Analysis of the rotational spectrum of C3v molecules by using factorization and diagonalization of the energy matrix: Application to CH3C15N

A method is given for the analysis of the rotational spectrum in the ground and excited states of C_3v molecules; it consists in a direct diagonalization of the energy matrix including all elements whose contribution can become significant for the analysis up to the sixth order of approximation.The method of factoring the energy matrix into four submatrices A₁, A₂, E, E, according to the symmetry species of the full point group C_3v, is given. The programm enables the calculation of the rotational frequencies and also carries out by a least-squares method the fitting of the molecular constants for vibrational states v = 0 (ground state) and v_E = 1, 2, 3, and 4, separately or simultaneously over several of these states.The analysis of the rotational spectrum of CH₃C¹⁵N in the v₈ = 0, 1, 2 states is given as an example.     

The rovibrational levels of ammonia

In this paper we report variational rovibrational studies on ammonia and its isotopomers. We use six internal coordinates (one of which describes the umbrella motion). The expansion functions are products of one-dimensional functions of these internal coordinates, multiplied by appropriate functions of the Euler angles to describe the rotational motion. We use a previously published high accuracy six-dimensional potential energy surface [LEONARD, C., HANDY, N. C., CARTER, S., and BOWMAN, J. M., 2002, Spectrachim. Acta, 58, 825]. We derive the full kinetic energy operator for the rovibrational motion in these coordinates. This operator has been completely checked to give a hermitian secular matrix. All matrix elements are evaluated numerically by quadrature. The symmetry of the expansion functions is fully described in D_3h, C_2v and C_s. It is not possible to perform the calculations in D_3h, but complete degeneracy in the appropriate levels is obtained with the C_2v program. The algebraic complexity of this program has been far greater than for any other variational study we have undertaken for a tetra-atomic molecule.

We present J = 0, 1, 2 energy levels for the experimentally observed band origins of NH₃, and J = 0, 1 energy levels for the ground state and fundamentals of NH₂D, ND₂H and ND₃. For the asymmetric isotopomers, identical results are obtained for both C_2v and C_s, thus confirming the validity of the method. The levels we obtain are completely converged. Agreement with observation is of the order of 0.5% (of course being dependent upon the accuracy of the potential energy surface); therefore the ordering of the rotational levels and their splitting is completely predicted and understood.     

Rotational excitation of CH<Subscript>4</Subscript> by He atoms

Quantum close-coupling and coupled-state approximation scattering calculations for rotational energy transfer of rotationally excited CH₄ due to collisions with He are presented for collision energies between 10⁻⁷ and 3000 cm⁻¹ using the MP4 potential of Calderoni et al. [J. Chem. Phys. 121, 8261 (2004)]. State-to-state cross sections and rate coefficients from selected initial rotational states of CH₄ in symmetries A, E, and F are studied from the ultra-cold to the thermal regime. Comparison of the cross sections with available theoretical results and experimental data show good agreement. Applications to astrophysics and cold laboratory environments are briefly addressed.     

Forbidden rotational transitions in symmetric top molecules

The intensities of the forbidden Δk = ±6 and ±4 transitions in symmetric top molecules arising from rotational intensity borrowing are reported. A perturbation theoretical approach has been used to study the mixing of wavefunctions produced by the additional splitting term in the rotational Hamiltonian of C_3v or C_4v-type molecules. Numerical values are presented for PH₃, PD₃, and BrF₅ molecules. The importance of these results in structural analysis and astrophysical studies is discussed.     

Electron impact ionization cross-section of C2, C3, Si2, Si3, SiC,SiC2 and Si2C

Total ionization cross-sections for C₂, C₃, Si₂, Si₃, SiC, SiC₂ and Si₂C molecules have been calculated by electron impact. Spherical complex optical potential formalism has been employed for obtaining the inelastic cross-sections for these molecules. Then by applying complex scattering potential-ionization contribution method, total ionization cross-sections are derived. These cross-sections are calculated in the energy range from ionization threshold to 2?keV. There are no measurements available in the literature to the best of our knowledge with which our results can be compared. The results show a linear relationship between maximum ionization cross-section and square root of the ratio of polarizability to ionization potential, depending on its atomicity. This gives a confirmation for the consistency of the data reported here. Present work is a maiden attempt to find electron impact ionization cross-section for these molecules, except for C₂ and C₃.     

O3+与H2碰撞中非解离电荷转移过程的全量子计算

应用全量子的分子轨道强耦合方法,研究了基态的O³⁺(2s²2p ²P)与氢分子碰撞的非解离电荷转移过程,计算了不同方位角(25°,45°,89°),能量分别为100,500,1000和5000eV/u时的单电子俘获的振动分辨的态选择截面及相应的微分截面.分子轨道强耦合计算中采用了自旋耦合价带理论计算的三原子分子势能面和径向耦合矩阵元.对氢分子的自身转动,采用无限阶的冲量近似方法;对体系的电子运动同H₂或H^{+< 关键词： 非解离电荷转移过程 全量子的分子轨道强耦合方法 无限阶冲量近似 振动冲量近似国家自然科学基金(批准号：10604011 10574020)和国家高技术研究发展计划(863)惯性约束聚变领域资助的课题.}     

CARS spectroscopy of molecules and clusters in supersonic jets

Supersonic molecular beams of D₂, CH₄, NH₃, and C₂H₄ are investigated in the expansion region employing collinear coherent anti-Stokes Raman spectroscopy (CARS). The analysis of rotationally resolved CARS spectra allows the determination of temperatures in the beam. The rotational relaxation as a function of stagnation pressure and separation from the nozzle is studied by recording theQ branch for D₂ and the ₃ R andS branches for CH₄. Rotational temperatures for NH₃ are determined by investigating the complete ₃ band. At strong stagnation conditions broad structures arise which can be attributed to the formation of NH₃ clusters. For C₂H₄ the ₅ band with resolved rotational structure is reported. Again, at larger distances from the nozzle, broad structures are observed. They are assigned to the ₁ and ₅ vibrations in the C₂H₄ cluster.     

Role of intramolecular interactions in Raman spectra of N2 and O2 molecules

The effect of vibration-rotation interactions and anharmonicities on the polarizabilities matrix elements, Raman scattering cross-sections, and depolarization degrees of N₂ and O₂ molecules for vibrational transitions v→v, v+1, v+2, v+3 have been investigated.     

Dependence of transport characteristics of molecules on the rotational quantum number

We derive a simple analytic formula that describes the relative difference of transport collision rates, Δv/v, for collisions of molecules and atoms in the rovibrational excitation of the former by light, as a function of the rotational quantum numbers of the combining (i.e., affected by radiation) levels of the molecules. (The relative difference of transport collision rates can be measured in light-induced drift, or LID, experiments and is proportional to the LID effect.) The formula is valid in the energy sudden approximation and is based on the well-known factorization formula for cross sections of RT-transitions in linear molecules that collide with atoms. We show that in this approximation the factor Δv/v is the sum of two independent terms, the vibrational term (Δv/v)_vib and the rotational term (Δv/v)_rot. Each term can be measured individually in LID experiments. Zh. éksp. Teor. Fiz. 113, 1649–1660 (May 1998)     

Coherent anti-Stokes Raman spectroscopy (CARS) of thev 3 band of methane in supersonic molecular beams

Supersonic molecular beams of methane are investigated in the expansion region using coherent anti-Stokes Raman scattering (CARS). Raman spectra of thev ₃ vibration with resolved rotational structure at low temperatures are reported. Comparison with calculated CARS spectra shows that the rotational distribution in the beam may be well described by a Boltzmann distribution. Temperatures are the same for all three nuclear spin modifications within the experimental error.     

Infrared combination bands of CH4 in crystal fields

Overtone and combination bands were observed between 1000 and 5000 cm^–1 for CH₄ molecules in several crystal fields: solid phases I and II, and diluted alloys with Kr. In the anisotropic field of phase II, a full (rotation/libration)-vibration spectrum was observed in the combination bands 2v ₄,v ₂+v ₄, andv ₃+v ₄. Here, all lines could be assigned to transitions of either D_2d or O_h molecules. The structure ofv ₃–v ₄,v ₂+2v ₄,v ₁+v ₄,v ₂+v ₃ and 3v ₄ bands could not be resolved. In phase I, all spectra show the characteristic features of rotational diffusion, while in a Kr matrix a rotovibrational structure could again be observed in the overtone and combination bands.     

Positrons — an alternative probe to electron scattering

Interaction of positrons with atoms and molecules differs from electron interaction due to the difference in polarity of the charge. This makes positrons an alternative tool to study atomic and molecular structure. Recent measurements of the total cross-sections for positron scattering at low energies on He, Ar, H₂, N₂, C₆H₆, C₆H₁₂, C₆H₇N carried out at Trento University [Karwasz et al., Acta Phys. Pol. 127, 666 (2005)] are discussed and compared to electron scattering results. All measured total cross-sections exhibit an increase with decreasing positron energy in the limit of zero energy; H₂, N₂, Ar, show regions of constant cross-section which are a few eV-wide, characteristic of scattering on a hard-sphere potential. Helium shows two resonant structures much below the positronium formation threshold. They may be attributed to virtual positronium formation. In conclusion, positron scattering is complementary to electron scattering. The total cross-sections do not show Ramsuaer minima but constant values, and new resonances appear.     

The laser-induced fluorescence spectroscopy of gold monoxide: B2Σ−－X2Π3/2 transition

The electronic spectrum of the gaseous gold monoxide molecule has been investigated in the range of 16000－18500?cm^?1 using laser induced fluorescence spectroscopy and single vibronic level emission spectra. Five rotationally resolved vibronic bands are observed and assigned to the transitions B²Σ^? (v'?=?0－4) －X²п_3/2 (v''?=?0), in which the 0－0 transition is observed for the first time. The molecular constants of the excited state B²Σ^? are obtained by a rotational analysis of the spectra. The spin-orbit coupling constant and the vibrational constants of the ground state X²п_i are determined with the accuracy improved by one order of magnitude. The lifetimes of most observed bands are also measured for the first time.     

The inter molecular potential of NH+ 4-Ar II. Calculations and experimental measurements for the rotational structure of the v 3 band

The mid-infrared spectrum of the v ₃,(t ₂) transition of the NH⁺ ₄-Ar complex has been recorded at rotational resolution using photofragmentation spectroscopy. The spectrum is divided into perpendicular and parallel subbands corresponding to transitions between different hindered internal rotor states. The P and R branches of the strongest perpendicular subbands are rotationally resolved providing rotational and centrifugal distortion constants. The widths of individual rotational lines are limited by the laser bandwidth of 0.02 cm^?1, giving a lower limit of 250 ps for the lifetime of the excited states. Effective intermolecular separations for each internal rotor state are determined from its rotational constant, after correction for the contribution due to Coriolis coupling between the internal and total rotational angular momenta. The absolute energies, rotational and distortion constants for the first few intermolecular bending and stretching levels of the ground intramolecular vibrational state are determined in a numerical solution to the rotation-intermolecular vibration Hamiltonian, employing a three-dimensional ab initio intermolecular potential. The results are compared with the experimental constants in order to assess the accuracy of the calculated potential. The relative energy levels from this calculation are also compared with those from a two-dimensional representation of the potential energy surface (‘fixed-R’ model) in order to judge directly the influence of the radial dependence of the potential.     

Calculation of absolute electron-impact ionization cross-sections of dimers and trimers

We report calculations of the electron-impact ionization cross-sections of selected dimers (homonuclear diatomic molecules) and trimers (homonuclear triatomic molecules) using a method which relies only on macroscopic quantities in conjunction with a “defect concept”. The empirically determined defect describes the deviation of the cluster (dimer, trimer) cross-sections from a simple linear dependence on the cluster size. We compare the calculated cross-sections to experimental data for the dimers S₂ and F₂ and the trimer O₃ and we present predictions for the ionization cross-sections of Br₂, I₂, C₂ and C₃ for which no experimental data are available. Lastly, we extend the method to the calculation of ionization cross-sections for the fullerenes C₆₀ and C₇₀. Received 6 December 1999 and Received in final form 10 April 2000     

The rotational spectrum of 13C2HD in the ground and excited bending states

The pure rotational spectrum of ¹³C₂HD was recorded in the range 100–700 GHz. Lines belonging to the ground vibrational state were observed from J^″ = 1 to J^″ = 11. Several absorption lines were also detected in the bending states v₄ = 1 (Π), v₅ = 1 (Π), v₄ = 2 (Σ⁺ and Δ), v₅ = 2 (Σ⁺ and Δ), v₄ = v₅ = 1 (Σ^?, Σ⁺ and Δ), v₄ = 3 (Π and Φ) and v₅ = 3 (Π and Φ). The transition frequencies measured in this work were fitted together with all the infrared lines available in the literature. The global fit allowed a very accurate determination of the vibrational, rotational and ?-type interaction parameters for the bending states of this molecule.     

Probing the isomer,fluorination and bond effects in C<Subscript>3</Subscript>H<Subscript>6</Subscript>, cyclo-C<Subscript>3</Subscript>H<Subscript>6</Subscript> and C<Subscript>3</Subscript>F<Subscript>6</Subscript> molecules using electron impact

We have carried out experimental and theoretical studies on electron scattering from the C₃H₆ isomers and C₃F₆ molecules and we report on total, differential as well as theoretical integral elastic cross-sections for these molecules. Vibrational excitation functions are also presented for the typical vibrational peaks in C₃H₆ and cyclo-C₃H₆ for the angle of 90^○, impact energy range of 1–16 eV and loss energies of 0.12 eV and 0.13 eV, respectively. In the cross-sections, clear differences in peak positions and magnitudes between the C₃H₆ isomers can be viewed as the isomer effect. The same is observed between C₃H₆ and C₃F₆ in a clear manifestation of the fluorination effect. The resemblance of the π^* shape resonance in the cross-sections, observed at about 2.2 eV for C₃H₆ and 3.5 eV for C₃F₆, to those in C₂H₄ and C₂F₄ clearly points to the effect of the double bond in the molecular structures for these molecules. Theoretical analysis is performed to provide rationales for the scattering dynamics.     

Bond charge parameters from integrated infrared intensities

A procedure is outlined to analyze the infrared absorption intensities of fundamental vibration bands in terms of “bond charge parameters”. The method is illustrated for some small C_2v- and C_3v-type molecules: SO₂, NF₃, and PF₃. The values obtained for the “bond charge reorganizations” and “effective bond charges” for SO, NF, and PF bonds are discussed. The method offers the possibility of calculating rotational contributions without the use of a reference molecule.     

Raman band shapes and the dynamics of liquid N2O4

The Raman spectra of the totally symmetric A _g modes, v ₁, v ₂ and v ₃, of the N₂O₄ molecule have been measured in the liquid state at 262, 279 and 297 K. The vibrational and the rotational correlation functions are calculated. The long-time exponential decay of the rotational correlation functions of all the A _g modes reflects an asymptotic diffusional behaviour of molecular reorientation. The rotational relaxation rate is found to increase with increasing temperature. A marked point of inflection from the short time inertial correlation to the long time exponential decay appears at about 0·35 ps for the v ₂ mode. This is an indication of orientational rebound arising from the librational motion in a temporary solvent cage. The isotropic bandwidth increases in the order v ₁ < v ₂ < v ₃, which is also the order of decreasing vibrational frequency. The temperature dependence of the peak frequency and of the bandwidth are also found to increase in the same order. These observations are analysed qualitatively in terms of two models of vibrational dephasing which take into account the effect of vibrational anharmonicity.     

Spontaneous Raman scattering: a useful tool for investigating the afterglow of nanosecond scale discharges in air

Nanosecond scale discharges are considered an interesting way for assisting combustion by enhancing either flame stabilization or ignition. Better understanding of energy deposit and radical species production processes is still required under pressure conditions normally encountered in combustion. The purpose of the present paper is to show that spontaneous Raman scattering, seldom used to investigate nanosecond pulsed discharges, is a useful measurement method for investigating the energy deposit of these discharges. The advantage of spontaneous Raman scattering is described by analyzing N₂ and O₂ spectra during the post-discharge of a filamentary nanosecond air discharge under atmospheric pressure, using phase-locked average spectra. The main advantages of spontaneous Raman scattering measurements are that they allow line-wise probing of different species with the same experimental setup and the determination of vibrational distribution by comparison with theoretical modeling over a wide range of vibrational levels (from v=0 to v=20 for N₂). The model proposed takes into account the high level of vibrational excitation and the strong non-equilibrium observed, allowing the characterization of the vibrational relaxation over the complete post-discharge duration. Although the rotational structure is not resolved, the rotational temperature and thus translational temperature are determined with a moderate uncertainty for T above 500 K.