CLOSED-FORM ANALYTICAL SOLUTIONS FOR THE CALCULATION OF THE MOMENTS OF THE MOLECULAR ELECTRON-DENSITY

Moments of the molecular electron density can be related directly to s everal experimental observables, but formerly they have only been accu rately calculated through methods which lack consistency with standard quantum chemical methods. Here we report analytical solutions to the basic molecular integrals required to compute the moments of the molec ular electron charge density over Gaussian basis functions. These are derived and cast into a practical closed form, suitable to interface w ith modem codes for the calculation of the molecular electronic struct ure. Illustrative calculations for the hydrogen molecule, at both the Hartree-Fock acid the full configuration interaction levels of theory, are shown and discussed in connection with observables linked directl y to some of the calculated moments.