Wavefunctions derived from experiment. I. Motivation and theory

An experimental wavefunction is one that has an assumed form and that is also fitted to experimental measurements according to some well defined procedure. In this paper, the concept of extracting wavefunctions from experimental data is critically examined and past efforts are reviewed. In particular, the importance of scattering experiments for wavefunction fitting schemes is highlighted in relation to the more familiar model, the Hamiltonian paradigm. A general and systematically improvable method for fitting a wavefunction to experimental data is proposed. In this method, the parameters in a model wavefunction are determined according to the variational theorem but subject to an imposed constraint that an agreement statistic between the calculated and observed experimental data has a certain acceptable value. Advantages of the method include the fact that any amount of experimental data can be used in the fitting procedure irrespective of the number of parameters in the model wavefunction, the fact that a unique answer is obtained for a given choice of the model wavefunction, and the fact that the method can be used to model different experiments simultaneously. The wavefunction fitting method is illustrated by developing the theory for extracting a single-determinant wavefunction for a fragment of a molecular crystal, using data obtained from elastic X-ray scattering data. Effects due to thermal motion of the nuclei, secondary extinction of the X-ray scattering and different choices for the crystal fragment are treated.