The generation and use of delocalized internal coordinates in geometry optimization

1996 ◽  
Vol 105 (1) ◽  
pp. 192-212 ◽  
Author(s):  
Jon Baker ◽  
Alain Kessi ◽  
Bernard Delley
Keyword(s):  
Geometry Optimization ◽  
Internal Coordinates

Geometry optimization in redundant internal coordinates

1992 ◽  
Vol 96 (4) ◽  
pp. 2856-2860 ◽  
Author(s):  
P. Pulay ◽  
G. Fogarasi
Keyword(s):  
Geometry Optimization ◽  
Internal Coordinates

Geometry optimization of solids using delocalized internal coordinates

2001 ◽  
Vol 335 (3-4) ◽  
pp. 321-326 ◽  
Author(s):  
Jan Andzelm ◽  
R.D. King-Smith ◽  
George Fitzgerald
Keyword(s):  
Geometry Optimization ◽  
Internal Coordinates

Geometry optimization of periodic systems using internal coordinates

2005 ◽  
Vol 122 (12) ◽  
pp. 124508 ◽  
Author(s):  
Tomáš Bučko ◽  
Jürgen Hafner ◽  
János G. Ángyán
Keyword(s):  
Geometry Optimization ◽  
Periodic Systems ◽  
Internal Coordinates

scholarly journals Geometry Optimization Speedup Through a Geodesic Approach to Internal Coordinates

2021 ◽  
Author(s):  
Eric Hermes ◽  
Khachik Sargsyan ◽  
Habib Najm ◽  
Judit Zádor
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Displacement Vector ◽  
Geometry Optimization ◽  
Molecular Geometry ◽  
Internal Coordinates ◽  
Derivatives Of

We present a new geodesic-based method for geometry optimization in a basis of redundant internal coordinates. Our method updates the molecular geometry by following the geodesic generated by a displacement vector on the internal coordinate manifold, which dramatically reduces the number of steps required to reach convergence. Our method can be implemented in any existing optimization code, requiring only implementation of derivatives of the Wilson B-matrix and the ability to solve an ordinary differential equation.

scholarly journals Geometry Optimization Speedup Through a Geodesic Approach to Internal Coordinate Optimization

2021 ◽  
Author(s):  
Eric Hermes ◽  
Khachik Sargsyan ◽  
Habib Najm ◽  
Judit Zádor
Keyword(s):  
Molecular Structure ◽  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Newton Method ◽  
Displacement Vector ◽  
Geometry Optimization ◽  
Internal Coordinates ◽  
Derivatives Of ◽  
Method Approach

We present a new geodesic-based method for geometry optimization in a basis of redundant internal coordinates.<br>This method realizes displacements along internal coordinates by following the geodesic generated by the displacement vector on the internal coordinate manifold.<br>Compared to the traditional Newton method approach to taking displacements in internal coordinates, this geodesic approach substantially reduces the number of steps required to reach convergence on a molecular structure minimization benchmark.<br>This new geodesic method can in principle be implemented in any existing optimization code, and only requires the implementation of derivatives of the Wilson B-matrix and the ability to solve a relatively inexpensive ordinary differential equation.

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