TY - JOUR
T1 - Computation of Internal Coordinates, Derivatives, and Gradient Expressions
T2 - Torsion and Improper Torsion
AU - Tuzun, Robert E.
AU - Noid, Donald W.
AU - Sumpter, Bobby G.
PY - 2000/5
Y1 - 2000/5
N2 - Laplacians and gradient dot products are required for the recently developed internal coordinate quantum Monte Carlo method. New formulas are presented for these quantities for torsion and improper torsion angles. The Laplacians can also be used to economize calculation of sets of second derivatives used in molecular mechanics and other methods. Formulas for torsion angle gradient dot products and Laplacians, and completely new formulas for improper torsion, are presented. In addition, calculations of cos τ and sin τ, some suitable for energy subroutines and others for force subroutines, are shown. Finally, in a related development, several sets of conditions for three atom linearity or four atom planarity involving internal coordinate derivatives are reported.
AB - Laplacians and gradient dot products are required for the recently developed internal coordinate quantum Monte Carlo method. New formulas are presented for these quantities for torsion and improper torsion angles. The Laplacians can also be used to economize calculation of sets of second derivatives used in molecular mechanics and other methods. Formulas for torsion angle gradient dot products and Laplacians, and completely new formulas for improper torsion, are presented. In addition, calculations of cos τ and sin τ, some suitable for energy subroutines and others for force subroutines, are shown. Finally, in a related development, several sets of conditions for three atom linearity or four atom planarity involving internal coordinate derivatives are reported.
KW - Gradient
KW - Internal coordinate quantum Monte Carlo
KW - Molecular dynamics
KW - Molecular mechanics
UR - http://www.scopus.com/inward/record.url?scp=0043230292&partnerID=8YFLogxK
U2 - 10.1002/(SICI)1096-987X(200005)21:7<553::AID-JCC4>3.0.CO;2-1
DO - 10.1002/(SICI)1096-987X(200005)21:7<553::AID-JCC4>3.0.CO;2-1
M3 - Article
AN - SCOPUS:0043230292
SN - 0192-8651
VL - 21
SP - 553
EP - 561
JO - Journal of Computational Chemistry
JF - Journal of Computational Chemistry
IS - 7
ER -