interactions among the electrons of an atom, an effective nuclear charge Zer can be used in place of z in the hydrogenic vnlm and En. formulas of the Background Material to generate approximate atomic orbitals to be filled by electrons in a many-electron atom For example, in the crudest approximation of a carbon atom, the two ls electrons experience the full nuclear attraction so Zeff=6 for them, whereas the 2s and 2p electrons are screened by the two ls electrons, so Zer= 4 for them. Within this approximation, one then occupies two ls orbitals with Z=6, two 2s orbitals with Z-4 and two 2p orbitals with Z=4 in forming the full six-electron product wave function of the lowest-energy state of carbon ,2,…,6)=v1so(1)v1s(2)v20(3)…v1pof阝 However, such approximate orbitals are not sufficiently accurate to be of use in quantitative simulations of atomic and molecular structure. In particular, their energies do not properly follow the trends in atomic orbital(AO)energies that are taught in introductory chemistry classes and that are shown pictorially in Fig 6.13 interactions among the electrons of an atom, an effective nuclear charge Zeff can be used in place of Z in the hydrogenic yn,l,m and En,l formulas of the Background Material to generate approximate atomic orbitals to be filled by electrons in a many-electron atom. For example, in the crudest approximation of a carbon atom, the two 1s electrons experience the full nuclear attraction so Zeff =6 for them, whereas the 2s and 2p electrons are screened by the two 1s electrons, so Zeff = 4 for them. Within this approximation, one then occupies two 1s orbitals with Z=6, two 2s orbitals with Z=4 and two 2p orbitals with Z=4 in forming the full six-electron product wave function of the lowest-energy state of carbon Y(1, 2, …, 6) = y1s a(1) y1sba(2) y2s a(3) … y1p(0) b(6). However, such approximate orbitals are not sufficiently accurate to be of use in quantitative simulations of atomic and molecular structure. In particular, their energies do not properly follow the trends in atomic orbital (AO) energies that are taught in introductory chemistry classes and that are shown pictorially in Fig. 6.1