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2014-09-04T06:24:37Z

References

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	~~{{Distinguish\|Slater–Condon rules}}~~		Friends contact her Claude Gulledge. Bookkeeping is what she does. To perform croquet is some thing that I've done for years. Delaware is our birth location.<br><br>my homepage - extended car warranty - [http://plus-Iq.com/profile-1669/info/ Read the Full Content],

	~~In [[quantum chemistry]], '''Slater's rules''' provide numerical values for the [[effective nuclear charge]] concept~~. ~~In a many-electron atom, each electron~~ is ~~said to experience less than the actual [[atomic nucleus\|nuclear charge]] owing to [[Shielding effect\|shielding]] or [[Electric field screening\|screening]] by the other electrons~~. ~~For each electron in an atom, Slater's rules provide a value for the screening constant, denoted by ''s'', ''S'', or ''σ'', which relates the effective and actual nuclear charges as~~

	~~:<math>Z_{\mathrm{eff}}= Z - s.\,</math>~~

	The rules were devised [[semi-empirical]]ly by [[John C. Slater]] and published in 1930.<ref name="slater57">{{cite journal\|last=Slater\|first=J. C.\|year=1930\|title=Atomic Shielding Constants\|url=http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/04/008.pdf\|journal=Phys. Rev.\|volume=36\|issue=1\|pages=57–64\|doi=10.1103/PhysRev.36.57\|bibcode=1930PhRv...36...57S}}</ref>

	Revised values of screening constants based on computations of atomic structure by the [[Hartree-Fock method]] were obtained by [[Enrico Clementi]] ''et al'' in the 1960s.<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\|issue=4\|bibcode=1967JChPh..47.1300C}}</ref>

	~~==Rules==~~

	Firstly,<ref name="slater57"/><ref>{{cite book\|last=Miessler\|first=Gary L.\|coauthors=Tarr, Donald A.\|title=Inorganic Chemistry\|publisher=Prentice Hall\|year=2003\|pages=38\|isbn=978-0-13-035471-6}}</ref> the electrons are arranged into a sequence of groups in order of increasing [[principal quantum number]] n, and for equal n in order of increasing [[azimuthal quantum number]] l, except that ~~s- and p- orbitals are kept together.~~
	~~:[1s] [2s,2p] [3s,3p] [3d] [4s,4p] [4d] [4f] [5s, 5p] [5d] etc.~~
	~~Each group is given a different shielding constant which depends upon the number and types of electrons in those groups preceding it.~~

	~~The shielding constant for each group is formed as the ''sum'' of the following contributions:~~

	~~#An amount of 0.35 from each ''other'' electron within the~~ '~~'same'' group except~~ for ~~the [1s] group, where the other electron contributes only 0~~.~~30.~~
	~~#If the group~~ is ~~of the [s p] type, an amount of 0.85 from each electron with principal quantum number (n) one less and an amount of 1.00 for each electron with an even smaller principal quantum number~~
	#If the group is of the [d] or [f], type, an amount of 1.00 for each electron inside it. This includes i) electrons with a smaller principal quantum number and ii) electrons with an equal principal quantum number and a smaller [[azimuthal quantum number]] (''l'')

	~~In tabular form, the rules are summarized as:~~

	~~{\| class="wikitable"~~
	\|-
	~~! Group~~
	~~! Other electrons in the same group~~
	~~! Electrons in group(s) with [[principal quantum number]] n and [[azimuthal quantum number]] < ''l''~~
	~~! Electrons in group(s) with [[principal quantum number]] n-1~~
	~~! Electrons in all group(s) with [[principal quantum number]] < n-1~~
	\|-
	~~\| [1s]~~
	~~\| 0.30~~
	~~\| N/A~~
	~~\| N/A~~
	~~\| N/A~~
	\|-
	~~\| [''n''s,''n''p]~~
	~~\| 0.35~~
	~~\| N/A~~
	~~\| 0.85~~
	~~\| 1~~
	\|-
	~~\| [''n''d] or [''n''f]~~
	~~\| 0.35~~
	~~\| 1~~
	~~\| 1~~
	~~\| 1~~
	\|-
	\|}

	~~==Example==~~

	An example provided in Slater's original paper is for the [[iron]] atom which has nuclear charge 26 and electronic configuration 1s<sup>2</sub>2s<sup>2</sub>2p<sup>6</sub>3s<sup>2</sub>3p<sup>6</sub>3d<sup>6</sub>4s<sup>2</sub>. ~~The screening constant, and subsequently the shielded (or effective) nuclear charge for each electron is deduced as:~~<~~ref name="slater57"/~~>

	:<~~math~~>
	~~\begin{matrix}~~
	~~4s &: 0.35 \times 1& + &0.85 \times 14 &+& 1.00 \times 10 &=& 22.25 &\Rightarrow& Z_{\mathrm{eff}}(4s)=3.75\\~~
	~~3d &: 0.35 \times 5& & &+& 1.00 \times 18 &=& 19.75 &\Rightarrow& Z_{\mathrm{eff}}(3d)=6.25\\~~
	~~3s,3p &: 0.35 \times 7& + &0.85 \times 8 &+& 1.00 \times 2 &=& 11.25 &\Rightarrow& Z_{\mathrm{eff}}(3s,3p)=14.75\\~~
	~~2s,2p &: 0.35 \times 7& + &0.85 \times 2 & & &=& 4.15 &\Rightarrow& Z_{\mathrm{eff}}(2s,2p)=21.85\\~~
	~~1s &: 0.30 \times 1& & & & &=& 0.30 &\Rightarrow& Z_{\mathrm{eff}}(1s)=25.7~~
	~~\end{matrix}~~
	~~</math>~~
	~~Note that the effective nuclear charge is calculated by subtracting the screening constant from the corresponding atomic number.~~

	~~==Motivation==~~

	The rules were developed by John C. Slater in an attempt to construct simple analytic expressions for the [[atomic orbital]] of any electron in an atom. Specifically, for each electron in an atom, Slater wished to determine shielding constants (''s'') and "effective" quantum numbers (''n''*) such that

	~~:<math>\psi_{n^{}s}(r) = r^{n^{}~~-~~1}\exp\left(~~-~~\frac{(Z-s)r}{n^{*}}\right)</math>~~

	provides a reasonable approximation to a single-electron wave function. Slater defined ''n''* by the rule that for n = 1, 2, 3, 4, 5, 6 respectively; ''n''* = 1, 2, 3, 3.7, 4.0 and 4.2. This was an arbitrary adjustment to fit calculated atomic energies to experimental data.

	~~Such a form was inspired by the known wave function spectrum of~~ [~~[hydrogen-like atom]]s which have the radial component~~

	:~~<math>R_{nl}(r) = r^{l}f_{nl}(r)\exp\left(-\frac{Zr}{n}\right),<~~/~~math>~~

	~~where ''n'' is the (true) [[principal quantum number]], ''l'' the [[azimuthal quantum number]], and ''f''<sub>''nl''<~~/~~sub>(''r'') is an oscillatory polynomial with ''n'' - ''l'' ~~-~~ 1 nodes~~.<ref>{{cite book\|last=Robinett\|first=Richard W.\|title=Quantum Mechanics Classical Results, Modern Systems, and Visualized Examples\|publisher=Oxford University Press\|location=New York\|year=2006\|pages=503\|isbn=978-0-13-120198-9}}</ref> Slater argued on the basis of previous calculations by [[Clarence Zener]]<ref>{{cite journal\|last=Zener\|first=Clarence\|year=1930\|title=Analytic Atomic Wave Functions\|journal=Phys. Rev.
	~~\|volume=36\|issue=1\|pages=51–56\|doi=10.1103~~/~~PhysRev.36.51\|bibcode = 1930PhRv...36...51Z }}<~~/~~ref> that~~ the presence of radial nodes was not required to obtain a reasonable approximation. He also noted that in the asymptotic limit (far away from the nucleus), his approximate form coincides with the exact hydrogen-like wave function in the presence of a nuclear charge of ''Z''-''s'' and in the state with a principal quantum number n equal to his effective quantum number ''n''*.

	~~Slater then argued, again based on the work of Zener, that the total energy of a ''N''-electron atom with a wavefunction constructed from orbitals of his form should be well approximated as~~

	~~:<math>E = -\sum_{i=1}^{N}\left(\frac{Z-s_{i}}{n^{*}_{i}}\right)^{2}.</math>~~

	Using this expression for the total energy of an atom (or ion) as a function of the shielding constants and effective quantum numbers, Slater was able to compose rules such that spectral energies calculated agree reasonably well with experimental values for a wide range of atoms. Using the values in the iron example above, the total energy of a neutral iron atom using this method is -2497.2 [[Rydberg constant\|Ry]], while the energy of an iron cation lacking a single 1s electron is -1964.6 Ry. The difference, 532.6 Ry, can be compared to the experimental (circa 1930) [[K-edge\|K absorption limit]] of 524.0 Ry.<ref name="slater57"/>

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Atomic physics]]~~
	~~[[Category:Chemical bonding]]~~
	~~[[Category:Quantum chemistry]]~~

en>KLBot2: Bot: Migrating 1 interwiki links, now provided by Wikidata on :d:Q1049381

2013-04-25T05:44:57Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:Q1049381

← Older revision		Revision as of 07:44, 25 April 2013
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	~~Hi there~~. My name is ~~Sophia Meagher even though~~ it is ~~not~~ the ~~title on my beginning certificate~~. ~~Invoicing~~ is ~~what I do~~. ~~Kentucky~~ is ~~exactly where I~~'~~ve always been living~~. ~~To play lacross~~ is ~~something I truly enjoy performing~~.<br><br>~~Also visit my blog post~~; ~~certified psychics~~ ([~~http:~~//~~www~~.~~aseandate~~.~~com~~/~~index~~.~~php?m~~=~~member_profile&p~~=~~profile&id~~=~~13352970 navigate~~ to this ~~web~~-~~site~~])		{{Distinguish\|Slater–Condon rules}}

			In [[quantum chemistry]], '''Slater's rules''' provide numerical values for the [[effective nuclear charge]] concept. In a many-electron atom, each electron is said to experience less than the actual [[atomic nucleus\|nuclear charge]] owing to [[Shielding effect\|shielding]] or [[Electric field screening\|screening]] by the other electrons. For each electron in an atom, Slater's rules provide a value for the screening constant, denoted by ''s'', ''S'', or ''σ'', which relates the effective and actual nuclear charges as

			:<math>Z_{\mathrm{eff}}= Z - s.\,</math>

			The rules were devised [[semi-empirical]]ly by [[John C. Slater]] and published in 1930.<ref name="slater57">{{cite journal\|last=Slater\|first=J. C.\|year=1930\|title=Atomic Shielding Constants\|url=http://astrophysics.fic.uni.lodz.pl/100yrs/pdf/04/008.pdf\|journal=Phys. Rev.\|volume=36\|issue=1\|pages=57–64\|doi=10.1103/PhysRev.36.57\|bibcode=1930PhRv...36...57S}}</ref>

			Revised values of screening constants based on computations of atomic structure by the [[Hartree-Fock method]] were obtained by [[Enrico Clementi]] ''et al'' in the 1960s.<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\|issue=4\|bibcode=1967JChPh..47.1300C}}</ref>

			==Rules==

			Firstly,<ref name="slater57"/><ref>{{cite book\|last=Miessler\|first=Gary L.\|coauthors=Tarr, Donald A.\|title=Inorganic Chemistry\|publisher=Prentice Hall\|year=2003\|pages=38\|isbn=978-0-13-035471-6}}</ref> the electrons are arranged into a sequence of groups in order of increasing [[principal quantum number]] n, and for equal n in order of increasing [[azimuthal quantum number]] l, except that s- and p- orbitals are kept together.
			:[1s] [2s,2p] [3s,3p] [3d] [4s,4p] [4d] [4f] [5s, 5p] [5d] etc.
			Each group is given a different shielding constant which depends upon the number and types of electrons in those groups preceding it.

			The shielding constant for each group is formed as the ''sum'' of the following contributions:

			#An amount of 0.35 from each ''other'' electron within the ''same'' group except for the [1s] group, where the other electron contributes only 0.30.
			#If the group is of the [s p] type, an amount of 0.85 from each electron with principal quantum number (n) one less and an amount of 1.00 for each electron with an even smaller principal quantum number
			#If the group is of the [d] or [f], type, an amount of 1.00 for each electron inside it. This includes i) electrons with a smaller principal quantum number and ii) electrons with an equal principal quantum number and a smaller [[azimuthal quantum number]] (''l'')

			In tabular form, the rules are summarized as:

			{\| class="wikitable"
			\|-
			! Group
			! Other electrons in the same group
			! Electrons in group(s) with [[principal quantum number]] n and [[azimuthal quantum number]] < ''l''
			! Electrons in group(s) with [[principal quantum number]] n-1
			! Electrons in all group(s) with [[principal quantum number]] < n-1
			\|-
			\| [1s]
			\| 0.30
			\| N/A
			\| N/A
			\| N/A
			\|-
			\| [''n''s,''n''p]
			\| 0.35
			\| N/A
			\| 0.85
			\| 1
			\|-
			\| [''n''d] or [''n''f]
			\| 0.35
			\| 1
			\| 1
			\| 1
			\|-
			\|}

			==Example==

			An example provided in Slater's original paper is for the [[iron]] atom which has nuclear charge 26 and electronic configuration 1s<sup>2</sub>2s<sup>2</sub>2p<sup>6</sub>3s<sup>2</sub>3p<sup>6</sub>3d<sup>6</sub>4s<sup>2</sub>. The screening constant, and subsequently the shielded (or effective) nuclear charge for each electron is deduced as:<ref name="slater57"/>

			:<math>
			\begin{matrix}
			4s &: 0.35 \times 1& + &0.85 \times 14 &+& 1.00 \times 10 &=& 22.25 &\Rightarrow& Z_{\mathrm{eff}}(4s)=3.75\\
			3d &: 0.35 \times 5& & &+& 1.00 \times 18 &=& 19.75 &\Rightarrow& Z_{\mathrm{eff}}(3d)=6.25\\
			3s,3p &: 0.35 \times 7& + &0.85 \times 8 &+& 1.00 \times 2 &=& 11.25 &\Rightarrow& Z_{\mathrm{eff}}(3s,3p)=14.75\\
			2s,2p &: 0.35 \times 7& + &0.85 \times 2 & & &=& 4.15 &\Rightarrow& Z_{\mathrm{eff}}(2s,2p)=21.85\\
			1s &: 0.30 \times 1& & & & &=& 0.30 &\Rightarrow& Z_{\mathrm{eff}}(1s)=25.7
			\end{matrix}
			</math>
			Note that the effective nuclear charge is calculated by subtracting the screening constant from the corresponding atomic number.

			==Motivation==

			The rules were developed by John C. Slater in an attempt to construct simple analytic expressions for the [[atomic orbital]] of any electron in an atom. Specifically, for each electron in an atom, Slater wished to determine shielding constants (''s'') and "effective" quantum numbers (''n''*) such that

			:<math>\psi_{n^{}s}(r) = r^{n^{}-1}\exp\left(-\frac{(Z-s)r}{n^{*}}\right)</math>

			provides a reasonable approximation to a single-electron wave function. Slater defined ''n''* by the rule that for n = 1, 2, 3, 4, 5, 6 respectively; ''n''* = 1, 2, 3, 3.7, 4.0 and 4.2. This was an arbitrary adjustment to fit calculated atomic energies to experimental data.

			Such a form was inspired by the known wave function spectrum of [[hydrogen-like atom]]s which have the radial component

			:<math>R_{nl}(r) = r^{l}f_{nl}(r)\exp\left(-\frac{Zr}{n}\right),</math>

			where ''n'' is the (true) [[principal quantum number]], ''l'' the [[azimuthal quantum number]], and ''f''<sub>''nl''</sub>(''r'') is an oscillatory polynomial with ''n'' - ''l'' - 1 nodes.<ref>{{cite book\|last=Robinett\|first=Richard W.\|title=Quantum Mechanics Classical Results, Modern Systems, and Visualized Examples\|publisher=Oxford University Press\|location=New York\|year=2006\|pages=503\|isbn=978-0-13-120198-9}}</ref> Slater argued on the basis of previous calculations by [[Clarence Zener]]<ref>{{cite journal\|last=Zener\|first=Clarence\|year=1930\|title=Analytic Atomic Wave Functions\|journal=Phys. Rev.
			\|volume=36\|issue=1\|pages=51–56\|doi=10.1103/PhysRev.36.51\|bibcode = 1930PhRv...36...51Z }}</ref> that the presence of radial nodes was not required to obtain a reasonable approximation. He also noted that in the asymptotic limit (far away from the nucleus), his approximate form coincides with the exact hydrogen-like wave function in the presence of a nuclear charge of ''Z''-''s'' and in the state with a principal quantum number n equal to his effective quantum number ''n''*.

			Slater then argued, again based on the work of Zener, that the total energy of a ''N''-electron atom with a wavefunction constructed from orbitals of his form should be well approximated as

			:<math>E = -\sum_{i=1}^{N}\left(\frac{Z-s_{i}}{n^{*}_{i}}\right)^{2}.</math>

			Using this expression for the total energy of an atom (or ion) as a function of the shielding constants and effective quantum numbers, Slater was able to compose rules such that spectral energies calculated agree reasonably well with experimental values for a wide range of atoms. Using the values in the iron example above, the total energy of a neutral iron atom using this method is -2497.2 [[Rydberg constant\|Ry]], while the energy of an iron cation lacking a single 1s electron is -1964.6 Ry. The difference, 532.6 Ry, can be compared to the experimental (circa 1930) [[K-edge\|K absorption limit]] of 524.0 Ry.<ref name="slater57"/>

			==References==
			{{reflist}}

			[[Category:Atomic physics]]
			[[Category:Chemical bonding]]
			[[Category:Quantum chemistry]]

en>Jan Krieg at 15:07, 23 July 2012

2012-07-23T15:07:39Z

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Hi there. My name is Sophia Meagher even though it is not the title on my beginning certificate. Invoicing is what I do. Kentucky is exactly where I've always been living. To play lacross is something I truly enjoy performing.<br><br>Also visit my blog post; certified psychics ([http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 navigate to this web-site])