A Tight-Binding Model for Molecular Dynamics of Carbon-Hydrogen Systems
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G. KOPIDAKIS, C.Z. WANG, C.M. SOUKOULIS AND K.M. HO Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011
ABSTRACT A model for studying carbon-hydrogen systems with molecular dynamics (MD) is developed based on an empirical tight-binding approach for the calculation of the interatomic forces. The parameters involved are obtained by fitting to the structure of methane. The transferability of the model is tested by reproducing accurately several electronic, structural, and vibrational properties of hydrocarbon molecules. Ab initio results on carbon clusters with hydrogen are compared with the results obtained with our model. INTRODUCTION There exists a variety of systems containing carbon and hydrogen with an important role in several areas of materials research, such as organic chemistry, polymers, and condensed matter physics. The unique ability of carbon to form strong covalent bonds with coordination numbers that range from two to four, results in many different bondings (single, double, triple, conjugated) and configurations (linear, planar, ring, tetrahedral, cage structures, graphite, diamond). In recent years there is a growing interest in understanding the
properties of hydrogenated amorphous carbon, both from the fundamental and the technological point of view. In order to study the dynamics of carbon-hydrogen systems one needs to have a reliable way of calculating the interatomic forces. Classical MD methods [1] can handle a large number of atoms for relatively long simulation times but fail to describe electronic properties. First principles MD [21 describe accurately the interatomic interactions but are limited to small systems and short times. Tight-binding MD (TBMD) is a scheme that preserves the main quantum mechanical features of the systems while allowing for computer simulations of relatively large systems and long times. This scheme has been proven to be very succesful in describing carbon systems [3] and in this work we develop a tight-binding model for carbon-hydrogen interactions for use in MD simulations. THE TIGHT-BINDING MODEL Within the tight-binding molecular dynamics (TBMD) scheme, the system is described by the Hamiltonian: H =E
± Z(I)PTIHTBI#) + Erep + i
(1)
2
The first term in (1) is the kinetic energy of the atoms (i = 1, .. , N) with momentum, pA, and mass, m,, the second term is the electronic band structure energy, i.e., the sum of the 73 Mat. Res. Soc. Symp. Proc. Vol. 358 01995 Materials Research Society
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1.2
11.1
1.3
C-H distance (A)
Fig. I Occupied energy levels for CH4 from TB model (line) and from LDA (square dots). eigenvalues over all occupied electronic states, and the third term includes all the repulsive energies. The electronic eigenvalues are obtained by solving the empirical tight-binding Hamiltonian, HTB. The matrix elements of HTBs are adjustable parameters that are determined by fitting to ab initio results. The diagonal elements are the atomic orbital energies of the corresponding atom and the
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