Physical Chemistry 2, Part 25: Slater's Rules, and Trial Wavefunctions

In multi-electron atoms, electrons experience an effective nuclear charge (Z*) that is less than the actual nuclear charge due to electron shielding, which can be calculated using Slater's rules: electrons in the same group shield 0.35 units, electrons in the previous principal quantum number shield 0.85 units for s/p orbitals, and electrons two or more levels below shield 1 unit; for d/f orbitals, all electrons to the left shield 1 unit. This explains why trial wavefunction calculations for helium predict a nuclear charge of 27/16 (~1.69) rather than the actual atomic number 2, as the effective nuclear charge felt by electrons is reduced by shielding. Common trial wavefunctions include products of hydrogen wavefunctions (most accurate but slow), sums of Gaussian curves (fastest but least accurate), and Slater-type orbitals (intermediate accuracy/speed).