What is the maximum number of electrons that can be accommodated in a shell n 3 L 1 and M =- 1?

Principal energy levels in atomic physics

This article is about the orbits of electrons. For valence shell, see Valence electron.

"Atomic shell" redirects here. For the weapon, see Nuclear artillery.

In chemistry and atomic physics, an electron shell may be thought of as an orbit followed by electrons around an atom's nucleus. The closest shell to the nucleus is called the "1 shell" (also called the "K shell"), followed by the "2 shell" (or "L shell"), then the "3 shell" (or "M shell"), and so on farther and farther from the nucleus. The shells correspond to the principal quantum numbers (n = 1, 2, 3, 4 ...) or are labeled alphabetically with the letters used in X-ray notation (K, L, M, ...). A useful guide when understanding electron shells in atoms is to note that each row on the conventional periodic table of elements represents an electron shell.

Each shell can contain only a fixed number of electrons: the first shell can hold up to two electrons, the second shell can hold up to eight (2 + 6) electrons, the third shell can hold up to 18 (2 + 6 + 10) and so on. The general formula is that the nth shell can in principle hold up to 2(n2) electrons.[1] For an explanation of why electrons exist in these shells, see electron configuration.[2]

Each shell consists of one or more subshells, and each subshell consists of one or more atomic orbitals.

History

The 1913 Bohr model of the atom attempted an arrangement of electrons in their sequential orbits, however, at that time Bohr continued to increase the inner orbit of the atom to eight electrons as the atoms got larger. Bohr built his 1913 model of electrons in elements thus:[3]

"From the above we are led to the following possible scheme for the arrangement of the electrons in light atoms:

Periodic table of Bohr in 1913 showing electron configurations in his second paper where he went to the 24th element.[4][5]

The shell terminology comes from Arnold Sommerfeld's modification of the Bohr model. During this period Bohr was working with Walther Kossel, whose papers in 1914 and in 1916 called the orbits "shells".[6][7] Sommerfeld retained Bohr's planetary model, but added mildly elliptical orbits (characterized by additional quantum numbers ℓ and m) to explain the fine spectroscopic structure of some elements.[8] The multiple electrons with the same principal quantum number (n) had close orbits that formed a "shell" of positive thickness instead of the circular orbit of Bohr's model which orbits called "rings" were described by a plane.[9]

The existence of electron shells was first observed experimentally in Charles Barkla's and Henry Moseley's X-ray absorption studies. Moseley's work did not directly concern the study of electron shells, because he was trying to prove that the periodic table was not arranged by weight, but by the charge of the protons in the nucleus.[10] However, because in a neutral atom, the number of electrons equals the number of protons, this work was extremely important to Niels Bohr who mentioned Moseley's work several times in his interview of 1962.[11] Moseley was part of Rutherford's group, as was Niels Bohr. Moseley measured the frequencies of X-rays emitted by every element between calcium and zinc, and found that the frequencies became greater as the elements got heavier, leading to the theory that electrons were emitting X-rays when they were shifted to lower shells.[12] This led to the conclusion that the electrons were in Kossel's shells with a definite limit per shell, labeling the shells with the letters K, L, M, N, O, P, and Q.[5][13] The origin of this terminology was alphabetic. Barkla, who worked independently from Moseley as an X-ray spectrometry experimentalist, first noticed two distinct types of scattering from shooting X-rays at elements in 1909 and named them "A" and "B". Barkla described these two types of X-ray diffraction: the first was unconnected with the type of material used in the experiment, and could be polarized. The other second diffraction beam he called "fluorescent" because it depended on the irradiated material.[14] It was not known what these lines meant at the time, but in 1911 Barkla decided there might be scattering lines previous to "A", so he began at "K".[15] However, later experiments indicated that the K absorption lines are produced by the innermost electrons. These letters were later found to correspond to the n values 1, 2, 3, etc. that were used in the Bohr model. They are used in the spectroscopic Siegbahn notation.

The work of assigning electrons to shells was continued from 1913 to 1925 by many chemists and a few physicists. Niels Bohr was one of the few physicists who followed the chemist's work[16] of defining the periodic table, while Arnold Sommerfeld worked more on trying to make a relativistic working model of the atom that would explain the fine structure of the spectra from a classical orbital physics standpoint through the Atombau approach.[5] Einstein and Rutherford, who did not follow chemistry, were unaware of the chemists who were developing electron shell theories of the periodic table from a chemistry point of view, such as Irving Langmuir, Charles Bury, J.J. Thomson, and Gilbert Lewis, who all introduced corrections to Bohr's model such as a maximum of two electrons in the first shell, eight in the next and so on, and were responsible for explaining valency in the outer electron shells, and the building up of atoms by adding electrons to the outer shells.[17][5] So when Bohr outlined his electron shell atomic theory in 1922, there was no mathematical formula for the theory. So Rutherford said he was hard put "to form an idea of how you arrive at your conclusions".[18][19] Einstein said of Bohr's 1922 paper that his "electron-shells of the atoms together with their significance for chemistry appeared to me like a miracle – and appears to me as a miracle even today".[20] Arnold Sommerfeld, who had followed the Atombau structure of electrons instead of Bohr who was familiar with the chemists' views of electron structure, spoke of Bohr's 1921 lecture and 1922 article on the shell model as "the greatest advance in atomic structure since 1913".[5][21][18] However, the electron shell development of Niels Bohr was basically the same theory as that of the chemist Charles Rugeley Bury in his 1921 paper.[22][5][23]

As work continued on the electron shell structure of the Sommerfeld-Bohr Model, Sommerfeld had introduced three "quantum numbers n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing."[24] Because we use k for the Boltzmann constant, the azimuthal quantum number was changed to ℓ. When the modern quantum mechanics theory was put forward based on Heisenberg's matrix mechanics and Schrödinger's wave equation, these quantum numbers were kept in the current quantum theory but were changed to n being the principal quantum number, and m being the magnetic quantum number.

However, the final form of the electron shell model still in use today for the number of electrons in shells was discovered in 1923 by Edmund Stoner, who introduced the principle that the nth shell was described by 2(n2). Seeing this in 1925, Wolfgang Pauli added a fourth quantum number, "spin", during the old quantum theory period of the Sommerfeld-Bohr Solar System atom to complete the modern electron shell theory.[5]

Subshells

Each shell is composed of one or more subshells, which are themselves composed of atomic orbitals. For example, the first (K) shell has one subshell, called 1s; the second (L) shell has two subshells, called 2s and 2p; the third shell has 3s, 3p, and 3d; the fourth shell has 4s, 4p, 4d and 4f; the fifth shell has 5s, 5p, 5d, and 5f and can theoretically hold more in the 5g subshell that is not occupied in the ground-state electron configuration of any known element.[2] The various possible subshells are shown in the following table:

• The first column is the "subshell label", a lowercase-letter label for the type of subshell. For example, the "4s subshell" is a subshell of the fourth (N) shell, with the type (s) described in the first row.
• The second column is the azimuthal quantum number (ℓ) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.
• The third column is the maximum number of electrons that can be put into a subshell of that type. For example, the top row says that each s-type subshell (1s, 2s, etc.) can have at most two electrons in it. In each case the figure is 4 greater than the one above it.
• The fourth column says which shells have a subshell of that type. For example, looking at the top two rows, every shell has an s subshell, while only the second shell and higher have a p subshell (i.e., there is no "1p" subshell).
• The final column gives the historical origin of the labels s, p, d, and f. They come from early studies of atomic spectral lines. The other labels, namely g, h and i, are an alphabetic continuation following the last historically originated label of f.

Number of electrons in each shell

Each subshell is constrained to hold 4ℓ + 2 electrons at most, namely:

• Each s subshell holds at most 2 electrons
• Each p subshell holds at most 6 electrons
• Each d subshell holds at most 10 electrons
• Each f subshell holds at most 14 electrons
• Each g subshell holds at most 18 electrons

Therefore, the K shell, which contains only an s subshell, can hold up to 2 electrons; the L shell, which contains an s and a p, can hold up to 2 + 6 = 8 electrons, and so forth; in general, the nth shell can hold up to 2n2 electrons.[1]

Although that formula gives the maximum in principle, in fact that maximum is only achieved (in known elements) for the first four shells (K, L, M, N). No known element has more than 32 electrons in any one shell.[26][27] This is because the subshells are filled according to the Aufbau principle. The first elements to have more than 32 electrons in one shell would belong to the g-block of period 8 of the periodic table. These elements would have some electrons in their 5g subshell and thus have more than 32 electrons in the O shell (fifth principal shell).

Subshell energies and filling order

Further information: Aufbau principle

n + ℓ {\displaystyle n+\ell }

Although it is sometimes stated that all the electrons in a shell have the same energy, this is an approximation. However, the electrons in one subshell do have exactly the same level of energy, with later subshells having more energy per electron than earlier ones. This effect is great enough that the energy ranges associated with shells can overlap.

The filling of the shells and subshells with electrons proceeds from subshells of lower energy to subshells of higher energy. This follows the n + ℓ rule which is also commonly known as the Madelung rule. Subshells with a lower n + ℓ value are filled before those with higher n + ℓ values. In the case of equal n + ℓ values, the subshell with a lower n value is filled first.

Because of this, the later shells are filled over vast sections of the periodic table. The K shell fills in the first period (hydrogen and helium), while the L shell fills in the second (lithium to neon). However, the M shell starts filling at sodium (element 11) but does not finish filling till copper (element 29), and the N shell is even slower: it starts filling at potassium (element 19) but does not finish filling till ytterbium (element 70). The O, P, and Q shells begin filling in the known elements, but they are not complete even at the heaviest known element, oganesson (element 118).

List of elements with electrons per shell

The list below gives the elements arranged by increasing atomic number and shows the number of electrons per shell. At a glance, the subsets of the list show obvious patterns. In particular, every set of five elements (in   electric blue) before each noble gas (group 18, in   yellow) heavier than helium have successive numbers of electrons in the outermost shell, namely three to seven.

Sorting the table by chemical group shows additional patterns, especially with respect to the last two outermost shells. (Elements 57 to 71 belong to the lanthanides, while 89 to 103 are the actinides.)

The list below is primarily consistent with the Aufbau principle. However, there are a number of exceptions to the rule; for example palladium (atomic number 46) has no electrons in the fifth shell, unlike other atoms with lower atomic number. The elements past 108 have such short half-lives that their electron configurations have not yet been measured, and so predictions have been inserted instead.

See also

Wikimedia Commons has media related to Electron shell diagrams.

• Periodic table (electron configurations)
• Electron counting
• 18-electron rule
• Core charge

References

1. ^ a b Re: Why do electron shells have set limits ? madsci.org, 17 March 1999, Dan Berger, Faculty Chemistry/Science, Bluffton College
2. ^ a b Electron Subshells. Corrosion Source.
3. ^ See Wikipedia periodic table.
4. ^ Niels Bohr, "On the Constitution of Atoms and Molecules, Part II Systems containing only a Single Nucleus Philosophical Magazine 26:857--875 (1913)
5. ^ a b c d e f g Kragh, Helge. "Niels Bohr’s Second Atomic Theory". Historical Studies in the Physical Sciences, vol. 10, University of California Press, 1979, pp. 123–86, https://doi.org/10.2307/27757389.
6. ^ W. Kossel, "Über Molekülbildung als Folge des Atombaues", Ann. Phys., 1916, 49, 229-362 (237).
7. ^ Translated in Helge Kragh, Aarhus, LARS VEGARD, ATOMIC STRUCTURE, AND THE PERIODIC SYSTEM, Bull. Hist. Chem., VOLUME 37, Number 1 (2012), p.43.
8. ^ Donald Sadoway, Introduction to Solid State Chemistry, Lecture 5 Archived 29 June 2011 at the Wayback Machine
9. ^ Bohr, Niels (1913). On the Constitution of Atoms and Molecules, Part I. _Philosophical Magazine_ 26:1--25.
10. ^ Uhler, Horace Scudder. "On Moseley’s Law for X-Ray Spectra". Proceedings of the National Academy of Sciences of the United States of America, vol. 3, no. 2, National Academy of Sciences, 1917, pp. 88–90, http://www.jstor.org/stable/83748.
11. ^ Niels Bohr interview 1962 Session III https://www.aip.org/history-programs/niels-bohr-library/oral-histories/4517-3
12. ^ Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.4.
13. ^ Barkla, Charles G. (1911). "XXXIX.The spectra of the fluorescent Röntgen radiations". Philosophical Magazine. Series 6. 22 (129): 396–412. doi:10.1080/14786440908637137. Previously denoted by letters B and A (...). The letters K and L are, however, preferable, as it is highly probable that series of radiations both more absorbable and more penetrating exist.
14. ^ Michael Eckert, Disputed discovery: the beginnings of X-ray diffraction in crystals in 1912 and its repercussions, January 2011, Acta crystallographica. Section A, Foundations of crystallography 68(1):30-39 This Laue centennial article has also been published in Zeitschrift für Kristallographie [Eckert (2012). Z. Kristallogr. 227 , 27–35].
15. ^ Charles G. Barkla M.A. D.Sc. (1911) XXXIX. The spectra of the fluorescent Röntgen radiations, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 22:129, 396-412, DOI: 10.1080/14786440908637137
16. ^ T.Hirosigeand S.Nisio,"Formation of Bohr's Theory of Atomic Constitution",Jap. Stud.Hist.Set.,No. 3(1964),6-28.
17. ^ See Periodic Table for full history.
18. ^ a b Niels Bohr Collected Works, Vol. 4, p. 740. Postcard from Arnold Sommerfeld to Bohr, 7 March 1921.
19. ^ Pais, Abraham (1991), Niels Bohr’s Times, in Physics, Philosophy, and Polity (Oxford: Clarendon Press), quoted p. 205.
20. ^ Schilpp, Paul A. (ed.) (1969), Albert Einstein: Philosopher-Scientist (New York: MJF Books). Collection first published in 1949 as Vol. VII in the series The Library of Living Philosophers by Open Court, La Salle, IL, Einstein, Albert 'Autobiographical Notes', pp.45-47.
21. ^ Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.7.
22. ^ Bury, Charles R. (July 1921). "Langmuir's Theory of the Arrangement of Electrons in Atoms and Molecules". Journal of the American Chemical Society. 43 (7): 1602–1609. doi:10.1021/ja01440a023. ISSN 0002-7863.
23. ^ The Genesis of the Bohr Atom, John L. Heilbron and Thomas S. Kuhn, Historical Studies in the Physical Sciences, Vol. 1 (1969), pp. vi, 211-290 (81 pages), University of California Press,p. 285-286.
24. ^ Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.5.
25. ^ Jue, T. (2009). "Quantum Mechanic Basic to Biophysical Methods". Fundamental Concepts in Biophysics. Berlin: Springer. p. 33. ISBN 978-1-58829-973-4.
26. ^ Orbitals. Chem4Kids. Retrieved on 1 December 2011.
27. ^ Electron & Shell Configuration Archived 28 December 2018 at the Wayback Machine. Chemistry.patent-invent.com. Retrieved on 1 December 2011.

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Chemical property of transition metals

The 18-electron rule is a chemical rule of thumb used primarily for predicting and rationalizing formulas for stable transition metal complexes, especially organometallic compounds.[1] The rule is based on the fact that the valence orbitals in the electron configuration of transition metals consist of five (n−1)d orbitals, one ns orbital, and three np orbitals, where n is the principal quantum number. These orbitals can collectively accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it is said to have achieved the same electron configuration as the noble gas in the period. The rule is not helpful for complexes of metals that are not transition metals, and interesting or useful transition metal complexes will violate the rule because of the consequences deviating from the rule bears on reactivity. The rule was first proposed by American chemist Irving Langmuir in 1921.[1][2]

Applicability

The rule usefully predicts the formulas for low-spin complexes of the Cr, Mn, Fe, and Co triads. Well-known examples include ferrocene, iron pentacarbonyl, chromium carbonyl, and nickel carbonyl.

Ligands in a complex determine the applicability of the 18-electron rule. In general, complexes that obey the rule are composed at least partly of π-acceptor ligands (also known as π-acids). This kind of ligand exerts a very strong ligand field, which lowers the energies of the resultant molecular orbitals so that they are favorably occupied. Typical ligands include olefins, phosphines, and CO. Complexes of π-acids typically feature metal in a low-oxidation state. The relationship between oxidation state and the nature of the ligands is rationalized within the framework of π backbonding.

Consequences for reactivity

Compounds that obey the 18-electron rule are typically "exchange inert". Examples include [Co(NH3)6]Cl3, Mo(CO)6, and [Fe(CN)6]4−. In such cases, in general ligand exchange occurs via dissociative substitution mechanisms, wherein the rate of reaction is determined by the rate of dissociation of a ligand. On the other hand, 18-electron compounds can be highly reactive toward electrophiles such as protons, and such reactions are associative in mechanism, being acid-base reactions.

Complexes with fewer than 18 valence electrons tend to show enhanced reactivity. Thus, the 18-electron rule is often a recipe for non-reactivity in either a stoichiometric or a catalytic sense.

Duodectet rule

Computational findings suggest valence p-orbitals on the metal participate in metal-ligand bonding, albeit weakly.[3] However, Weinhold and Landis within the context of natural bond orbitals do not count the metal p-orbitals in metal-ligand bonding,[4] although these orbitals are still included as polarization functions. This results in a duodectet (12-electron) rule for five d-orbitals and one s-orbital only.

The current consensus in the general chemistry community is that unlike the singular octet rule for main group elements, transition metals do not strictly obey either the 12-electron or 18-electron rule, but that the rules describe the lower bound and upper bound of valence electron count respectively.[5][6] Thus, while transition metal d-orbital and s-orbital bonding readily occur, the involvement of the higher energy and more spatially diffuse p-orbitals in bonding depends on the central atom and coordination environment.[7][8]

Exceptions

π-donor or σ-donor ligands with small interactions with the metal orbitals lead to a weak ligand field which increases the energies of t2g orbitals. These molecular orbitals become non-bonding or weakly anti-bonding orbitals (small Δoct). Therefore, addition or removal of electron has little effect on complex stability. In this case, there is no restriction on the number of d-electrons and complexes with 12–22 electrons are possible. Small Δoct makes filling eg* possible (>18 e−) and π-donor ligands can make t2g antibonding (<18 e−). These types of ligand are located in the low-to-medium part of the spectrochemical series. For example: [TiF6]2− (Ti(IV), d0, 12 e−), [Co(NH3)6]3+ (Co(III), d6, 18 e−), [Cu(OH2)6]2+ (Cu(II), d9, 21 e−).

In terms of metal ions, Δoct increases down a group as well as with increasing oxidation number. Strong ligand fields lead to low-spin complexes which cause some exceptions to the 18-electron rule.

16-electron complexes

An important class of complexes that violate the 18e rule are the 16-electron complexes with metal d8 configurations. All high-spin d8 metal ions are octahedral (or tetrahedral), but the low-spin d8 metal ions are all square planar. Important examples of square-planar low-spin d8 metal Ions are Rh(I), Ir(I), Ni(II), Pd(II), and Pt(II). At picture below is shown the splitting of the d subshell in low-spin square-planar complexes. Examples are especially prevalent for derivatives of the cobalt and nickel triads. Such compounds are typically square-planar. The most famous example is Vaska's complex (IrCl(CO)(PPh3)2), [PtCl4]2−, and Zeise's salt [PtCl3(η2-C2H4)]−. In such complexes, the dz2 orbital is doubly occupied and nonbonding.

Many catalytic cycles operate via complexes that alternate between 18-electron and square-planar 16-electron configurations. Examples include Monsanto acetic acid synthesis, hydrogenations, hydroformylations, olefin isomerizations, and some alkene polymerizations.

Other violations can be classified according to the kinds of ligands on the metal center.

Bulky ligands

Bulky ligands can preclude the approach of the full complement of ligands that would allow the metal to achieve the 18 electron configuration. Examples:

• Ti(neopentyl)4 (8 e−)
• Cp*2Ti(C2H4) (16 e−)
• V(CO)6 (17 e−)
• Cp*Cr(CO)3 (17 e−)
• Pt(PtBu3)2 (14 e−)
• Co(norbornyl)4 (13 e−)
• [FeCp2]+ (17 e−)

Sometimes such complexes engage in agostic interactions with the hydrocarbon framework of the bulky ligand. For example:

• W(CO)3[P(C6H11)3]2 has 16 e− but has a short bonding contact between one C–H bond and the W center.
• Cp(PMe3)V(CHCMe3) (14 e−, diamagnetic) has a short V–H bond with the 'alkylidene-H', so the description of the compound is somewhere between Cp(PMe3)V(CHCMe3) and Cp(PMe3)V(H)(CCMe3).

High-spin complexes

High-spin metal complexes have singly occupied orbitals and may not have any empty orbitals into which ligands could donate electron density. In general, there are few or no π-acidic ligands in the complex. These singly occupied orbitals can combine with the singly occupied orbitals of radical ligands (e.g., oxygen), or addition of a strong field ligand can cause electron-pairing, thus creating a vacant orbital that it can donate into. Examples:

• CrCl3(THF)3 (15 e−)
• [Mn(H2O)6]2+ (17 e−)
• [Cu(H2O)6]2+ (21 e−, see comments below)

Complexes containing strongly π-donating ligands often violate the 18-electron rule. These ligands include fluoride (F−), oxide (O2−), nitride (N3−), alkoxides (RO−), and imides (RN2−). Examples:

• [CrO4]2− (16 e−)
• Mo(=NR)2Cl2 (12 e−)

In the latter case, there is substantial donation of the nitrogen lone pairs to the Mo (so the compound could also be described as a 16 e− compound). This can be seen from the short Mo–N bond length, and from the angle Mo–N–C(R), which is nearly 180°. Counter-examples:

• trans-WO2(Me2PCH2CH2PMe2)2 (18 e−)
• Cp*ReO3 (18 e−)

In these cases, the M=O bonds are "pure" double bonds (i.e., no donation of the lone pairs of the oxygen to the metal), as reflected in the relatively long bond distances.

π-donating ligands

Ligands where the coordinating atom bear nonbonding lone pairs often stabilize unsaturated complexes. Metal amides and alkoxides often violate the 18e rule

Combinations of effects

The above factors can sometimes combine. Examples include

• Cp*VOCl2 (14 e−)
• TiCl4 (8 e−)

Higher electron counts

Some complexes have more than 18 electrons. Examples:

• Cobaltocene (19 e−)
• Nickelocene (20 e−)
• The hexaaquacopper(II) ion [Cu(H2O)6]2+ (21 e−)
• TM(CO)8− (TM = Sc, Y, La) (20 e−)

Often, cases where complexes have more than 18 valence electrons are attributed to electrostatic forces – the metal attracts ligands to itself to try to counterbalance its positive charge, and the number of electrons it ends up with is unimportant. In the case of the metallocenes, the chelating nature of the cyclopentadienyl ligand stabilizes its bonding to the metal. Somewhat satisfying are the two following observations: cobaltocene is a strong electron donor, readily forming the 18-electron cobaltocenium cation; and nickelocene tends to react with substrates to give 18-electron complexes, e.g. CpNiCl(PR3) and free CpH.

In the case of nickelocene, the extra two electrons are in orbitals which are weakly metal-carbon antibonding; this is why it often participates in reactions where the M–C bonds are broken and the electron count of the metal changes to 18.[9]

The 20-electron systems TM(CO)8− (TM = Sc, Y, La) have a cubic (Oh) equilibrium geometry and a singlet (1A1g) electronic ground state. There is one occupied valence MO with a2u symmetry, which is formed only by ligand orbitals without a contribution from the metal AOs. But the adducts TM(CO)8− (TM=Sc, Y, La) fulfill the 18-electron rule when one considers only those valence electrons, which occupy metal–ligand bonding orbitals.[10]

See also

• Electron counting – Formalism used for classifying compounds
• Ligand field theory – Molecular orbital theory applied to transition metal complexes
• d electron count – Description of the electron configuration
• Tolman's rule – Rule describing chemical reactions

References

1. ^ a b Langmuir, I. (1921). "Types of Valence". Science. 54 (1386): 59–67. Bibcode:1921Sci....54...59L. doi:10.1126/science.54.1386.59. PMID 17843674.
2. ^ Jensen, William B. (2005). "The Origin of the 18-Electron Rule". J. Chem. Educ. 82 (1): 28. Bibcode:2005JChEd..82...28J. doi:10.1021/ed082p28.
3. ^ Frenking, Gernot; Shaik, Sason, eds. (May 2014). "Chapter 7: Chemical bonding in Transition Metal Compounds". The Chemical Bond: Chemical Bonding Across the Periodic Table. Wiley-VCH. ISBN 978-3-527-33315-8.
4. ^ Landis, C. R.; Weinhold, F. (2007). "Valence and extra-valence orbitals in main group and transition metal bonding". J. Comput. Chem. 28 (1): 198–203. doi:10.1002/jcc.20492. PMID 17063478.
5. ^ Frenking, Gernot; Fröhlich, Nikolaus (2000). "The Nature of the Bonding in Transition-Metal Compounds". Chem. Rev. 100 (2): 717–774. doi:10.1021/cr980401l. PMID 11749249.
6. ^ Zhao, Lili; Holzmann, Nicole; Schwerdtfeger, Peter; Frenking, Gernot (2019). "Chemical Bonding and Bonding Models of Main-Group Compounds". Chem. Rev. 119 (14): 8781–8845. doi:10.1021/acs.chemrev.8b00722. PMID 31251603. S2CID 195761899.
7. ^ Bayse, Craig; Hall, Michael (1999). "Prediction of the Geometries of Simple Transition Metal Polyhydride Complexes by Symmetry Analysis". J. Am. Chem. Soc. 121 (6): 1348–1358. doi:10.1021/ja981965+.
8. ^ King, R.B. (2000). "Structure and bonding in homoleptic transition metal hydride anions". Coordination Chemistry Reviews. 200–202: 813–829. doi:10.1016/S0010-8545(00)00263-0.
9. ^ Girolami, Gregory; Rauchfuss, Thomas; Angelici, Robert (1999). "Experiment 20". Synthesis and Technique in Inorganic Chemistry. Sausalito, California: University Science Books. ISBN 978-0-935702-48-4.
10. ^ Jin, Jiaye; Yang, Tao; Xin, Ke; Wang, Guanjun; Jin, Xiaoyang; Zhou, Mingfei; Frenking, Gernot (2018-04-25). "Octacarbonyl Anion Complexes of Group Three Transition Metals [TM(CO)8]− (TM=Sc, Y, La) and the 18-Electron Rule". Angewandte Chemie International Edition. 57 (21): 6236–6241. doi:10.1002/anie.201802590. ISSN 1433-7851. PMID 29578636.

Further reading

• Tolman, C. A. (1972). "The 16 and 18 electron rule in organometallic chemistry and homogeneous catalysis". Chem. Soc. Rev. 1 (3): 337. doi:10.1039/CS9720100337.

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