ 1) were determined for all assigned subbands, and accurate molecular constants were determined using the effective Hamiltonian for linear polyatomic molecules defined by Yamada, Birss, and Aliev [J. Mol. Spectrosc.112,347–356 (1985).]. The analysis of the rotational constants in terms of the rotation–vibration interaction constants is presented. The equilibrium rotational constantBewas found to be 0.1664056(69) cm−1for C15NC15N.

Vibrational magnetism of HCN and its isotopomers using rotational London atomic orbitals

Abstract We present correlated calculations of the rotational and vibrational g factors of HCN and its isotopomers. The vibrational g factor of a linear polyatomic molecule is calculated as the rotational g factor of a slightly bent molecule in the equilibrium configuration of its circular polarized vibrational state. Results close to the Hartree-Fock limit are obtained using rotational London atomic orbitals, and correlation is accounted for by using large Restricted Active Space wave functions. The results are compared with experimental results and other theoretical calculations.

Algebraic approach to molecular spectra: Two-dimensional problems

The Lie algebraic approach is extended to two-dimensional problems (rotations and vibrations in a plane). Bending vibrations of linear polyatomic molecules are discussed. The algebraic approach is particularly well suited to treat coupled bending modes. The formalism needed to treat coupled benders is introduced and a sample case, acetylene, is analyzed in terms of two coupled local benders.

Rotational and rovibrational spectrum of C 15NC 15N in the region of the bending modes ν4, ν5, the combination band ν4 + ν5 and the Fermi interacting modes ν3, 2 ν4

The high-resolution gas-phase Fourier transform infrared spectrum of the doubly 15N-substituted isocyanogen, C 15NC 15N, has been measured in the spectral regions 160–240 cm −1 and 390–1110 cm −1 with unapodized resolutions of 0.0017 and 0.0021 cm −1 respectively. In these experiments we were able to measure the band systems due to the excitation of the bending modes ν 5 and ν 4 at 190.9 cm −1 and 458.1 cm −1, a combination band system of the two bending modes ν 4 + ν 5 at 649.7 cm −1, as well as two band systems arising from a Fermi interaction between the twofold excited bending mode 2 ν 4 and the stretching mode ν 3 at 869.9 cm −1 and 960.2 cm −1 respectively. Furthermore, we have measured and assigned pure rotational transitions of C 15NC 15N in the vibrational ground state and in excited vibrational bending states lying in the microwave and the millimeter wave region between 19.9 and 20.2 GHz, 29.9 and 30.4 GHz and 120 and 440 GHz. Constants of a power series in J( J + 1) for numerous rovibrational subbands, as well as accurate molecular constants using the effective hamiltonian for linear polyatomic molecules, defined by Yamada et al. [J. Mol. Spectrosc., 112 (1985) 347], were determined.

Born-Oppenheimer effects and vibration-rotational spectra of linear molecules

A quantitative treatment of adiabatic and non-adiabatic effects in the vibration-rotational spectra of a linear polyatomic molecule is applied to the available spectral data of carbon dioxide. The results include a potential-energy function in displacement coordinates up to the sixth power and parameters corresponding to adiabatic and non-adiabatic effects for the primary vibrational and rotational quantities that are independent of nuclear masses, the equilibrium internuclear distance R BO e = (1·159 979 2 ± 0·000 002 2) × 10-10 m, and an estimate of the rotational g factor that agrees with the value more accurately determined from experiments on molecular beams.

Calculations of the polycentric linear molecule H 32+ with the finite element method

A fully numerical two-dimensional solution of the Schrödinger equation is presented for the linear polyatomic molecule H 3 2+ using the finite element method (FEM). The Coulomb singularities at the nuclei are rectified by using both a condensed element distribution around the singularities and special elements. The accuracy of the results for the lσ and 2σ orbitals is of the order of 10 −7 au.

Mean-field approach to the algebraic treatment of molecules: Linear molecules.

We study recently proposed algebraic models [F. Iachello, Chem. Phys. Lett. 78, 581 (1981); F. Iachello and R. D. Levine, J. Chem. Phys. 77, 3046 (1982); F. Iachello, S. Oss, and R. Lemus, J. Mol. Spectrosc. 146, 56 (1991); F. Iachello and S. Oss, ibid. 149, 132 (1991)] for diatomic and linear polyatomic molecules in the mean-field approximation. In this approach, we recover the harmonic molecular spectra efficiently and accurately and, more importantly, we are able to explore the geometrical meaning of boson operators and to suggest boson Hamiltonians that have closer links to molecular geometries.

Rotational spectrum of CNCN in excited vibrational states

The millimeter-wave rotational spectrum of isocyanogen, CNCN, was measured in the frequency range from 70 to 340 GHz in the vibrational ground state and in the excited vibrational bending states ( v 4 v 5) = (00), (10), (01), (02), (03), (11). Accurate molecular constants were determined using the effective Hamiltonian for linear polyatomic molecules defined by K. M. T. Yamada, F. W. Birss, and M. R. Aliev [ J. Mol. Spectrosc. 112, 347–356 (1985)]. The rotational transitions J = 2 ← 1 and J = 3 ← 2 were measured in the microwave regions 20 690–20 970 and 29 940–30 420 MHz, respectively, in order to search for rotational transitions arising from molecules in the vibrational states ν 3 and 2 ν 4 coupled by a Fermi resonance predicted by P. Botschwina and P. Sebald [ Chem. Phys. 141, 311–323 (1990)]. This resonance could be found and confirmed from the pure rotational transitions. The spectroscopic constants B v and D v as well as several vibration-rotational constants for each vibrational state of CNCN were determined.

String-like model for internal rotations in linear polyatomic molecules: new dynamical variables

A recently proposed model for linear polyatomic molecules is investigated. New dynamical quantum variables ( e 's), associated to internal rotations and generic of these models, are exhibited. The e 's and the angular momentum operators generate a rank-two semisimple Lie algebra. The associated Lie group is non-compact. The self-adjointness of the Hamiltonian is established.

Vibronic coupling in Rydberg series of linear molecules

Vibronic coupling of Σ and Π Rydberg series in linear polyatomic molecules is analyzed within a simple multi-channel quantum-defect-type model. The static (potential-energy surfaces of Rydberg states) and dynamic (absorption and photoionization cross sections) aspects of the model are analyzed. The model describes non-Born-Oppenheimer vibronic effects in low Rydberg members, resonant inter-Rydberg perturbations in the range of intermediate principal quantum numbers, as well as vibronically induced autoionization of high Rydberg levels in a coherent manner.

String-like model for linear polyatomic molecules and polymers

A three-dimensional string-like system of quantum particles is considered, in which each particle interacts with its two neighbours, through oscillator-like forces. In the high-frequency limit, a new quantum Hamiltonian is obtained. As a test of physical consistency, the latter implies, in classical statistical mechanics, some polymer-like features, like rubber elasticity.

A systematic study of molecular vibrational anharmonicity and vibration-rotation interaction by self-consistent-field higher-derivative methods. Linear polyatomic molecules

The inclusion of the anharmonicity of molecular vibrations is an important aspect of the goal of making highly accurate theoreticalpredictions of the spectroscopic properties of molecules. Recently developed analytic third derivative methods for selfconsistent-field(SCF) wavefunctions have made it possible to determine the complete cubic and quartic force fields of polyatomic molecules, thus allowing the treatment of anharmonic effects. Here we continue our systematic evaluation of the performance of such theoretical methods by studying several linear molecules which are well characterized experimentally, viz., HCN, DCN, CO 2, N 2O, OCS, C 2H 2, and C 2D 2. A number of anharmonic molecular properties have been determined, including vibration-rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, rotational constants which include zero-point vibrational corrections, and vibrational and rotational l-type doubling constants. These anharmonic molecular constants are not as well converged with respect to basis set enlargement as those which were previously determined for asymmetric top molecules, apparently because all the molecules considered here contain multiple bonds. However, the reported anharmonic constants at the SCF level of theory are still in reasonably good agreement with the corresponding experimental constants. Significant improvements in accuracy are achieved by incorporating electron correlation at the configuration interaction singles and doubles (CISD) level of theory. Standard spectroscopic perturbationtheory methods are used in this study, which are directly and immediately applicable to larger molecular systems than those studied here.

Angular Distribution of the Multipole and Multiphoton Photofragmentation of Molecules

AbstractThe effect of higher‐order photo‐excitation on the angular distribution of photo‐dissociated molecular fragments is studied. A general formalism is derived that will cover non‐linear as well as linear polyatomic molecules and will permit comparison of the processes of different orders. Some of the higher‐order processes, e.g., magnetic dipole and electric quadrupole, will give rise to azimuthal‐angle (Φ) besides polar‐angle (θ) dependence of the fragments. Using a molecule of D3h, Symmetry as an example, a comprehensive study is made of all possible excitations allowed by symmetry in this point group for one‐photon electric/magnetic dipole and three‐photon electric‐dipole transitions. Plane wave approximation is used for the relative motion of the random and non‐rotating molecules which dissociate instantaneously with a velocity large compared with thermal motion. These basic angular factors may be used in future extensions to rotating and vibrating molecules and to time‐delayed dissociations and to vibronically excited fragment states, etc.