Cluster-surface and cluster-cluster interactions: Ab initio calculations and modeling of asymptotic van der Waals forces

We present fully ab initio calculations of van der Waals coefficients for two different situations: (i) the interaction between hydrogenated silicon clusters and (ii) the interactions between these nanostructures and a nonmetallic surface (a silicon or a silicon carbide surface). The methods used are very efficient and allow the calculation of systems containing hundreds of atoms. The results obtained are further analyzed and understood with the help of simple models. These models can be of interest for molecular-dynamics simulations of silicon nanostructures on surfaces, where they can give a very fast yet sufficiently accurate determination of the van der Waals interaction at large separations.

[1]  Dependences of the van der Waals atom-wall interaction on atomic and material properties , 2005, quant-ph/0503038.

[2]  Efficient calculation of van der Waals dispersion coefficients with time-dependent density functional theory in real time: application to polycyclic aromatic hydrocarbons. , 2007, The Journal of chemical physics.

[3]  Cheng Chin,et al.  Impact of the Casimir-Polder potential and Johnson noise on Bose-Einstein condensate stability near surfaces. , 2004, Physical review letters.

[4]  L. Reining,et al.  Energy dependence of the exchange-correlation kernel of time-dependent density functional theory: A simple model for solids , 2005 .

[5]  H. Casimir,et al.  Influence of Retardation on the London–van der Waals Forces , 1946, Nature.

[6]  H. Rydberg,et al.  UNIFIED TREATMENT OF ASYMPTOTIC VAN DER WAALS FORCES , 1998, cond-mat/9805352.

[7]  Hinds,et al.  Direct measurement of the van der Waals interaction between an atom and its images in a micron-sized cavity. , 1992, Physical review letters.

[8]  N. Vast,et al.  Long-range contribution to the exchange-correlation kernel of time-dependent density functional theory , 2004 .

[9]  H. Rydberg,et al.  Dispersion Coefficients for van der Waals Complexes, Including C60–C60 , 1999 .

[10]  Evert Jan Baerends,et al.  A density-functional theory study of frequency-dependent polarizabilities and Van der Waals dispersion coefficients for polyatomic molecules , 1995 .

[11]  Arup Banerjee,et al.  Comparison of van der Waals coefficient C6 of sodium clusters obtained via spherical jellium background model and all-electron ab initio method , 2007, J. Comput. Methods Sci. Eng..

[12]  E. Lifshitz The theory of molecular attractive forces between solids , 1956 .

[13]  D. Langreth,et al.  Van Der Waals Interactions In Density Functional Theory , 2007 .

[14]  Patrick Norman,et al.  C6 dipole-dipole dispersion coefficients for the n-alkanes : Test of an additivity procedure , 2004 .

[15]  J. G. Snijders,et al.  Time-dependent density functional result for the dynamic hyperpolarizabilities of C60. , 1997 .

[16]  W. Kohn,et al.  Van der Waals interaction between an atom and a solid surface , 1976 .

[17]  Patrick Norman,et al.  Polarization propagator calculations of the polarizability tensor at imaginary frequencies and long-range interactions for the noble gases and n-alkanes , 2003 .

[18]  Robert Moszynski,et al.  Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes , 1994 .

[19]  F. Shimizu Specular reflection of very slow metastable neon atoms from a solid surface. , 2001, Physical review letters.

[20]  E. A. Cornell,et al.  Thermally Induced Losses in Ultra-Cold Atoms Magnetically Trapped Near Room-Temperature Surfaces , 2003 .

[21]  H. Appel,et al.  octopus: a tool for the application of time‐dependent density functional theory , 2006 .

[22]  Patrick Norman,et al.  Complex polarization propagator method for calculation of dispersion coefficients of extended pi-conjugated systems: the C6 coefficients of polyacenes and C60. , 2005, The Journal of chemical physics.

[23]  J. Israelachvili Intermolecular and surface forces , 1985 .

[24]  Erika Hult,et al.  Trends in atom/molecule-surface van der Waals interactions , 1997 .

[25]  Yu Tian,et al.  Adhesion and friction in gecko toe attachment and detachment , 2006, Proceedings of the National Academy of Sciences.

[26]  H. Casimir,et al.  The Influence of Retardation on the London-van der Waals Forces , 1948 .

[27]  Xavier Andrade,et al.  Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities. , 2007, The Journal of chemical physics.

[28]  Senatore,et al.  Nonlinear response of closed-shell atoms in the density-functional formalism. , 1987, Physical review. A, General physics.

[29]  Matthieu Verstraete,et al.  First-principles computation of material properties: the ABINIT software project , 2002 .

[30]  Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals. , 2005, Physical review letters.

[31]  S. Karna,et al.  Frequency-dependent hyperpolarizabilities of haloforms from ab initio SCF calculations , 1990 .

[32]  D. Langreth,et al.  Density Functional for van der Waals Forces at Surfaces. , 1996, Physical review letters.

[33]  Martins,et al.  Efficient pseudopotentials for plane-wave calculations. , 1991, Physical review. B, Condensed matter.

[34]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[35]  Werner Hanke,et al.  Dielectric theory of elementary excitations in crystals , 1978 .

[36]  L. Reining,et al.  Time-dependent density-functional theory for extended systems , 2007 .

[37]  D Kielpinski,et al.  Bose-Einstein condensates near a microfabricated surface. , 2003, Physical review letters.

[38]  Á. Rubio,et al.  Assessment of exchange-correlation functionals for the calculation of dynamical properties of small clusters in time-dependent density functional theory , 2001, cond-mat/0102234.

[39]  G. Bertsch,et al.  Real-space computation of dynamic hyperpolarizabilities , 2001 .

[40]  F. Capasso,et al.  Nonlinear micromechanical Casimir oscillator. , 2001, Physical review letters.

[41]  J. Lennard-jones,et al.  Processes of adsorption and diffusion on solid surfaces , 1932 .

[42]  D. Hamann,et al.  Norm-Conserving Pseudopotentials , 1979 .

[43]  L. Hedin Effects of Recoil on Shake-Up Spectra in Metals , 1980 .

[44]  M. Dekieviet,et al.  Experimental observation of quantum reflection far from threshold. , 2002, Physical review letters.

[45]  L. Reining,et al.  Electronic excitations: density-functional versus many-body Green's-function approaches , 2002 .

[46]  Xavier Gonze,et al.  A brief introduction to the ABINIT software package , 2005 .

[47]  F. Capasso,et al.  Quantum Mechanical Actuation of Microelectromechanical Systems by the Casimir Force , 2001, Science.

[48]  D. Wood,et al.  Effective medium theory of optical properties of small particle composites , 1977 .

[49]  J. Garnett,et al.  Colours in Metal Glasses and in Metallic Films , 1904 .

[50]  A. Banerjee,et al.  Calculation of van der Waals coefficients in hydrodynamic approach to time-dependent density functional theory , 2002 .

[51]  S. Saltiel,et al.  Exploring the van der Waals atom-surface attraction in the nanometric range , 2006, physics/0605134.

[52]  E. Gross,et al.  Time-dependent density functional theory. , 2004, Annual review of physical chemistry.

[53]  A. Zunger,et al.  Self-interaction correction to density-functional approximations for many-electron systems , 1981 .

[54]  R. Girlanda,et al.  Optical properties of semiconductors within the independent-quasiparticle approximation. , 1993, Physical review. B, Condensed matter.

[55]  H. C. Hamaker The London—van der Waals attraction between spherical particles , 1937 .

[56]  M. W. Cole,et al.  The interaction between an atom and a surface at large separation , 1981 .

[57]  D. M. Bishop,et al.  Near-resonant absorption in the time-dependent self-consistent field and multiconfigurational self-consistent field approximations , 2001 .

[58]  P. Norman,et al.  Electric dipole polarizabilities and C6 dipole-dipole dispersion coefficients for sodium clusters and C60. , 2006, The Journal of chemical physics.

[59]  J. Chelikowsky,et al.  Ab initio absorption spectra and optical gaps in nanocrystalline silicon. , 2001, Physical review letters.

[60]  S. Patil,et al.  Damping functions for the pairwise sum model of the atom–surface potential , 2002 .

[61]  Stefano de Gironcoli,et al.  Phonons and related crystal properties from density-functional perturbation theory , 2000, cond-mat/0012092.

[62]  M. Marques,et al.  Identification of fullerene-like CdSe nanoparticles from optical spectroscopy calculations , 2006, cond-mat/0605517.

[63]  J. Chelikowsky,et al.  Ab initio absorption spectra of CdSe clusters , 2001 .

[64]  R. Gebauer,et al.  Efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy. , 2005, Physical review letters.

[65]  A. Banerjee,et al.  Van der Waals coefficients for alkali metal clusters and their size dependence , 2006 .

[66]  Angel Rubio,et al.  Excitonic effects in solids described by time-dependent density-functional theory. , 2002, Physical review letters.

[67]  Á. Rubio,et al.  octopus: a first-principles tool for excited electron-ion dynamics. , 2003 .