Damped Dispersion Research Articles

The torsional dependence of an interaction potential: the CH 3OHHe system

An interaction potential for the methanol-helium system was calculated, consisting of an SCF part plus a damped dispersion contribution. A double-zeta basis set was used for the methanol, augmented with one set of polarization functions on each atom. The He basis was a ( 6s 3s ) set augmented with two p-functions. The counterpoise method was used to help correct the basis set superposition error. Interaction energies were computed as a function of the relative position of the HE ( R, θ, φ) as well as of the methanol conformation, described by the single angle γ. The SCF potential was found to be relatively more repulsive at the methyl end of the molecule compared to the Billing site-site potential. A φ-shift approximation was found to predict fairly accurately the γ-dependence of the potential from the staggered conformation interaction alone. The anisotropy of the potential was analyzed using an expansion in products of spherical harmonics in θ, φ and exp(inγ) functions, in which it was shown that only n values which are multiples of three appear. The resulting expansion coefficients are those needed for the matrix elements of the potential between two rotational-torsional states in the close-coupling formation of the scattering problem. It was found that the torsional anisotropy is much weaker than the overall anisotropy and that the φ and γ anisotropies are strongly coupled.

A b i n i t i o potential energy surfaces of Ar–H2O and Ar–D2O

We present an ab initio potential energy surface for the van der Waals system argon–water. The points on the surface are computed as a sum of Heitler–London short range repulsion, damped dispersion, and damped induction. Damping is done in the manner first proposed by Tang and Toennies. We give the surface analytically in the form of a spherical harmonic expansion through l=7. The expansion coefficients are represented by functions depending on the distance between the centers of mass of the monomers. We also present an Ar–D2O potential obtained from the Ar–H2O potential by translating the center of mass of the water molecule. An analytic formula for the translation of polarizabilities is derived and applied to the computation of the long range energy of Ar–D2O. The short range part of the energy is translated numerically. Finally, the potential is checked by comparison of computed interaction virial coefficients with experimental data.

Repulsive ion—atom and ion—ion potentials from charge density overlap integrals

The short-range repulsive potentials for different combinations of the alkali ions Na +, K +, Rb + and Cs + and inert gas atoms, and between the same alkali ions are estimated using a recently suggested combining rule procedure. The comparison with ab initio first-order SCF calculations indicates an error of less than 20% for the combining rule procedure. Well parameters for the full potentials for the alkali ion-inert gas systems including the damped dispersion and polarizability terms are given and compared with values from ion mobility and ion beam experiments.

Computation of the short range repulsion energy from correlated monomer wavefunctions in van der Waals dimers containing He, Ne, and N2

The first order Coulomb plus exchange energy between two closed shell monomers is computed in a non-orthogonal natural orbital formalism. SD-CI monomer wavefunctions were used in order to account for the intramolecular correlation effect. Approximations to the SD-CI wavefunctions and some restraints to the dimer orbital basis are investigated for He2. These result in a method which is applicable to larger dimers. This method is applied to dimers consisting of He, Ne, and N2. It is shown that it is possible to obtain reliable potential energy surfaces from this short range contribution, combined with damped dispersion energy terms.

A comparison between calculated and experimental relaxation phenomena in binary gaseous mixtures N2-He, Ne and Ar

The usefulness of available anisotropic potential energy surfaces for the calculation of collision cross sections governing relaxation phenomena is considered for binary mixtures of N2 with the noble gases He, Ne and Ar. The relaxation phenomena specifically considered are collision broadening of the depolarized Raman and Rayleigh spectra of scattered light. In addition, the relaxation cross section associated with the position on the magnetic field by pressure, B/p, axis of the viscomagnetic effect in such binary mixtures is examined. Six N2-He potentials, eight N2-Ne potentials and seven N2-Ar potentials have been considered in the present study. Of the N2-He potentials, one is satisfactory as far as these relaxation phenomena are concerned; a set of six Hartree-Fock plus damped dispersion (HFD) potentials seem to be reasonable for the N2-Ne system, and three HFD potentials seem reasonable for the N2-Ar system. However, when the present results are combined with transport property requirements, only one...

New anisotropic potential energy surfaces for N2-Ne and N2-Ar

New anisotropic potential energy surfaces of the Hartree-Fock plus damped dispersion (HFD) type have been obtained for the N2-Ne and N2-Ar interactions. The SCF energies utilized in constructing the short-range part of the interactions were computed at 20 points on each surface by using basis sets of double zeta plus polarization quality. Anisotropic C 6 and C 8 dispersion coefficients, utilized in constructing the long-range part of the interaction, have been calculated with a recently obtained combining rule. Several procedures are introduced for estimating the anisotropic damping factors used in the description of the correlation energy contributions in the HFD model. The essential differences amongst the surfaces reported here arise from these estimates. Comparisons are made with other available anisotropic N2-Ne and N2-Ar surfaces. The predictive ability of all surfaces with respect to the temperature dependence of the interaction second virial coefficient, B 12(T), has also been tested. For the N2-Ne system only the present HFD3 surface gives good agreement with the experimental interaction second virial coefficients over a wide temperature range. Similarly, for the N2-Ar system the surface of Candori et al. [1983, Chem. Phys. Lett., 102, 412], which was partially determined using the second virial coefficient data, and the present HFD1 surface give good agreement with experimental virial data.

Calculated high-pressure properties of solid acetylene and possible polymerization paths

Results of theoretical calculations at 0 K on the two known structures of solid acetylene using the modified Gordon–Kim plus damped dispersion model are reported. The lattice energy of the low temperature Cmca structure is compared to that of the high temperature Pa3 structure at zero pressure and found to be slightly less stable, though a very small pressure (about 0.25 kbar) stabilizes the Cmca structure relative to the Pa3 structure. Agreement between the experimental structure and energy for the Cmca structure and our present results is good. Structural properties of the Cmca structure were calculated to 100 kbar as well as the pressure dependence of the Ag libron mode. A possible high-pressure path for the polymerization of solid Cmca acetylene that would lead to a well-ordered polymer was proposed, but calculations of C–C distances suggest that a more cross-linked product would be favored.

Dissociation of compound ions in a high electric field: Atomic tunneling, orientational, and isotope effects.

Dissociation of compound ions, ${\mathrm{HeRh}}^{2+}$, has been studied with a combined technique of pulsed-laser-stimulated field desorption and time-of-flight spectroscopy. It is found that $^{4}\mathrm{HeRh}^{2+}$ ions can dissociate in a field of a few V/A\r{} by atomic tunneling several hundred femtoseconds after their formation. This dissociation time is believed to be one of the fastest reaction times ever successfully measured. The tunneling effect is confirmed with a strong isotope effect observed when $^{4}\mathrm{He}$ is replaced with $^{3}\mathrm{He}$. The field dissociation can occur most readily when the ions are rotated by 180\ifmmode^\circ\else\textdegree\fi{} from their original field-desorption orientation. This orientation effect produces a secondary peak in the time-of-flight spectral line of ${\mathrm{Rh}}^{2+}$. The experimental results can be satisfactorily explained by using a realistic interaction U(r) between a He atom and a ${\mathrm{Rh}}^{2+}$ ion. This potential is constructed from an effective-medium model of the repulsion, an induced dipole attraction, and damped dispersion interaction terms.

He-atom interaction with the (001) surfaces of LiF and NaCl.

Calculations are presented of the potential energy of a He atom near the (001) surfaces of LiF and NaCl. Ingredients in this interaction are a repulsion, computed from the substrate charge density with the effective-medium theory, a sum of damped dispersion attractions contributed by the individual ions, and a small induced dipole energy. The net interaction has a qualitatively reasonable attractive strength. The corrugation, however, is \ensuremath{\sim}1.5--2 times larger than is inferred from He-beam diffraction intensities. Hypothetical explanations are briefly discussed.

Proton magnetic resonance study of the H2–Ne potential energy surface

Measurements of the proton spin-lattice relaxation time (T1) carried out at 18.775 MHz in two H2–Ne mixtures are presented. Values for T1/ρ)∞lin, accurate to within 2% are deduced for ten temperatures between 99 and 296 K. These data are compared with values obtained from close-coupled scattering calculations for a Hartree–Fock plus damped dispersion (HFD) model potential energy surface, allowing a refined anisotropic contribution to be determined.

Rotationally inelastic scattering and potential calculations for He + CH4

In two crossed beam experiments total differential and rotationally inelastic cross sections have been measured for He + CH4 in the angular range from 3° to 70° in the c.m. system. At the low collision energy of E = 34·1 meV state resolved cross sections for the 0–3, 1–2 and 1–3 transition have been observed. All cross sections show well resolved diffraction oscillations. The inelastic cross sections are much smaller than the elastic ones. At the collision energy of E = 75·5 meV energy loss spectra have been measured, which are, at large angles, dominated by inelastic transitions. The data are compared with quantum coupled-states calculations based on a potential model of the Hartree-Fock-dispersion type, where high quality SCF-calculations are combined with damped dispersion coefficients. The gross features of the measurements are reproduced by adjusting one parameter in the damping function. However, discrepancies arise in predicting some of the inelastic cross sections at low energies.

Rotationally inelastic scattering and potential calculations for Ne + CH4

In a crossed molecular beam experiment total differential cross sections and differential energy loss spectra have been measured for Ne + CH4 at 88·8 meV. The energy loss spectra taken at centre-of-mass deflection angles from 45° to 145° show appreciable energy transfer in the backward direction with a maximal energy transfer corresponding to final rotational states of j′ = 4. The total differential cross sections exhibit diffraction oscillations in the forward direction. These two data sets are compared with calculations performed in the accurate centrifugal sudden approximation both for the A- and T-symmetry of the CH4 molecule. The non-spherical potential surface, which includes the anisotropic T 3 and T 4 is determined from accurate SCF-calculations and a damped dispersion contribution using the HFD-model. The general features of the experimental data are reproduced using a simple universal damping function. However, discrepancies concerning the isotropic potential well depth and the repulsive anisotropy remain. The comparison with other methane-rare gas interactions reveals an increase of the attractive minimum and a decrease of the relative repulsive anisotropy going from He to Ar.

CEPA calculations of potential energy surfaces for open-shell systems.

Abstract Quantum-chemical ab initio calculations have been performed for the van der Waals interaction between helium and oxygen atoms in their respective ground states: He( 1 S)+ O( 3 P). As long as fine-structure effects are neglected, there are two low-lying electronic states, 3 Σ − and 3 Π resulting from the degeneracy of the O( 3 P) ground state. Both states are purely repulsive at the SCF level, after inclusion of electronic correlation by the CEPA method they exhibit shallow van der Waals (dispersion) minima at large interatomic separation: R ϵ = 3.61 A, ϵ = 1.0 meV ( 3 Σ − ) and R ϵ = 3.05 A, ϵ = 2.3 meV ( 3 Π). The analysis of the results shows the very slow convergence of the dispersion interaction with increasing basis size, while SCF repulsion and the repulsion due to the change of the intra-atomic correlation are obtained reasonably accurately with moderate basis stes. Van der Waals coefficients C 6 , C 8 , C 10 , potential curves of the type HFD (i.e. Hartree-Fock plus damped dispersion) and the influence of fine-structure effects (mainly spin-orbit coupling) on the shape of the adiabatic potential curves are discussed as well.

Vibrational relaxation of CO (n=1) in collisions with H2. I. Potential energy surface and test of dynamical approximations

We present a fully quantal dynamical study of vibrational relaxation of CO in collisions with H2 treating H2 as a structureless projectile. The potential energy surface consists of a SCF part, including explicitly the variation with the CO bond distance, and a damped long range dispersion part. This potential model contains only two free parameters in the damping function which have been determined previously by fitting rotationally inelastic beam data for D2–CO. The dynamical calculations are performed within the infinite order sudden approximation (IOSA) and the coupled states approximation (CSA). The IOSA relaxation cross sections are generally a factor of ∼1.5 smaller than the CSA cross sections independent on the initial rotational state of CO for j≲4–6. The relaxation rate constants are very sensitive to small changes of the interaction potential. After readjusting one of the damping parameters (within a range still acceptable with the beam data) the IOSA rate constants agree very well with the experimental ones for ortho H2. It is demonstrated that on the same level of approximation the present rate constants are about three times larger than those obtained from the potential energy surface of Poulsen.

Vibrational relaxation of CO (n=1) in collisions with H2. II. Influence of H2 rotation

Vibrational relaxation of CO (n1=1) in collision with ortho, para H2 is studied quantum mechanically, with the rotational degree of freedom of H2 included. This represents extension of our earlier study [Ref. 11, J. Chem. Phys. 81, 0000 (1984)], where H2 was treated as a structureless particle. The potential surface, described in detail in Ref. 11, consists of a SCF part, which includes explicitly the variation with the CO bond distance, and a damped long range dispersion contribution. The relaxation cross sections are calculated within the infinite order sudden approximation (IOSA) for CO rotation and within the coupled states approximation (CSA) for H2 rotation. Many of the trends clearly present in the cross sections can be understood in terms of the distorted wave approximation (DWA). The calculated relaxation rates in para H2 agree well (within a factor of 2) with the experimental results. However, judging from a limited number of calculated cross sections for relaxation in ortho H2, the ortho H2 relaxation rates would be comparable in magnitude to the para rates, in disagreement with experiment. Extensive comparison is made with the work of Poulsen and Billing (Ref. 12) and a number of significant, even qualitative differences regarding magnitude of some simultaneous CO vibrational and H2 rotational transitions are discussed.

Anisotropic intermolecular forces from Hartree-Fock plus damped dispersion (HFD) calculations

The semiempirical HFD model of intermolecular forces is extended to strongly anisotropic atom-diatom systems. A single-centre representation of the dispersion energy is found to be inadequate, and a method of partitioning dispersion forces between two centres of attraction is developed, based on the A tensor of the diatomic molecule. The method is tested on the systems Ar-HCl and Ar-HF, for which accurate data sensitive to the potential anisotropy are available, and gives promising results. The quality of the SCF potential used is crucial, and it appears that for Ar-HCl the results are limited by deficiencies in the SCF potentials available. For Ar-HF, the dispersion coefficients are not well known, and the HFD method provides a single-parameter functional form capable of reproducing all the available data.

A comparison of the predictions of various model N2–He potential energy surfaces with experiment

Predictions of beam scattering and bulk gas phenomena based upon five different model potential energy surfaces for the N2–He system are compared with experiment. The surfaces considered are our recent HFD1 and HFD2 surfaces based on the Hartree–Fock plus damped dispersion (HFD) model, the surface of Habitz, Tang, and Toennies (HTT) based upon the Tang–Toennies model, the surface of Keil, Slankas, and Kuppermann (KSK) and a modification (KKM3) of the KSK surface. The physical observables against which these surfaces are tested include total differential scattering cross sections, state-to-state inelastic differential scattering cross sections, interaction second virial coefficients, shear viscosity and binary diffusion coefficients, and the relaxation cross section for the Senftleben–Beenakker effect on the shear viscosity. None of the surfaces is in complete agreement with all of these observables. For the interaction second virial coefficients, the shear viscosity and binary diffusion coefficients, the HFD1 surface is the only one to predict values within most of the experimental error bars. The relaxation cross section is correctly predicted only by the KKM3 surface which was essentially fitted to it. The HFD1, HFD2, and HTT surfaces are all in good agreement with the state-to-state inelastic cross sections. The KSK surface gives the best agreement with the total differential cross section. It appears that an accurate N2–He surface cannot be obtained from simple models, and its determination will require multiproperty fits.

An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients

Starting from our earlier model [J. Chem. Phys. 66, 1496 (1977)] a simple expression is derived for the radial dependent damping functions for the individual dispersion coefficients C2n for arbitrary even orders 2n. The damping functions are only a function of the Born–Mayer range parameter b and thus can be applied to all systems for which this is known or can be estimated. For H(1S)–H(1S) the results are in almost perfect agreement with the very accurate recent ab initio damping functions of Koide, Meath, and Allnatt. Comparisons with less accurate previous calculations for other systems also show a satisfactory agreement. By adding a Born–Mayer repulsive term [A exp(−bR)] to the damped dispersion potential, a simple universal expression is obtained for the well region of the atom–atom van der Waals potential with only five essential parameters A, b, C6, C8, and C10. The model has been tested for the following representative systems: H2 3Σ, He2, and Ar2 as well as NaK 3Σ and LiHg, which include four chemically different types of van der Waals interactions for which either very precise theoretical or experimental data is available. For each system the ab initio dispersion coefficients together with the well-known parameters ε and Rm were used to determine A and b from the model potential. With these values the reduced potentials were calculated and found to agree with the experimental potentials to better than 1% and always less than the experimental uncertainties. Some of the implications of the new model are discussed.

Interaction of hydrogen atoms with polyatomic molecules studied by means of scattering experiments and hybrid Hartree-Fock plus damped dispersion calculations

Total differential collision cross sections for the scattering of H atoms from ethane (C/sub 2/H/sub 6/), propane (C/sub 2/H/sub 8/), acetylene (C/sub 2/H/sub 2/), and O/sub 2/ have been measured and information on the spherical and nonspherical parts of the interaction potential extracted by means of scattering calculations which make use of the infinite-order sudden (IOS) approximation. The interactions of three other systems, H + Ar, H + CH/sub 4/, and H + CO, previously measured in our laboratory have been calculated by means of hybrid Hartree-Fock plus damped dispersion (HFD) energy calculation and found to be in good agreement with the experimental potentials. A model is then constructed to derive the main features of the interaction of H atoms with the higher hydrocarbons from the knowledge of the H + CH/sub 4/ interaction. The predictions of this model are found to be in excellent agreement with the experimental parameters for both the spherical and nonspherical parts of the potentials. 4 figures, 9 tables.

On the interatomic potentials for noble gas mixtures

Recently, a relatively simple scheme for the construction of isotropic intermolecular potentials has been proposed and tested for the like species interactions involving He, Ne, Ar, Kr and H 2. The model potential has an adjustable parameter which controls the balance between its exchange and Coulomb energy components. The representation of the Coulomb energy contains a damped multipolar dispersion energy series (which is truncated through O( R −10) and provides additional flexibility through adjustment of the dispersion energy coefficients, particularly C 8 and C 10, within conservative error estimates. In this paper the scheme is tested further by application to interactions involving unlike noble gas atoms where the parameters in the potential model are determined by fitting mixed second virial coefficient data as a function of temperature. Generally the approach leads to potential of accuracy comparable to the best available literature potentials which are usually determined using a large base of experimental and theoretical input data. Our results also strongly indicate the need of high quality virial data.