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International Journal of Nonlinear Analysis and Applications، جلد ۱۵، شماره ۴، صفحات ۲۱۷-۲۲۰
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عنوان انگلیسی Calculation of cartesian internal molecular coordinates
چکیده انگلیسی مقاله For the solution of a variety of problems which concern molecular structures, it is often necessary to calculate the Cartesian coordinates of the atoms from a set of geometric parameters. In order to fully utilize symmetry operations in the calculation of Cartesian coordinates, it is necessary to construct the molecule within a primary coordinate system. This is accomplished by introducing a set of four dummy atoms, by which unit vectors are specified. One atom is placed at the origin and the others at unit distances along each of the three Cartesian axes. in this framework according to the attachment procedures described below. The atoms of a molecule are positioned through the use of a secondary coordinate system. A base coordinate system is defined by the positions of three atoms, numbered 1, 2, and 3. The origin is taken at Atom 1, the negative x-axis passes through Atom 2, and Atom 3 lies in the first or second quadrant of the xy plane. In order to define the angles, the following conventions are adopted: for a general atom j, the atom to which it was attached is called $j^{prime}$, and the atom to which $j^{prime}$ was attached is called $j^{prime prime}$, and the atom to which $j^{prime prime}$ was attached is called $j^{prime prime prime}$. Two special cases where these definitions do not suffice are atoms attached to Atom 1 and to Atom 2. Where j is attached to Atom 2, Atom 1 is taken as $j^{prime prime}$ and Atom 3 as $j^{prime prime prime}$. Where j is attached to Atom 1, Atom 2 is taken as $j^{prime prime}$ and Atom 3 as $j^{prime prime prime}$. The program described is being used extensively for specifying molecular structures for electron diffraction investigations. Other current uses are in programs for x-ray diffraction of polymers, for estimating magnitudes of energy via postulated force field functions, and in molecular orbital calculations.
کلیدواژه‌های انگلیسی مقاله Calculation, Cartesian Coordinates, Internal Molecular Coordinates
نویسندگان مقاله Arezo Moradi |
Department of Statistics, Faculty of Basic Science, University of Kurdistan, Sanandaj, Iran

Aida Azuji |
Department of Biophysics, North Tehran Branch, Islamic Azad University, Tehran, Iran

نشانی اینترنتی https://ijnaa.semnan.ac.ir/article_7819_9d608bd620886123d3e4081bfe07c410.pdf
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