Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states. Part II: Theoretical investigation of oxalyl chloride

The structures of the oxalyl chloride molecule (COCl)₂ in the ground and the four lowest (two singlet and two triplet) excited electronic states were investigated by means of the CASPT2(8-6)/cc-pVTZ technique. The equilibrium geometric parameters, harmonic vibrational frequencies, and adiabatic energies of the electronic transitions were determined for all states under investigation. The calculations predicted the existence of the trans- and gauche- conformers in the ground state and the trans- and cis-conformers in all excited states. For the ground electronic state, the conformer energy difference and the barriers to conformational transitions were estimated using extrapolation to the complete basis set within a Valence Focal-Point Analysis procedure. The internal rotation in the excited electronic states was found to be strongly coupled with the non-planar symmetric CCOCl wagging. Two-dimensional potential energy surface sections along internal rotation and non-planar coordinates were constructed, and the corresponding anharmonic vibrational problems for the trans-conformer were solved.     

Effect of side by side interactions on the thermodynamic properties of adsorbed CO molecules on the Ni(111) surface: a cluster model study

The effect of electrostatic interactions on vibrational frequencies and thermodynamic properties of CO adsorbate on the Ni(111) surface is calculated by taking the first and second nearest-neighbour interactions into account. In order to obtain reasonable results, the cluster model of various surface adsorption sites with CO adsorbate is partially optimized, using Density Functional Theory and also the MP2 method for the hcp site. Comparison between DFT and MP2 results shows that DFT results are more reliable for this system. The stretching and bending frequencies of CO adsorbate are calculated using both Partial Hessian Analysis and Cluster–Adsorbate Coupling methods. Stretching and bending frequencies are both shifted by the side by side interactions. The coupling of surface phonons and adsorbate vibrations reduces the side effects. The largest side effects on the vibrational internal energy, isochoric heat capacity, entropy and total Helmholtz free energy of adsorbed CO molecule calculated using the CAC method are found for 0.5 ML coverage. The results of the CAC method are better, but the PHA method can be used as a simple upper bound estimation. The adsorptive phase acts as an intelligent material in such a way that it changes its configuration in order to reduce the side effects.     

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.     

Coupled cluster ab initio potential energy surfaces for CO… He and CO… H2

Ab initio potential energy surfaces including the vibrational coordinate dependence are presented for CO… He and CO… H₂ using the coupled cluster method with Brueckner orbitals. The interaction energy is calculated using the supermolecule approach. The calculation of rate constants for the vibrational relaxation of CO(v = 1) by He and their comparison with the experimentally measured values over the temperature range 40–300 K is used to test the accuracy of the CO… He surface. Comparison with results from an earlier surface calculated by symmetry adapted perturbation theory shows that the two surfaces have similar scattering characteristics and reproduce the experimental measurements to a similar level of accuracy. The potential surface for the CO… H₂ system is presented as raw data in anticipation of future calculations.     

The vibrational energy levels of ammonia

A variational 6-dimensional method is used to determine the low lying vibrational energy levels of ammonia. The six internal coordinates were chosen to be appropriate for the symmetry and inversion motion of the molecule; they were the three NH bond lengths, r1, r2, r3, the unique angle β which each bond makes with the trisector of them, and two (of the three) angles, θ2 and θ3, between the bonds when projected on to a plane perpendicular to the trisector. The Wilson G matrix was determined for these internal coordinates both by computer algebra and by hand. An appropriate Jacobian for the motion was determined and the full Hermitian kinetic energy operator was obtained using the Podolsky transformation. Expansion functions were in the usual product form. Special attention was given to the θ2, θ3 expansion functions so that appropriate A1, A2 and E symmetry vibrational modes were obtained explicitly. Matrix elements of the kinetic energy operator were expressed in terms of one-dimensional integrals.Variational calculations have been performed with two six-dimensional surfaces: (i) that due to Martin, Lee and Taylor; and (ii) that due to Spirko and Kraemer. Although some of the vibrational levels for both surfaces are accurate, both have inadequacies: (a) because it is a Taylor expansion about an equilibrium, based on ab initio calculations, with no attention paid to planarity; and (b) because the non-inversion part of the surface was treated perturbatively in its derivation, and in fact some of the quartic displacement powers have negative coefficients. Therefore, neither surface gave good results overall, and there is a need for a refined 6 dimensional NH3 surface.     

Indeterminancy of the potential matrix in redundant coordinates

The use of redundant internal coordinates in vibrational problems leads to an indeterminate potential matrix. Two formulations are given which express the indeterminancy by sets of arbitrary parameters. All potential matrices related by these formulations within a given set of internal coordinates lead to the same vibrational eigenvalues and eigenvectors. The indeterminancy is illustrated by examples and by possible application in practical normal coordinate analysis.     

Conformational stability and vibrational study of phenylacetyl chloride

The Fourier transform infrared spectroscopy and Fourier transform Raman spectra of phenylacetyl chloride were recorded and analyzed in the range 3500–400 and 3500–200 cm^?1 at room temperature, respectively. In order to obtain the structural information and conformational stabilities, a potential energy surface scan for internal rotation was carried out at the B3LYP/6‐31G(d) level. The potential energy surface reveals that the title compound has two minimal conformers (A and B). The optimized geometries, structural parameters, stabilities, energies, thermodynamic parameters, vibrational wavenumbers, infrared intensities, and Raman activities for the two conformers (A and B) have been obtained by employing B3LYP and MP2 calculations with 6‐311++G (d, p) basis sets. The conformational energy difference between A and B is very small, indicating that the B conformer coexists with the A conformer. The detailed vibrational assignments of vibrational spectra of each conformer have been made on the basis of the potential energy distributions analysis. The highest occupied molecular orbital –lowest unoccupied molecular orbital energy gap and molecular electrostatic potential of the two conformers have been also calculated for comparison of their chemical activities. Copyright © 2015 John Wiley & Sons, Ltd.     

Vibrational spectra and normal coordinate analysis on structure of chlorambucil and thioguanine

A normal coordinate analysis on chlorambucil and thioguanine has been carried out with a set of symmetry coordinates following Wilson’s F-G matrix method. The potential constants evaluated for these molecules are found to be in good agreement with literature values thereby confirming the vibrational assignments. To check whether the chosen set of vibrational frequencies contribute maximum to the potential energy associated with the normal coordinates of the molecule, the potential energy distribution has been evaluated.      

Anharmonic potential function of 1,1-dichloroethylene

A simple anharmonic potential containing 18 quadratic, 6 cubic, and 6 quartic constants is proposed to fit 124 vibrational frequencies of 1,1-dichloroethylene and its ³⁷Cl isotope in the region from 10 000 to 350 cm^?1. The level patterns in the first and the second overtone regions of the CH₂ stretching vibrations are explained by the absence of large higher-order interaction terms between the two CH stretching coordinates.     

Quantum theory of energy exchange in direct encounters of polyatomic molecules with nonrigid surfaces

Recently developed effective mass theory of vibrational, rotational and translational energy exchange in molecular collisions is extended naturally to polyatomic molecules colliding with nonrigid surfaces. Considering the processes where the short-range forces are of prevailing importance, we transform the Hamiltonian into the form which enables us to eliminate the coordinates which are cyclic in the limit of zero range forces and can thus be expected to be approximately ignorable when forces are of short, but finite, range. Instead of three rotational and three translational coordinates we are thus left with one only relevant generalized coordinate. The mass corresponding to this coordinate can easily be calculated; it depends on the mass and the moments of inertia of the molecule, and on the segment of the potential surface on which the system evolves. The motion of the only relevant generalized coordinate is then quantized. The inelastic scattering problem is treated within first-order in the distorted wave expansion. In the cases where this may be expected to be inadequate, more advanced approximation schemes developed in scattering theory could be applied as well. The excitations of bulk phonons and also of vibrational modes localized on the surface are included in the theory. As an application, energy transfer in collisions of CO₂ molecules with Pt and Ag surfaces is studied (since this is the experimentally most studied case involving molecules of more than two atoms), and the results are compared with the experiments and with the recent semiclassical stochastic trajectory calculations in which the transfer of vibrational energy to rotations is neglected and the solid's vibrations are treated by a quasiclassical approximation. Excellent agreement was found between the present theory and the trajectory calculations mentioned for all three gas temperatures considered (290, 580 and 1160 K) in the case of small change in vibrational energy and high surface temperature, i.e., under the conditions where the agreement between the two methods could possibly be expected because of the approximations involved.     

A Theoretical Study of the Methyl and Aldehyde Torsion FIR Spectra in Symmetric Propanal Isotopomers

This paper is an extension of the techniques developed by us [A. Vivier-Bunge, V. H. Uc, and Y. G. Smeyers, J. Chem. Phys. 109, 2279 (1998)] for standard propanal. In that paper the potential energy surface for the simultaneous methyl and asymmetric aldehydic torsions was calculated at RHF/MP2 level using the 6-311(3df,p) basis set for propanal. The fit of the energy values to symmetry-adapted functional forms was carried out by using the 28 energy values which retain the C(3) dynamical symmetry of the methyl group in the optimization procedure. With this potential, as well as with the kinetic parameters and the electric dipole moment variations, the FIR frequencies and intensities for the methyl and aldehyde torsions of seven symmetric isotopomers of propanal were determined theoretically using two-dimensional calculations. The calculated spectra of propanal and three of its isotopomers were compared with the available experimental data. It is found that the calculations for the cis conformer satisfactorily reproduce the aldehyde and methyl torsion spectra and furnish also methyl torsionally excited progressions for the aldehyde torsion modes. The methyl torsion frequencies agree especially well whenever the methyl group is nondeuterated. The small deviations encountered for the deuterated compound are probably due to some mass effect, such as the zero-point vibrational energy correction, which is not taken into account in the present calculations. Finally, the influence of the deuteration on the intensities is discussed. Copyright 2000 Academic Press.     

A General Variational Algorithm to Calculate Vibrational Energy Levels of Tetraatomic Molecules

A general variational method for calculating vibrational energy levels of tetraatomic molecules is presented. The quantum mechanical Hamiltonian of the system is expressed in a set of coordinates defined by three orthogonalized vectors in the body-fixed frame without any dynamical approximation. The eigenvalue problem is solved by a Lanczos iterative diagonalization algorithm, which requires the evaluation of the action of the Hamiltonian operator on a vector. The Lanczos recursion is carried out in a mixed grid/basis set, i.e., a direct product discrete variable representation (DVR) for the radial coordinates and a nondirect product finite basis representation (FBR) for the angular coordinates. The action of the potential energy operator on a vector is accomplished via a pseudo-spectral transform method. Six types of orthogonal coordinates are implemented in this algorithm, which is capable of describing most four-atom systems with small and/or large amplitude vibrational motions. Its application to the molecules H₂CO, NH₃, and HOOH and the van der Waals cluster He₂Cl₂ is discussed.     

Effective one-dimensional equation of motion for nuclear fission

An approach for describing the dynamics of nuclear fission in the framework of generalized quantum mechanics is discussed. The collective kinetic energy is assumed to be two dimensional, and the reduced mass is allowed to vary with the coordinates. The generalized calculus of variation is employed for minimizing the action after being properly quantized as required by Hamilton's principle, employing a curvilinear coordinate system. The corresponding Euler Lagrange equation is identified as the required generalized equation of motion. The proposed generalized two-dimensional equation of motion is separated into a vibrational eigenvalue equation and a set of coupled-channel one-dimensional equations which describe the translational motion, by exploiting the completeness of the vibrational eigenfunctions. Such a system of coupled equations can be decoupled by replacing the coupling matrix elements by a nonlocal interaction, which can be rendered local after employing the effective mass approximation. As a consequence this differential equation is provided with an effective mass, an effective potential barrier, and a differential boundary term which is responsible for restoring the self-adjointness of the kinetic energy differential operator.     

Geometry,vibrational frequencies,and ionization potentials for CO/Ni(100); explanation of the disappearance of the 5σ peak in pes

Using a cluster of 14 Ni atoms to model a Ni(100) surface, we used ab initio methods [generalized valence bond (GVB)] to study CO chemisorbed at the on-top site. Reported are the optimum geometry, vibrational frequencies, and ionization potentials. We propose a new explanation for the two lowest levels of free CO (5σ and 1π) reducing to one level of chemisorbed CO.     

Potential energy function of polyatomic molecules: Fourth-order approximation of the potential energy function of CO2: Spectroscopic constants of nine isotopic species

In this paper are given the values of the coefficients involved in the fourthorder expansion, with respect to mass-independent internal coordinates, of the potential energy function of CO₂. This function is applied to the computation of the vibrational energy levels of nine isotopic species of this molecule. A comparison between experimental and theoretical results is given along with the spectroscopic constants of these nine species. The coefficients appearing in the expansion of the potential energy function with respect to dimensionless normal coordinates are also given for each of these molecules.     

The rovibrational structure of the He-CO complex from a model interaction potential

The full dimensional potential energy surface for the He-CO complex, V(R,Ø r_co), has been calculated using a recently developed scheme which combines density functional theory with the long range dispersion contributions obtained from perturbative theory. Then the two adiabatic surfaces obtained by the integration of the full potential over the vibrational coordinate of CO have been used to calculate the bound states of the van der Waals complex for both v_co = 0 and v_co = 1. Calculations of the wavefunctions and of the frequencies of various rotational and rovibrational transitions is seen to provide good overall agreement with the available experiments on the title system.     

Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ²T_VIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C₃ molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191–207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C₃. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations.     

The coadsorption of potassium and co on the pt(111) crystal surface: A TDS,HREELS and UPS study

The interaction of CO with a potassium covered Pt(111) surface is investigated using thermal desorption (TDS), high resolution electron energy loss (HREELS) and ultraviolet photoelectron (UPS) spectroscopies. When submonolayer amounts of potassium are preadsorbed, the adsorption energy of CO increases from 25 to 36 kcal/mole, while substantial shifts in the site occupancy from the linear to the bridged site are observed. The CO stretching vibrational frequencies are shown to decrease continuously with either increasing potassium coverage or decreasing CO coverage. A minimum CO stretching frequency of 1400 cm^?1 is observed, indicative of a CO bond order of 1.5. The work function decreases by up to 4.5 eV at submonolayer potassium coverages, but then increases by 1.5 eV upon CO co-adsorption. The results indicate that the large adsorption energy, vibrational frequency and work function changes are due to molecular CO adsorption with a substantial charge donation from potassium through the platinum substrate and into the 2π¹_CO orbital.     

A refined potential energy surface and the rovibrational states for the electronic ground state of ozone

A potential energy surface for the electronic ground state of ozone has been optimized by using a variational procedure with the exact vibrational Hamiltonian in bond length-bond angle coordinates. In the optimization, the ab initio force field of Borowski, P., Andersson, K., Malmquist, P.-A., and Roos, B. O., 1992, J. chem. Phys., 97, 5568 is taken as the starting point, and the recent observed vibrational band origins up to 4900 cm^-1 reported by Floud, J.-M., Barbe, A., Camy-Peyret, C., and Plateaux, J. J., 1996, J. molec. Spectrosc., 177, 34 are involved. The root mean square error of this fit for the 39 observed vibrational energy levels is 0.83 cm^-1. In order to test the refined potential, the rovibrational energy levels up to J = 15 are calculated and compared with the observed values.     

An effective scaling frequency factor method for scaling of harmonic vibrational frequencies: The use of redundant primitive coordinates

A modified effective scaling frequency factor (ESFF) method that takes advantage of the potential energy distribution (PED) coefficients calculated in the basis of redundant primitive internal coordinates is presented. This approach is simpler and more flexible than that based on the natural internal coordinates. The sets of optimal scaling factors for routine 9- and 11-parameter ESFF calculations based on B3LYP/6-311G∗∗ force fields are derived from Baker’s training set of 30 molecules (660 frequencies). The calculated root-mean-square (RMS) deviations for all frequencies are 11.42 and 11.44 cm⁻¹ for 9- and 11-parameter scaling, respectively. They are somewhat lower than in the case of ordinary ESFF calculations. The new sets of factors seem to be particularly well suited for scaling of frequencies in the middle region of the vibrational spectra (1000-2500 cm⁻¹) - the RMS values in this range are 8.37 for 9-, and 9.56 cm⁻¹ for 11-parameter scaling. These values are to be compared with 9.20 and 10.29 cm⁻¹, respectively, calculated within the natural coordinates based ESFF formalism.