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Orthogonal coordinates for the dynamics of four bodies and for the representation of potentials of tetra‐atomic molecules
Author(s) -
Ragni Mirco,
Bitencourt Ana Carla P.,
Aquilanti Vincenzo
Publication year - 2007
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21481
Subject(s) - orthogonal coordinates , dihedral angle , representation (politics) , tetra , kinetic energy , classical mechanics , surface (topology) , potential energy surface , molecule , kinematics , potential energy , rotation (mathematics) , molecular dynamics , physics , generalized coordinates , euler angles , cluster (spacecraft) , bipolar coordinates , curvilinear coordinates , coordinate system , chemistry , quantum mechanics , mathematics , geometry , computer science , hydrogen bond , politics , medicinal chemistry , political science , law , programming language
We discuss systems of orthogonal coordinates for the dynamical treatment of four particles, generated by making extensive use of the concept of kinematic rotations, which act on coordinates of the particles and are represented by matrices only dependent on their masses. The explicit representations of the kinetic rotation matrices are given: this allows us to define alternative particle schemes, such as those based on the Jacobi and Radau‐Smith vectors, as well as on mixed types of vectors, of possible interest for specific molecules or aggregates. A list is given of relevant formulas connecting these coordinate sets to the geometrical parameters (internuclear distances, bond and dihedral angles) of use for the representation of the potential energy surface of four atomic systems. Applications are indicated for molecular and cluster physics. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007