Internal coordinates and orthogonality: features of the pseudoinverse of the Eliashevich–Wilsonian B-matrix
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.
KeywordsInternal coordinates Reciprocal internal displacement coordinates Non-orthogonal B-matrix Pseudoinverse Sayvetz conditions GDIIS
Unable to display preview. Download preview PDF.