On the application of complete orthonormal atomic basis sets to x-rays diffracted by a thermally excited molecule

The application of a formalism developed for an orthonormal basis set molecular orbital theory enables a separation of the electron density into unique one-center terms. This separation permits easy incorporation of thermal motion into the molecular X-ray scattering factor and allows comparison of theoretical and experimental electron and charge densities. If theoretical basis functions are employed, the number of parameters needed to characterize the electron density is shown to be equal to the number of basis functions.