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QUANTUM CHEMISTRY COMPUTATIONS IN MOMENTUM SPACE 145
With the above results, it is possible to write the expanded momentum space form of the
Hartree-Fock equations :
The equations to be fulfilled by momentum space orbitals contain convolution integrals
which give rise to momentum orbitals shifted in momentum space. The so-called
form factor F and the interaction terms Wij defined in terms of current momentum
coordinates are the momentum space counterparts of the core potentials and Coulomb
and/or exchange operators in position space. The nuclear field potential transfers a
momentum to electron i, while the interelectronic interaction produces a momentum
transfer between each pair of electrons in turn. Nevertheless, the total momentum of the
whole molecule remains invariant thanks to the contribution of the nuclear momenta [7].
2.2 ORBITAL AND TOTAL ENERGIES
The calculation of in momentum space is analogous to that in position space. Starting
with the r-representation, and expressing the quantity as the inverse Fourier
transform of one easily finds that:
The one-electron energy has the same expression in the p-representation as in the
position space where the different contributions can be expressed as follows :
Kinetic energy term. Its expression is straightforward to write :
