Variational calculation of dynamic polarizabilities

The finite field method of obtaining static multipole polarizabilities is extended to the calculation of dynamic polarizabilities. The first-order frequency dependent wavefunction is obtained variationally using a trial function, λ(ω)ψ₁(0). ψ₁(0) is the first-order wavefunction obtained in the static calculation. The results are applied to the approximation of the dynamic polarizability at imaginary frequencies. These are then used to calculate the coefficients for the inverse power series representation of the interatomic potential energy. The method has been applied to two simple cases, hydrogen and helium. For hydrogen the present method yields results close to the exact values for the static dipole polarizability and the dipole-dipole van der Waals coefficient; C₆. In the case of helium a simple Hartree-Fock function was perturbed but the results are still encouraging with the dipole-dipole van der Waals coefficient, C₆, calculated to within 7% of the accurate value.     

The non-empirical calculation of second-order molecular properties by means of effective states. II. Effective TDCHF spectra for NO+ CO,CO2, and C2H2

Time-dependent coupled Hartree-Fock calculations have been performed in the large bases molecules NO⁺, CO. CO₂ and C₂H₂. Some first- and second-order properties are presented, in particular the isotropic dispersion interaction coefficients C₆⁰⁰⁰, C₈⁰⁰⁰ and C₁₀⁰⁰⁰ for all possible van der Waals dimers consisting of these monometers. These coefficients, and also the corresponding long-range anisotropic interaction coefficients, can be calculated easily for any of these dimers using the effective TDCHF multipole spectra presented in this paper. Formulas to this end are given.     

Accurate ab initio determination of the van der Waals interaction in the X 2Σ+ ground state of LiHe

Accurate quantum-chemical ab initio calculations have been performed at the SCF and CEPA (coupled electron pair approximation) levels for the van der Waals interaction in the X ² Σ ⁺ ground state of LiHe. An extended basis set has been used and the counterpoise correction for the basis set superposition error (BSSE) has been applied. The calculated potential energy curve has a very shallow minimum at 11.56 a ₀ with a well depth of only 1.49 cm^?1. This is too small to allow for a bound vibrational level. The analysis of the results shows that the interaction mainly consists of the Pauli repulsion between Li(1s ²2s) and He (1s ²), which is decaying exponentially, and the attractive London dispersion energy. Van der Waals coefficients C₆, C₈, and C₁₀ have been determined by a least squares fit to the long-range part of the calculated potential curve.     

Accurate DMBE Potential Energy Surface For the N(2D) + H2(1Σ g + ) Reaction Using an Improved Switching Function Formalism

A single-sheeted double many-body expansion (DMBE) potential energy surface is reported for the 1 ² A′′ state of NH₂. To approximate its true multi-sheeted nature, a novel switching function that imposes the correct behavior at the H₂(X ¹Σ _g ⁺)+ N(² D) and NH(X ³Σ^-) + H(² S) dissociation limits has been suggested. The new DMBE form is shown to fit with high accuracy an extensive set of new ab initio points (calculated at the multi-reference configuration interaction level using the full valence complete active space as reference and aug-cc-pVQZ and aug-cc-pV5Z basis sets) that have been semiempirically corrected at the valence regions by scaling the n-body dynamical correlation terms such as to account for the finite basis set size and truncated configuration interaction expansion. A detailed study of the N(² D) ... H₂(X ¹Σ _g ⁺) van der Waals region has also been carried out. These calculations predict a nearly free rigid-rotor with two shallow van der Waals wells of C _2v and C _{∞ v} symmetries. Such a result contrasts with previous cc-pVTZ calculations which predict a single T-shaped van der Waals structure. Except in the vicinity of the crossing seam, which is replaced by an avoided intersection, the fit shows the correct physical behavior over the entire configurational space. The topographical features of the new DMBE potential energy surface are examined in detail and compared with those of other potential functions available in the literature. Amongst such features, we highlight the barrier for linearization (11,802 cm^-1) which is found to overestimate the most recent empirical spectroscopic estimate by only 28 cm^-1. Additionally, the T-shaped N(² D) ... H₂ van der Waals minimum is predicted to have a well depth of 90 cm^-1, being 11 cm^-1 deeper than the C _{∞ v} minimum. The title DMBE form is therefore recommendable for dynamics studies of both non-reactive and reactive N(² D)+H₂ collisions.     

Semiclassical calculation of energy transfer in polyatomic molecules. XI. Cross sections and rate constants for Ar + CO2

Data from electron gas calculation on the short-range potential and theoretical van der Waals coefficients C_n (n = 6, 8) have been used to construct a potential surface for the Ar+CO₂ system. The surface has been used to calculate: second virial coefficient, viscosity and diffusion coefficient, rotational relaxation rates, rate constants for vibrational transitions in CO₂ and high-enery/small-angle differential cross sections.     

CEPA calculations of potential energy surfaces for open-shell systems.: III. Van der Waals interaction between O(3P) and He(1S)

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(¹S)+ O(³P). As long as fine-structure effects are neglected, there are two low-lying electronic states, ³Σ^? and ³Π resulting from the degeneracy of the O(³P) 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_? = 3.61 Å, ? = 1.0 meV (³Σ^?) and R_? = 3.05 Å, ? = 2.3 meV (³Π). 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 C₆, C₈, C₁₀, 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.     

Interaction potential for He/H2 including the region of the van der waals minimum

The energy of He/H₂ in its ground state is calculated in an ab-initio way using the IEPA PNO method for three different H-H distances, three different angles and for distances between He and the midpoint of H₂ ranging from 3 to 20a₀.A van der Waals minimum of ≈21°K is found for the linear arrangement and a saddle point of ≈14°K for the C_2v geometry. The computed hypersurface is compared with experiment and with the R^?6 term known from perturbation theory. The anisotropy of the potential is much larger than what is predicted asymptotically.     

Non-statistical behavior in the dissociative photoionization of the 1,3-butadiene/sulfur dioxide van der Waals complex

Dissociative photoionization of the van der Waals complex of 1,3-butadiene and SO₂ to yield the fragment ion C₄H₆-SO⁺ is reported. From     

Ionic Liquids: Dissecting the Enthalpies of Vaporization

We calculate the heats of vaporisation for imidazolium‐based ionic liquids [C_nmim][NTf₂] with n=1, 2, 4, 6, 8 by means of molecular dynamics (MD) simulations and discuss their behavior with respect to temperature and the alkyl chain length. We use a force field developed recently. The different cohesive energies contributing to the overall heats of vaporisations are discussed in detail. With increasing alkyl chain length, the Coulomb contribution to the heat of vaporisation remains constant at around 80 kJ mol^?1, whereas the van der Waals interaction increases continuously. The calculated increase of about 4.7 kJ mol^?1 per CH₂‐group of the van der Waals contribution in the ionic liquid exactly coincides with the increase in the heats of vaporisation for n‐alcohols and n‐alkanes, respectively. The results support the importance of van der Waals interactions even in systems completely composed of ions.     

Long-Range van der Waals Interactions in Density Functional Theory

The early difficulties in accounting for long-range van der Waals interactions in the framework of density functional theory (DFT) have been overcome to a certain extent in recent works by several groups, and those interactions can be computed numerically. In this paper a derivation of the analytical form of the attractive van der Waals interaction between two neutral atoms with polarizabilities α₁ and α₂ at large distance R, namely E _int=−C ₆ α₁ α₂/R ⁶ is performed within the context of DFT. Use is made of the properties of the Coulomb correlation hole, and it is shown that nonlocal Coulomb correlations are responsible for long-range dispersion interactions.     

Intermolecular vibronic spectroscopy of small Van Der Waals clusters: phenol- and aniline-(argon)2 complexes

We report the clear observation and assignment of the symmetric stretching and bending van der Waals modes in two three-bodyC _2v complexes, phenol- and aniline-(Ar)₂, using resonant two-photon ionization.     

Application of significant structure theory of liquids to critical phenomena. Calculation of critical-point exponents

Three critical-point exponents β, δ, γ and the corresponding coefficients B, D and G are calculated using significant structure theory. The results are compared with those obtained from the van der Waals equation, Berthelot's equation and the Dieterici equation. The significant structure theory and the van der Waals equation behave similarly in the critical region. All these equations of state predict a finite C_ν at the critical point.     

Self-consistent-field × α cluster calculations for the ground state Ne2 molecule

The ground ¹Σ⁺_g state potential curve for Ne₂ is calculated in the SCF × α approximation. The molecule is found to dissociate too slowly and to give no van der Waals minimum.     

Multipole interaction in high energy approximation. Calculation of the total collision cross section

For molecules of cylindrical symmetry the total collision cross section is calculated in the high energy approximation, taking into account various long range intermolecular interactions. Results are obtained for the limiting cases that the rotational motion of the molecules is fast or slow with respect to the duration of the molecular interaction. The assumption is made that either one multipole term of the intermolecular potential predominates or that all multipole terms can essentially be treated as a small perturbation of the van der Waals r^?6 interaction.     

Rotationally resolved ultraviolet spectra of benzene-noble gas van der Waals clusters

Sub-Doppler electronic spectra with hundreds of resolved rotational lines are now available for benzene-Ar dimers and trimers. From their analysis the structure of these clusters is precisely determined. The analysis of two bands, 6 ₀ ¹ and 16 ₀ ² , of C₆H₆ · Ar is presented in detail. It leads to accurate values of the van der Waals bond length in the electronic ground and excited state. The change in frequency upon clustering is found to be a factor of 17 larger for the overtone of the out-of-plane modev ₁₆ than for the in-plane vibrationv ₁. This can be tentatively explained by an interaction of the low frequency out-of-plane motion of the ring with the van-der-Waals motion of the Ar atom.     

Fragmentation of neutral van der Waals clusters with visible laser light: a new variant of the Raman effect?

We have observed strong photodissociation (using visible laser light) of neutral van der Waals clusters (Ar, N₂, O₂, CO₂, SO₂, NH₃) produced by supersonic expansion and detected by electron ionization/mass spectrometer. Several tests were performed, all of them supporting this surprising discovery. We suggest that Raman induced photodissociation (RIP) is responsible for this phenomenon. This first observation of Raman induced photodissociation provides a new technique for the study of neutral van der Waals clusters.     

Correlation of the prigogine-flory theory with isothermal compressibility and excess enthalpy data for benzene +n-alkane mixtures

Isothermal compressibilitiesκ _T for benzene + n-alkane systems at 25, 35, 45, and 60°C have been used to check the Prigogine-Flory theory using the van der Waals and Lennard-Jones potentials in order to study the energy-volume dependence. The Flory interaction parameter χ₁₂ has also been calculated for those set of systems at four temperatures. The variation of χ₁₂ with the number of carbon atoms in the n-alkane was studied. Three excess functions have been obtained from χ₁₂ for the equimolecular mixture: (?V ^E/?p)_T which is related toκ _T ^E , the excess enthalpy H ^E , and the excess volume V ^E . Except for H ^E theoretical predictions using a Lennard-Jones potential are in good agreement with the experimental data. A similar treatment has been performed for the same set of systems but using H ^E data at 25°C. The theory, using a van der Waals potential, predicts correctly the variation of the three excess functions with the chain length of the n-alkane but using a Lennard-Jones potential results in better agreement for the order in the magnitude of these excess functions.     

Electronic properties of divalent-metal clusters

The transition from van der Waals to metallic bonding expected to occur in divalent-metal clusters (e.g., Be _n , Mg _n , Hg _n ) as a function of cluster size is discussed. Theoretical results for several electronic properties reflecting this transition in Hg _n -clusters are briefly reviewed and compared with available experiments. The limitations of the present theory particularly concerning the role of correlations and van der Waals interactions are discussed and possible improvements are suggested.     

Electron-gas interaction potentials for collisions of CaCl(X 2Σ+) and KCl(X 1Σ+) with Ar

Interaction potentials for CaCl(X ²Σ⁺)-Ar and KCl(X ¹Σ⁺)-Ar have been determined. They include a Gordon-Kim electron-gas repulsive part smoothly joined to the long-range van der Waals potential. The van der waals potential for KClAr was taken from Meyer and Toennies. For CaClAr, the necessary molecular parameter were estimated from the Rittner model, which predicts both the dipole and quadrupole moments fairly accurately. The CaClAr interaction potential is quite different from that of KClAr. Due to the outer 4s electron on the Ca⁺ ion. the CaClAr potential exhibits a deep minimum in the odd-order Legendre terms which is expected to have a large effect on the cross sections for collisional rotational excitation. The KClAr potential determined here also shows significant differences in the repulsive and well regions from that predicted by Meyer and Toennies using a site-site model for the repulsive contribution.