Subject: QUESTIONS:ELECTRON CORRELATION

From: "E. Lewars" <[email-masked]>
Date: Tue, 7 Jul 1998 11:42:07 -0400 (EDT)

Tues, 1998 July 7

            SOME QUESTIONS ABOUT ELECTRON CORRELATION AND THE
            HARTREE-FOCK METHOD

Hello,

The HF method (HFM), even at the basis set limit, gives an energy which is
higher than the exact expectation value of the Hamiltonian, the energy
difference being the correlation energy.  The higher value of the HF energy is
said to be due to overestimation of *potential* energy  ("the HF method always
underestimates the kinetic energies of the electrons"--Pilar, 2nd ed, p 286),
specifically electron-electron repulsion.  The HFM is also said to
underestimate the coulomb hole ("the coulomb hole is neglected almost
completely" -- Pilar, p 296/297) and to overestimate the fermi hole (Pilar 296).

  So the HFM gives an energy that is too high, because it overestimates el-el
potential E ; as far as *kinetic* energy goes, the HFM would give an energy
that is too *low*.

QUESTIONS:

1)  Does anyone question any of the above statements?

2)  If the fermi hole is  overestimated, should this decrease el-el
repulsion, since the fermi hole means a region around each el. unfriendly to
other electrons of the same spin--if any two electrons avoid one another they
repel one another less;  in which case:

3)  Shouldn't the neglect of the *coulomb hole* be the real cause of the over-
estimation of el-el repulsion?  In other words, shold not most of the el-el
repulsion in the HFM be between electrons of *opposite* spin (electrons of the
same spin avoiding one another because of the Pauli effect (i.e. because of
the fermi hole)?

4)  Overestimation of the fermi hole is simply a result of using a one-
determinant wavefunction--right?

5)  Is there a way to see *intuitively* that the HFM must overestimate
electron-electron repulsion and underestimate electron kinetic energy?

   Thanks
    E. Lewars
========================