Hartree-fock-roothaan theory of electron momentum distiributions, compton profiles and the expectation values of momentums of molecules and some applications

Hartree-Fock-Roothaan Theory of Electron Momentum Distiributions, Compton Profiles and the Expectation Values of Momentums of Molecules and Some Applications Electron momentum distributions, Compton profiles and expectation values of momentums used extensively in the investigation of the electronic structure of atoms, molecules and crystals. Shifted Compton line due to Doppler effect is called as Compton profile. In other words; Compton profile is the projection of electron momentum on the scattering vector. It is quite time consuming and expensive to get atomic or molecular electron momentum distributions and Compton profiles experimentally for all energy values. Therefore, it is quite important to calculate electron momentum distributions, Compton profiles and expectation values of momentums theoretically. Electron momentum distributions, Compton profiles and expectation values of momentums for atoms are studied in literature frequently and there is not deficiency in their theory. However, the studies in literature about these properties of molecules are especially applications studies on some special molecules or numeric calculations. That is, there are not full theoretical, general and analytical studies about the calculation electron momentum distributions, Compton profiles and expectation values of momentums for molecules. In the first stage of this work, general and analytical expressions of electron momentum distributions, Compton profiles and expectation values of momentums for molecules have been derived by using Hartree-Fock-Roothaan method and computer programs for these expressions have been constructed in Maple-16 symbolic programming language. In the second section of this study, using obtained expressions for electron momentum distributions, Compton profiles and expectation values of momentums, related properties of molecules H2+, H2, HeH+, LiH, Li2, HF, F2, H2O and CH4 have been calculated, and the availability of the proposed theory and the constructed computer programs have been investigated by comparing the obtained results with the available literature values.