General internal coordinate gradient vectors and the vibrational kinetic energy operator of centrally-connected penta-atomic systems. Part I.
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.
Manson
Steven A
SA
Chemistry Department, University of Aberdeen, Meston Walk, Aberdeen AB24 3UE, UK.
Law
Mark M
MM
D003198:Computer Simulation; D007700:Kinetics; D008433:Mathematics; D008956:Models, Chemical; D011789:Quantum Theory; D014732:Vibration