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This is an abstract for a poster to be presented at the Fifth Foresight Conference on Molecular Nanotechnology. There will be a link from here to the full article when it is available on the web.A comparative analysis of the overlap matrix evaluation results obtained within LCAO, from one side, by using the standard Slater type atomic orbital basis set and, from the other hand, by using the new numerical method with given accuracy for each matrix element has been made. It was shown that, accounting for approximately the same calculation CPU times, the new method provides much more accurate results. Moreover, it is impossible to reach the calculation accuracy of 0.0001 % using the standard method due to the huge number of basis functions. The calculation time using the new numerical method with the mentioned above accuracy is only of 0.1 second.