Craig Interpolation in the Presence of Non-linear Constraints

2011 ◽  
pp. 240-255 ◽  
Author(s):  
Stefan Kupferschmid ◽  
Bernd Becker
Keyword(s):  
Linear Constraints ◽  
Craig Interpolation ◽  
Non Linear

scholarly journals Automated handling of complex chemical structures in Z-matrix coordinates - the chemcoord library

2021 ◽  
Author(s):  
Oskar Weser ◽  
Björn Hein Hanke ◽  
Ricardo Mata
Keyword(s):  
Structural Changes ◽  
Molecular System ◽  
Linear Constraints ◽  
Analytical Geometry ◽  
Cartesian Coordinates ◽  
Chemical Structures ◽  
Automated Method ◽  
Non Linear ◽  
Linearly Constrained ◽  
Automated Handling

In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimisations with non-linear constraints. Analytical gradients for the transformation between the coordinate systems were derived for the first time, which allows analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimisation was coupled with a Symbolic Algebra package to support arbitrary non-linear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. Sample applications are provided for a number of common chemical reactions and illustrative examples where these new algorithms can be used to automatically produce chemically reasonable structure interpolations, or to perform non-linearly constrained optimisations of molecules.

Algorithms for non-linear constraints

2009 ◽  
pp. 723-747
Author(s):  
Ross Baldick
Keyword(s):  
Linear Constraints ◽  
Non Linear

scholarly journals Optimization under non-linear constraints

1983 ◽  
Vol 11 (4) ◽  
pp. 343-346
Author(s):  
Leif Jansson ◽  
Erik Mellander
Keyword(s):  
Linear Constraints ◽  
Non Linear

On classical mechanical systems with non-linear constraints

2004 ◽  
Vol 49 (3-4) ◽  
pp. 385-417 ◽  
Author(s):  
Gláucio Terra ◽  
Marcelo H. Kobayashi
Keyword(s):  
Mechanical Systems ◽  
Linear Constraints ◽  
Non Linear
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