Effective nuclear charge

In an atom with one electron, that electron experiences the full charge of the positive nucleus. In this case, the effective nuclear charge can be calculated by Coulomb's law.

However, in an atom with many electrons, the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:

${\displaystyle Z_{\mathrm {eff} }=Z-S}$

where

Z is the number of protons in the nucleus (atomic number), and

S is the shielding constant.

S can be found by the systematic application of various rule sets, the simplest of which is known as "Slater's rules" (named after John C. Slater). Douglas Hartree defined the effective Z of a Hartree–Fock orbital to be:

${\displaystyle Z_{\mathrm {eff} }={\frac {\langle r\rangle _{\rm {H}}}{\langle r\rangle _{Z}}}}$

where

${\displaystyle \langle r\rangle _{\rm {H}}}$ is the mean radius of the orbital for hydrogen, and

${\displaystyle \langle r\rangle _{Z}}$ is the mean radius of the orbital for a proton configuration with nuclear charge Z.

Updated effective nuclear charge values were provided by Clementi et al. in 1963 and 1967.[1][2] In their work, screening constants were optimized to produce effective nuclear charge values that agree with SCF calculations. Though useful as a predictive model, the resulting screening constants contain little chemical insight as a qualitative model of atomic structure.

Nuclear charge is the electric charge of a nucleus of an atom, equal to the number of protons in the nucleus times the elementary charge. In contrast, the effective nuclear charge is the attractive positive charge of nuclear protons acting on valence electrons, which is always less than the total number of protons present in a nucleus due to the shielding effect[3]

• Atomic orbitals
• Core charge
• d-block contraction (or scandide contraction)
• Electronegativity
• Lanthanide contraction
• Shielding effect
• Slater-type orbitals
• Valence electrons
• Weak charge

• Brown, Theodore; LeMay, H.E.; & Bursten, Bruce (2002). Chemistry: The Central Science (8th revised edition). Upper Saddle River, New Jersey 07458: Prentice-Hall. ISBN 0-13-061142-5.