Can correlation bring electrons closer together?

Abstract

We discuss the exact Coulomb hole for the ground state of the helium atom and helium-like ions. We find that the correlated wavefunction yields a smaller probability of finding the electrons at large separations than does the Hartree-Fock wavefunction, leading to the counterintuitive conclusion that correlation brings distant electrons closer together. This effect becomes less pronounced as the nuclear charge increases.

Hooke’s law correlation in two-electron systems

“…Contrary to the Coulomb correlation [41,49], in the Moshinsky atom the correlation increases the likelihood of finding the two electrons close together and decreases the probability of larger values of u. It implies that the Hooke hole is positive for small u and negative for larger u.…”

Distribution of r12· p12in quantum systems

“…The depth of ∆X(x) decreases as Z increases but the depth of ∆P (u) is almost constant as it is squeezed toward the origin. ∆P (u) exhibits a secondary hole, discussed in detail by Pearson et al [18], but this subtle correlation effect is not visitble in ∆X(x).…”

“…In (2), u = r 1 − r 2 , u = |u| ≡ r 12 and Ω u is the angular part of u. P (u) gives the probability density for finding two particles separated by a distance u and has been widely studied [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Anisotropic intracule densities and electron correlation in H2: A quantum Monte Carlo study

“…The existence of a similar long-range Coulomb hole in the ground-state He atom has recently been confirmed. 25 The The anisotropic Coulomb hole shows a large reduction in the probability density for finding electrons close together in both the z and directions. The hole extends almost to the value of the bond length in the z-direction and even further in the -direction.…”