title: General internal coordinate gradient vectors and the vibrational kinetic energy operator of centrally-connected penta-atomic systems. Part I.
abstract: New internal coordinate gradients, s-vectors, are derived using geometric algebra. The internal coordinates are based on a completely general description of the molecular geometry in terms of internal vectors. The internal coordinate gradients allow kinetic energy operators to be easily expressed in terms of orthogonal or non-orthogonal coordinate systems. Using this approach, a new exact vibrational kinetic energy operator for centrally-connected penta-atomic systems is derived for an internal polyspherical coordinate system based on orthogonal internal vectors. Difficulties associated with the well known coordinate redundancy in centrally-connected penta-atomic systems are discussed and overcome.
authors.affiliation: Chemistry Department, University of Aberdeen, Meston Walk, Aberdeen AB24 3UE, UK.
authors.forename: Steven A
authors.initials: SA
authors.lastname: Manson
authors.forename: Mark M
authors.initials: MM
authors.lastname: Law
mesh_terms: D003198:Computer Simulation; D007700:Kinetics; D008433:Mathematics; D008956:Models, Chemical; D011789:Quantum Theory; D014732:Vibration