By Taro Udagawa
This ebook offers the multi-component first-principles tools that may take account of the quantum impression of sunshine debris reminiscent of proton and positron, in addition to electron. specifically, the authors introduce their multi-component molecular orbital (MC_MO) tools and multi-component 'hybrid kind' density useful idea (MC_DFT). utilizing those multi-component approach, the authors can examine many chemical phenomena, H/D isotope influence, positronic structures, and so forth. The authors convey a few examples of MC_MO and MC_DFT works.
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54 Taro Udagawa and Masanori Tachikawa  H. Iikura, T. Tsuneda, T. Yanai, K. Hirao, J. Chem. , 115 (2001) 3540.  M. Kamiya, T. Tsuneda, K. Hirao, J. Chem. Phys. 117 (2002) 6010.  T. Sato, T. Tsuneda, K. Hirao, Mol. Phys. 103 (2005) 1151.  J. F. Capitani, R. F. Nalewajski, R. G. , J. Chem. , 76 (1982) 568.  P. C. Jain, R. M. Singru, K. P. Gopinathan, Eds. Positron Annihilation (World Scientific, Singapore, 1985).  J. M. Humberston, E. A. G. Armous, Eds, Atomic Physics with Positrons, NATO ASI Series Vol.
Application of the Multi-Component Methods 35 The energy derivatives with respect to the GTF exponents have been evaluated in the scale of their natural logarithms. Individual exponent optimization is carried out for p and p GTFs, and a single exponent for d-type GTFs. To avoid the redundancy problem of the basis functions, the GTF center for electronic s-type GTFs on each side is assumed to have identical values through the optimization, and also for electronic p-type GTFs. Since all variational parameters are optimized in multi-dimensional energy hypersurface, possible problems of redundancy or multiple energy minima are checked by using different initial conditions for the GTF exponent; the same results are obtained in most cases.
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Multi-Component Molecular Orbital Theory by Taro Udagawa