A Semi-Empirical Methodology to Study Bulk Silica System
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ABSTRACT A semi-empirical methodology [1,2] developed to model and simulate covalently bonded networked systems is modified to study the heteroatomic mixtures of silica. This methodology is capable of grasping the essential qualitative and quantitative features of the coupling between the electronic coordinates and the geometric structure. The methodology is used to simulate and to probe the structural and thermodynamic properties of the bulk crystalline, amorphous solid and the melt states of silica.
INTRODUCTION Heteroatomic networked materials that exhibit a modest electronegativity difference between the different types of atoms generally form covalent bonds that contain significant ionic character. The ionic character is a result of charge transference (i.e. a shift of electron density) from the less electronegative atom to the one with greater electronegativity and thus leads to a partial charge on each atom. In these systems, as the bonds stretch and vibrate the partial charge fluctuates around an equilibrium value. Moreover, as a bond breaks the dissociation pathway will be either homolytic (covalent) or heterolytic (ionic) depending upon which pathway is the most stable. In principle, such a description can be obtained using quantum chemical approaches as in simulations based on density functional theory [3,4]. However, this approach remains computationally intensive for use in large scale molecular dynamics (MD) simulations. Although empirical model potentials have proven to be successful and useful, they have not succeeded in capturing details of the electronic fluctuations. In this work, we present a simulation methodology that incorporates a semiempirical calculation into a classical simulation approach. This method is capable of grasping the essential qualities of ionic character in an otherwise covalent bond, and we show that it provides an excellent description of silica. In the present work, a set of constant volume molecular dynamics simulations has been performed to examine the crystalline, liquid and amorphous states of silica. Extended HMickel theory [5] (EHT) is used to model the nearest neighbor bonding interactions in a pairwise localized molecular orbital environment. It provides a set of electronic coordinates given by the rotational and hybridization states of the valence orbitals. The modified Buckingham [6] (exp-6) potential is used to model the nonbonded neighbor interactions. This approach provides a quantitative measure of self diffusion in the melt as a function of temperature, and gives a melt structure whose pair distribution function is in good agreement with experimental and other simulation results.
POTENTIAL MODEL The total potential energy of the system for a given configuration of N atoms is determined by
ET=
Z
2
(ZET
+ + Es,.3'+ Elm., ±
Eiko
+ Eab
(1)
where the first sum is over all atoms in the system, the second sum is over all bonded neighbors, and the third sum is over all nonbonded neighbors within a specified cutoff 61 0 Mat. Res. Soc. Symp. Proc. Vol. 408
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