Transformation of the effective rotational Hamiltonian of nonrigid X 2 Y molecules

The transformation of the effective rotational Hamiltonian H of nonrigid X ₂ Y molecules to the form having a minimum number of diagonals in the basis of rotational functions of a symmetric top is discussed. Such a transformation is a generalization of the reduction transformation performed for the polynomial effective Hamiltonian H. It is shown that in the general case the transformation substantially changes the form of the initial Hamiltonian, which restricts the region of applicability (J<J*) of the reduced Hamiltonian represented in a class of elementary functions in terms of angular momentum operators. The values of the rotational quantum number J* are estimated for the (000) ground and (010) vibrational states of the H₂O molecule.     

Variational Calculation of Energies of Highly Excited Rovibrational States of CO2

Accurate variational calculations of energies of highly excited rovibrational states of ¹²C¹⁶O₂ using a Lanczos recursion are presented. In a first step, we use experimental rovibrational transition frequencies to determine by a least-square fitting procedure a potential energy surface for the CO₂ molecule. This potential energy surface is expressed as a multidimensional power series expansion in the normal coordinates. It is then used to determine all the rovibrational energies for symmetry e levels up to a rotational number J=200, a vibrational energy of 13 000 cm⁻¹, and a vibrational angular momentum l=13.     

A new resonance in thee-H2-scattering

A short-lived compound state of the systeme-H₂ in the energy region from 13.5 to 15 eV has been investigated. It desintegrates preferably into theC ¹ π _u v=0, 1, 2, 3,... vibrational states of H₂. Excitation functions and angular dependences of these states have been measured. The H₂ vibrational levels are situated at 13.63, 13.93, 14.20, 14.70, 14.92,... eV. The shape of the potential energy curve and the internuclear distance of the compound state should be very similar to that of theC ¹ π _u resp.D ¹ π _u state ofH ₂.     

Calculation of vibrational energy levels of triatomic molecules with the C2v and Cs symmetries by summing divergent series of the Rayleigh-Schr?dinger perturbation theory

The Rayleigh-Schr?dinger perturbation theory is applied to calculation of vibrational energy levels of triatomic molecules with the C _2v and C _s symmetries: SO₂, H₂S, F₂O, HOF, HOCl, and DOCl. Particular attention is given to the states coupled by anharmonic resonances; for such states, the perturbation theory series diverge. To sum these series, the known methods of Padé, Padé-Borel, and Padé-Hermite and the method of power moments are used. For low-lying levels, all the summation methods give satisfactory results, while the method of quadratic Padé-Hermite approximants appears to be more efficient for high-excited states. Using these approximants, the structure of singularities of the vibrational energy, as a function in the complex plane, is studied.     

The rotational dependence of diagonal Coriolis coupling

The diagonal Coriolis coupling in degenerate vibrational states of symmetric- or spherical-top molecules has a rotational dependence of degree three in the components of the total angular momentum vector. A general formula is obtained for the coefficients of these terms and is specialized to the cases of symmetric tops (particularly C_3v molecules), where the coefficients are Maes' constants η_tJ and η_tK, and of cubic spherical tops, where the coefficients are Hecht's constants F_t (t ∈ E), F_uS and F_uT (u ∈ F_1,2). It is shown that these coefficients obey certain sum rules in which many of the contributions cancel. The values of the sums can be expressed in terms of the ordinary quartic centrifugal constants D_J, D_JK, and D_K for a symmetric top, or D and D_T for a cubic spherical top. The sum rules for methane are approximately satisfied by the experimental values of the constants.     

Product state distributions and rotational polarization for the crossed beam reactions of Ca with F2 and NF3

Product state distributions of the CaF products from the thermal crossed beam reactions Ca + F₂ and Ca + NF₃ have been measured using laser induced fluorescence (LIF) techniques. We obtain information about the rotational and vibrational distributions by generating synthetic band profiles and comparing them with those observed. The inverted vibrational distributions indicate direct reaction mechanisms. For Ca + F₂ the fractionf′ of energy is nearly half going into product translation and the remainder being devided nearly equally between product rotation and vibration. For Ca + NF₃ the largest fraction of the available reaction exoergicity goes into vibrational excitation of the newly formed CaF products. In addition, we have probed the rotational polarization of CaF product molecules. This gives direct information on the role of angular momentum alignment in reactive scattering.     

An application of a representation theorem for entropy functionals

The vibrational predissociation of HD₂ ⁺ is modelled in terms of quantum-mechanical tunnelling through a minimal centrifugal barrier at given total angular momentum, J, and with statistical intermode coupling behind the barrier. It is shown that the observed strong preference for the H⁺ + D ₂ predissociation channel (over D⁺ + HD) is consistent with an experimental preference for J values in the range 0 < J < 25, a range which is also shown to be consistent with the observed H₃ ⁺ preferred range of kinetic energy release. A correlation between the total angular momentum and the kinetic energy release is also predicted.     

Calculated energy levels and intensities for the ν1 and 2ν2 bands of HDO

A Hamiltonian taking explicitly into account both Fermi and Coriolis interactions has been set up for triatomic molecules of symmetry C_s and used to reproduce, very satisfactorily, the available rotational energy levels of the {(100), (020)} interacting states of HDO, providing us with realistic wavefunctions as well as precise rotational constants and vibrational energies. Then, to calculate line intensities, these wavefunctions were used together with suitably chosen transition moment operators expanded up to degree 2 in $\text{J}$ and having the correct symmetry in the C_s group, leading to hybrid bands of both A and B type., Using this formalism, it has been possible to determine, from the fit of the existing experimental intensities, the coefficients appearing in the expansions of the transition moment operators of the 2ν₂ and ν₁ bands of HDO. In this way, we have improved upon the F-factor formalism which needs much more parameters to reproduce the line intensities with the same precision. Finally, using the transition moments as well as the wavefunctions and energy levels deduced from the diagonalization of the Hamiltonian matrix, we have calculated the whole spectrum of the ν₁ and 2ν₂ bands of HDO.     

Ro-vibrational states of triplet H3 (aΣu): The lowest 19 bands

We have performed extensive calculations of the ro-vibrational states of triplet H₃⁺, using the method of hyperspherical harmonics and our recently reported double many-body expansion potential energy surface. The rotational term values of the lowest 19 states are presented here for a total angular momentum of J?10.     

The microwave spectrum,conformation, and vibration-rotation interaction of N-cyanopyrrolidine

The microwave spectrum of N-cyanopyrrolidine was observed and assigned in the ground and nine excited states. In the lowest two states, split 3.9 cm^?1 by a ring-puckering, nitrogen-inversion motion, the rotational constants are (for v = 0) A = 6585.05 ± 3.83, B = 1919.54 ± 0.05, C = 1583.84 ± 0.05, and (for v = 1) A = 6575.31 ± 6.01, B = 1922.37 ± 0.08, C = 1586.44 ± 0.08 MHz. Deviations from rigid rotor behavior in the lowest two states were described and analyzed by inclusion of a Hamiltonian term coupling the states via the internal vibrational angular momentum. The observed conformation of the five-membered ring system was found to be the envelope equatorial form. The tunneling motion which interconverts equivalent conformers has been discussed, and the qualitative nature of the potential energy surface has been described and compared to the parent unsubstituted molecule.     

The 260 nm absorption spectrum of benzene: Selection rules and band contours of vibrational angular momentum components

The role of vibrational degeneracies and vibrational angular momentum in the 260 nm absorption spectrum of benzene is further examined. Degenerate Herzberg-Teller terms are set down through third order with specific identification of vibrational symmetries capable of inducing intensities (Table II). These terms provide a basis for predicting the Δv selection rules, the signed vibrational angular momentum selection rules, and the vibrational angular momentum component energy splittings for all vibronic transitions. A new parameter, χ, is developed which can be used to predict the rotational band contour of any vibronic component transition. These developments underlie the systematic reexamination of assignments which is given in Paper III of this series.     

Ion-electron coincidence study of the thermal He(23S) + H2 Penning reaction

A new Penning-electron-Penning-ion coincidence method is described. It is applied to the study of the thermal reaction of He(2³S) with H₂. The main results reported are separate electron energy spectra that are coincident with the three different ions formed: HeH₂⁺, HeH⁺ and H₂⁺. Based on these results it is shown that the Penning reaction of the He(2³S)/H ₂ system proceeds in two well-separated steps: (i) ionization at distances R (HeH₂) ? 6a₀ in which H₂⁺ (v) is formed in different vibrational states; and (ii) reactive collision of H₂⁺ (v) with He. For the second step the variation of the branching ratios with vibrational quantum numbers v = 0 to v = 10 is derived, and it is shown that these branching ratios may be regarded as relative vibrational-energy-dependent cross-sections for the collision of H₂⁺ (v) with He at an average relative kinetic energy of ～20 meV.     

Some effects of spin-orbit interaction on rotational levels and rotational line intensities in vibrationally unexcited 2A, 2E, and 2F electronic states of open-shell XY4 molecules

Rotational energy levels in vibronic ground states of ²A, ²E, and ²F electronic states of open-shell XY₄ molecules, as well as rotational line intensities for allowed transitions between such states, are discussed, including the effects of spin-orbit interaction and tetrahedral splittings. Jahn-Teller effects are assumed to be small, and are only taken into account implicitly, through their contributions to various parameters in the effective Hamiltonian. Qualitative information is obtained by considering several limiting-case coupling schemes among the electron spin angular momentum S, the electron orbital angular momentum L, and the pure rotational angular momentum R. These limiting cases are similar in spirit to Hund's coupling cases in diatomic molecules, but differ sufficiently from the latter to make detailed correspondences unhelpful. Quantitative information on rotational energy levels and line intensities is obtained numerically by diagonalizing a Hamiltonian matrix set up in a basis set characterized by uncoupled moleculefixed projections of S, L, and the total angular momentum J, and symmetrized so that all basis set functions belong to a definite species in the subgroup D_2d of the true point group T_d. Hamiltonian matrix elements are determined by ladder operator techniques. Three sample calculated spectra, corresponding to $\text{p(}{}^2\text{F}{}_2\text{)-s(}{}^2\text{A}{}_1\text{)}$, $\text{d(}{}^2\text{E)-p(}{}^2\text{F}{}_2\text{)}$, and $\text{d(}{}^2\text{F}{}_2\text{)-p(}{}^2\text{F}{}_2\text{)}$ are presented. As one might expect, when the spin-orbit constant A is set equal to zero, then both qualitative and quantitative aspects of the rotational-electronic problem in open-shell XY₄ molecules can be mapped easily onto discussions of the rotation-vibration problem from the CH₄ literature.     

The interacting states (020), (100), and (001) of H217O and H218O

A fit of about 350 rotational levels of the (020), (100), and (001) vibrational states has been performed for H₂¹⁷O as well as for H₂¹⁸O leading to the determination of 51 rotational and coupling constants for each isotopic species. The Fermi-type interaction and the two Coriolis-type interactions have been taken into account by appropriate rotation-vibration operators and the v-diagonal part of the Hamiltonian is, for each vibrational state, a Watson-type Hamiltonian. The results are very satisfactory since 87% of the experimental levels are reproduced within 15 × 10^?3 cm^?1.     

Photoelectron spectra of ethylene and of the six deuterated derivatives

The photoelectron spectra of C₂H₄ and of six deuterated molecules of ethylene — C₂D₄, C₂D₃H, C₂H₃D, cis-C₂H₂D₂, trans-C₂H₂D₂ and gem-C₂H₂D₂ — have been recorded with the 584-Å resonance line of He. The adiabatic ionization potentials of the X²B_3u and the ²B_3g states of the seven isotopic components have been determined with an accuracy of about 7 meV. The ionization potentials of the other excited electronic states have been measured with a lower accuracy owing to a less well defined onset. The measured ionization potentials of C₂H₄ are 10.514 eV, 12.431 eV, 14.4₃ eV, 15.7₄ eV and 18.7 eV. The vibrational structure of the first electronic band shows that the two normal modes ν₂ (symmetric CC stretching) and ν₃ (symmetric HCH bending) are excited simultaneously. The measured vibrational frequencies show no abnormal isotopic effect if the assignment given in the literature for the ν₂ and ν₃ modes in C₂H₄⁺ are reversed and if a stronger excitation of the ν₃ symmetric bending mode in the least deuterated compounds is assumed. The vibrational modes most strongly excited in the second and third electronic bands are ν₁ (symmetric CH stretching) and ν₃, and in the fourth band ν₃.     

Influence of short-and long-range interaction forces on the efficiency of collisional vibrational energy transfer in the vibrational quasi-continuum

Based on measurements of the time-resolved delayed fluorescence, the influence of universal interactions on the collisional vibrational energy transfer is studied in mixtures of vibrationally excited polyatomic molecules (acetophenone, benzophenone, and anthraquinone) with inert bath gases (Ar, C₂H₄, SF₆, CCl₄, and C₅H₁₂). From the dependences of the decay rates of delayed fluorescence on bath gas pressure, the efficiencies of the establishment of vibrational (V-V relaxation) and thermal (V-T relaxation) equilibrium after excitation of molecules into the vibrational quasi-continuum of a triplet state are estimated. The main emphasis is on studying the dependences of the efficiency of collisional vibrational energy transfer on temperature and the molecular characteristics of collision partners. It is found that the efficiency increases with the complication of the structure of bath gases for the V-V process and decreases upon the increasing of their mass for the V-T process. For the temperature range 273–553 K, the negative temperature dependence of the V-V transfer probability and the positive (Landau-Teller) dependence of the V-T transfer probability were obtained. It is concluded that the above regularities reflect the dominant role of long-range attractive forces in initiating the quasi-resonant V-V transfer and of short-range repulsive forces in the V-T transfer of vibrational energy.     

Quasiclassical calculation of the chemical reaction Ba＋C3HTBr → BaBr＋C3H7

<正>The quasi-classical trajectory（QCT） method based on the extended London-Eyring-Polanyi-Sato potential energy surface is used to investigate the product vibrational distribution,angular distribution and angle-resolved kinetic distribution of the reaction Ba+C₃H₇Br→BaBr+C₃H₇ at 2.58 kcal/mol.The calculated results show that the product BaBr vibrational distribution is quite hot,the vibrational population peaks are located at v = 12,and the angular product distribution tends to backward scattering.The calculated angle-resolved kinetic distribution shows that the kinetic distribution is obviously related to angle.The QCT results are always qualitatively acceptable and sometimes even quantitatively.     

Mechanisms of inelastic scattering of low-energy protons by C6H6, C60, C6F12, and C60F48 molecules

The mechanisms of inelastic scattering of low-energy protons with a kinetic energy of 2–7 eV by C₆H₆, C₆F₁₂, C₆₀, and C₆₀F₄₈ molecules are studied using the methods of quantum chemistry and nonempirical molecular dynamics. It is shown that, for the C₆H₆ + proton and C₆₀ + proton systems, starting from a distance of 6 Å from the carbon skeleton, the electronic charge transfer from the aromatic molecule to H⁺ occurs with a probability close to unity and transforms the H⁺ ion into a hydrogen atom and the neutral C₆H₆ and C₆₀ molecules into cation radicals. The mechanism of interaction of low-energy protons with C₆F₁₂ and C₆₀F₄₈ molecules has a substantially different character and can be considered qualitatively as the interaction between a neutral molecule and a point charge. The Coulomb perturbation of the system arising from the interaction of the noncompensated proton charge with the Mulliken charges of fluorine atoms results in an inversion of the energies of the electronic states localized, on the one hand, on the positively charged hydrogen ion and, on the other hand, on the C₆F₁₂ and C₆₀F₄₈ molecules. As a result, the neutral molecule + proton state becomes the ground state. In turn, this inversion makes the electronic charge transfer energetically unfavorable. Quantum-chemical and molecular-dynamics calculations on different levels of theory showed that, for fluorine derivatives of some aromatic structures (C₆F₁₂, C₆₀F₄₈), the barriers to proton penetration through carbon hexagons are two to four times lower than for the corresponding parent systems (C₆H₆, C₆₀). This effect is explained by the absence of active π-electrons in the case of fluorinated molecules.