Lithium quadrupole properties and Van der Waals constants using pseudo-state techniques

Pseudo-spectral techniques are used to evaluate the moments of the quadrupole oscillator strength distribution for the ground-state Li atom and the dipole-quadrupole Van der Waals constants for the ground-state Li-Li, Li-He and Li-H interactions. The analysis of the pseudo-state data allows an error to be assigned to each calculated Li quadrupole property and Van der Waals constant. The pseudo-state approach also allows a quantitative estimate of the contributions of the Li atom quadrupole resonance, principal series and inner shell transitions to each Li atom quadrupole properly. The convergence of the sum over states expressions for the quadrupole properties of Li is quite different than for the corresponding dipole properties.     

Dipole properties of PH3, PF3, PF5, PCl3, SiCl4, GeCl4, and SnCl4

Experimental and theoretical photoabsorption cross sections combined with constraints provided by the Kuhn–Reiche–Thomas sum rule, the high-energy behaviour of the dipole oscillator strength density, static dipole polarisabilities, and molar refractivity data when available are used to construct dipole oscillator strength distributions for PH₃, PF₃, PF₅, PCl₃, SiCl₄, GeCl₄, and SnCl₄. The distributions are used to predict dipole sum rules S(k), mean excitation energies I(k), and van der Waals C₆ coefficients.     

Re-evaluation of some lithium dipole properties and dipole-dipole and dipole-quadrupole van der Waals constants

Our previous one-centre pseudo-state results for some ground-state Li atom dipole oscillator strength sums, the dipole-dipole dispersion energy constants for the Li-Li, Li-H and Li-He ground-state interactions and the dipole-quadrupole dispersion energy constant for the Li-Li interaction are re-evaluated in the light of a more reliable selection for the resonance dipole oscillator strength of the Li atom. These and some of our previous lithium pseudo-state results are compared with corresponding literature values.     

Many-body study of van der Walls interaction involving lithium and rare-gas atoms and its contribution to hyperfine shifts

Using linked cluster many-body perturbation theory, the frequency-dependent dipole polarizabilitiesa(ω) has been calculated for the lithium atom. The value ofa(ω) at the static limit (169.04a ₀ ³ ) matches well with other available theoretical values and experimental results. These values have been used to calculate the van der Waals constants for interactions of lithium, helium and neon atoms. The values of the van der Waals constants for dipole-dipole interaction in atomic units are −22.9, −44.8, −1465.8, 184950.0, 2011.8, 3896.5, 30.3, 59.0 and 115.1 for Li-He, Li-Ne, Li-Li, Li-Li-Li, Li-Li-He, Li-Li-Ne, Li-He-He, Li-He-Ne and Li-Ne-Ne interactions respectively. Obtaining the suitable response functions for lithium and helium atoms, the long range contribution to Δa(r)/a ₀ in the study of fractional frequency shift in hyperfine pressure and temperature shift measurements is obtained as −541 atomic units.     

Messungen der van der Waals-Wechselwirkung zwischen Edelgasatomen

Total cross sections for collisions of Helium atoms with other rare gases have been measured by modulated molecular beam technique. The results are used to determine the interaction constants of the van der Waals potential (V(r)～ ?C/r ⁶). For this purpose, an indirect procedure is adopted, since the well known approximation ofMassey andMohr (Q～C ^2/5) is not applicable for Helium scattering experiments at thermal energies. The van der Waals constants obtained are in agreement with values determined from experimental data on transport properties in gases.     

Use of simulated infrared spectra to test N2-Ar pair potentials and dipole moment surfaces

Infrared spectra of the ¹⁴N₂-Ar van der Waals complex have been simulated by performing exact quantum mechanical calculations using two recent potential energy surfaces, one having a modified Morse-Morse-spline-van der Waals form and the other an exchange-Coulomb (XC) modelform. Frequencies and intensities have been calculated for some 10⁵ spectral transitions amongst the bound states of the complex, and simulations of the mid-infrared (2290-2370 cm^-1) spectrum of the complex at 77 K constructed from superpositions of lines, each of which has been assigned a Lorentzian lineshape with a linewidth appropriate to the experimental conditions. The roles of the various terms in the effective dipole moment surface proposed by Ayllon et al. (1990, Molecular Physics, 71, 1043) have also been examined, and a modification made which yields improved agreement with the experimental mid-infrared spectrum obtained by McKellar (1988, Journal of Chemical Physics, 88, 4190). Based upon the present calculations, the 48 most intense bands of the simulated spectrum of the ¹⁴N₂-Ar van der Waals complex have been given vibrational assignments. The spectrum simulated from the modified Morse-type potential surface, when employed together with the present modified dipole moment surface, shows distinctly better agreement with experiment than does the spectrum simulated from either the XC or the earlier empirical potential energy surface. Far-infrared spectra have also been simulated at 5 K and at 77 K using an appropriate effective dipole surface, and compared with the calculation of Ayllon et al.     

High precision calculation of multipolar dynamic polarizabilities and two- and three-body dispersion coefficients of atomic hydrogen

In this paper we investigate a variationally stable procedure for multipolar dynamic polarizabilities calculation as well as the two- and three-body van der Waals coefficients of the hydrogen atom. This approach provides precise, fast convergent values for real and imaginary frequency-dependent 2 ^L -pole dynamic polarizabilities. Highly accurate two- and three-body van der Waals dispersion coefficients are calculated from dynamic polarizabilities at imaginary photon frequencies. The present approach is also precise for higher interaction orders. The results are compared with previous calculations found in the literature.     

Investigation of the electronic structure of Be2+He and Be+He,and static dipole polarisabilities of the helium atom

The potential energy and spectroscopic constants of the ground and many excited states of the Be⁺He van der Waals system have been investigated using a one-electron pseudo-potential approach, which is used to replace the effect of the Be²⁺ core and the electron-He interactions by effective potentials. Furthermore, the core–core interactions are incorporated. This permits the reduction of the number of active electrons of the Be⁺He van der Waals system to only one electron. Therefore, the potential energy of the ground state as well as the excited states is performed at the SCF level and considering the spin–orbit interaction. The core–core interaction for Be²⁺He ground state is included using accurate CCSD (T) calculations. Then, the spectroscopic properties of the Be⁺He electronic states are extracted and compared with the previous theoretical and experimental studies. This comparison has shown a very good agreement for the ground and the first excited states. Moreover, the transition dipole moment has been determined for a large and dense grid of internuclear distances including the spin orbit effect. In addition, a vibrational spacing analysis for the Be²⁺He and Be⁺He ground states is performed to extract the He atomic polarisability.     

Bonding analysis for NgMOH (Ng=Ar,Kr and Xe; M=Cu and Ag)

The structures and stabilities of a new class of species, noble-gas–coinage-metal hydroxides NgMOH (Ng =?Ar, Kr and Xe; M =?Cu and Ag), are investigated at the MP2 theoretical level. All species are found to be in Cs symmetry with an approximate linear Ng–M–O moiety. The noble-gas–coinage-metal bond lengths are in the range of the respective covalent and van der Waals limits, showing a different degree of approach to the former along the series Ar–Kr–Xe for Ng–Cu and Ng–Ag bonds, respectively. The dissociation energies of noble-gas–coinage-metal bonds are relatively large as compared to the van der Waals complexes. Besides the charge-induced dipole contribution, other effects –?higher-order charge-induction energies, dispersion interaction, etc., should be considered to explain the noble-gas–coinage-metal bonding mechanism. The present results suggest that the title species are stable enough to be prepared experimentally.     

On the additivity of atomic and molecular dipole properties and dispersion energies using H,N, O,H2, N2, O2, NO,N2O,NH3 and H2O as models

The zeroth-order theory of intermolecular forces is used to derive additivity relations for rotationally averaged molecular dipole properties and dispersion energy constants by assuming that a molecule is comprised of non-interacting atoms or molecules. Some of the additivity rules are new and others, for example the mixture rule for dipole oscillator strength distributions (DOSDs), Bragg's rule for stopping cross sections and Landolt's rule for molecular refractivities, are well known. The additivity rules are tested by using previously constructed DOSDs and reliable values for the dipole oscillator strength sums S_k , L_k and I_k , and dispersion energy constants C ₆, for H, N, O, H₂, N₂, O₂, NO, N₂O, NH₃ and H₂O as models. It is found that additivity is generally unreliable for estimating molecular properties corresponding to k < -2. Generally for k ≥ -2 and for C ₆, and if the hydrogen molecule is used to represent the hydrogen atom in the additivity rules, the additivity relations yield results that are reliable to within ?20 per cent and the estimates improve substantially as k increases. The effects of molecule formation on DOSDs is examined by comparing the various molecular DOSDs with the sum of the DOSDs for the atoms making up the molecules. Molecule formation results in a net decrease in the amount of dipole oscillator strength for low excitation energies and a compensating net increase for higher energies in a region extending from the absorption threshold to about 100 eV. This is shown to imply that estimates of the stopping average energy I ₀, obtained by using bona fide atomic I ₀ values, are lower bounds to the correct molecular I ₀ results.     

A comparison of self broadening and shift of helium,neon and argon emission lines

Self broadening (van der Waals and resonance) and shift of Ne emission lines and van der Waals broadening and shift of He emission lines have been measured using a high pressure (0.5–3.0 atom), low current discharge. These results are compared with previous measurements in Ar and He to obtain a complete comparison of self broadening and shift of He, Ne and Ar emission lines. Oscillator strengths for the resonance transitions are obtained from the resonance broadening coefficients. The trend of the van der Waals broadening coefficients for the three noble gases is correctly predicted by a theory due to HINDMARSHet al.⁽⁴⁾ in which a Lennard-Jones potential is used in the impact theory formalism. The measured line shifts cannot be accounted for by this theory and reflect the need for more accurate quantum mechanical calculations.     

Bemerkung zur Bestimmung der van der Waals-Konstanten aus Streuquerschnitten

The attempt has been made by several authors to clear up the discrepancy between van der Waals constants determined from scattering cross sections for thermal energies and theoretical values using measured oscillator strengths. The present paper discusses three sources of error not accounted for properly in the earlier work. The appropriate corrections discussed in this paper lead to a satisfactory agreement between experiment and theory.     

Theoretical study of the spectral and structural parameters of van der Waals complexes of the Li+ cation with the H2, D2, and T2 isotopomers of the hydrogen molecule

The three-dimensional vibrational problem for the isolated binary complexes formed by the Li⁺ cation with all the isotopomers of the hydrogen molecule is solved by the variational method using sufficiently exact nonempirical adiabatic surfaces of the potential energy and the dipole moment. Information on the largeamplitude vibrations was obtained for the first time, and the anharmonic effects caused by the interaction of the different internal degrees of freedom in these weakly bound van der Waals complexes were consistently taken into account. The frequencies and intensities of many spectral transitions are determined, and the average values of geometrical parameters and the dipole moment are calculated for the ground and excited vibrational states.     

N.M.R. studies of cis-1,2-difluoroethylene and vinyl fluoride in a nematic solvent

Constrained anisotropic dipole oscillator strength techniques are used to obtain reliable values for a wide range of anisotropic and isotropic dipole properties of NO, including most anisotropic components of the dipole-dipole dispersion energy coefficients for the interaction of NO with NO, O₂, H₂, N₂, CO, He, Ne, Ar, Kr and Xe. Some of the anisotropic constraints required for our calculations are obtained via dipole sum rules from ab initio, multi-reference configuration interaction wavefunctions for NO. The individual dipole properties of NO considered include the dipole oscillator strength sums S_k , k = 2,1,0(? 1/2)? 2,? 3,? 4,..., the logarithmic dipole sums L_k and mean excitation energies I_k , k = 2(? 1)? 2, and, as a function of wavelength, the dynamic polarizability and its anisotropy, the total depolarizaiton ratio, and the Rayleigh scattering cross-section. Our constrained dipole oscillator strength results are often the only reliable, and often the only available, values for many of the properties and dispersion energies considered.     

Observation of a high lying van der Waals mode in the intermolecular potential of Ar-CO

A continuous two-dimensional jet expansion in combination with an infrared diode laser spectrometer has been used to record a new subband of the weakly bound complex Ar-CO in the 2168cm^?1 region. Twenty-two transitions were assigned to a thus far unobserved K _a = 0 van der Waals state at 36.765 cm^?l above the ground state. This is the highest van der Waals mode of Ar-CO reported so far. These high lying energy levels will provide a very sensitive test for future ab initio and Semiempirical potential energy surfaces.     

LiAr, LiKr and LiXe excimers: Photochemical formation of the - bands

We investigated the photochemical formation of lithium-rare-gas excimers in the 3 state through the reaction of Li₂(2(C)) and the ground-state rare-gas atom. Lithium-rare-gas vapor mixture was prepared in the heat-pipe oven. We populated the 2(C)state of the Li₂ molecule using the XeCl excimer laser wavelength at 308 nm or the PTP dye laser wavelength at about 335 nm. The 3-1 transitions were observed with peaks at 414, 420 and 435 nm for LiAr, LiKr and LiXe, respectively. We estimated thermally averaged rate constants for these photochemical reactions, which are cm³s^-1 for LiAr, cm ³ s^-1 for LiKr and cm³s^-1 for LiXe. Ab initio potential-energy curves and transition dipole moments for LiKr were calculated applying the SCF MRDCI method. Available data for the LiAr and LiKr excimers are presented, including potential-energy curves, electronic transition dipole moments, and spectroscopic constants. Possible photochemical formation of these molecules in the excited states is discussed. We performed the quantum-mechanical spectral simulations of the LiAr and LiKr 3-1 transitions, using ab initio potential-energy curves. Received: 2 October 1998 / Received in final form: 25 January 1999     

Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C_s/epsilon and C_b/epsilon where C_s and C_b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C_s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2–3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.     

Van der Waals attraction between cylinders,rods or fibers

In a first step, we calculate the van der Waals energy between two cylinders by pairwise integration of unscreenedr ⁻⁶ interactions between any two molecules. It turns out proportional tod ^−3/2 at small separations and proportional tod ⁻⁵ at large separationsd of the cylinders. In a second step, we use an integration method for multiplet interactions, which relates the latter to screening and represents the van der Waals energy by macroscopic reaction fields. We expand these reaction fields in terms of modified Bessel functions. The van der Waals energy evolves from a sum over the numberl of field reflections, from a frequency integral over the dielectric constants involved, and from a wave number integral over the radii and the separation of the cylinders. The lowest order term verifies the results found by integration of pair interactions, yet replaces the unscreened polarizabilities of the atoms by the screened dielectric constants of the media. The higher order reflection termsl≧2 likewise turn out to be proportional tod ^−3/2 at small separationsd, but decrease in weight more rapidly than 1/l ³. Their contribution at large separation is proportional tod ^−(4l+1). From a comparison of our results with those obtained for spheres and half-spaces, we conclude that retardation entails ad ^−5/2 and ad ⁻⁶ law at small and large separations, respectively. This suggestion is confirmed by preliminary calculations based on the Helmholtz equation.     

A search for colour van der Waals interaction

It is suggested that the strength of nuclear colour van der Waals interaction, if present, can be determined by measuring deviations from Rutherford scattering of charged hadrons from nuclei, at energies well below the Coulomb barrier. Experimental limit on the strength of such a potential is obtained asλ<50, when the colour van der Waals potential is given byV(r)=λ(hc/r ₀)(r ₀/r)⁷, withr ₀, the scaling length, taken as 1 fm. This limit is obtained from an analysis of existing experiments and by performing scattering experiments of 3–4.6 MeV protons from a²⁰⁸Pb target.     

Theoretical estimates of the trineutron and tetraneutron binding energies

The trineutron and tetraneutron binding energies are calculated using an interaction which reproduces ³H, ³He, ⁴H, ⁴He, and ⁴Li ground-state properties. A 4?ω model space and completely symmetrized translationally invariant harmonic oscillator eigenstates are used in the analysis. The calculation yields a ³n eigenvalue within the range suggested in an experiment by Ohlsen et al. The ⁴n eigenvalue is consistent with the location of the first T = 2 level in the ⁴He system.