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On the general transformation from molecular geometric parameters to cartesian coordinates
Author(s) -
Essén Hanno
Publication year - 1983
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540040203
Subject(s) - cartesian coordinate system , dihedral angle , log polar coordinates , bipolar coordinates , orthogonal coordinates , position (finance) , transformation (genetics) , coordinate system , generalized coordinates , analytic geometry , mathematics , geometry , physics , mathematical analysis , molecule , chemistry , quantum mechanics , finance , economics , gene , hydrogen bond , biochemistry
This article presents a general method and accurate algorithm for calculating the Cartesian coordinates ( x a , y a , z a ) from an arbitrary triple of distances r ( a , i ), angles, θ( a , j , k ), or dihedral angles ϕ( a , l , m , n ), specifying the position of the nucleus a relative to nuclei i , ⃜, n with known Cartesian coordinates. There is a brief discussion of the requirements on the 3 N ‐6 geometric parameters in order for them to determine the shape of an N ‐atomic molecule.