An alternative to orthogonalisation of wavefunctions and calculation of X-ray spectral intensities

Simplifying assumptions made while considering complex systems often lead to non-orthogonal sets of wavefunctions. A procedure is suggested for employing such non-orthogonal wavefunctions without first orthogonalising them. The method involves the use of a basis reciprocal to the basis of the non-orthogonal functions. The relative intensities of K alpha 1, K beta 1 and K beta 2 X-ray spectral lines calculated by the proposed method are in fair agreement with available experimental data.