A gas-phase elementary-reaction mechanism of diamond growth by a vapor depostion process is proposed. The rate constants for-all reactions included in the model have been computed using the species and their transition-state parameters predicted by molecular orbital ab intio at HF/6-31G^* level The calculated results quantitatively agree with experimental data on the concentration of gas-phase species and substrate temperature.

The value of potential barrier of H abstraction from hydrogeneted diamond (111) surface is critical to understand nucleation and growth dynamics of diamond film under the condition of Chemical Vapor Deposition.The previous theoretical works on the value are far from accord based upon different MO methods.On use of a series of cluster models and some kinds of MO methods the potential barrier is systematically studied here.After determinating the MNDO approach reliability for this problem,the corrected theoretical value is given as well.

The potential energy curves between methyl and diamond (Ⅲ) surface are calculated by Ami semi-empirical molecular orbital method, which are found to be in close agreement with the substrate models. It provides much information for studying the dynamic processes of the nucleation and growth of diamond films, and more general adsorption as well.

With regard to evaluation of auxiliary function I_μ(x)up to arbitrary accuracy, it is required that the forward recurrence scheme of the function can be used as far as possible. Applying a new inequality found by us, we have set up a criterion which can accurately decide whether the requirement can be met.

Two inequalities of incomplete Gamma function are given for the domain v∈[0,-∞) and z∈(-∞,0].Based upon the inequalities, we derive the round off error propagation regularity of the forward recurrence scheme. Our numerical experiments indicate that the relative error predicated by our regularity almost coincides with that from authentic regularity in the whole domain of v and z.