Thermal energy charge transfer reactions of Ar+ ions with HBr and DBr molecules

HBr⁺ (A²Σ⁺-X²Π_i) and DBr⁺ (A²Σ⁺-X²Π_i) emissions are found up to v′=1 and v^′=2, respectively, from the thermal energy charge transfer reactions of Ar⁺ with HBr and DBr molecules in a flowing afterglow apparatus. Both A-state vibrational distributions have a peak at the lowest vibrational level, which are inconsistent with those expected from the energy resonance and/or Franck-Condon factors for ionization. This discrepancy is explained in terms of the distortion of target molecules by approach of reactant ions. Both A-state rotational distributions show that energies partitioned into rotation decrease with increasing vibrational levels, whereas the internal energy is nearly constant for all vibrational levels. The vibrational and rotational distributions obtained suggest that the reaction occurs at a relatively short distance and the product has a broad translational energy distribution.     

Triatom-triatom collisions: Fixed angle close-coupling study of vibrational excitation in the 12CO2+13CO2 system

A close-coupling approach to the calculation of quantal vibrational transition probabilities for the fixed angle scattering of a linear triatomic molecule with another linear triatomic molecule is described. The method is applied to the ¹²CO₂+¹³C0₂ collisional system. For a calculated inelastic transition probability to have an appreciable magnitude, it is found that the amount of energy transferred in a transition must be very small and just one quantum of energy must be exchanged between either the symmetric stretch or the asymmetric stretch vibrational modes of ¹²C0₂ and ¹³CO₂. For collisional energies away from threshold, the probabilities for transitions involving the symmetric stretch ¹²CO₂ and ¹³CO₂ modes are insensitive to long range multipole terms in the potential energy surface, while the probabilities for energy exchange between the asymmetric stretch modes are considerably diminished when the long range terms are removed from the potential energy surface. A brief discussion is presented on the possibilities of extending the technique to the calculation of vibrational excitation cross sections for three-dimensional triato—triatom collisions.     

Ab initio computation of vibrational relaxation rate coefficients for the collisions of CO2 with helium and neon atoms

Ab initio calculations of rate coefficients are reported for the vibrational relaxation of CO₂ molecules in collision with helium and neon atoms. Self consistent-field computations have been performed to parameterise simple three-dimensional potential energy functions which have been used in vibrational close-coupling, rotational infinite-order-sudden calculations of rate coefficients. Excellent agreement is obtained between the calculated and experimental rate coefficients for the deactivation of the (01₁0) vibrational level in the He + CO₂ system at temperatures of 300 K and above. The ab initio predictions of rate coefficients for relaxation of CO₂ vibrational levels such as (10⁰0) and (02⁰0) should be useful in computer simulations of CO₂ lasers.     

Large configuration interaction calculations of nuclear spin-spin coupling constants: III. Vibrational effects in ammonia

Large configuration interaction calculations of the proton—proton coupling constant for several geometrical configurations of the ammonia molecules are reported. The analytical expressions for the energy surface and the coupling constant as functions of two cartesian displacement coordinates are fitted to the calculated values. The potential is used for the calculation of the vibrational wavefunctions for ¹⁵NH₃ and ¹⁵ND₃ species and the vibrational averaging of the coupling constant is carried out using these functions. Though the value of the coupling constants shows a very strong geometry dependence, the vibrational corrections are found to be small. A possible correlation of the proton—proton coupling constant with an angular parameter in the NH₂ group in RNH₂ compounds is indicated.     

Time-dependent Wave Packet Quantum Scattering Study of Reaction S(3P)+H2→HS+H on a New ab initio Potential Energy Surface 3A'

A new potential energy surface is presented for the triplet state ³A' of the chemical reaction S(³P)+H₂ from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference config-uration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8～2.2 eV. Both the centrifugal-sudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H₂ initially in the vibrational states v=0～3 (j=0). It is found that initial vibrational excitation enhances the title reaction.     

Improved Calculation of Vibrational Energy Levels in F2 Molecule using the RKR Method

The potential energy curves of the ground state X²∑⁺_g of the fluorine molecule have been ac-curately reconstructed employing the Ryderg-Klein-Rees (RKR) method extrapolated by a Hulburt and Hirschfeler potential function for longer internuclear distances. Solving the cor-responding radial one-dimensional Schr?dinger equation of nuclear motion yields 22 bound vibrational levels above v=0. The comparison of these theoretical levels with the experimen-tal data yields a mean absolute deviation of about 7.6 cm^-1 over the 23 levels. The highest vibrational level energy obtained using this method is 13308.16 cm?1 and the relative de-viation compared with the experimental datum of 13408.49 cm^-1 is only 0.74%. The value from our method is much closer and more accurate than the value obtained by the quantum mechanical ab initio method by Bytautas. The reported agreement of the vibrational levels and dissociation energy with experiment is contingent upon the potential energy curve of the F₂ ground state.     

Basis-independent potential energy curves for the neutral diatomics of Li,Na and K evaluated by means of Hartree-Fock and different density functional potentials

Summary The solution of the Schrödinger equation for diatomic molecules when the finite element method is used gives the possibility to evaluate highly accurate basis-independent potential energy curves. In this work such types of numerically accurate potential energy curves on the HF level have been evaluated for Li₂, Na₂ and K₂ and could be used as benchmarks in the optimization of basis sets. A comparison between recent LCAO HF calculations in which extended basis sets are used and the accurate values determined in this work show that there is a difference in total energy of 4×10^–5 and 10^–3 a.u. for Li, Li₂, and Na, Na₂, respectively. Evaluated dissociation energies are, however, due to the cancellation of numerical errors in much better agreement. Further, it is found that different exchange correlation potentials for the heavier molecules such as those given by von Barth-Hedin and Vosko, Wilk and Nusair reproduce experimental properties such as dissociation energies, vibrational frequencies almost as well as those achieved with advanced CI methods. TheX potential gives accurate bond lengths for Na₂ and K₂, whereas the dissociation energies are too small.     

The calculation of vibrational energy levels of polyatomic molecules including anharmonic effect using contact transformation perturbation method

Using contact transformation perturbation method based on the Taylor expansion of the potential energy function in terms of dimensionless normal coordinates up to sixth‐order, the vibrational energy levels in terms of force constants are derived. The contact transformation theory has been applied to simplify the calculation of perturbation effects. To calculate the second‐order vibrational energy correction, the third and fourth‐order terms of potential function have been placed in the first‐order perturbation Hamiltonian and the second‐order Hamiltonian contains hexatic ones. We present expressions which give relations between the fourth‐ and sixth‐order terms in dimensionless normal coordinates of the potential and the anharmonicity coefficients. For illustration, a set of vibrational energies levels of SO₂, and H₂O molecules including anharmonic effects has been calculated. © 2013 Wiley Periodicals, Inc.     

Accurate Theoretical Study of LiS Radical and Its Singly Charged Cation and Anion in their Ground Electronic State

Potential energies of LiS(²Π), LiS^-(¹Σ⁺) and LiS⁺(³Σ^-) are calculated by using the multireference configuration interaction method including Davidson correction and the augmented correlation-consistent basis sets aug-cc-PV(X+d)Z (X=T, Q). Such obtained potential energies are subsequently extrapolated to the complete basis set limit. Both the core-valence correction and the relativistic effect are also considered. The analytical potential energy functions are then obtained by fitting such accurate energies utilizing a least-squares fitting procedure. By using such analytical potential energy functions, we obtain the accurate spectroscopic parameters, complete set of vibrational levels and classical turning points. The present results are compared well with the experimental and other theoretical work.     

Vibrational calculations in formaldehyde: the CH stretch system

An alternative procedure for the calculation of highly excited vibrational levels in S0 formaldehyde was developed to apply to larger molecules. It is based on a new set of symmetrized vibrational valence coordinates. The fully symmetrized vibrational kinetic energy operator is derived in these coordinates using the Handy expression [Molec. Phys. 61, 207 (1987)]. The potential energy surface is expressed as a fully symmetrized quartic expansion in the coordinates. We have performed ab initio electronic computations using GAMESS to obtain all force constants of the S0 formaldehyde quartic force field. Our large scale vibrational calculations are based on a fully symmetrized vibrational basis set, in product form. The vibrational levels are calculated one by one using an artificial intelligence search/selection procedure and subsequent Lanczos iteration, providing access to extremely high vibrational energies. In this work special attention has been given to the CH stretch system by calculating the energies up to the fifth CH stretch overtone at ∼16000 cm⁻¹, but the method has also been tested on two highly excited combination levels including other lower frequency modes.      

Infrared and Raman spectra, conformational stability, ab initio calculations and vibrational assignment for 1,2-pentadiene (ethyl allene)

The infrared (3500-50 cm⁻¹) and Raman (3500-20 cm⁻¹) spectra of 1,2-pentadiene, H₂C=C=C(H)CH₂CH₃ (ethyl allene), have been recorded for both the gaseous and solid states. Additionally, the Raman spectrum of the liquid has been obtained with qualitative depolarization values. In the fluid phases both the cis and gauche conformers have been identified, with the gauche rotamer being the predominant form although it may not be the conformer of lowest energy. In the solid state only the cis conformer remains after repeated annealing of the crystal. The asymmetric torsion of the cis conformer is observed as a series of Q-branch transitions beginning at 103.4 cm⁻¹ and falling to lower frequency. An estimate of the potential function governing conformer interconversion is provided. A complete assignment of the normal modes for the cis conformer is given and several of the fundamentals are assigned for the gauche rotamer. Ab initio electronic structure calculations of energies, conformational geometries, vibrational frequencies, and potential energy functions have been made to complement and assist the interpretation of the infrared and Raman spectra. In particular, the transitions among torsional energy levels for both the symmetric (methyl) and asymmetric (ethyl) motions have been calculated. The results are compared to the corresponding quantities for some similar molecules.     

Applications of an adiabatic rotational model to the Ar…O2 van der Waals molecule

In this paper a separation of vibrational and rotational motions is applied to describe the metastable levels of the ArO₂ van der Waals molecule. The potential energy surface is written as a sum of atom—atom pairwise Morse functions, the parameters being obtained by fitting the potential of Pirani and Vecchiocattivi at the equilibrium configuration. The results agree fairly well with experimental data about infrared absorption, assuming a J = 2 → 1 transition, where J is the quantum number associated to the total angular momentum of the complex. Also, close coupling three-dimensional calculations about the ArO₂ collision show a good agreement with some energies previously calculated. The widths for rotational predissociation have been estimated by this procedure to be of the order of 1 cm^?1.     

On the vibrational dependence of electron impact ionization of diatomic molecules

The dependence of the Na₂ electron impact ionization rate is measured as a function of vibrational excitation in a crossed molecule-electron beamm arrangement at collision energiesE _coll ≤ 3 eV above the ionization threshold. Specific vibrational distributions in theX ¹∑ _g ⁺ state with average vibrational energies of 0.17 eV, 0.276 eV, and 0.349 eV, are prepared via Franck-Condon pumping using a narrow-band cw laser. Enhancement of the ionization rate is observed only at impact energies near the ionization threshold where the ionization rate increases linearly as a function of vibrational excitation. Analysis of the experimental data is based on three model calculations. The first of these calculations equates vibrational energy with kinetic energy and agrees well with the experimental data. A second, more refined model allows for differences in state-to-state ionization rates and uses Franck-Condon factors to estimate transition probabilities, but leads to a less favorable agreement. The third one employs a semi-classical formulation of the Franck-Condon principle. It provides the best agreement with the experimental data. In contrast with an earlier study of electron impact ionization of diatomic molecules [20], we find no evidence of dynamical modification of the ionization rate, due to vibrational motion of the nuclei, at the present level of accuracy of our data and analysis.     

Virtual screening of borate derivatives as high-performance additives in lithium-ion batteries

We report a new three-dimensional potential energy surface for the He–CS₂ complex including the Q ₃ normal mode for the υ ₃ antisymmetric stretching vibration of the CS₂ molecule. The potential energies were calculated at the coupled-cluster singles and doubles with noniterative inclusion of connected triples level with augmented correlation-consistent quadruple-zeta basis set plus midpoint bond functions. Two vibrationally averaged potentials with CS₂ at both the ground (υ = 0) and the first excited (υ = 1) υ ₃ vibrational states were generated from the integration of the three-dimensional potential over the Q ₃ coordinate. Both potentials have a T-shaped global minimum and two equivalent linear local minima. The radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm were applied to calculate the rovibrational energy levels. Our calculated results show that the two potentials support eight vibrational bound states. The calculated band origin shift of the complex (0.1759 cm^?1) agrees very well with the observed one (0.1709 cm^?1). The predicted infrared spectra and spectroscopic constants based on the two averaged potentials are in excellent agreement with the available experimental values.     

Inversion Vibrational Energy Levels of PH3+(X2A2") Calculated by a New Two-dimension Variational Method

A new 2-D variational method is proposed to calculate the vibrational energy levels of the symmetric P-H stretching vibration (v1) and the symmetric umbrella vibration (inversion vibration) (v2) of PH₃⁺(X²A₂") that has the tunneling effect. Because the symmetric internal Cartesian coordinates were employed in the calculations, the kinetic energy operator is very simple and the inversion vibrational mode is well characterized. In comparison with the often used 1-D model to calculate the inversion vibrational energy levels, this 2-D method does not require an assumption of reduced mass, and the interactions between the v1 and v2 vibrational modes are taken into consideration. The calculated vibrational energy levels of PH₃⁺ are the first reported 2-D calculation, and the average deviation to the experimental data is less than 3 cm^-1 for the first seven inversion vibrational energy levels. This method has also been applied to calculate the vibrational energy levels of NH₃. The application to NH₃ is less successful, which shows some limitations of the method compared with a full dimension computation.     

Ab initio energies and tunneling lifetimes of the doubly charged AH2+ (A = Mg—Ar) diatomics

Potential energy curves for the ground and low-lying excited states of the AH²⁺ (A = Mg—Ar) dications have been calculated using high-level ab initio methods with large atomic orbital basis sets. Quasi-bound potential energy curves with local minima and deprotonation barriers have been found for most of the dications studied. The energies, tunneling lifetimes, and widths of the quasi-bound states have been calculated by numerical solution of the radial Schrodinger equation using the Numeov method. All these dications except ArH²⁺ have low-lying states which support quasi-bound vibrational states. The ArH²⁺ dication has a ²∏_i potential energy curve with a minimum so shallow that it does not support any quasi-bound vibrational states. Results of our calculations are compared with previous ab initio calculations and available experimental data. © 1995 John Wiley & Sons, Inc.     

Determination of vibrational level spacings of van der waals molecules from the Lennard-Jones potential

An approximate expression for the eigenvalues for van der Waals molecules by use of the Lennard-Jones (12-6) potential in the WKB approximation is presented. The expression is applied to the rare gas molecules. Ar₂, Kr₂, and Xe₂ by fitting the potential function to the observed potential parameters. Calculated results of vibrational energy spacings for these molecules agree well with the experiment and other calculations which are based on numerical integration of the Schrödinger equation. For Xe₂, the energy spacing expression is used to determine the thermodynamic functions of the van der Waals bond.     

<Emphasis Type="Italic">Ab initio</Emphasis> spectroscopic studies of non-rigid molecules: an application to acetic acid

The torsional levels of various isotopologues of acetic acid are determined from an ab initio potential energy surface using a flexible model depending on the OH-torsion and the methyl-torsion coordinates. Previous calculations for CH₃–COOH and CH₃–COOD are review and first theoretical energies of the one-deuterated species CH₂D–COOH are provided. The zero point vibrational energy correction and an exact definition for the methyl-torsional coordinate have been considered. The levels are compared with previous calculations (Senent in Mol Phys 99:1311, 2001) and experimental data (Havey et al. in J Mol Spectrosc 229:151, 2005). Isotopic effects on the torsional barriers and energies are discussed. For CH₂D–COOD, the deuteration splits by 25 cm⁻¹ the zero vibrational energy level.     

Variational calculations on the vibrational level structure of S0 HDCO

We perform converged high precision variational calculations to determine the frequencies of the vibrational levels in S₀ HDCO, extending up to 5000 cm^?1 of vibrational excitation energy. For these calculations we use our specific vibrational method (recently employed for studies on H₂CO and D₂CO), consisting of a combination of a search/selection algorithm and a Lanczos iteration procedure and based on the Martin, Lee, Taylor potential energy surface for formaldehyde. The calculated level structure is compared to the recently measured frequencies by Ellsworth et al. in order to improve their assignments and further clarify the vibrational mixing pattern and vibrational resonances in HDCO that are very different from the other more symmetric formaldehyde species H₂CO and D₂CO studied recently.     

Variational calculation of vibrational energies of triatomic molecules using SCF optimized modes

A self-consistent field optimization of the vibrational coordinates for nonlinear triatomic molecules is presented. The optimal coordinates are obtained by making a three-dimensional rotational transformation of the normal modes and determining the rotation angles as those for which the SCF energy is stationary. The utility of the optimized coordinates in full variational calculations of vibrational energies is studied for the molecules of H₂O, O₃, H₂D⁺, H₂T⁺, and D₂T⁺. For H₂O and O₃, the optimization procedure leads to the local mode representation. It is shown that the use of the optimal coordinates in variational calculations allows a large reduction of the dimension of the Hamiltonian matrix to be diagonalized in order to reach convergence.