Many-body Contributions Research Articles

Casimir-Lifshitz interaction between dielectrics of arbitrary geometry: A dielectric contrast perturbation theory

The general theory of electromagnetic-fluctuation-induced interactions in dielectric bodies as formulated by Dzyaloshinskii, Lifshitz, and Pitaevskii is rewritten as a perturbation theory in terms of the spatial contrast in (imaginary) frequency dependent dielectric function. The formulation can be used to calculate the Casimir-Lifshitz forces for dielectric objects of arbitrary geometry, as a perturbative expansion in the dielectric contrast, and could thus complement the existing theories that use perturbation in geometrical features. We find that expansion in dielectric contrast recasts the resulting Lifshitz energy into a sum of the different many-body contributions. The limit of validity and convergence properties of the perturbation theory is discussed using the example of parallel semi-infinite objects for which the exact result is known.

The multiscale coarse-graining method. III. A test of pairwise additivity of the coarse-grained potential and of new basis functions for the variational calculation

The multiscale coarse-graining (MS-CG) method, proposed by Izvekov and Voth [J. Phys. Chem. B 109, 2469 (2005); Izvekov and VothJ. Chem. Phys. 123, 134105 (2005)], is a method for determining the effective potential energy function for a coarse-grained model of a fluid using data obtained from molecular dynamics (MD) simulation of the corresponding atomically detailed model. The method has been given a rigorous statistical mechanical basis [Noid et al. J. Chem. Phys. 128, 244114 (2008); Noid et al., J. Chem. Phys. 128, 244115 (2008)]. The coarse-grained (CG) potentials obtained using the MS-CG method are an approximate variational solution for the exact many-body potential of mean force for the coarse-grained sites. In this paper we apply this method to study the many-body potential of mean force among solutes in a simple model of a solution of Lennard-Jones particles. We use a new set of basis functions for the variational calculation that is useful when the coarse-grained potential is approximately equal to an arbitrarily complicated pairwise additive, central interaction among the sites of the coarse-grained model. For this model, pairwise additivity of the many-body potential of mean force is a very good approximation when the solute concentration is low, and it becomes less accurate for high concentrations, indicating the importance of many-body contributions to the coarse-grained potential. The best possible pairwise additive CG potential of the solute particles is found to be quite long ranged for all concentrations except those for which the mole fraction of solute is very close to unity. We discuss strategies for construction of short-ranged potentials for efficient but accurate CG MD simulation. We also discuss how the choice of basis functions for the variational calculation can be used to provide smoothing of the calculated CG potential function to overcome statistical sampling error in the atomistic simulation data used for the generation of the potential.

Unified approach to structure factors and neutrino processes in nucleon matter

We present a unified approach to neutrino processes in nucleon matter based on Landau's theory of Fermi liquids that includes one and two quasiparticle-quasihole pair states as well as mean-field effects. We show how rates of neutrino processes involving two nucleons may be calculated in terms of the collision integral in the Landau transport equation for quasiparticles. Using a relaxation time approximation, we solve the transport equation for density and spin-density fluctuations and derive a general form for the response functions. We apply our approach to neutral-current processes in neutron matter, where the spin response function is crucial to the calculation of neutrino elastic and inelastic scattering and neutrino-pair bremsstrahlung and absorption from strongly interacting nucleons. We calculate the relaxation rates using modern nuclear interactions and including many-body contributions, and find that rates of neutrino processes are reduced compared with estimates based on the one-pion exchange interaction, which is used in current simulations of core-collapse supernovae.

Brillouin scattering studies of liquid argon at high temperatures and high pressures

Brillouin scattering measurements were performed on liquid argon in a diamond anvil cell at various solidification points up to 503 K. With the measured results from the 60 degree platelet- and 180 degree back-scattering geometries, the sound velocity, refractive index, experimental equation of state, and adiabatic bulk modulus of liquid argon as a function of pressure were determined. The discrepancy between experimental and previous calculated equation of state indicates that the many-body contribution to the density of liquid argon increases with increasing pressure and decreases with increasing temperature. By analyzing the Brillouin spectra in the coexistence of liquid and solid phase regions, the volume change and latent heat of solid-liquid transformation along the equilibrium curve have been also obtained for the first time.

Popular Kohn-Sham density functionals strongly overestimate many-body interactions in van der Waals systems

We find spuriously large repulsive many-body contributions to binding energies of rare gas systems for the first three rungs of Jacob's Ladder within Kohn-Sham density functional theory. While the description of van der Waals dimers is consistently improved by the pairwise London C-6/R-6 correction, inclusion of a corresponding three-body Axilrod-Teller C-9/R-9 term only increases the repulsive error. Our conclusions based on extensive solid state and molecular electronic structure calculations are particularly relevant for condensed phase van der Waals systems.

Convergence of all-order many-body methods: Coupled-cluster study for Li

We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, $2{p}_{1∕2}$, and $2{p}_{3∕2}$ states of Li atom. The calculations are complete through the fourth order of many-body perturbation theory for energies and through the fifth order for matrix elements and subsume certain chains of diagrams in all orders. A nearly complete many-body calculation allows us to draw conclusions on the convergence pattern of the coupled-cluster method. Our analysis suggests that the high-order many-body contributions to energies and matrix elements scale proportionally and provide a quantitative ground for semiempirical fits of ab initio matrix elements to experimental energies.

Polarizable continuum model with the fragment molecular orbital‐based time‐dependent density functional theory

The polarizable continuum model (PCM) for describing the solvent effect was combined with the fragment molecular orbital-based time-dependent density functional theory (TDDFT). Several levels of the many-body expansion were implemented, and the importance of the many-body contributions to the singlet-excited states was discussed. To calibrate the accuracy, we performed a number of the model calculations using our method and the regular TDDFT in solution, applying them to phenol and polypeptides at the long-range corrected BLYP/6-31G* level. It was found that for systems up to 192 atoms the largest error in the excitation energy was 0.006 eV (vs. the regular TDDFT/PCM of the full system). The solvent shifts and the conformer effects were discussed, and the scaling was found to be nearly linear. Finally, we applied our method to the lowest singlet excitation of the photoactive yellow protein (PYP) in aqueous solution and determined the excitation energy to be in reasonable agreement with experiment. The excitation energy analysis provided the contributions of individual residues, and the main factors as well as their solvent shifts were determined.

Many-body effects on surface stress, surface energy and surface relaxation of fcc metals

The results of an investigation aimed at isolating the role played by pair-wise and many-body contributions in determining the surface stress, surface energy and surface relaxation for clean, low-index fcc metal surfaces are presented. General expressions for surface stress and surface energy are developed for generic embedded atom method (EAM) potentials and are contrasted with results derived from central-force pair potentials. Calculations are presented for specific forms. We find that these pair-wise and many-body contributions usually act in opposition to each other. Pair potentials tend to produce compressive surface stress contributions and favor outward surface relaxations, while the many-body component produces tensile surface stress contributions and favors inward relaxations. We also bring to light certain relationships between surface and bulk thermodynamic properties within the framework of these models. It is shown how surface stress can be expressed in an approximate form involving terms proportional to the product of an elastic modulus and the neighbor spacing characteristic of the material, and constants of proportionality that depend only on surface orientation. This form provides a good fit to a set of first-principles results as well. Finally, we demonstrate how various surface properties display a strong correlation with the ratio of bulk-to-shear moduli, B eq/ G eq.

Many-body decomposition of the binding energies for OH⋅(H2O)2 and OH⋅(H2O)3 complexes

We use ab initio electronic structure methods to calculate the many-body decomposition of the binding energies of the OH.(H2O)n (n=2,3) complexes. We employ MP2 and CCSD(T) levels of theory with aug-cc-pVDZ and aug-cc-pVTZ basis sets and analyze the significance of the nonpairwise interactions between OH radical and the surrounding water molecules. We also evaluate the accuracy of our newly developed potential function, the modified Thole-type model, for predicting the many-body terms in these complexes. Our analysis of the many-body contributions to the OH.(H2O)n binding energies clearly shows that they are just as important in the OH interactions with water as they are for interactions in pure water systems.

S-pairing in neutron matter: I. Correlated basis function theory

S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of [S. Fantoni, Nucl. Phys. A 363 (1981) 381], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two-body order of the cluster expansion, but considering the one-body density and the corresponding energy vertex corrections at the first order of the Power Series expansion. Based on these approximations, we have derived a system of Euler equations for the correlation factors and for the BCS amplitudes, resulting in correlated nonlinear gap equations, formally close to the standard BCS ones. These equations have been solved for the momentum independent part of several realistic potentials (Reid, Argonne v 14 and Argonne v 8 ′ ) to stress the role of the tensor correlations and of the many-body effects. Simple Jastrow correlations and/or the lack of the density corrections enhance the gap with respect to uncorrelated BCS, whereas it is reduced according to the strength of the tensor interaction and following the inclusion of many-body contributions.

Ultrafast Optical Spectroscopy of Spectral Fluctuations in a Dense Atomic Vapor

Transient four-wave mixing experiments with 100 fs pulses in a dense potassium vapor probe the electronic energy fluctuations that lead to optical decoherence. Echo-peak shift experiments yield a biexponential two-time correlation function of energy level fluctuations. Molecular dynamics simulations show that the slow component is a many-body excitonic contribution arising from long-range resonant interactions. The decay of the correlation function occurs on comparable time scales in theory and experiment.

Hydration properties of Al3+ ion using empirical ion-water potential by Monte Carlo simulation

In this work, hydration properties of Al3+ ion are investigated by statistical mechanics Monte Carlo simulations in the NpT ensemble at 298.15 K and 1 atm using an effective ion-water potential model whose parameters were developed through empirical search in configurational energy space during the course of simulations to fitting structural experimental data of the first hydration shell. Computed structural results for coordination numbers and ion-water oxygen distances for both first and second coordination shells are obtained in very good agreement with experimental observations. The hydration enthalpy predicted from this simple model is also in very good agreement with experimental values and it is quite similar to the one obtained by Wasserman et al. from the hydrated ion model. Many-body contributions investigated for an [Al(H2O)6]3+ cluster using the density functional theory in ab initio quantum mechanical calculations provide support to the effectiveness of the ion-water pair potential developed concerning many-body effects of water molecules around the ion incorporated in the fitted parameters.

Complex coordinate rotation and relativistic Hylleraas-CI: helium isoelectronic series

A combination of the Hylleraas-CI (Hy-CI) and complex coordinate rotation (CCR) methods has been applied to study the nuclear charge dependence of the eigenvalues of the Dirac–Coulomb (DC) Hamiltonian corresponding to the ground states of helium isoelectronic series atoms. It has been shown that the CCR, due to the separation of the localized states from the unphysical Brown–Ravenhall continuum, removes the instabilities of the bound-state eigenvalues observed in large-basis set Hy-CI results. The Hy-CI–CCR results are in very good agreement with the most accurate ones available in the literature. Surprisingly, the difference between the DC Hy-CI–CCR eigenvalues and the eigenvalues of the positive-energy projected no-pair Hamiltonian is equal, up to the numerical accuracy of the results, to (Zα)3/6π, i.e. to (Zα)3 relativistic many-body perturbation theory contribution for electron–electron Coulomb interaction operator. An excellent agreement between the Hy-CI–CCR eigenvalues shifted by (Zα)3/6π and the no-pair ones confirms the very high accuracy achieved in both approaches. The numerical accuracy of the Hy-CI–CCR DC eigenvalues is estimated to eight significant figures.

Many-body effects of dispersion interaction

The role of many-body (MB) dispersion forces have been analyzed for strands, films, and cubic lattices in the framework of a model Hamiltonian that allows exact solution of the multiparticle Shrodinger equation. For the systems investigated the MB contribution may be as large as 7% of specific dispersion energy and 11% of solvation energy. Nonadditivity becomes particularly important for aggregation in solution, where its effect may be several times larger than the pairwise contribution. For all systems considered, the three-body Axilrod-Teller approximation was insufficient to predict the magnitude and in some cases even the sign of the full MB effect.

Noniterative inclusion of the triply and quadruply excited clusters: The locally renormalized perspective

Noniterative inclusion of the higher-order clusters has been a subject of intensive studies aimed at developing a well balanced description of individual many-body contributions for entire ground-state potential energy surfaces. In traditional approaches, the connected quadruples are estimated directly based on perturbative arguments, which leads to excellent agreement with full CI results near the equilibrium geometry and increasingly worse energies for larger internuclear stretches. As a possible improvement to this situation, two techniques are considered as especially promising: perturbative approaches based on the similarity transformed Hamiltonians and renormalization schemes both in global and local formulations. Following the latter strategy we adopted the recently introduced numerator–denominator connected expansion (NDC) [K. Kowalski, P. Piecuch, J. Chem. Phys. 122 (2005) 074107] as an effective tool for designing new forms of noniterative corrections accounting for the joint effect of triples and quadruples. The performance of the ensuing locally renormalized CCSD(TQ) approaches (LR-CCSD(TQ)) is illustrated on several examples that require either going beyond the triples approximation or describing very subtle effects encountered in van der Waals complexes. Comparisons with other noniterative approaches are also made and some issues regarding the size-extensivity of the locally renormalized methods are addressed.

Electric Quadrupole Moments of theDStates of Alkaline-Earth-Metal Ions

The electric quadrupole moment for the 4d(2)D(5/2) state of (88)Sr(+); one of the most important candidates for an optical clock, has been calculated using the relativistic coupled-cluster theory. This is the first application of this theory to determine atomic electric quadrupole moments. The result of the calculation is presented and the important many-body contributions are highlighted. The calculated electric quadrupole moment is (2.94 +/- 0.07)ea(2)(0), where a(o) is the Bohr radius and the electronic charge while the measured value is (2.6 +/- 0.3) ea(2)(0). This is so far the most accurate determination of the electric quadrupole moment for the above mentioned state. We have also calculated the electric quadrupole moments for the metastable 4d(2)D(3/2) state of 88(Sr(+) and for the 3d(2)D(3/2.5/2) and 5d(2)D(3/2.5/2) states of (43)Ca(+) and (138)Ba(+), respectively.

From first-principles to material properties

Many modeling problems in materials science involve finite temperature simulations with a realistic representation of the interatomic interactions. These problems often necessitate the use of large simulation cells or long run times, which puts them outside the range of direct ab initio simulation. In ionic systems, it is possible to introduce physically motivated model potentials for the interactions, in which additional degrees of freedom provide a ‘cartoon’ of the response of the electronic structure of the ions to their changing coordination environments and allow the compact representation of many-body contributions to the interaction energy. These potentials may then be parameterized by fitting the predicted forces and multipoles to a large body of information generated from ab initio calculations. The resulting potentials are predictive, of ab initio accuracy and have a high degree of transferability between different systems.

Van der Waals forces between nanoclusters: Importance of many-body effects

van der Waals interactions between nanoclusters have been calculated with a self-consistent, coupled dipole method. The method accounts for all many-body (MB) effects. Comparison is made between the exact potential energy, V, and the values obtained with two alternative methods: the sum of two-body interactions and the sum of two-body and three-body interactions. For all cases considered, the three-body term alone does not accurately represent the MB contributions to V. MB contributions are especially large for shape-anisotropic clusters.

Many-body contributions to the equation of state for highly compressed solid helium

To investigate the significance of various many_body effects on the equation of state (EOS) of solid helium,the interaction energy of hcp crystal structure is expanded as a sum of two_ to five_body potentials in the present work. Each short_range many_body term between helium atom clusters is computed by means of Hartree_Fock (HF) self_consistent_field (SCF) method. It is indicated that at high densities the many_body expansion formula is an alternative series, in which two_, and four_body terms are positive, whereas three_ and five_body terms are negative. According to such an expansion of crystal interaction energy, the equation of state of solid helium at 0 K is obtained. The specific characteristics of each of the up to five_body contributions in highly compressed helium are discussed. Between 0.26 to 0.23nm, the interaction energy may be well described by two_ and three_body interactions. Over a distance range 0.23—0.20nm, truncated many_body expansion after the four_body term recovers the main part of atomic potential energy. Below 0.20nm the five_body contributions have to be included. The sum of two_ to five_body term accurately reproduces the atomic potential energy from 0.20 to 0.175nm. The inclusion up to five_body potential satisfactorily describes the available experimental data from 7.5 to 2.5 cm3/mol, corresponding to 1—60 GPa.

Multireference configuration interaction calculations for complexes of positronium and B, C, N, and O atoms

Positronium (Ps) binding energies for complexes of Ps and atoms with open shell electrons, PsX (X=B, C, N, and O), are calculated using the multireference singly and doubly excited configuration interaction (MRSDCI) method. The effectiveness of this method for the complexes is verified. The MRSDCI calculations are carried out with a frozen-core approximation so as to incorporate only the most important valence correlation effects. Many-body correlation effects and contributions from higher angular momentum orbitals are estimated by extrapolation techniques. The resulting Ps binding energies agree well with the results of diffusion Monte Carlo simulations by Bressanini et al. (Phys Rev A 57:1678,1998) and by Jiang and Schrader (J Chem Phys 109:9430,1998). For PsO the Ps binding energy obtained by Jiang and Schrader is about 1.8 times larger than that of Bressanini et al.; the present calculated value is close to that of Jiang and Schrader.