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Internal coordinates and orthogonality: features of the pseudoinverse of the Eliashevich–Wilsonian B-matrix

  • F. Kalincsák
  • G. PongorEmail author
Chapter
Part of the Highlights in Theoretical Chemistry book series (HITC, volume 12)

Abstract

It is shown that the system of unit vectors corresponding to the internal coordinates is non-orthogonal generally. The deduction starts with the well-known orthonormality of unit vectors of the Cartesian coordinates. The crucial point of the GDIIS method is discussed regarding a “partially isomorphic” relationship between two vector spaces. Some features of the pseudoinverse of the Eliashevich–Wilsonian matrix B are deduced and discussed: these are analogous to the conditions formulated originally for the elements of the B-matrix.

Keywords

Internal coordinates Reciprocal internal displacement coordinates Non-orthogonal B-matrix Pseudoinverse Sayvetz conditions GDIIS 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Inorganic Chemistry, Institute of ChemistryEötvös Loránd UniversityBudapestHungary

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