Electron density nonlinear transformations

Nonlinear Transformations of Fuzzy Electron Density Fragments... 

Based on these vectors, a simple, nonlinear transformation is defined that places all the n nuclei to the required locations and also transforms the electronic density so that it follows the nuclear distortion. The transformation for the electron density is not unique and is coordinate-dependent for most dimensions, however, the coordinate dependence is small if the distortion of the nuclear arrangement is small. The transformation based on this approach is expected to provide the best results if the dimension of vectors a( ) is 3 (equivalent to the case of linear homotopy for four nuclei, discussed in section 4.5), or 9 (ten nuclei), or 19 (20 nuclei), and in general, for cases where all coordinate products up to a given overall degree are included as components of the vectors a( ). 

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