Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

arXiv:0708.0341v1 [physics.atm-clus] 2 Aug 2007 Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters Arup Banerjeea, Aparna Chakrabartib, and Tapan K. Ghantyc (a) Laser Physics Application Division, Raja Ramanna Centre for Advanced Technology Indore 452013, India (b) Semiconductor Laser Section, Raja Ramanna Centre for Advanced Technology Indore 452013, India (c) Theoretical Chemistry Section, Chemistry Group, Bhabha Atomic Research Centre, Mumbai 400 085, India Abstract In this paper we employ all-electron ab-initio time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) C6 of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical aver- age of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C6 and static polarizability are quite accurate and very close to the exper- imental results. We examine the relationship between volume of the cluster and van der Waals coefficient and find that to a very high degree of correlation C6 scales as square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N2 molecule interactions. 1 I. INTRODUCTION The long range dispersive or van der Waals forces play a significant role in the description of many physical and chemical phenomena such as adhesion, surface tension, physical adsorp- tion, etc. These forces originate from the correlations between electron density fluctuations at widely separated locations. The van der Waals interaction between two neutral polariz- able molecules has R−6 dependence (provided orientational averages have been performed), where R is the separation between the two molecules. The van der Waals coefficient C6 asso- ciated with the R−6 dependent dispersive interaction describes the dipole-dipole interaction between two polarizable systems. This paper is devoted to the ab-initio time-dependent den- sity functional theory (TDDFT) based calculation of C6 for sodium-cluster-cluster, sodium- cluster-argon-atom, and sodium-cluster-nirogen-molecule interactions. For our calculations we consider closed-shell sodium clusters containing up to 20 atoms. The knowledge of van der Waals coefficient C6 is useful for the description of cluster- cluster collisions [1] and also for characterizing the orientation of clusters in bulk matter [2, 3]. We note here that large body of theoretical [4, 5, 6, 7, 8, 9] and experimental [6, 10, 11, 12, 13] work on the electronic and optical response properties of sodium atom clusters exists in the literature. Majority of the theoretical calculations on sodium clusters have been performed by employing density functional theory (DFT) or its time dependent version TDDFT within the spherical jellium background model (SJBM) (see the reviews [5, 8]). The SJBM replaces the discrete ionic structure of clusters by a spherically symmetric uniform positive charge background and thus making it possible to carry out calculations for the optical response properties of reasonably large clusters of around 100 atoms [5, 14]. Parallel to the jellium model calculations, several DFT and TDDFT based all-electron ab- initio and pseudopotential calculations devoted to the ground state and the optical response properties of sodium clusters taking into account the actual geometrical arrangement of the sodium atoms have been reported in the literature [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25]. However, these calculations could handle clusters with smaller sizes than the ones that could be studied by performing jellium based calculations. We note here that only very few papers devoted to the calculation of the van der Waals co- efficients and their measurements exist in the literature. In Refs. [26, 27, 28], time-dependent Kohn-Sham (TDKS) equation of TDDFT within SJBM was employed to calculate the van 2 der Waals coefficients. On the other hand, in Ref. [29], a purely density-based modified Thomas-Fermi approach within TDDFT has been applied to calculate the coefficients. It is only very recently that the first all-electron ab-initio calculation of the van der Waals coefficient C6 of small sized closed shell sodium cluster containing up to 20 atoms has been reported in the literature [30]. In Ref. [30] calculations have been carried out by employing linear complex polarization propagator approach in conjunct

…(Full text truncated)…

This content is AI-processed based on ArXiv data.