Effective nuclear charge

Effective Nuclear Charge Diagram

The effective nuclear charge (often symbolized as or ) is the net positive charge experienced by an electron in a multi-electron atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons. The effective nuclear charge experienced by the outer shell electron is also called the core charge. It is possible to determine the strength of the nuclear charge by the oxidation number of the atom.

Calculation

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 from 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:

where

Z is the number of protons in the nucleus (atomic number), and
S is the average number of electrons between the nucleus and the electron in question (the number of non-valence electrons).

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:

where

is the mean radius of the orbital for hydrogen, and
is the mean radius of the orbital for an electron configuration with nuclear charge Z.

Values

Updated values of screening constants were provided by Clementi et al.[1][2]

Effective Nuclear Charges
  H   He
Z1   2
1s1.000   1.688
  LiBe   BCNOFNe
Z34   5678910
1s2.6913.685   4.6805.6736.6657.6588.6509.642
2s1.2791.912   2.5763.2173.8474.4925.1285.758
2p     2.4213.1363.8344.4535.1005.758
  NaMg   AlSiPSClAr
Z1112   131415161718
1s10.62611.609 12.59113.57514.55815.54116.52417.508
2s6.5717.392 8.2149.0209.82510.62911.43012.230
2p6.8027.826 8.9639.94510.96111.97712.99314.008
3s2.5073.308 4.1174.9035.6426.3677.0687.757
3p 4.0664.2854.8865.4826.1166.764
  KCaScTiVCrMnFeCoNiCuZnGaGeAsSeBrKr
Z192021222324252627282930313233343536
1s18.49019.47320.45721.44122.42623.41424.39625.38126.36727.35328.33929.32530.30931.29432.27833.26234.24735.232
2s13.00613.77614.57415.37716.18116.98417.79418.59919.40520.21321.02021.82822.59923.36524.12724.88825.64326.398
2p15.02716.04117.05518.06519.07320.07521.08422.08923.09224.09525.09726.09827.09128.08229.07430.06531.05626.047
3s8.6809.60210.34011.03311.70912.36813.01813.67614.32214.96115.59416.21916.99617.79018.59619.40320.21921.033
3p7.7268.6589.40610.10410.78511.46612.10912.77813.43514.08514.73115.36916.20417.01417.85018.70519.57120.434
4s3.4954.3984.6324.8174.9815.1335.2835.4345.5765.7115.8425.9657.0678.0448.9449.75810.55311.316
3d 7.1208.1418.9839.75710.52811.18011.85512.53013.20113.87815.09316.25117.37818.47719.55920.626
4p 6.2226.7807.4498.2879.0289.338
  RbSrYZrNbMoTcRuRhPdAgCdInSnSbTeIXe
Z373839404142434445464748495051525354
1s36.20837.19138.17639.15940.14241.12642.10943.09244.07645.05946.04247.02648.01048.99249.97450.95751.93952.922
2s27.15727.90228.62229.37430.12530.87731.62832.38033.15533.88334.63435.38636.12436.85937.59538.33139.06739.803
2p33.03934.03035.00335.99336.98237.97238.94139.95140.94041.93042.91943.90944.89845.88546.87347.86048.84749.835
3s21.84322.66423.55224.36225.17225.98226.79227.60128.43929.22130.03130.84131.63132.42033.20933.99834.78735.576
3p21.30322.16823.09323.84624.61625.47426.38427.22128.15429.02029.80930.69231.52132.35333.18434.00934.84135.668
4s12.38813.44414.26414.90215.28316.09617.19817.65618.58218.98619.86520.86921.76122.65823.54424.40825.29726.173
3d21.67922.72625.39725.56726.24727.22828.35329.35930.40531.45132.54033.60734.67835.74236.80037.83938.90139.947
4p10.88111.93212.74613.46014.08414.97715.81116.43517.14017.72318.56219.41120.36921.26522.18123.12224.03024.957
5s4.9856.0716.2566.4465.9216.1067.2276.4856.640(empty)6.7568.1929.51210.62911.61712.53813.40414.218
4d 15.95813.07211.23811.39212.88212.81313.44213.61814.76315.87716.94217.97018.97419.96020.93421.893
5p 8.4709.1029.99510.80911.61212.425

See also


References

  1. Clementi, E.; Raimondi, D. L. (1963). "Atomic Screening Constants from SCF Functions". J. Chem. Phys. 38 (11): 2686–2689. Bibcode:1963JChPh..38.2686C. doi:10.1063/1.1733573.
  2. Clementi, E.; Raimondi, D. L.; Reinhardt, W. P. (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". Journal of Chemical Physics. 47: 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.

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