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1465:) elements, ending a point of contention and confusion. Part of the confusion originates from the fact that d-functions are essential in the basis sets used to describe these compounds (or else unreasonably high energies and distorted geometries result). Also, the contribution of the d-function to the molecular wavefunction is large. These facts were incorrectly interpreted to mean that d-orbitals must be involved in bonding.
513:
1650:, the p/s ratio is closer to 2. A similar trend is seen for the other 2p elements. Substitution of fluorine for hydrogen further decreases the p/s ratio. The 2p elements exhibit near ideal hybridisation with orthogonal hybrid orbitals. For heavier p block elements this assumption of orthogonality cannot be justified. These deviations from the ideal hybridisation were termed hybridisation defects by
128:. Pauling pointed out that a carbon atom forms four bonds by using one s and three p orbitals, so that "it might be inferred" that a carbon atom would form three bonds at right angles (using p orbitals) and a fourth weaker bond using the s orbital in some arbitrary direction. In reality, methane has four C–H bonds of equivalent strength. The angle between any two bonds is the
533:
1554:
1516:
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160:. For drawing reaction mechanisms sometimes a classical bonding picture is needed with two atoms sharing two electrons. Hybridisation theory explains bonding in alkenes and methane. The amount of p character or s character, which is decided mainly by orbital hybridisation, can be used to reliably predict molecular properties such as acidity or basicity.
635:
525:
304:
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However, computational VB groups such as
Gerratt, Cooper and Raimondi (SCVB) as well as Shaik and Hiberty (VBSCF) go a step further to argue that even for model molecules such as methane, ethylene and acetylene, the hybrid orbitals are already defective and nonorthogonal, with hybridisations such as
625:
forming a total of three sp orbitals with one remaining p orbital. In ethene, the two carbon atoms form a σ bond by overlapping one sp orbital from each carbon atom. The π bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap. Each carbon atom forms covalent
1736:
Bonding orbitals formed from hybrid atomic orbitals may be considered as localized molecular orbitals, which can be formed from the delocalized orbitals of molecular orbital theory by an appropriate mathematical transformation. For molecules in the ground state, this transformation of the orbitals
439:
According to quantum mechanics the lowest energy is obtained if the four bonds are equivalent, which requires that they are formed from equivalent orbitals on the carbon. A set of four equivalent orbitals can be obtained that are linear combinations of the valence-shell (core orbitals are almost
1629:
Hybridisation of s and p orbitals to form effective sp hybrids requires that they have comparable radial extent. While 2p orbitals are on average less than 10% larger than 2s, in part attributable to the lack of a radial node in 2p orbitals, 3p orbitals which have one radial node, exceed the 3s
1605:
Although ideal hybrid orbitals can be useful, in reality, most bonds require orbitals of intermediate character. This requires an extension to include flexible weightings of atomic orbitals of each type (s, p, d) and allows for a quantitative depiction of the bond formation when the molecular
1362:
In some general chemistry textbooks, hybridization is presented for main group coordination number 5 and above using an "expanded octet" scheme with d-orbitals first proposed by
Pauling. However, such a scheme is now considered to be incorrect in light of computational chemistry calculations.
1616:
For molecules with lone pairs, the bonding orbitals are isovalent sp hybrids. For example, the two bond-forming hybrid orbitals of oxygen in water can be described as sp to give the interorbital angle of 104.5°. This means that they have 20% s character and 80% p character and does
913:, spd hybridisation is used to model the shape of these molecules. These molecules tend to have multiple shapes corresponding to the same hybridization due to the different d-orbitals involved. A square planar complex has one unoccupied p-orbital and hence has 16 valence electrons.
1767:
Molecules with multiple bonds or multiple lone pairs can have orbitals represented in terms of sigma and pi symmetry or equivalent orbitals. Different valence bond methods use either of the two representations, which have mathematically equivalent total many-electron
1787:, a localized orbital theory containing modernized analogs of classical (valence bond/Lewis structure) bonding pairs and lone pairs. For the hydrogen fluoride molecule, for example, two F lone pairs are essentially unhybridized p orbitals, while the other is an sp
1630:
orbitals by 20–33%. The difference in extent of s and p orbitals increases further down a group. The hybridisation of atoms in chemical bonds can be analysed by considering localised molecular orbitals, for example using natural localised molecular orbitals in a
136:
orbitals. Each hybrid is denoted sp to indicate its composition, and is directed along one of the four C–H bonds. This concept was developed for such simple chemical systems, but the approach was later applied more widely, and today it is considered an effective
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This means that in practice, hybrid orbitals do not conform to the simple ideas commonly taught and thus in scientific computational papers are simply referred to as sp, spd or sd hybrids to express their nature instead of more specific integer values.
1339:
388:) molecule, with a hypothetical bond angle of 90° corresponding to the angle between two p orbitals on the same atom. However the true H–C–H angle in singlet methylene is about 102° which implies the presence of some orbital hybridisation.
1682:) can be constructed out of four resonance structures attributing the ejected electron to each of the four sp orbitals. A linear combination of these four structures, conserving the number of structures, leads to a triply degenerate T
1573:
While the simple model of orbital hybridisation is commonly used to explain molecular shape, hybridisation is used differently when computed in modern valence bond programs. Specifically, hybridisation is not determined
1783:) representation. In contrast, for multiple lone pairs, most textbooks use the equivalent orbital representation. However, the sigma-pi representation is also used, such as by Weinhold and Landis within the context of
391:
The carbon atom can also bond to four hydrogen atoms in methane by an excitation (or promotion) of an electron from the doubly occupied 2s orbital to the empty 2p orbital, producing four singly occupied orbitals.
1578:
but is instead variationally optimized to find the lowest energy solution and then reported. This means that all artificial constraints, specifically two constraints, on orbital hybridisation are lifted:
893:
2250:
David L. Cooper; Terry P. Cunningham; Joseph
Gerratt; Peter B. Karadakov; Mario Raimondi (1994). "Chemical Bonding to Hypercoordinate Second-Row Atoms: d Orbital Participation versus Democracy".
1872:
Pauling, L. (1931), "The nature of the chemical bond. Application of results obtained from the quantum mechanics and from a theory of paramagnetic susceptibility to the structure of molecules",
288:
associated with an orbital is proportional to the square of the wavefunction, the ratio of p-character to s-character is λ = 3. The p character or the weight of the p component is Nλ = 3/4.
2279:
Richard D. Harcourt; Thomas M. Klapötke (2003). "Increased valence (qualitative valence bond) descriptions of the electronic structures of electron-rich fluorine-containing molecules".
569:
between the carbons and only three σ bonds are formed per carbon atom. In sp hybridisation the 2s orbital is mixed with only two of the three available 2p orbitals, usually denoted 2p
281:
246:
176:
can be solved exactly. In heavier atoms, such as carbon, nitrogen, and oxygen, the atomic orbitals used are the 2s and 2p orbitals, similar to excited state orbitals for hydrogen.
2479:
Andrei M. Tokmachev; Andrei L. Tchougreeff; Igor A. Misurkin (2001). "Ionization potentials within semiempirical antisymmetrized product of strictly localized geminals approach".
1741:
to the delocalized orbital description for ground state total energy and electron density, as well as the molecular geometry that corresponds to the minimum total energy value.
90:. For example, in a carbon atom which forms four single bonds, the valence-shell s orbital combines with three valence-shell p orbitals to form four equivalent sp mixtures in a
436:
The energy released by the formation of two additional bonds more than compensates for the excitation energy required, energetically favoring the formation of four C-H bonds.
626:
C–H bonds with two hydrogens by s–sp overlap, all with 120° bond angles. The hydrogen–carbon bonds are all of equal strength and length, in agreement with experimental data.
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2613:
1102:
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geometry deviates from ideal bond angles. The amount of p-character is not restricted to integer values; i.e., hybridizations like sp are also readily described.
1118:
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of 109°28' (around 109.5°). Pauling supposed that in the presence of four hydrogen atoms, the s and p orbitals form four equivalent combinations which he called
2577:
1041:
98:
and atomic bonding properties and are symmetrically disposed in space. Usually hybrid orbitals are formed by mixing atomic orbitals of comparable energies.
1674:
is applied to localized hybrids, quantum mechanics requires that the (in this case ionized) wavefunction obey the symmetry of the molecule which implies
168:
Orbitals are a model representation of the behavior of electrons within molecules. In the case of simple hybridization, this approximation is based on
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1012:
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in addition to hybridisation, which implies that each resonance structure has its own hybridisation scheme. All resonance structures must obey the
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imply that a hybrid orbital is formed from one s and four p orbitals on oxygen since the 2p subshell of oxygen only contains three p orbitals.
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2018:
1995:
1969:
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Bayse, Craig; Hall, Michael (1999). "Prediction of the
Geometries of Simple Transition Metal Polyhydride Complexes by Symmetry Analysis".
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Hybrid orbitals are assumed to be mixtures of atomic orbitals, superimposed on each other in various proportions. For example, in
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938:
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published a paper definitively excluding the role of d-orbital hybridisation in bonding in hypervalent compounds of second-row (
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1185:
823:
312:
129:
91:
2388:
Kaupp, Martin (2014) . "Chapter 1: Chemical bonding of main group elements". In
Frenking, Gernod & Shaik, Sason (eds.).
740:, which can be used to predict molecular geometry based on empirical rules rather than on valence-bond or orbital theories.
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1526:
1458:
1413:
991:
82:(with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form
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leaves the total many-electron wave function unchanged. The hybrid orbital description of the ground state is, therefore
317:
Hybridisation describes the bonding of atoms from an atom's point of view. For a tetrahedrally coordinated carbon (e.g.,
1790:
hybrid orbital. An analogous consideration applies to water (one O lone pair is in a pure p orbital, another is in an sp
1727:
736:, since the angles between bonds are approximately equal to the angles between hybrid orbitals. This is in contrast to
38:
3095:
2444:
Shaik, Sason; Danovich, David; Hiberty, Philippe (2022). "On the nature of the chemical bond in valence bond theory".
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Geometry and singlet-triplet energy gap in methylene: A critical review of experimental and theoretical determinations
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781:
643:
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is explained by sp hybridization. In this model, the 2s orbital is mixed with only one of the three p orbitals,
94:
arrangement around the carbon to bond to four different atoms. Hybrid orbitals are useful in the explanation of
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260:
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For multiple bonds, the sigma-pi representation is the predominant one compared to the equivalent orbital (
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249:
376:
This diagram suggests that the carbon atom could use its two singly occupied p-type orbitals to form two
2989:
2791:
1675:
1481:
2559:
2223:
Magnusson, E. (1990). "Hypercoordinate molecules of second-row elements: d functions or d orbitals?".
1334:{\displaystyle \theta =\arccos \left(\pm {\sqrt {{\frac {1}{3}}\left(1-{\frac {2}{x}}\right)}}\right)}
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2100:
1910:
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381:
1642:, the calculated p/s ratio is approximately 3 consistent with "ideal" sp hybridisation, whereas for
1141:, the p-orbitals are unoccupied and sd hybridisation is used to model the shape of these molecules.
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McMurray, J. (1995). Chemistry
Annotated Instructors Edition (4th ed.). Prentice Hall. p. 272.
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formed by p–p overlap. Each carbon also bonds to hydrogen in a σ s–sp overlap at 180° angles.
196:
153:
142:
1613:: "Atomic character concentrates in orbitals directed towards electropositive substituents".
712:) consists of sp–sp overlap between the two carbon atoms forming a σ bond and two additional
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2453:
2426:
2344:
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Frenking, Gernot; Shaik, Sason, eds. (2014). "Chapter 3: The NBO View of
Chemical Bonding".
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Other carbon compounds and other molecules may be explained in a similar way. For example,
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bond consists of 25% s character and 75% p character and is thus described as sp (read as
2333:"The role of radial nodes of atomic orbitals for chemical bonding and the periodic table"
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state. The difference in energy between each ionized state and the ground state would be
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1914:
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One misconception concerning orbital hybridization is that it incorrectly predicts the
1610:
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172:, similar to those obtained for the hydrogen atom, the only neutral atom for which the
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1957:
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109:
83:
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112:
first developed the hybridisation theory in 1931 to explain the structure of simple
3069:
2586:
1717:. This gives rise to the two unique peaks on the photoelectron spectrum of methane.
737:
700:
resulting in two sp orbitals and two remaining p orbitals. The chemical bonding in
329:
200:
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never involved in bonding) s and p wave functions, which are the four sp hybrids.
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253:
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2817:
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Kaupp, Martin (2001). ""Non-VSEPR" Structures and
Bonding in d(0) Systems".
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Gillespie, R.J. (2004), "Teaching molecular geometry with the VSEPR model",
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that hybridisation is restricted to integer values (isovalent hybridisation)
701:
532:
325:), the carbon should have 4 orbitals directed towards the 4 hydrogen atoms.
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63:
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2209:
512:
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2202:
10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-#
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that hybrid orbitals are orthogonal to one another (hybridisation defects)
2684:
2136:. Cambridge: Cambridge University Press. pp. 367, 374–376, 381–383.
713:
489:
188:
113:
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2174:
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17:
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2417:
Kutzelnigg, W. (August 1988). "Orthogonal and non-orthogonal hybrids".
1900:
Brittin, W. E. (1945). "Valence Angle of the
Tetrahedral Carbon Atom".
1827:
1678:
in valence bond theory. For example, in methane, the ionised states (CH
1635:
1553:
1515:
562:
318:
252:(here 1/2) and pσ is a p orbital directed along the C-H axis to form a
180:
117:
106:
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2332:
2134:
Valency and bonding: A Natural Bond
Orbital Donor-Acceptor Perspective
2113:
1922:
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1643:
649:
547:
184:
496:(that is, four single covalent bonds) of equal length and strength.
1754:
1696:
1694:, which yields two values in agreement with experimental results.
909:
are the five d, one s and three p orbitals with the corresponding
756:, sp hybridization is used to model the shape of these molecules.
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2901:
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634:
524:
303:
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The Chemical Bond: Chemical Bonding Across the Periodic Table
888:{\displaystyle \theta =\arccos \left(-{\frac {1}{x}}\right)}
511:
501:
2569:
2308:
The Chemical Bond: Fundamental Aspects of Chemical Bonding
752:
are the one s and three p orbitals with the corresponding
42:
1964:(1st ed.). Oxford University Press. p. 105.
256:. The ratio of coefficients (denoted λ in general) is
59:
Mixing (superposition) of atomic orbitals in chemistry
1265:
849:
561:
For this molecule, carbon sp hybridises, because one
263:
209:
2510:. New Jersey: Wiley-Interscience. pp. 104–106.
1609:
The hybridization of bond orbitals is determined by
738:
valence shell electron-pair repulsion (VSEPR) theory
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2935:
2865:
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2830:
2805:
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2770:
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General Chemistry tutorial on orbital hybridization
1851:(2nd ed.). Pearson Prentice-Hal. p. 100.
1759:
The symmetry-adapted and hybridized lone pairs of H
2389:
2127:
2125:
2123:
1987:, Third Edition Marye Anne Fox James K. Whitesell
1939:(3rd ed., Oxford University Press 1960) p.111–120.
1847:Housecroft, Catherine E.; Sharpe, Alan G. (2005).
1333:
887:
275:
240:
145:. It gives a simple orbital picture equivalent to
1713:), both of which result from the ionization of CH
2533:Discovering Chemistry with Natural Bond Orbitals
728:Shapes of the different types of hybrid orbitals
332:configuration is 1s 2s 2p or more easily read:
2913:
2607:
2155:
2153:
2058:. Tetrahedron, volume 41, issue 8, page 1531
8:
2506:Sason S. Shaik; Phillipe C. Hiberty (2008).
488:, four sp hybrid orbitals are overlapped by
156:, one of the most compelling examples being
152:Hybridisation theory is an integral part of
2570:Hybrid orbital 3D preview program in OpenGL
1776:of the set of occupied molecular orbitals.
26:
2920:
2906:
2898:
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2776:
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2575:Understanding Concepts: Molecular Orbitals
2531:Weinhold, Frank; Landis, Clark R. (2012).
2481:International Journal of Quantum Chemistry
2132:Weinhold, Frank; Landis, Clark R. (2005).
648:The chemical bonding in compounds such as
2348:
2112:
1722:Localized vs canonical molecular orbitals
1670:of many molecules. While this is true if
1309:
1288:
1286:
1264:
870:
848:
558:) has a double bond between the carbons.
265:
262:
222:
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2535:. Hoboken, N.J.: Wiley. pp. 67–68.
2508:A Chemist's Guide to Valence Bond Theory
2419:Journal of Molecular Structure: THEOCHEM
2253:Journal of the American Chemical Society
1875:Journal of the American Chemical Society
1563:Hybridisation in computational VB theory
1490:
1477:, a better treatment would be to invoke
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276:{\displaystyle \color {blue}{\sqrt {3}}}
241:{\displaystyle N(s+{\sqrt {3}}p\sigma )}
183:, the C hybrid orbital which forms each
32:This is an accepted version of this page
2949:Sickle Cell Anemia, a Molecular Disease
1839:
28:
2560:Covalent Bonds and Molecular Structure
1751:Sigma-pi and equivalent-orbital models
1457:In 1990, Eric Alfred Magnusson of the
1347:Hybridisation of hypervalent molecules
1818:Linear combination of atomic orbitals
7:
141:for rationalizing the structures of
2963:How to Live Longer and Feel Better
2337:Journal of Computational Chemistry
658:
583:
542:trigonal planar molecular geometry
442:
394:
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264:
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3023:International League of Humanists
2645:Introduction to quantum mechanics
1668:ultraviolet photoelectron spectra
1240:sd hybridisation (63.4°, 116.6°)
1211:sd hybridisation (65.9°, 114.1°)
1190:sd hybridisation (70.5°, 109.5°)
1552:
1533:
1514:
720:Hybridisation and molecule shape
2997:Pauling Electronegativity Scale
2943:The Nature of the Chemical Bond
2446:The Journal of Chemical Physics
1937:The Nature of the Chemical Bond
732:Hybridisation helps to explain
199:describes this hybrid as an sp
1658:sp instead of sp for methane.
313:tetrahedral molecular geometry
235:
213:
1:
2956:Vitamin C and the Common Cold
2293:10.1016/S0022-1139(03)00012-5
2281:Journal of Fluorine Chemistry
2093:Journal of Chemical Education
2064:10.1016/S0040-4020(01)96393-8
1745:Two localized representations
1459:University of New South Wales
380:with two hydrogen atoms in a
2431:10.1016/0166-1280(88)80273-2
1728:Localized molecular orbitals
1551:
1544:
1532:
1525:
1513:
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1103:Tricapped trigonal prismatic
1119:Capped square antiprismatic
1087:Bicapped trigonal prismatic
905:As the valence orbitals of
748:As the valence orbitals of
492:1s orbitals, yielding four
284:in this example. Since the
74:) is the concept of mixing
3122:
1748:
1725:
1701:Two distinct states for CH
1598:
1569:Modern valence bond theory
1566:
1350:
828:sp hybridisation (109.5°)
641:
577:. The third 2p orbital (2p
539:
310:
3055:Intravenous ascorbic acid
2630:
2565:Hybridisation flash movie
2310:. John Wiley & Sons.
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1042:Capped trigonal prismatic
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2832:Molecular orbital theory
807:sp hybridisation (120°)
786:sp hybridisation (180°)
581:) remains unhybridised.
39:latest accepted revision
3018:Linus Pauling Institute
2054:Isaiah Shavitt (1985),
1808:Isovalent hybridisation
1601:Isovalent hybridisation
1595:Isovalent hybridisation
1475:computational chemistry
1171:sd hybridisation (90°)
509:translates into :
2331:Kaupp, Martin (2007).
2190:Angew Chem Int Ed Engl
2013:Paula Yurkanis Bruice
1774:unitary transformation
1764:
1718:
1546:Pentagonal bipyramidal
1437:Pentagonal bipyramidal
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1013:Pentagonal bipyramidal
889:
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292:Types of hybridisation
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250:normalisation constant
242:
130:tetrahedral bond angle
2985:Orbital hybridisation
1785:natural bond orbitals
1772:and are related by a
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1662:Photoelectron spectra
1625:Hybridisation defects
1567:Further information:
1499:Resonance structures
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1137:complexes with a low
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527:
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499:The following :
306:
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68:orbital hybridisation
3050:Vitamin C megadosage
1803:Crystal field theory
1732:Natural bond orbital
1632:natural bond orbital
1508:Trigonal bipyramidal
1391:Trigonal bipyramidal
1353:Hypervalent molecule
1263:
1257:Interorbital angles
1058:Square antiprismatic
958:Trigonal bipyramidal
847:
841:Interorbital angles
565:is required for the
261:
207:
174:Schrödinger equation
3060:Linus Pauling Award
2980:Valence bond theory
2772:Valence bond theory
2266:10.1021/ja00089a033
2237:10.1021/ja00178a014
2105:2004JChEd..81..298G
1915:1945JChEd..22..145B
1888:10.1021/ja01355a027
1849:Inorganic Chemistry
1813:Ligand field theory
1495:Coordination number
1370:Coordination number
1148:Coordination number
920:Coordination number
763:Coordination number
750:main group elements
88:valence bond theory
29:Page version status
3096:Molecular geometry
3045:Molecular medicine
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1441:spd hybridisation
1418:spd hybridisation
1395:spd hybridisation
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1236:Trigonal prismatic
1167:Trigonal pyramidal
1107:spd hybridisation
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2847:Molecular orbital
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2640:Quantum mechanics
2542:978-1-118-11996-9
2517:978-0-470-03735-5
2458:10.1063/5.0095953
2350:10.1002/jcc.20522
2317:978-3-527-66471-9
2260:(10): 4414–4426.
2231:(22): 7940–7951.
2175:10.1021/ja981965+
2163:J. Am. Chem. Soc.
2143:978-0-521-83128-4
2114:10.1021/ed081p298
2080:978-0-131-40221-8
2031:"Acids and Bases"
2019:978-0-130-17858-9
2007:Organic Chemistry
1996:978-0-7637-3586-9
1985:Organic Chemistry
1971:978-0-19-850346-0
1962:Organic Chemistry
1952:; Greeves, Nick;
1950:Clayden, Jonathan
1923:10.1021/ed022p145
1793:hybrid orbital).
1692:ionization energy
1672:Koopmans' theorem
1634:(NBO) scheme. In
1560:
1559:
1455:
1454:
1344:
1343:
1324:
1317:
1296:
1126:
1125:
1029:Capped octahedral
907:transition metals
901:spd hybridisation
898:
897:
878:
698:
697:
623:
622:
482:
481:
434:
433:
374:
373:
307:Four sp orbitals.
270:
227:
197:Quantum mechanics
154:organic chemistry
143:organic compounds
47:22 September 2024
16:(Redirected from
3113:
3091:Chemical bonding
2922:
2915:
2908:
2899:
2837:
2777:
2758:Exchange-coupled
2660:
2623:Chemical bonding
2616:
2609:
2602:
2593:
2547:
2546:
2528:
2522:
2521:
2503:
2497:
2496:
2493:10.1002/qua.1060
2476:
2470:
2469:
2441:
2435:
2434:
2414:
2408:
2407:
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2385:
2379:
2378:
2352:
2328:
2322:
2321:
2303:
2297:
2296:
2276:
2270:
2269:
2247:
2241:
2240:
2225:J. Am. Chem. Soc
2220:
2214:
2213:
2196:(1): 3534–3565.
2185:
2179:
2178:
2169:(6): 1348–1358.
2157:
2148:
2147:
2129:
2118:
2117:
2116:
2088:
2082:
2072:
2066:
2052:
2046:
2045:
2043:
2041:
2035:Orgo Made Simple
2027:
2021:
2004:
1998:
1982:
1976:
1975:
1946:
1940:
1933:
1927:
1926:
1897:
1891:
1890:
1882:(4): 1367–1400,
1869:
1863:
1862:
1844:
1556:
1537:
1518:
1491:
1450:
1427:
1404:
1366:
1340:
1338:
1337:
1332:
1330:
1326:
1325:
1323:
1319:
1318:
1310:
1297:
1289:
1287:
1207:Square pyramidal
1144:
1139:d electron count
1135:transition metal
1129:sd hybridisation
976:Square pyramidal
916:
911:18-electron rule
894:
892:
891:
886:
884:
880:
879:
871:
759:
744:sp hybridisation
659:
584:
536:Ethene structure
443:
395:
335:
286:electron density
282:
280:
279:
274:
271:
266:
247:
245:
244:
239:
228:
223:
147:Lewis structures
102:History and uses
21:
3121:
3120:
3116:
3115:
3114:
3112:
3111:
3110:
3101:Stereochemistry
3081:
3080:
3079:
3074:
3027:
3006:
3002:Pauling's rules
2968:
2931:
2926:
2896:
2887:
2861:
2822:
2801:
2797:Lewis structure
2762:
2733:
2689:
2651:
2626:
2620:
2556:
2551:
2550:
2543:
2530:
2529:
2525:
2518:
2505:
2504:
2500:
2478:
2477:
2473:
2443:
2442:
2438:
2416:
2415:
2411:
2404:
2387:
2386:
2382:
2330:
2329:
2325:
2318:
2305:
2304:
2300:
2278:
2277:
2273:
2249:
2248:
2244:
2222:
2221:
2217:
2187:
2186:
2182:
2159:
2158:
2151:
2144:
2131:
2130:
2121:
2090:
2089:
2085:
2073:
2069:
2053:
2049:
2039:
2037:
2029:
2028:
2024:
2005:
2001:
1983:
1979:
1972:
1948:
1947:
1943:
1934:
1930:
1899:
1898:
1894:
1871:
1870:
1866:
1859:
1846:
1845:
1841:
1836:
1799:
1762:
1753:
1747:
1734:
1726:Main articles:
1724:
1716:
1712:
1708:
1704:
1689:
1685:
1681:
1664:
1649:
1641:
1627:
1603:
1597:
1571:
1565:
1471:
1449:
1445:
1426:
1422:
1403:
1399:
1375:Molecular shape
1360:
1358:Octet expansion
1355:
1349:
1302:
1298:
1282:
1278:
1261:
1260:
1251:
1247:
1233:
1221:
1217:
1197:
1177:
1131:
1113:
1094:
1081:
1068:
1049:
1036:
1023:
1003:
983:
969:
949:
903:
866:
862:
845:
844:
835:
814:
803:Trigonal planar
793:
746:
722:
711:
707:
646:
638:Two sp orbitals
632:
580:
576:
572:
557:
553:
544:
522:
494:σ (sigma) bonds
487:
387:
324:
315:
299:
294:
259:
258:
248:, where N is a
205:
204:
170:atomic orbitals
166:
158:Baldwin's rules
126:atomic orbitals
123:
104:
80:hybrid orbitals
76:atomic orbitals
60:
55:
54:
53:
52:
51:
50:
34:
22:
15:
12:
11:
5:
3119:
3117:
3109:
3108:
3103:
3098:
3093:
3083:
3082:
3076:
3075:
3073:
3072:
3067:
3062:
3057:
3052:
3047:
3042:
3035:
3033:
3029:
3028:
3026:
3025:
3020:
3014:
3012:
3008:
3007:
3005:
3004:
2999:
2994:
2993:
2992:
2987:
2976:
2974:
2970:
2969:
2967:
2966:
2960:
2952:
2946:
2939:
2937:
2933:
2932:
2927:
2925:
2924:
2917:
2910:
2902:
2893:
2892:
2889:
2888:
2886:
2885:
2883:Antibonding MO
2880:
2878:Non-bonding MO
2875:
2869:
2867:
2863:
2862:
2860:
2859:
2854:
2849:
2843:
2841:
2834:
2828:
2827:
2824:
2823:
2821:
2820:
2815:
2809:
2807:
2803:
2802:
2800:
2799:
2794:
2789:
2787:Hybrid orbital
2783:
2781:
2774:
2768:
2767:
2764:
2763:
2761:
2760:
2755:
2750:
2744:
2742:
2735:
2734:
2732:
2731:
2726:
2721:
2716:
2711:
2706:
2700:
2698:
2691:
2690:
2688:
2687:
2682:
2677:
2672:
2666:
2664:
2657:
2656:Types of bonds
2653:
2652:
2650:
2649:
2648:
2647:
2637:
2635:Atomic orbital
2631:
2628:
2627:
2621:
2619:
2618:
2611:
2604:
2596:
2590:
2589:
2584:
2580:2013-04-11 at
2572:
2567:
2562:
2555:
2554:External links
2552:
2549:
2548:
2541:
2523:
2516:
2498:
2487:(3): 109–117.
2471:
2436:
2409:
2402:
2380:
2343:(1): 320–325.
2323:
2316:
2298:
2271:
2242:
2215:
2180:
2149:
2142:
2119:
2099:(3): 298–304,
2083:
2067:
2047:
2022:
1999:
1977:
1970:
1958:Wothers, Peter
1954:Warren, Stuart
1941:
1928:
1903:J. Chem. Educ.
1892:
1864:
1857:
1838:
1837:
1835:
1832:
1831:
1830:
1825:
1820:
1815:
1810:
1805:
1798:
1795:
1770:wave functions
1760:
1749:Main article:
1746:
1743:
1723:
1720:
1714:
1710:
1706:
1702:
1687:
1686:state and an A
1683:
1679:
1663:
1660:
1647:
1639:
1626:
1623:
1599:Main article:
1596:
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1419:
1416:
1411:
1407:
1406:
1396:
1393:
1388:
1384:
1383:
1380:
1379:Hybridisation
1377:
1372:
1359:
1356:
1351:Main article:
1348:
1345:
1342:
1341:
1329:
1322:
1316:
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1301:
1295:
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1199:
1195:
1191:
1188:
1183:
1179:
1178:
1175:
1172:
1169:
1164:
1160:
1159:
1156:
1155:Hybridisation
1153:
1150:
1130:
1127:
1124:
1123:
1121:
1115:
1114:
1111:
1108:
1105:
1100:
1096:
1095:
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1089:
1083:
1082:
1079:
1076:
1070:
1069:
1066:
1063:
1060:
1055:
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1038:
1037:
1034:
1031:
1025:
1024:
1021:
1018:
1015:
1010:
1006:
1005:
1001:
997:
994:
989:
985:
984:
981:
978:
972:
971:
967:
963:
960:
955:
951:
950:
947:
944:
941:
936:
932:
931:
928:
927:Hybridisation
925:
922:
902:
899:
896:
895:
883:
877:
874:
869:
865:
861:
858:
855:
852:
842:
838:
837:
833:
829:
826:
821:
817:
816:
812:
808:
805:
800:
796:
795:
791:
787:
784:
779:
775:
774:
771:
770:Hybridisation
768:
765:
745:
742:
734:molecule shape
721:
718:
709:
705:
696:
695:
692:
689:
686:
683:
679:
678:
675:
672:
669:
666:
663:
631:
628:
621:
620:
617:
614:
611:
608:
604:
603:
600:
597:
594:
591:
588:
578:
574:
570:
555:
551:
521:
518:
485:
480:
479:
476:
473:
470:
467:
463:
462:
459:
456:
453:
450:
447:
432:
431:
428:
425:
422:
419:
415:
414:
411:
408:
405:
402:
399:
385:
378:covalent bonds
372:
371:
368:
365:
362:
359:
355:
354:
351:
348:
345:
342:
339:
322:
298:
295:
293:
290:
269:
237:
234:
231:
226:
221:
218:
215:
212:
195:) hybridised.
165:
162:
121:
103:
100:
84:chemical bonds
58:
56:
36:
30:
27:
25:
24:
23:
14:
13:
10:
9:
6:
4:
3:
2:
3118:
3107:
3104:
3102:
3099:
3097:
3094:
3092:
3089:
3088:
3086:
3071:
3068:
3066:
3065:Pauling Field
3063:
3061:
3058:
3056:
3053:
3051:
3048:
3046:
3043:
3040:
3037:
3036:
3034:
3030:
3024:
3021:
3019:
3016:
3015:
3013:
3009:
3003:
3000:
2998:
2995:
2991:
2988:
2986:
2983:
2982:
2981:
2978:
2977:
2975:
2971:
2964:
2961:
2958:
2957:
2953:
2950:
2947:
2944:
2941:
2940:
2938:
2934:
2930:
2929:Linus Pauling
2923:
2918:
2916:
2911:
2909:
2904:
2903:
2900:
2884:
2881:
2879:
2876:
2874:
2871:
2870:
2868:
2864:
2858:
2855:
2853:
2850:
2848:
2845:
2844:
2842:
2838:
2835:
2833:
2829:
2819:
2816:
2814:
2813:Covalent bond
2811:
2810:
2808:
2804:
2798:
2795:
2793:
2790:
2788:
2785:
2784:
2782:
2778:
2775:
2773:
2769:
2759:
2756:
2754:
2751:
2749:
2746:
2745:
2743:
2741:
2736:
2730:
2727:
2725:
2724:5 (quintuple)
2722:
2720:
2719:4 (quadruple)
2717:
2715:
2712:
2710:
2707:
2705:
2702:
2701:
2699:
2697:
2692:
2686:
2683:
2681:
2678:
2676:
2673:
2671:
2668:
2667:
2665:
2661:
2658:
2654:
2646:
2643:
2642:
2641:
2638:
2636:
2633:
2632:
2629:
2624:
2617:
2612:
2610:
2605:
2603:
2598:
2597:
2594:
2588:
2585:
2583:
2582:archive.today
2579:
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2568:
2566:
2563:
2561:
2558:
2557:
2553:
2544:
2538:
2534:
2527:
2524:
2519:
2513:
2509:
2502:
2499:
2494:
2490:
2486:
2482:
2475:
2472:
2467:
2463:
2459:
2455:
2452:(9): 090901.
2451:
2447:
2440:
2437:
2432:
2428:
2424:
2420:
2413:
2410:
2405:
2403:9781234567897
2399:
2396:. Wiley-VCH.
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2263:
2259:
2255:
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2226:
2219:
2216:
2211:
2207:
2203:
2199:
2195:
2191:
2184:
2181:
2176:
2172:
2168:
2165:
2164:
2156:
2154:
2150:
2145:
2139:
2135:
2128:
2126:
2124:
2120:
2115:
2110:
2106:
2102:
2098:
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2081:
2077:
2071:
2068:
2065:
2061:
2057:
2051:
2048:
2036:
2032:
2026:
2023:
2020:
2016:
2012:
2008:
2003:
2000:
1997:
1993:
1990:
1986:
1981:
1978:
1973:
1967:
1963:
1959:
1955:
1951:
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1800:
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1502:
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1443:
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1371:
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1314:
1311:
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1242:
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1234:
1228:
1225:
1224:
1213:
1210:
1208:
1205:
1202:
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1198:
1192:
1189:
1187:
1184:
1181:
1180:
1173:
1170:
1168:
1165:
1162:
1161:
1157:
1154:
1151:
1149:
1146:
1145:
1142:
1140:
1136:
1128:
1122:
1120:
1117:
1116:
1109:
1104:
1101:
1097:
1090:
1088:
1085:
1084:
1077:
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1071:
1064:
1059:
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1052:
1045:
1043:
1040:
1039:
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1030:
1027:
1026:
1019:
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1011:
1007:
1004:
998:
995:
993:
990:
987:
986:
979:
977:
974:
973:
970:
964:
959:
956:
952:
945:
942:
940:
939:Square planar
937:
934:
933:
929:
926:
923:
921:
918:
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914:
912:
908:
900:
881:
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769:
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751:
743:
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739:
735:
726:
719:
717:
715:
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110:Linus Pauling
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73:
72:hybridization
69:
65:
48:
44:
40:
33:
19:
3070:4674 Pauling
2984:
2962:
2954:
2951:(1949 paper)
2942:
2936:Publications
2786:
2729:6 (sextuple)
2696:multiplicity
2532:
2526:
2507:
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2484:
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2038:. Retrieved
2034:
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2006:
2002:
1988:
1984:
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1961:
1944:
1936:
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1858:0130-39913-2
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1665:
1656:
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1615:
1608:
1604:
1589:
1575:
1572:
1473:In light of
1472:
1456:
1361:
1229:
1132:
1074:Dodecahedral
904:
747:
731:
699:
654:triple bonds
647:
624:
560:
545:
508:
498:
483:
438:
435:
390:
375:
330:ground state
327:
316:
300:
203:of the form
201:wavefunction
192:
178:
167:
151:
133:
105:
79:
78:to form new
71:
67:
61:
46:
37:This is the
31:
2959:(1970 book)
2945:(1939 book)
2663:By symmetry
2425:: 403–419.
2287:(1): 5–20.
1935:L. Pauling
1823:MO diagrams
1611:Bent's rule
1186:Tetrahedral
1133:In certain
824:Tetrahedral
704:(ethyne) (C
567:double bond
563:π (pi) bond
92:tetrahedral
3085:Categories
2873:Bonding MO
2857:MO diagram
2714:3 (triple)
2709:2 (double)
2704:1 (single)
1909:(3): 145.
1834:References
1739:equivalent
1652:Kutzelnigg
1527:Octahedral
1486:octet rule
1479:sigma bond
1414:Octahedral
992:Octahedral
754:octet rule
642:See also:
540:See also:
311:See also:
254:sigma bond
2990:Resonance
2818:Lone pair
2792:Resonance
2680:Delta (δ)
2670:Sigma (σ)
2359:0192-8651
1781:bent bond
1676:resonance
1482:resonance
1469:Resonance
1382:Examples
1307:−
1284:±
1276:
1267:θ
1158:Examples
930:Examples
868:−
860:
851:θ
773:Examples
702:acetylene
382:methylene
328:Carbon's
233:σ
193:s-p-three
139:heuristic
114:molecules
64:chemistry
2973:Concepts
2840:Concepts
2780:Concepts
2578:Archived
2466:36075734
2375:12677737
2367:17143872
2210:11592184
2009:3rd Ed.
1960:(2001).
1797:See also
1705:exist (A
1576:a priori
1463:period 3
490:hydrogen
189:hydrogen
164:Overview
124:) using
116:such as
43:reviewed
18:Sp2 bond
3032:Related
3011:Founded
2753:Singlet
2748:Triplet
2685:Phi (φ)
2101:Bibcode
2040:23 June
1911:Bibcode
1828:VALBOND
1636:methane
714:π bonds
650:alkynes
353:
319:methane
181:methane
118:methane
107:Chemist
3041:(wife)
2965:(1986)
2675:Pi (π)
2625:theory
2539:
2514:
2464:
2400:
2373:
2365:
2357:
2314:
2208:
2140:
2078:
2017:
1994:
1968:
1855:
1644:silane
1273:arccos
1152:Shape
1078:Mo(CN)
1000:Mo(CO)
966:Fe(CO)
924:Shape
857:arccos
782:Linear
767:Shape
573:and 2p
548:ethene
185:carbon
134:hybrid
2371:S2CID
1709:and T
1646:, SiH
1214:Ta(CH
652:with
484:In CH
2852:LCAO
2740:spin
2537:ISBN
2512:ISBN
2462:PMID
2398:ISBN
2363:PMID
2355:ISSN
2312:ISBN
2206:PMID
2138:ISBN
2076:ISBN
2042:2015
2015:ISBN
2011:2001
1992:ISBN
1989:2003
1966:ISBN
1853:ISBN
1730:and
1638:, CH
1244:W(CH
1194:TiCl
980:MnCl
946:PtCl
70:(or
2738:By
2694:By
2489:doi
2454:doi
2450:157
2427:doi
2423:169
2345:doi
2289:doi
2285:123
2262:doi
2258:116
2233:doi
2229:112
2198:doi
2171:doi
2167:121
2109:doi
2060:doi
1919:doi
1884:doi
1619:not
1174:CrO
1110:ReH
1091:ZrF
1065:ReF
1046:TaF
1033:MoF
1020:ZrF
832:CCl
811:BCl
694:2p
665:↑↓
662:C*
619:2p
590:↑↓
587:C*
478:sp
449:↑↓
446:C*
430:2p
401:↑↓
398:C*
384:(CH
370:2p
344:↑↓
341:↑↓
120:(CH
86:in
62:In
45:on
3087::
2485:85
2483:.
2460:.
2448:.
2421:.
2369:.
2361:.
2353:.
2341:28
2339:.
2335:.
2283:.
2256:.
2227:.
2204:.
2194:40
2192:.
2152:^
2122:^
2107:,
2097:81
2095:,
2033:.
1956:;
1917:.
1907:22
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1878:,
1654:.
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1488:.
1446:IF
1433:7
1423:SF
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1387:5
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1203:5
1182:4
1163:3
1099:9
1054:8
1009:7
988:6
954:5
935:4
820:4
799:3
790:CO
778:2
691:2p
688:sp
685:sp
682:1s
677:↑
674:↑
671:↑
668:↑
630:sp
616:sp
613:sp
610:sp
607:1s
602:↑
599:↑
596:↑
593:↑
550:(C
520:sp
475:sp
472:sp
469:sp
466:1s
461:↑
458:↑
455:↑
452:↑
427:2p
424:2p
421:2s
418:1s
413:↑
410:↑
407:↑
404:↑
367:2p
364:2p
361:2s
358:1s
350:↑
347:↑
338:C
321:CH
297:sp
149:.
66:,
41:,
2921:e
2914:t
2907:v
2615:e
2608:t
2601:v
2545:.
2520:.
2495:.
2491::
2468:.
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2433:.
2429::
2406:.
2377:.
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2320:.
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2212:.
2200::
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2146:.
2111::
2103::
2062::
2044:.
1974:.
1925:.
1921::
1913::
1886::
1861:.
1763:O
1761:2
1715:4
1711:2
1707:1
1703:4
1688:1
1684:2
1680:4
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1640:4
1448:7
1425:6
1402:5
1328:)
1321:)
1315:x
1312:2
1304:1
1300:(
1294:3
1291:1
1280:(
1270:=
1250:6
1248:)
1246:3
1230:C
1220:5
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1216:3
1196:4
1176:3
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1093:8
1080:8
1067:8
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1035:7
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1002:6
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882:)
876:x
873:1
864:(
854:=
834:4
813:3
792:2
710:2
708:H
706:2
579:z
575:y
571:x
556:4
554:H
552:2
486:4
386:2
323:4
268:3
236:)
230:p
225:3
220:+
217:s
214:(
211:N
187:–
122:4
49:.
20:)
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