C6 Coefficients Research Articles

Intermolecular interaction between the pendant chain of perfluorinated ionomer and water

The intermolecular interaction energies between a water molecule and four models of pendant chains for perfluorinated ionomers, such as CF3OCF2CF2SO3H, CF3OCF2CF2SO3−, CF3CF2CF2COOH, CF3CF2CF2COO−, were analyzed by using a molecular orbital calculation. In order to investigate a variety of configurations, five hundred random configurations that water and monomer contact at their van der Waals surfaces were generated for each system. We employed an empirical correction method for dispersion energy defined by the equation Edisp = −fd(R)C6R−6, so as to reduce the computational costs. The C6 coefficients of this equation were optimized to reproduce the energies obtained at the MP2/aug-cc-pVDZ level of calculations, and then overall intermolecular interaction energies (Eint = EHF + Edisp) were evaluated as a summation of Edisp and intermolecular interaction energy at the HF/aug-cc-pVDZ level (EHF). From these analyses, we obtained the following conclusions. (1) The ether oxygen in the pendant chain cannot bind with water strongly due to fluorination. (2) De-protonations of sulfonic and carboxylic acids extend the region where water molecules sufficiently bind with pendant chains, and this effect would cause rich water absorption when these pendant chains form membranes. Therefore, the degree of proton disassociation would be one of the key factors for the water sorption ratio and membrane morphology. (3) The binding energy of the optimized configuration for CF3CF2CF2COO− + H2O is about 2.5 kcal mol−1 larger than that for the CF3OCF2CF2SO3− + H2O system because of the larger electron negativities of the oxygen atoms on deprotonated carboxylic acid compared with those on the sulfonic acid.

Electric Field Dependence of Dielectric Constant of the Sol-Gel Deposited Bax Sr1–x TiO3 Film—Thermodynamic Analysis

The measured dielectric constant as a function of electric field, at a frequency of 1MHz is reported for sol-gel deposited Barium-Strontium Titanate (BaxSr1–x TiO3) thin films with x = 0.0 to 0.6 at different temperatures and film thicknesses. The experimental data can be explained by Devonshire thermodynamic theory of free energy expansion in terms of power series of polarization. It is shown that the expansion upto the quadratic term is sufficient to explain the field dependence of dielectric constant. The coefficient C3 of the quadratic term is almost independent of electric field, thickness and temperature but appears to depend on composition and mechanical strains. The effect of strains on C3 shows that the electrostrictive coefficients Q 11, Q 12 and the elastic constants c 11 and c 12 are different in thin films with respect to the bulk.

Accurate relativistic many-body calculations of van der Waals coefficients C8 and C10 for alkali-metal dimers

We consider long-range interactions between two alkali-metal atoms in their respective ground states. We extend the previous relativistic many-body calculations of C6 dispersion coefficients [Phys. Rev. Lett. 82, 3589 (1999)] to higher-multipole coefficients C8 and C10. Special attention is paid to usually omitted contribution of core-excited states. We calculate this contribution within relativistic random-phase approximation and demonstrate that for heavy atoms core excitations contribute as much as 10% to the dispersion coefficients. We tabulate results for both homonuclear and heteronuclear dimers and estimate theoretical uncertainties. The estimated uncertainties for C8 coefficients range from 0.5% for Li2 to 4% for Cs2.

Many-Electron Problem in Terms of the Density: From Thomas–Fermi to Modern Density-Functional Theory

In this paper we focus on the use of electron density and current-density as basic variables in describing a many-electron system. We start with a discussion of the seminal Thomas–Fermi theory and its extension by Bloch for time-dependent hamiltonians. We then present modern density-functional theory (for both time-independent and time-dependent hamiltonians) and approximations involved in implementing it. Also discussed is perturbation theory in terms of electron density and its use for calculating various response properties and related quantities. In particular, van der Waals coefficient C6is calculated using density and current density in time-dependent perturbation theory. Throughout the paper, results for alkali-metal clusters are presented to demonstrate the strength of density-based theories.

Dipole oscillator strengths, dipole properties and dispersion energies for SiF4

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silicon tetrafluoride (SiF4) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental molar refractivity data and the Thomas-Reiche-Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums and mean excitation energies for the molecule. A pseudo-DOSD for SiF4 is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interaction of SiF4 with itself and with 43 other species and the triple-dipole dispersion energy coefficient C9 for (SiF4)3.

Intramolecular dependence of the frequency dependent polarizabilities of Li2(a 3Σ+ u) and Na2(a 3Σ+ u) and van der Waals dispersion coefficients for atom-diatom and diatom-diatom alkali dimers

An ab initio time dependent gauge invariant method (TDGI) has been used to compute the frequency dependent dipole and quadrupole polarizabilities of Li, Na, Li2(a3Σ+ u) and Na2(a3Σ+ u) and their dependence on the internuclear distance of the diatomic species. The dependence of the isotropic and anisotropic components of the static dipole polarizabilities on the diatomic distance was fitted to an analytical form which has an asymptotic form in agreement with the theoretical expression derived by Heijmen, T. G. A., Moszynski, R., Wormer, P. E. S., and van der Avoird, A., Molec. Phys., 89, 81. Long range two-body C6 coefficients have been evaluated for all combinations of atom-atom, atom-homonuclear diatom and homonuclear diatom-homonuclear diatom systems in which the diatomics are in the a 3Σ+ u state. Furthermore, the C8 coefficients for the atom-atom and atom-diatom interactions and the three-body C9 coefficients for the four atom-diatom systems have been obtained. For the atom-diatom case, the dipole-induced dipole C6 coefficients have been calculated for various diatomic distances up to 15 Å. The distance dependence of their isotropic C000 6 and anisotropic C202 6 components has been fitted to an analytical form similar to that used for the static dipole polarizabilities of the diatomics.

Photodissociation spectroscopy of stored CH+ ions: Detection, assignment, and close-coupled modeling of near-threshold Feshbach resonances

We have measured and theoretically analyzed a photodissociation spectrum of the CH+ molecular ion in which most observed energy levels lie within the fine-structure splitting of the C+ fragment and predissociate, and where the observed irregular line shapes and dipole-forbidden transitions indicate that nonadiabatic interactions lead to multichannel dynamics. The molecules were prepared in low rotational levels J″=0–9 of the vibrational ground state X 1Σ+ (v″=0) by storing a CH+ beam at 7.1 MeV in the heavy-ion storage ring TSR for up to 30 s, which was sufficient for the ions to rovibrationally thermalize to room temperature by spontaneous infrared emission. The internally cold molecules were irradiated with a dye laser at photon energies between 31 600–33 400 cm−1, and the resulting C+ fragments were counted with a particle detector. The photodissociation cross section displays the numerous Feshbach resonances between the two C+ fine-structure states predicted by theory for low rotation. The data are analyzed in two steps. First, from the overall structure of the spectrum, by identifying branches, and by a Le Roy–Bernstein analysis of level spacings we determine the dissociation energy D0=(32 946.7±1.1) cm−1 (with respect to the lower fine-structure limit) and assign the strongest features to the vibrational levels v′=11–14 of the dipole-allowed A 1Π state. The majority of the 66 observed resonances cannot be assigned in this way. Therefore, in a second step, the complete spectrum is simulated with a close-coupling model, starting from recent ab initio Born–Oppenheimer potentials. For the long-range induction, dispersion and exchange energies, we propose an analytical expression and derive the C6 coefficients. After a systematic variation of just the vibrational defects of the four Born–Oppenheimer potentials involved, the close-coupling model yields a quantitative fit to the measured cross section in all detail, and is used to assign most of the remaining features to the dipole-forbidden a 3Π state (v′=17–20), and some to the weakly bound c 3Σ+ state (v′=0–2). The model potentials, which reproduce the spectrum and compactly represent the spectroscopic data, should help to predict more accurately C++H scattering in the interstellar medium.

Dipole oscillator strength properties and dispersion energies for SiH4

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the silane (SiH4) molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength data. The constraints are furnished by experimental molar refractivity data and the Thomas–Reiche–Kuhn sum rule. The DOSD is used to evaluate a variety of isotropic dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecule. A pseudo-DOSD for SiH4 is also presented which is used to obtain reliable results for the isotropic dipole–dipole dispersion energy coefficients C6, for the interaction of silane with itself and with forty-four other species, and the triple–dipole dispersion energy coefficient C9 for ðSiH4Þ 3 . 2002 Elsevier Science B.V. All rights reserved.

Dipole oscillator strength properties and dispersion energies for CI2

A recommended isotropic dipole oscillator strength distribution (DOSD) has been constructed for the chlorine molecule through the use of quantum mechanical constraint techniques and experimental dipole oscillator strength and molar refractivity data. It has been used to evaluate a variety of dipole oscillator strength sums, logarithmic dipole oscillator strength sums, and mean excitation energies for the molecule. A pseudo-DOSD for C12 is also presented which is used to obtain reliable results for the isotropic dipole-dipole dispersion energy coefficients C6, for the interaction of Cl2 with itself and forty-two other species, and the triple-dipole dispersion energy coefficient C9 for (Cl2)3.

Calculation of van der Waals coefficients in hydrodynamic approach to time-dependent density functional theory

In this paper we employ hydrodynamic formulation of time-dependent density-functional theory to obtain coefficient C6 of the long-range part of the van der Waals interaction between alkali-metal clusters of large sizes. Such a calculation becomes computationally very demanding in the orbital-based Kohn–Sham formalism, but is quite simple in the hydrodynamic approach. This is because in hydrodynamic formulation, electron density and current density, rather than the orbitals, are employed as basic variables. We show that for intercations between the clusters of same sizes, C6 scales as the sixth power of the cluster radius and approaches the classically predicted value for large size clusters.

Halogen Bond in (CH3)nX (X = N, P, n = 3; X = S, n = 2) and (CH3)nXO (X = N, P, n = 3; X = S, n = 2) Adducts with CF3I. Structural and Energy Analysis Including Relativistic Zero-Order Regular Approximation Approach in a Density Functional Theory Framework

Density functional theory (DFT) calculations on the geometry and bonding energy of the X- - -I intermolecular interaction of CF3I and (CH3)nX (X = N, P, n = 3; X = S, n = 2) and (CH3)nXO (X = N, P, n = 3; X = S, n = 2) are reported. The effect of the basis set, Effective Core Potential (ECP), and relativistic corrections have been investigated to gain insight into the origin and nature of this interaction. Energy decomposition in terms of different contributions allows us to understand the different donor behavior of second and third row atoms toward perfluorinated iodo hydrocarbon compounds, suggesting that bond energies are mainly due to orbital contribution. TD-DFT calculations of the van der Waals coefficient C6 for CF3I- - -N(CH3)3 and CF3I- - -P(CH3)3 adducts estimate values of −2.02 and −1.30 kcal/mol, respectively, for their dispersion energy, thus representing only a small contribution to the total bonding energy (−5.64 and −5.76 kcal/mol, respectively). The role of competition between intra- and...

A method for modeling the formation of caii lines in the spectra of irradiated stellar atmospheres

We have developed a method for calculating deviations from LTE of level populations and profiles of selected spectral lines in stellar atmospheres in the presence of external radiation. The influence of Thomson scattering at the frequencies of the external radiation is considered. The method used to calculate model irradiated atmospheres in a semi-grey approximation has been improved. We have modified the NONLTE3 code used to determine the level populations to make it suitable for irradiated atmospheres. A model for the CaII atom including 42 energy levels of CaII, the ground state of CaIII, and 80 linearized transitions was constructed for these calculations. This atomic model takes into account the effect of all relevant collisional processes and radiative processes at the frequencies of the internal and external radiation. We investigated the correctness of the non-LTE calculations for the CaII ion by analyzing 16 lines of ionized calcium in the solar spectrum. The influence of uncertainties in the atomic data on the non-LTE level populations and CaII line profiles was also analyzed, and the van der Waals broadening coefficients C6 were refined. The scaling coefficient in the Dravin formula was taken to be 0.1. We found the non-LTE abundance corrections for most lines to be significant (Δlogɛ(Ca)=0.05−0.15dex), even under the conditions for the solar atmosphere. The lines of the λ=8498, 8542, 8662 A infrared triplet can be adequately described. Differences in the mean calcium abundance obtained using different model atmospheres are smaller than 0.02 dex. Our final estimate of the mean calcium abundance in the solar atmosphere is logɛ(Ca)=6.31, in good agreement with the meteoritic abundance, logɛ(Ca)=6.32.

Empirical correction to density functional theory for van der Waals interactions

An empirical method has been designed to account for the van der Waals interactions in practical molecular calculations with density functional theory. For each atom pair separated at a distance R, the method adds to the density functional electronic structure calculations an additional attraction energy EvdW=−fd(R)C6R−6, where fd(R) is the damping function which equals to one at large value of R and zero at small value of R. The coefficients C6 for pair interactions between hydrogen, carbon, nitrogen, and oxygen atoms have been developed in this work by a least-square fitting to the molecular C6 coefficients obtained from the dipole oscillator strength distribution method by Meath and co-workers. Two forms of the damping functions have been studied, with one dropping to zero at short distances much faster than the other. Four density functionals have been examined: Becke’s three parameter hybrid functional with the Lee-Yang-Parr correlation functional, Becke’s 1988 exchange functional with the LYP correlation functional, Becke’s 1988 exchange functional with Perdew and Wang’s 1991 (PW91) correlation functional, and PW91 exchange and correlation functional. The method has been applied to three systems where the van der Waals attractions are known to be important: rare-gas diatomic molecules, stacking of base pairs and polyalanines’ conformation stabilities. The results show that this empirical method, with the damping function dropping to zero smoothly, provides a significant correction to both of the Becke’s hybrid functional and the PW91 exchange and correlation functional. Results are comparable to the corresponding second-order Møller-Plesset calculations in many cases.

Long-range interactions for H(1s)-He(n 1,3P),H(1s)-Li(n 2P) and He(1 1S)-Li(n 2P)systems

The dispersion coefficients C6 for theH(1s)-He(n 1,3P), H(1s)-Li(n 2P) andHe(1 1S)-Li(n 2P) systems with n = 2,3 arecalculated using variational wavefunctions in Hylleraascoordinates.

Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment

We extend an approximate density functional theory (DFT) method for the description of long-range dispersive interactions which are normally neglected by construction, irrespective of the correlation function applied. An empirical formula, consisting of an R−6 term is introduced, which is appropriately damped for short distances; the corresponding C6 coefficient, which is calculated from experimental atomic polarizabilities, can be consistently added to the total energy expression of the method. We apply this approximate DFT plus dispersion energy method to describe the hydrogen bonding and stacking interactions of nucleic acid base pairs. Comparison to MP2/6-31G*(0.25) results shows that the method is capable of reproducing hydrogen bonding as well as the vertical and twist dependence of the interaction energy very accurately.

High-precision calculationsj of the 3,1 P 1 0 →1 S 0 E1 amplitudes for magnesium, calcium, and strontium

High-precision calculations of the 3,1 P 1 0 (ns np→1 S 0(ns 2) E1 amplitudes were carried out for magnesium, calcium, and strontium (n=3, 4, and 5, respectively). The following results were obtained for the reduced matrix element 〈1 P 1 0 ‖d‖ 1 S 0〉 of electric dipole moment operator: 4.03(2) au for Mg, 4.91(7) au for Ca, and 5.28(9) au for Sr. These matrix elements are necessary for calculating the van der Waals coefficients C 6, which are used in evaluating the atomic scattering lengths. The latter determine the dynamics and stability of the Bose-Einstein condensate.

Collision properties of ultracold 133Cs atoms

We present a theoretical analysis of numerous magnetically tunable Feshbach resonances measured by Chin et al. [preceding Letter, Phys. Rev. Lett. 85, 2717 (2000)] at fields of up to 25 mT. This analysis provides the most accurate characterization of the collisional properties of ground state Cs atoms currently available and clearly shows, in contrast to previous work, that Bose-Einstein condensation of 133Cs cannot be ruled out. The X1Sigma(+)(g) and a(3)Sigma(u) scattering lengths are constrained to (280+/-10)a(0) and (2400+/-100)a(0), respectively ( 1a(0) = 0.052 917 7 nm), and the van der Waals C6 coefficient to 6890+/-35 a.u.(1 a.u. = 0.095 734 5 x10(-24) &Jdot;nm(6)).

Dispersion coefficients for interactions between two metastable helium-like ions

The dispersion coefficients C6, C8 and C10 for the interactions between helium and helium-like ions in the metastable states of 2 1S and 2 3S with Z up to 10 are calculated using variational wave functions in Hylleraas coordinates.

Adiabatic perturbation theory for Van der Waals coefficients

The leading contribution to the Van der Waals C6 coefficient in an expansion with respect to the coupling strengths of the electrons is derived in terms of the Kohn–Sham (KS) orbitals and eigenvalues, and evaluated for noble gases and small molecules.

A Novel Constraint for the Simplified Description of Dispersion Forces

We propose a novel use of an exact constraint in the construction of simple approximations for response functions of interacting many-electron systems. Within its simplest local version, the resulting theory gives improved approximations for static atomic dipolar polarisabilities without the direct use of wavefunctions or semi-empirical cutoffs. It leads to correct van der Waals energies between distant planar systems, but over-corrects existing cutoff theories for the van der Waals C 6 coefficient for atoms. It is argued that a nonlocal-response version of the constrained theory will do better.