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| [[File:Effective Nuclear Charge.svg|thumb|Effective Nuclear Charge Diagram|400px|right|Effective Nuclear Charge Diagram]]
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| The '''effective nuclear charge''' (often symbolized as <math>Z_{\mbox{eff}}</math> or Z*) is the net positive charge or pull experienced by an [[electron]] in a multi-electron [[atom]] due to the protons in the nucleus. The term "effective" is used because the [[shielding effect]] of negatively charged electrons prevents higher orbital electrons from experiencing the full [[nuclear charge]] by 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 looking at the oxidation number of the atom.
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| ==Calculating the effective nuclear charge== | |
| In an atom with one electron, that electron experiences the full charge of the positive [[atomic nucleus|nucleus]]. In this case, the effective nuclear charge can be calculated from [[Coulomb's law]].
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| 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:
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| :<math>Z_{eff} = Z - S </math>
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| where
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| :''Z'' is the number of protons in the nucleus ([[atomic number]]), and
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| :''S'' is the average number of electrons between the nucleus and the electron in question (the number of nonvalence electrons).
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| ''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:
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| :<math>Z_{eff} = \frac{<r>_H}{<r>_Z} </math>
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| where
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| :''<r>''<sub>H</sub> is the mean radius of the orbital for hydrogen, and
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| :''<r>''<sub>Z</sub> is the mean radius of the orbital for an electron configuration with nuclear charge ''Z''.
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| Note: ''Z''<sub>eff</sub> is also often written ''Z''*.
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| ==Example==
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| Consider a [[sodium]] [[cation]], a [[fluorine]] [[anion]], and a neutral [[neon]] atom. Each has 10 electrons, and the number of nonvalence electrons is 2 (10 total electrons - 8 valence) but the effective nuclear charge varies because each has a different atomic number:
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| :<math>Z_{eff}(F^-) = 9 - 2 = 7+</math> | |
| :<math>Z_{eff}(Ne) = 10 - 2 = 8+</math>
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| :<math>Z_{eff}(Na^+) = 11 - 2 = 9+</math>
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| So, the sodium cation has the largest effective nuclear charge, and thus the smallest [[atomic radius]].
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| ==Values==
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| Updated values of screening constants were provided by Clementi ''et al''.<ref>{{cite journal|last=Clementi|first=E.|coauthors=Raimondi, D. L.|title=Atomic Screening Constants from SCF Functions|journal=J. Chem. Phys|year=1963|volume=38|issue=11|pages=2686–2689|doi=10.1063/1.1733573|bibcode = 1963JChPh..38.2686C }}</ref><ref name="clem67">{{cite journal|last=Clementi|first=E.|coauthors=Raimondi, D. L.; Reinhardt, W. P.|title=Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons|journal=Journal of Chemical Physics|year=1967|volume=47|pages=1300–1307|doi=10.1063/1.1712084|bibcode = 1967JChPh..47.1300C }}</ref>
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| {| style="text-align: right; border: none;" cellpadding="2" cellspacing="0"
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| |+ Effective Nuclear Charges
| |
| |- style="background: #||31.628||32.380||33.155||33.883||34.634||35.386||36.124||36.859||37.595||38.331||39.067||39.803
| |
| |-
| |
| |2p||33.039||34.030||35.003||35.993||36.982||37.972||38.941||39.951||40.940||41.930||42.919||43.909||44.898||45.885||46.873||47.860||48.847||49.835
| |
| |-
| |
| |3s||21.843||22.664||23.552||24.362||25.172||25.982||26.792||27.601||28.439||29.221||30.031||30.841||31.631||32.420||33.209||33.998||34.787||35.576
| |
| |-
| |
| |3p||21.303||22.168||23.093||23.846||24.616||25.474||26.384||27.221||28.154||29.020||29.809||30.692||31.521||32.353||33.184||34.009||34.841||35.668
| |
| |-
| |
| |4s||12.388||13.444||14.264||14.902||15.283||16.096||17.198||17.656||18.582||18.986||19.865||20.869||21.761||22.658||23.544||24.408||25.297||26.173
| |
| |-
| |
| |3d||21.679||22.726||25.397||25.567||26.247||27.228||28.353||29.359||30.405||31.451||32.540||33.607||34.678||35.742||36.800||37.839||38.901||39.947
| |
| |-
| |
| |4p||10.881||11.932||12.746||13.460||14.084||14.977||15.811||16.435||17.140||17.723||18.562||19.411||20.369||21.265||22.181||23.122||24.030||24.957
| |
| |-
| |
| |5s||4.985||6.071||6.256||6.446||5.921||6.106||7.227||6.485||6.640||(empty)||6.756||8.192||9.512||10.629||11.617||12.538||13.404||14.218
| |
| |-
| |
| |4d|| || ||15.958||13.072||11.238||11.392||12.882||12.813||13.442||13.618||14.763||15.877||16.942||17.970||18.974||19.960||20.934||21.893
| |
| |-
| |
| |5p|| colspan="12" | ||8.470||9.102||9.995||10.809||11.612||12.425
| |
| |}
| |
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| ==See also==
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| *[[Slater's rules]]
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| *[[Slater-type orbitals]]
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| *[[Electronegativity]]
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| ==References==
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| <references />
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| ==Resources==
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| *Brown, Theodore; LeMay, H.E.; & Bursten, Bruce (2002). ''Chemistry: The Central Science'' (8th revised edition). Upper Saddle River, NJ 07458: Prentice-Hall. ISBN 0-13-061142-5.
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| [[Category:Chemical bonding]]
| |
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