Helium atom overlap integral

Let us see what happens if we make similar calculations for the two helium atoms. In order to compare the future result with the H2 case, let us keep everything the same (the intemuclear distance R, the atomic orbitals, the overlap integral S, etc.), except that the number of electrons changes from two to four. This time, the calculation will be a little more tedious because four-electron wave functions are more complicated than two-electron functions. For instance, the function can be approximated as the product of the two Slater determinants-one for atom a, and the other for atom b ... 

R = 4 a.u. For this distance the overlap integral (see Appendix R, p. 1009) S = (l+R + - ) exp( —R) is 0.189. As we can see, the electron density has flown from the nuclei to the bond, (b) Two helium atoms. The only difference with respect to (a) is that two elections have been added. The visualization of p — pf ) reveals a compktely different pattern. This time the electron density has been removed from the bond region and increased in the region of the nuclei. 

The hypothetical molecule Hc2 would have a bond order of 0. In fact, the overlap integral in the denominator of the energy-level equations. Equations (7.22) and (7.23), means that the ungerade symmetry MO destabilizes this system slightly more than the stabilization gained by filling the l(Tg+ level. Accordingly, Hc2 is unstable with respect to isolated He atoms, and so helium is a monatomic gas. 

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