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Title: Van der Waals coefficients beyond the classical shell model

Abstract

Van der Waals (vdW) coefficients can be accurately generated and understood by modelling the dynamic multipole polarizability of each interacting object. Accurate static polarizabilities are the key to accurate dynamic polarizabilities and vdW coefficients. In this work, we present and study in detail a hollow-sphere model for the dynamic multipole polarizability proposed recently by two of the present authors (JT and JPP) to simulate the vdW coefficients for inhomogeneous systems that allow for a cavity. The inputs to this model are the accurate static multipole polarizabilities and the electron density. A simplification of the full hollow-sphere model, the single-frequency approximation (SFA), circumvents the need for a detailed electron density and for a double numerical integration over space. We find that the hollow-sphere model in SFA is not only accurate for nanoclusters and cage molecules (e.g., fullerenes) but also yields vdW coefficients among atoms, fullerenes, and small clusters in good agreement with expensive time-dependent density functional calculations. However, the classical shell model (CSM), which inputs the static dipole polarizabilities and estimates the static higher-order multipole polarizabilities therefrom, is accurate for the higher-order vdW coefficients only when the interacting objects are large. For the lowest-order vdW coefficient C{sub 6}, SFA and CSMmore » are exactly the same. The higher-order (C{sub 8} and C{sub 10}) terms of the vdW expansion can be almost as important as the C{sub 6} term in molecular crystals. Application to a variety of clusters shows that there is strong non-additivity of the long-range vdW interactions between nanoclusters.« less

Authors:
 [1]; ;  [2];  [3]; ;  [4]
  1. Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323 (United States)
  2. Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118 (United States)
  3. Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA and Department of Chemistry, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
  4. Department of Physics, Temple University, Philadelphia, Pennsylvania 19122 (United States)
Publication Date:
OSTI Identifier:
22415836
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 2; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; APPROXIMATIONS; ATOMS; COMPUTERIZED SIMULATION; DENSITY FUNCTIONAL METHOD; DIPOLES; ELECTRON DENSITY; FULLERENES; MOLECULAR CRYSTALS; MOLECULES; NANOSTRUCTURES; POLARIZABILITY; TIME DEPENDENCE; VAN DER WAALS FORCES

Citation Formats

Tao, Jianmin, E-mail: jianmint@sas.upenn.edu, Fang, Yuan, Hao, Pan, Scuseria, G. E., Ruzsinszky, Adrienn, and Perdew, John P.. Van der Waals coefficients beyond the classical shell model. United States: N. p., 2015. Web. doi:10.1063/1.4905259.
Tao, Jianmin, E-mail: jianmint@sas.upenn.edu, Fang, Yuan, Hao, Pan, Scuseria, G. E., Ruzsinszky, Adrienn, & Perdew, John P.. Van der Waals coefficients beyond the classical shell model. United States. doi:10.1063/1.4905259.
Tao, Jianmin, E-mail: jianmint@sas.upenn.edu, Fang, Yuan, Hao, Pan, Scuseria, G. E., Ruzsinszky, Adrienn, and Perdew, John P.. 2015. "Van der Waals coefficients beyond the classical shell model". United States. doi:10.1063/1.4905259.
@article{osti_22415836,
title = {Van der Waals coefficients beyond the classical shell model},
author = {Tao, Jianmin, E-mail: jianmint@sas.upenn.edu and Fang, Yuan and Hao, Pan and Scuseria, G. E. and Ruzsinszky, Adrienn and Perdew, John P.},
abstractNote = {Van der Waals (vdW) coefficients can be accurately generated and understood by modelling the dynamic multipole polarizability of each interacting object. Accurate static polarizabilities are the key to accurate dynamic polarizabilities and vdW coefficients. In this work, we present and study in detail a hollow-sphere model for the dynamic multipole polarizability proposed recently by two of the present authors (JT and JPP) to simulate the vdW coefficients for inhomogeneous systems that allow for a cavity. The inputs to this model are the accurate static multipole polarizabilities and the electron density. A simplification of the full hollow-sphere model, the single-frequency approximation (SFA), circumvents the need for a detailed electron density and for a double numerical integration over space. We find that the hollow-sphere model in SFA is not only accurate for nanoclusters and cage molecules (e.g., fullerenes) but also yields vdW coefficients among atoms, fullerenes, and small clusters in good agreement with expensive time-dependent density functional calculations. However, the classical shell model (CSM), which inputs the static dipole polarizabilities and estimates the static higher-order multipole polarizabilities therefrom, is accurate for the higher-order vdW coefficients only when the interacting objects are large. For the lowest-order vdW coefficient C{sub 6}, SFA and CSM are exactly the same. The higher-order (C{sub 8} and C{sub 10}) terms of the vdW expansion can be almost as important as the C{sub 6} term in molecular crystals. Application to a variety of clusters shows that there is strong non-additivity of the long-range vdW interactions between nanoclusters.},
doi = {10.1063/1.4905259},
journal = {Journal of Chemical Physics},
number = 2,
volume = 142,
place = {United States},
year = 2015,
month = 1
}
  • In this paper we present a derivation of time-dependent coupled Hartree--Fock (TDCHF) theory for the case of half-open shells. With this method frequency-dependent polarizabilities are calculated for the hydrogen and nitrogen atom, as well as for the diatomics CN, NH, and OH{sup +}. van der Waals coefficients of the half-open-shell systems with the H atom and the H{sub 2} molecule are computed. Other dispersion coefficients for dimers consisting of these monomers are available upon request.
  • Due to the absence of the long-range van der Waals (vdW) interaction, conventional density functional theory (DFT) often fails in the description of molecular complexes and solids. In recent years, considerable progress has been made in the development of the vdW correction. However, the vdW correction based on the leading-order coefficient C{sub 6} alone can only achieve limited accuracy, while accurate modeling of higher-order coefficients remains a formidable task, due to the strong non-additivity effect. Here, we apply a model dynamic multipole polarizability within a modified single-frequency approximation to calculate C{sub 8} and C{sub 10} between small molecules. We findmore » that the higher-order vdW coefficients from this model can achieve remarkable accuracy, with mean absolute relative deviations of 5% for C{sub 8} and 7% for C{sub 10}. Inclusion of accurate higher-order contributions in the vdW correction will effectively enhance the predictive power of DFT in condensed matter physics and quantum chemistry.« less
  • The shell model of atomic polarizability is generalized to include a statistical distribution of shell states for each instantaneous configuration of the cores. Effective Hamiltonians for motions of the cores are derived for both quantum and classical descriptions of the shells. This extends the shell model into a formalism useful for molecular dynamics. The fluctuations of the shell positions account for London dispersion interactions. The resulting equations may also have applications to other systems containing motions with disparate time scales.
  • Four grades of nuclear graphite with various microstructures were subjected to accelerated oxidation tests in helium with traces of moisture and hydrogen in order to evaluate the effects of chronic oxidation on graphite components in high temperature gas cooled reactors. Kinetic analysis showed that the Langmuir-Hinshelwood (LH) model cannot consistently reproduce all results. In particular, at high temperatures and water partial pressures oxidation was always faster than the LH model predicts, with stronger deviations for superfine grain graphite than for medium grain grades. It was also found empirically that the apparent reaction order for water has a sigmoid-type variation withmore » temperature which follows the integral Boltzmann distribution function. This suggests that the apparent activation with temperature of graphite reactive sites that causes deviations from the LH model is rooted in specific structural and electronic properties of surface sites on graphite. A semi-global kinetic model was proposed, whereby the classical LH model was modified with a temperature-dependent reaction order for water. The new Boltzmann-enhanced model (BLH) was shown to consistently predict experimental oxidation rates over large ranges of temperature (800-1100 oC) and partial pressures of water (3-1200 Pa) and hydrogen (0-300 Pa), not only for the four grades of graphite but also for the historic grade H-451. The BLH model offers as more reliable input for modeling the chemical environment effects during the life-time operation of new grades of graphite in advanced nuclear reactors operating at high and very high temperatures.« less