Long-range Coefficients Research Articles

Long-range dispersion coefficients for Li, Li+, and Be+ interacting with the rare gases

The long-range dispersion coefficients for the ground and excited states of Li, Li(+), and Be(+) interacting with the He, Ne, Ar, Kr, and Xe atoms in their ground states are determined. The variational Hylleraas method is used to determine the necessary lists of multipole matrix elements for He, Li, Li(+), and Be(+), while pseudo-oscillator strength distributions are used for the heavier rare gases. Some single electron calculations using a semiempirical Hamiltonian are also performed for Li and Be(+) and found to give dispersion coefficients in good agreement with the Hylleraas calculations. Polarizabilities are given for some of the Li and Li(+) states and the recommended (7)Li(+) polarizability including both finite-mass and relativistic effects was 0.192 486 a.u. The impact of finite-mass effects upon the dispersion coefficients has been given for some selected interatomic interactions.

Ab initio potential energy surfaces for NH(Σ3−)–NH(Σ3−) with analytical long range

We present four-dimensional ab initio potential energy surfaces for the three different spin states of the NH(Σ3−)–NH(Σ3−) complex. The potentials are partially based on the work of Dhont et al. [J. Chem. Phys. 123, 184302 (2005)]. The surface for the quintet state is obtained at the RCCSD(T)/augmented correlation-consistent polarized valence triple-zeta (aug-cc-pVTZ) level of theory and the energy differences with the singlet and triplet states are calculated at the complete active space with nth-order perturbation theory/aug-cc-pVTZ (n=2,3) level of theory. The ab initio potentials are fitted to coupled spherical harmonics in the angular coordinates, and the long range is further expanded as a power series in 1/R. The RCCSD(T) potential is corrected for a size-consistency error of about 0.5×10−6 Eh prior to fitting. The long-range coefficients obtained from the fit are found to be in good agreement with first and second-order perturbation theory calculations.

Quantum-Mechanical Study of the Collision Dynamics of O2(3Σg−) + O2(3Σg−) on a New ab Initio Potential Energy Surface

The quantum mechanical theory for the scattering of two identical rigid rotors is reviewed and applied to the collision of O2(3Sigma(g)-) molecules using a new accurate ab initio potential energy surface (PES) for the quintet state of the composite system. The PES is based on calculations using restricted coupled-cluster theory with singles, doubles, and perturbative triple excitations [RCCSD(T)] [Bartolomei; et al. J. Chem. Phys. 2008, 128, 214304.]. This PES is extended here for large intermolecular distances using the ab initio long-range coefficients of Hettema et al. [J. Chem. Phys. 1994, 100, 1297.]. Elastic and rotationally inelastic integral cross sections have been obtained by means of close coupling calculations in the subthermal energy range (center-of-mass velocities below 500 m/s). Results are compared with those obtained using a PES derived from molecular beam experiments [Aquilanti; et al. J. Am. Chem. Soc. 1999, 121, 10794.]. General agreement is found between both PESs, although the experimentally derived PES appears as somewhat more anisotropic at least for the studied energy range. There is, however, a significant difference in the absolute value of the elastic cross sections that is due to differences in the long-range dispersion interaction. The performance of the ab initio PES for higher velocities (relevant to experiments) is also explored by retaining just the isotropic component of the interaction. A satisfactory agreement is found for the shape of the glory pattern but shifted toward lower absolute values of the cross sections.

Si(3P) + OH(X2Π) Interaction: Long-Range Multipolar Potentials of the Eighteen Spin−Orbit States

Eighteen spin-orbit states are generated from the open-shell open-shell Si((3)P) + OH(X(2)Pi) interacting system. We present here the behavior of the associated long-range intermolecular potentials, following a multipolar expansion of the Coulombic interaction treated up to second order of the perturbation theory, giving rise to a series of terms varying in R(-n). In the present work, we have considered the electrostatic dipole-quadrupole (n = 4) and quadrupole-quadrupole (n = 5) interactions, as well as the dipole-induced dipole-induced dispersion (n = 6) and dipole-dipole-induced induction (n = 6) contributions. The diatomic OH is kept fixed at its ground state-averaged distance, (r)(v=0) = 1.865 bohr, so that the long-range potentials are two-dimensional potential energy surfaces (PESs) that depend on the intermolecular distance R and on the bending angle gamma = angleSiGH, where G represents the mass center of OH. From the calculated properties of the monomers, such as the dipole and quadrupole moments and static and dynamic polarizabilities, we have determined and tabulated the long-range coefficients of the multipolar expansion of the potentials for each matrix elements. The isolated monomer spin-orbit splittings have been included in the final matrix, whose diagonalization gives rise to 18 adiabatic potentials. Then, the adiabatic states have been compared to potential energies given by supermolecular ab initio calculations resulting in a general good overall agreement.

High sensitive photoassociation spectroscopy of the Cs molecular [formula omitted] and 1 g long-range states below the 6S 1/2 + 6P 3/2 limit

Highly sensitive photoassociation spectroscopy is reported using the modulation technique in a Cs atom magneto-optical trap. Spectral data are extended to red detunings of 70 cm −1 below the Cs 6S 1/2 + 6P 3/2 dissociation limit. Long vibrational progressions are assigned to the 0 u + and 1 g long-range molecular excited states. Some low-lying vibrational levels are first observed for the 0 u + and 1 g states. By fitting the experimental data using the semiclassical LeRoy–Bernstein equation, the long-range molecular coefficients C 3 of the 0 u + and 1 g states are obtained. The present C 3 values are closest to the theoretical values compared with the experimental results reported in earlier publications. Empirical potential curves in the long-range region are derived from these data.

Long-range multipolar potentials of the 18 spin-orbit states arising from the C(P3)+OH(X Π2) interaction

We present multipolar potentials at large intermolecular distances for the 18 doubly degenerate spin-orbit states arising from the interaction between the two open-shell systems, C((3)P) and OH(X (2)Pi). With OH fixed at its ground vibrational state-averaged distance r(0), the long-range potentials are two-dimensional potential energy surfaces (PESs) that depend on the intermolecular distance R and the angle gamma = CGH, where G represents the mass center of OH. The 18x18 diabatic potential matrix elements are built up from the perturbation theory up to second order and from a two-center expansion of the Coulombic interaction potential, resulting in a multipolar expansion of the potential expressed as a series of terms varying in R(-n). The expressions for the long-range coefficients of the expansion are explicitly given in terms of monomer properties such as permanent multipole moments, and static and dynamic polarizabilities. Accurate values for the monomer properties are used to properly determine the long-range interaction coefficients. The diagonalization of the full 18x18 potential matrix generates adiabatic long-range PESs in good agreement with their ab initio counterparts.

Inelastic processes in collisions ofNa(3s,3p)with He at thermal energies

Inelastic collisions of sodium due to low-energy helium are investigated using the quantum-mechanical molecular-orbital coupled-channel method. The calculations adopt adiabatic potentials and nonadiabatic radial and rotational couplings obtained with the multireference single- and double-excitation configuration interaction approach. The potentials are fitted to long-range dispersion coefficients and adjusted with a model interaction in the van der Waals well region. Collisional cross sections for energies between $0.001\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and $10\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and rate coefficients as a function of temperature between $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $10\phantom{\rule{0.2em}{0ex}}000\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ are obtained for $\mathrm{Na}(3p\ensuremath{\rightarrow}3s)$ quenching and $\mathrm{Na}(3s\ensuremath{\rightarrow}3p)$ excitation. The results are relevant to modeling non-LTE effects in Na D absorption lines in extrasolar planets and brown dwarfs.

Inelastic Collisions of Ultracold Heteronuclear Molecules in an Optical Trap

Ultracold RbCs molecules in high-lying vibrational levels of the a3Sigma+ ground electronic state are confined in an optical trap. Inelastic collision rates of these molecules with both Rb and Cs atoms are determined for individual vibrational levels, across an order of magnitude of binding energies. The long-range dispersion coefficients for the collision process are calculated and used in a model that accurately reproduce the observed scattering rates.

Long-range interactions of theSr+ion

A number of properties of the low-lying states of the ${\text{Sr}}^{+}$ ion are evaluated by diagonalizing a semiempirical Hamiltonian in a large dimension single electron basis. These properties include the oscillator strengths connecting the low-lying states, the quadrupole moments, and the polarizabilities. In addition, the long-range dispersion coefficients for the states of this ion interacting with a number of atoms are given. The polarizabilities and dispersion coefficients can be used to estimate frequency shifts of the ${\text{Sr}}^{+}$ $5s\ensuremath{\rightarrow}4d$ clock transition due to background fields, including the blackbody radiation shift, and shifts due to collisions with a buffer gas.

Non-Brownian Diffusion of Membrane Molecules in Nanopatterned Supported Lipid Bilayers

Molecules associated with the outer surface of living cells exhibit complex, non-Brownian patterns of diffusion. In this report, supported lipid bilayers were patterned with nanoscale barriers to capture key aspects of this anomalous diffusion in a controllable format. First, long-range diffusion coefficients of membrane-associated molecules were significantly reduced by the presence of the barriers, while short-range diffusion was unaffected. Second, this modulation was more pronounced for large molecular complexes than for individual lipids. Surprisingly, the quantitative effect of these barriers on long-range lipid diffusion could be accurately simulated using a simple, continuum-based model of diffusion on a nanostructured surface; we thus describe a metamaterial that captures the properties of the outer membrane of living cells.

Water Diffusion in a Synthetic Hectorite Clay Studied by Quasi-elastic Neutron Scattering

We present a quasi-elastic neutron scattering study of water dynamics confined in a model clay system, a synthetic hectorite with Na+ compensating counterions. As shown by water adsorption gravimetry and neutron/X-ray diffraction, the clay system has, unlike its natural counterparts, very well-defined swelling characteristics, with a clear appearance of a monohydrated and a bihydrated state. This simplifies to a great extent neutron scattering analysis and interpretation. Initially, microscopic relaxation times as well as long-range self-diffusion coefficients for water in Na-hectorite at ambient temperature are determined using the time-of-flight (TOF) and neutron spin echo (NSE) neutron scattering techniques, applying a simple model of isotropic (three-dimensional) translational diffusion. Results from the two techniques are in excellent agreement, giving diffusion coefficient of approximately 1.5 × 10-10 m 2 s-1 and 4.5 × 10-10 m 2 s-1 for the monohydrated and bihydrated state, respectively. Concentrat...

Accurate long-range coefficients for two excited like isotope He atoms:He(2P1)–He(2P1),He(2P1)–He(2P3), andHe(2P3)–He(2P3)

A general formalism is used to express the long-range potential energies in inverse powers of the separation distance between two like atomic or molecular systems with P symmetries. The long-range molecular interaction coefficients are calculated for the molecular symmetries {delta}, {pi}, and {sigma}, arising from the following interactions: He(2 {sup 1}P)-He(2 {sup 1}P), He(2 {sup 1}P)-He(2 {sup 3}P), and He(2 {sup 3}P)-He(2 {sup 3}P). The electric quadrupole-quadrupole term C{sub 5}, the van der Waals (dispersion) term C{sub 6}, and higher-order terms C{sub 8} and C{sub 10} are calculated ab initio using accurate variational wave functions in Hylleraas coordinates with finite nuclear mass effects. A comparison is made with previously published results where available.

Global fits of new intermolecular ground state potential energy surfaces for N 2–H 2 and N 2–N 2 van der Waals dimers

We have built new global fits for the ground state potential energy surfaces (PES) of N 2–H 2 and N 2–N 2 complexes using ab initio perturbative and supermolecular methods. The analytical expressions used in the four-dimensional fitting procedure require the knowledge of the multipole moments, the static and dynamic multipolar polarizabilities of each monomer, from which long-range electrostatic, induction and dispersion coefficients are evaluated. In agreement with previous work, we have found the most stable conformation of N 2–H 2 to be linear and that of N 2–N 2 to have a 45/50° canted parallel shape. The quality of present PESs have been checked by comparing between calculated and experimental second virial coefficients and integral scattering cross-sections, which are found to be in good agreement.

Long-range interactions forHe(nS)–He(n′S)andHe(nS)–He(n′P)

The energetically lowest five states of a helium atom are: He($1^1S$), He($2^3S$), He($2^1S$), He($2^3P$), and He($2^1P$). Long-range interaction coefficients $C_3$, $C_6$, $C_8$, $C_9$, and $C_{10}$ for all $S-S$ and $S-P$ pairs of these states are calculated precisely using correlated wave functions in Hylleraas coordinates. Finite nuclear isotope mass effects are included.

Keesom coefficients in gases

T-dependent long-range Keesom coefficients are evaluated up to the R −10 term for small values of the dimensionless parameter | a ℓ ℓ ′ | . For large values of | a ℓ ℓ ′ | corrections must be introduced mostly for the dipole–dipole term, the correct values of C 6 being best obtained from a recently derived asymptotic formula. The corresponding attractive energies are the isotropic electrostatic contributions to the interaction energy and are temperature-dependent. Comparison with long-range induction and dispersion energy results for some simple polar axially symmetric molecules in the gas phase shows that at R = 10 a 0 and T = 293 K the electrostatic dipole–dipole component is dominant for ∣ a 11∣ > 0.5. For centrosymmetric molecules the corresponding electrostatic contribution is usually negligible with respect to dispersion.

An enlarged basis Full-Cl calculation of C7 dispersion coefficients for the LiH–LiH homodimer

C 7 long-range dispersion coefficients for LiH–LiH are evaluated from Full-CI calculations of frequency-dependent dipole and dipole–quadrupole polarizabilities of ground state LiH at a few selected imaginary frequencies. The elementary dispersion constants are evaluated analytically from the Casimir–Polder integral using a recently proposed interpolation technique in its 2-term form which requires knowledge of just four polarizability values. The enlarged basis of 109 GTOs used in this work improves upon earlier results obtained by use of the smaller 58 GTOs basis set.

Intramolecular dependence of the frequency-dependent polarizabilities of K 2(a 3Σ u+) and van der Waals dispersion coefficients for X+K 2, X 2+K and X 2+K 2 (X=Li,Na,K)

The ab initio time-dependent gauge-invariant method has been used to compute the frequency-dependent dipole polarizabilities of the first triplet state of K 2(a 3Σ u +), and to study its dependence on the internuclear distance. Then, isotropic C 6 000 and anisotropic C 6 202 long-range coefficients of X( 2S)+K 2(a 3Σ u +), K( 2S)+X 2(a 3Σ u +) and X 2(a 3Σ u +)+K 2(a 3Σ u +) (X=Li,Na,K) have been evaluated using dynamic dipole polarizability values of K and K 2. From the determination of the dynamic quadrupole polarizability components of both interacting species, C 8 000, C 8 202 and C 8 404 have been also obtained for the X( 2S)+K 2(a 3Σ u +) and K( 2S)+X 2(a 3Σ u +) (X=Li,Na,K) interacting systems at the calculated equilibrium distance of K 2 (11.57 bohr), as well as the three-body C 9 long-range coefficients depending only on the dipole polarizability of K. Good agreement with the previous values of Marinescu and Starace [Phys. Rev. A 55 (1997) 2067] is obtained for these last coefficients.

Long-range interactions within the [formula omitted] molecule

The long-range interactions between the atoms and diatoms in their ground and first excited states as they appear as fragments on the water dissociation have been modeled. The computed long-range coefficients, which are function of the interaction angle and the interatomic distance of the diatomic, are used to build potential energy functions to represent the long-range energies within this system.

The existence of more than one jump process of hydrogen in palladium–silver alloys — an NMR study

The hydrogen dynamics in the α-phase of Pd 1− x Ag x H y has been studied by proton nuclear magnetic resonance (NMR) measurements. Jump frequencies of the hydrogen atoms in the metal lattice have been deduced from the dipolar spin-lattice relaxation rates Γ 1d by applying the BPP model. In PdH y , the temperature dependence of Γ 1d is well described by a single jump process for all hydrogen atoms. In contrast, in the palladium–silver alloys Pd 1− x Ag x H y , the Γ 1d data indicate more than one jump process with different activation energies. Two and three processes could be separated for x=0.1 and x=0.3, respectively. In both alloys, the diffusion process with the lowest activation energy ( E a=226 meV) is comparable to that in pure palladium. The jump processes with higher activation energies occur more frequently in Pd 0.7Ag 0.3 than in Pd 0.9Ag 0.1. This indicates higher energy-barriers for jumps between O-sites in silver-rich environments. Direct measurements of the long-range diffusion coefficients D were performed by pulsed-field-gradient (PFG)-NMR at temperatures up to 450 K. For both Pd 1− x Ag x H y samples, D( T) is well represented by a single Arrhenius law with the diffusion parameters D 0=3.0×10 −7 m 2 s −1 and E a=230 meV for x=0.1 and D 0=2.1×10 −7 m 2 s −1 and E a=260 meV for x=0.3. The diffusivities calculated from the jump frequencies of the hydrogen atoms are in good agreement with these PFG results and also with measurements using the time-lag technique.

Excited states dipole polarizabilities of calcium atom and long-range dispersion coefficients for the low-lying electronic states of Ca 2 and CaMg

The frequency-dependent dipole polarizabilities are calculated for the five lowest states 4 1S, 5 1S, 4 1P, 4 3P and 5 3S of Ca by using a time-dependent gauge invariant method. The difference of the polarizability (α( 3 P)−α( 1 S)) of 112.9 a.u., between the excited 3P state and the 4 1S ground state calculated from the TDGI method is in good agreement with the two experimental measurements of 96.5±16.4 and 90.4±13.8 a.u. obtained from the Stark frequency and phase shifts, respectively, by Morinaga et al. [Phys. Rev. A 54 (1996) 21]. As a consequence of our previous work referring to the Mg atom, the length formulation of the oscillator strengths has been used. Estimations of the long-range dispersion coefficients for the first molecular state dissociations of Ca 2 and CaMg are proposed. Most of the results are new, and predict a repulsive behaviour for the 1Π g, u and 3Σ + g, u states of the 4 1 S–4 1 P and 5 1 S–4 1 P interactions, respectively.