Long-range Coefficients Research Articles

Dynamic dipole polarizabilities forthe ground 4 1S and the low-lying 4 1,3P and5 1,3S excited states of Zn. Calculation oflong-range coefficients of Zn2

Dynamic dipole polarizabilities for the ground 4 1Sand the low-lying 4 1,3P and 5 1,3S excitedstates of Zn are calculated by the time-dependentgauge-invariant method and compared with otherexperimental and theoretical results. The wavefunctionsare obtained from multi-referenceconfiguration-interaction calculations using atwo-electron relativistic pseudopotential. Core-valencepolarization is accounted for by the use of asemi-empirical core-valence potential.Core-polarization effects are also considered whencalculating the oscillator strengths using a modifieddipole transition operator. Long-range coefficients forthe molecular states of Zn2 dissociating into: 4 1S+ 4 1S; 4 1S + 4 3P; 4 1S + 4 1P; 4 1S +5 1S and 4 1S + 5 3S are presented.

Kink dynamics in a lattice model with long-range interactions

This paper proposes a one-dimensional lattice model with long-range interactions which, in the continuum, keeps its nonlocal behaviour. In fact, the long-time evolution of the localized waves is governed by an asymptotic equation of the Benjamin-Ono type and allows the explicit construction of moving kinks on the lattice. The long-range particle interaction coefficients on the lattice are determined by the Benjamin-Ono equation.

Long-range dispersion coefficients for the low-lying electronic states of Mg 2 from the calculation of the frequency-dependent dipole polarizabilities of Mg in its ground and excited states

The frequency-dependent dipole polarizabilities are calculated for the five lowest states 3 1S; 4 1S; 3 1P; 3 3P and 4 3S of Mg by using our time-dependent gauge invariant method (TDGI). Estimations of the long-range dispersion coefficients for all the first-molecular states dissociations of Mg 2 are proposed. Accuracy of the results is checked through the calculations obtained from a length, a velocity and a mixed approach in the formulation of the oscillator strengths and the corresponding dynamic dipole polarizabilities. In all cases, the length results appear as a reference for the comparison with some previous works concerning the ground state. The long-range coefficients reported for almost all the low-lying states are new and predict a repulsive interaction between the 4 1S states.

Ground state potentials for alkaline-earth–helium diatoms calculated by the surface integral method

Using a recently derived simple formula the van der Waals ground state potential curves of alkaline-earth–helium pairs BeHe, MgHe, CaHe, SrHe, and BaHe have been calculated. The repulsive potential is based on exchange energies calculated from the surface integral method applied to multielectron systems. With the exception of the long-range dispersion coefficients all the input parameters are atomic properties of the free atoms. The agreement with the available potentials from the literature is reasonable.

Nonrelativisticab initiocalculation of the interaction potentials between metastable Ne atoms

We compute nonrelativistic ab initio electronic potential surfaces for two metastable 2p 3s neon atoms using a multiconfiguration all-electron valence-bond method. Spectroscopic constants and long-range C6 dispersion coefficients are presented for Sg/u , Pg/u , and Dg/u symmetries. In addition, we analyze the role of various atomic configurations in the formation of the neon dimer. Our results can be used to model the suppression of collision-induced ionization of metastable neon, which is believed to be a good candidate for Bose-Einstein condensation.

On the long-range and short-range behavior of potentials from reproducing kernel Hilbert space interpolation

The short-range and long-range asymptotic behavior of potential functions obtained from the reciprocal power reproducing kernel Hilbert space interpolation procedure [Ho and Rabitz, J. Chem. Phys. 104, 2584 (1996)] is analyzed. In the short-range region, the potential functions are polynomial in form: the method should not be used for extrapolation in this region. General formulae for the short-range and long-range expansion coefficients are presented. Potentials for He-Ar+ are discussed as examples.

Radial basis function networks for obtaining long range dispersion coefficients from second virial data

A new approach, consisting of using radial basis function networks to obtain the long-range part of diatomic potential energy functions from simulated second virial coefficients, is presented. From these simulated data the artificial neural network was able not only to learn but also to predict properties for systems that were not considered during the training process. Fifteen different diatomic systems were chosen and a leave-three-out approach was applied. A cross-validation procedure was used for analysing the network generalization properties and the relative average error achieved for the three systems was about 5%, providing accurate data for the long-range dispersion coefficients.

Comment on “Ab initio dynamic dipole polarizabilities for O2, its photoabsorption spectrum in the Schumann–Runge region, and long-range interaction coefficients for its dimer” [J. Chem. Phys. 109, 9802 (1998)

The oscillator-strength density calculated ab initio for the Schumann–Runge transition of O2 by Spelsberg and Meyer [J. Chem. Phys. 109, 9802 (1998)] is assessed against an up-to-date experimental database.

Response to “Comment on ‘Ab initio dynamic dipole polarizabilities for O2, its photoabsorption spectrum in the Schumann–Runge region, and long-range interaction coefficients for its dimer’ ” [J. Chem. Phys. 111, 11236 (1999)

The oscillator strengths of the discrete part of the Schumann–Runge band system is recalculated from single-state calculations using the adiabatic potential curve. Potential curves for three Πu3 states are computed. The integrated oscillator strength for the Πu3←Σu3 transition is recalculated from four-state coupled diabatic calculations.

Dynamic multipole polarizabilities, reduced spectra, and interaction coefficients for N2 and CO

Reliable ab initio reduced spectra that serve to calculate dynamic polarizabilities as well as long-range interaction coefficients are presented. The reduced spectra are constructed from perturbed functions that are computed in the single excitation multi-reference averaged coupled pair approach. The static dipole polarizabilities are of the same quality as values obtained in a recent study using elaborated coupled cluster expansions. The dynamic dipole polarizabilities are in excellent agreement with all experimental data available. The higher multipole polarizabilities (l⩽3) are also expected to be the most reliable ones up to date. The interaction coefficients for the N2–N2 interaction perfectly match the coefficients obtained from semiempirical anisotropic oscillator strength distributions. For the CO–CO interaction, however, the same quantities differ by up to 10%. We believe our coefficients to be accurate to 3%.

Dynamic multipole polarizabilities and reduced spectra for OH, application to the long-range part of the two lowest potential surfaces of the OH–CO complex

The formalism of the two-center expansion of the long-range interaction potential is extended to molecules which may be in a degenerate state. As a consequence of this degeneracy the common long-range interaction coefficients have to be replaced by “long-range interaction matrices.” The formalism is applied to the OH–CO complex and leads to an accurate description of the long-range part of its potential surfaces. The reduced spectra that represent the dynamic polarizabilities of the subsystems are obtained in the single excitation multi-reference averaged coupled pair approach. They also serve to calculate the interaction matrices.

Order-disorder process in the tetrahedral sites of albite

The crystal structure of albite from Stintino, Sardinia, Italy, was refined at different degrees of disorder to determine the (Si-Al) order-disorder process. Eight X-ray structure refinements were performed on single-crystal data collected at room temperature, after heating at 1050‐1090 °C for 3 to 12 days. Average long-range order coefficients S between 0.93 and 0.24 were obtained for different samples. The results indicate that in the (Si-Al) disordering process Al enriches the T1m site more than T2o and T2m sites. This trend continues until both T1o and T1m are occupied by 30% of Al, and T2o and T2m by 20% of Al. No evidence of complete disorder in T1 and T2 sites has been experimentally found to date. The (Si-Al) disordering process induces a clockwise rotation of the four-membered rings of tetrahedra parallel to the (100) plane. An inverse linear relationship between the isotropic equivalent displacement parameter of the Na atom, Beq(Na), and S is interpreted as positional disorder of Na. The variations in the Na-O bond lengths with increasing disorder are explained by the related variations in the bond strengths of tetrahedral cations.

Long-range dispersion and induction coefficients for the homodimers of Li 2, Na 2 and K 2

Long-range dispersion and induction coefficients for the homodimers of Li 2, Na 2, K 2 are evaluated in the L A L B M scheme using explicit formulae presented previously and numerical values of moments, polarizabilities and dispersion constants obtained from 2-term reduced spectra of the Kaiserslautern group. While induction coefficients are 5–8 times smaller than dispersion, induction anisotropies are always larger than the corresponding dispersion anisotropies for all homodimers.

Casimir-Polder long-range interaction potentials between alkali-metal atoms

A complete description of the multipolar Casimir-Polder effects between two alkali-metal atoms in the ground state is presented. We give both general and particular expressions for the electric-electric, electric-magnetic, magnetic-magnetic, diamagnetic-electric, and diamagnetic-magnetic two-photon multipole processes, many of which have not been discussed previously in literature, to our knowledge. The asymptotic behavior of the Casimir-Polder potential is studied in terms of the ${K}_{7}, {K}_{9},$ and ${K}_{11}$ long-range coefficients. We have established the range of validity of the Casimir-Polder potential by analyzing the first-order correction to the energy given by the matrix element of the contact interaction term between the atomic charge distributions. Numerical values for the Casimir-Polder long-range interaction potentials for both homonuclear and heteronuclear alkali-metal dimers are presented. Comparisons with previous analytical and numerical results are included.

Long-range coefficients for the low-lying electronic states of BeLi and Be2

Using the frequency-dependent dipole polarizabilities calculated for the five lowest states 2 1S, 2 3P, 2 1P, 3 3S and 3 1S of Be and for the 2 2S and 2 2P states of Li, from our time-dependent gauge invariant method, estimates of C6 were obtained for all the first molecular states dissociations: 2 1S+2 1S, 2 1S+2 3P, 2 1S+2 1P and 2 3P+2 3P of Be–Be and 2 2S+2 1S, 2 2P+2 1S and 2 2P+2 3P of Li–Be. Some higher interactions between these states were also estimated: 2 1S+3 1S, 3 3S+2 3P, 2 1P+2 1P, 3 1S+2 1P, 3 3S+3 3S, 2 1P+2 3P, and 3 1S+3 1S for the homonuclear system, 2 2P+2 1P and 2 2S+2 3P for the heteronuclear one. Experimentally, only the (X 1Σg+) ground state, and the two first (A 1Πu and B 1Σu+) states, which dissociate in 2 1S+2 1S and 2 1S+2 1P channels respectively, are known for Be2. The long-range coefficients reported for almost all of the low-lying states are new.

Long-range potentials for two-species alkali-metal atoms

We address a growing interest in trapping and cooling of mixed-species alkali-metal atoms. Long-range coefficients that arise in the multipole expansion of molecular potentials for unlike alkali-metal dimers are calculated. The coefficients for the heteronuclear alkali-metal dimers corresponding to different molecular symmetries that separate to $\mathrm{nS}\ensuremath{-}{n}^{\ensuremath{'}}S,nS\ensuremath{-}{n}^{\ensuremath{'}}P,nS\ensuremath{-}{n}^{\ensuremath{'}}D,$ and $\mathrm{nP}\ensuremath{-}{n}^{\ensuremath{'}}P$ atomic levels are computed with high precision. We consider cases where in the infinite separation limit, one atom is in the ground state and the other is in one of the lowest S, P, and D excited states and both atoms are in their lowest excited P states. We find the long-range potentials for $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{Rb}(6S)\ensuremath{-}\mathrm{C}\mathrm{s}(6S),\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P){ }^{1,3}\ensuremath{\Sigma},\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P){ }^{1,3}\ensuremath{\Sigma},$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{N}\mathrm{a}(3D){ }^{1,3}\ensuremath{\Sigma}$ molecules to be the most attractive. The $\mathrm{K}(4S)\ensuremath{-}\mathrm{R}\mathrm{b}(5P)$ dimer represents the best candidate molecule for ultracold photoassociative spectroscopy. We also find the $\mathrm{K}(4P)\ensuremath{-}\mathrm{C}\mathrm{s}(6P)$ and $\mathrm{Rb}(5S)\ensuremath{-}\mathrm{K}(4P)$ dimers to form, respectively, the most attractive and the most repulsive long-range potentials. The present calculation is in good agreement with experimentally determined value for the ${1/R}^{6}$ van der Waals coefficient for the interaction between $\mathrm{Cs}(6S)$ and $\mathrm{Li}(2P)$ atoms.

Ab initio dynamic dipole polarizabilities for O2, its photoabsorption spectrum in the Schumann–Runge region, and long-range interaction coefficients for its dimer

Perturbed states representing the response to an external electric field are obtained in the multireference averaged coupled pair functional formalism based on orbitals which are optimized in a perturbed multireference self-consistent field procedure. For each perturbing operator perturbed wave functions for several frequencies of the perturbing field are obtained simultaneously. From these sets of perturbed states reduced spectra are derived which represent effective oscillator strength distributions. The broad shape of the Schumann–Runge continuum leads to a poor description of the dynamic polarizability for frequencies approaching the first pole when only vertical transitions are considered. To account for this effect the absorption spectrum in the Schumann–Runge region is calculated and the polarizability is described up to the range of anomalous dispersion. The dynamic polarizabilities and the interaction coefficients are found to be in excellent agreement with experimental data where it is available. Significant differencies of up to 20% are observed between our anisotropic interaction coefficients and earlier estimates obtained from semiempirical anisotropic dipole oscillator strength distributions.

Long-range, collision-induced dipoles of Td–D∞h molecule pairs: Theory and numerical results for CH4 or CF4 interacting with H2, N2, CO2, or CS2

Compressed gases and liquids containing molecules of Td and D∞h symmetry absorb far-infrared radiation, due to transient dipole moments induced during molecular collisions. In earlier theoretical work on far-infrared absorption by CH4/N2 mixtures, good agreement was obtained between calculated and experimental spectra at low frequencies, but at higher frequencies—from 250 to 650 cm−1—calculated absorption intensities fell significantly below the experimental values. In this work, we focus on an accurate determination of the long-range, collision-induced dipoles of Td⋯D∞h pairs, including two polarization mechanisms not treated in the earlier line shape analysis: dispersion and nonuniformity in the local field gradient acting on the Td molecule. Since these mechanisms produce transitions with ΔJ=±3 or ±4 for CH4 and ΔJ=0 or ±2 for N2, their inclusion is expected to increase the calculated absorption intensities in the high frequency wings for CH4/N2 mixtures. This should improve agreement with the experimental spectra, and permit more accurate determination of anisotropic overlap terms in the collision-induced dipole. We give numerical values for the long-range dipole coefficients of CH4 or CF4 interacting with H2, N2, CO2, or CS2; the dipole coefficients have been derived with spherical-tensor methods and evaluated using single-molecule moments and susceptibilities from recent ab initio calculations or experiments. The dispersion dipoles are given rigorously in terms of integrals involving the imaginary-frequency polarizability α(iω) and the hyperpolarizabilities β(0;iω,−iω) and B(0;iω,−iω). To obtain numerical estimates for the dispersion dipoles, we have developed constant-ratio approximations that require only the static susceptibilities and C6 van der Waals coefficients.

Ab initio calculations of dipole polarizabilities of Na and K in their 32D-state and determination of long-range coefficients for S+D molecular states of Na2, K2, and NaK

Dynamic polarizabilities of Na and K in their first excited states are calculated with a time-dependent gauge-invariant (TDGI) method, using one-electron wave functions and pseudo-potentials. The values obtained for Na and K in the low-lying S and P states are compared to our previous all-electron results. Then, the dynamic polarizabilities of Na and K in their 3d D2 state are calculated in order to determine the long-range dispersion coefficients for the dissociative S+D states of Na2, K2, and NaK.

Long-range induction coefficients for like centrosymmetric linear molecules and an application to H 2–H 2

The C 8 and C 10 long-range induction coefficients for two like centrosymmetric linear molecules are derived explicitly using the irreducible properties of spherical tensor operators. An application to the H 2–H 2 system shows that whereas the isotropic induction coefficients are 50–100 times smaller than dispersion, the induction anisotropies γ n are always larger than the corresponding dispersion anisotropies.