Thermal desorption spectroscopy

2013-11-05T22:29:21Z

140.180.253.70: /* Desorption */ Physisorption occurs too.

:''Not to be confused with s-p mixing in Molecular Orbital theory. See [[Molecular orbital diagram]].

In [[chemistry]], '''hybridisation''' (or '''[[American and British English spelling differences#-ise, -ize (-isation, -ization)|hybridization]]''') is the concept of mixing [[atomic orbital]]s into new ''hybrid orbitals'' (with different energies, shapes, etc., than the component atomic orbitals) suitable for the pairing of electrons to form [[chemical bond]]s in [[valence bond theory]]. Hybrid orbitals are very useful in the explanation of [[molecular geometry]] and atomic bonding properties. Although sometimes taught together with the [[VSEPR|valence shell electron-pair repulsion (VSEPR) theory]], valence bond and hybridisation are in fact not related to the VSEPR model.<ref>{{citation | last= Gillespie | first=R.J. | year=2004 | title=Teaching molecular geometry with the VSEPR model | journal=Journal of Chemical Education | volume=81 | issue=3 | pages=298–304 | doi=10.1021/ed081p298 |bibcode = 2004JChEd..81..298G }}</ref>

== Historical development ==

[[Chemist]] [[Linus Pauling]] first developed the hybridisation theory in order to explain the structure of [[molecule]]s such as [[methane]] (CH4).<ref>{{citation | last=Pauling | first=L. | year=1931 | title=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 | journal=[[Journal of the American Chemical Society]] | volume=53 |issue=4 | pages=1367–1400 | doi=10.1021/ja01355a027 }}</ref> This concept was developed for such simple chemical systems, but the approach was later applied more widely, and today it is considered an effective [[heuristic]] for rationalising the structures of [[organic compounds]].

Orbitals are a model representation of the behaviour of electrons within molecules. In the case of simple hybridisation, this approximation is based on atomic orbitals, similar to those obtained for the hydrogen atom, the only neutral atom for which the [[Schrödinger equation]] 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. Hybrid orbitals are assumed to be mixtures of these atomic orbitals, superimposed on each other in various proportions. It provides a [[quantum mechanics|quantum mechanical]] insight to [[Lewis structure]]s. Hybridisation theory finds its use mainly in organic chemistry.

== spx and sdx terminology ==
This terminology describes the weight of the respective components of a hybrid orbital. For example, in methane, the C hybrid orbital which forms each [[carbon]]–[[hydrogen]] bond consists of 25% s character and 75% p character and is thus described as sp3 (read as ''s-p-three'') hybridised. [[Quantum mechanics]] describes this hybrid as an sp3 [[wavefunction]] of the form N(s + {{sqrt|3}}pσ), where N is a [[normalization constant]] (here 1/2) and pσ is a p orbital directed along the C-H axis to form a [[sigma bond]]. The ratio of coefficients (denoted λ in general) is [[square root of 3|{{sqrt|3}}]] in this example. Since the [[electron density]] associated with an orbital is proportional to the square of the wavefunction, the ratio of p-character to s-character is λ2 = 3. The p character or the weight of the p component is N2λ2 = 3/4.

For atoms forming equivalent hybrids with no lone pairs, there is a correspondence to the number and type of orbitals used. For example, sp3 hybrids are formed from one s and three p orbitals. However, in all other cases, there is no such correspondence. The two bond-forming hybrid orbitals of oxygen in water can be described as sp4, which means that they have 20% s character and 80% p character, but does ''not'' imply that they are formed from one s and four p orbitals. As a result, the amount of ''p''-character is not restricted to integer values; i.e., hybridisations like ''sp''2.5 are also readily described. For more information see [[variable hybridization]].

An analogous notation is used to describe sdx hybrids. For example, the [[permanganate ion]] (MnO4–) has sd3 hybridisation with orbitals that are 25% s and 75% d.

== Types of hybridisation ==

=== sp3 hybrids ===
[[Image:AE4h.svg|thumb|150px|Four sp3 orbitals.]]
Hybridisation describes the bonding atoms from an atom's point of view. That is, for a tetrahedrally coordinated carbon (e.g., [[methane]] CH4), the carbon should have 4 orbitals with the correct symmetry to bond to the 4 hydrogen atoms.

Carbon's [[ground state]] configuration is 1s2 2s2 2p''x''1 2p''y''1 or more easily read:

{| cellpadding=4px align=center
| rowspan=2 |C||↑↓||↑↓||↑||↑|| 
|-
|{{overline|1s}}
|{{overline|2s}}
|{{overline|2p''x''}}
|{{overline|2p''y''}}
|{{overline|2p''z''}}
|}

The carbon atom can utilize its two singly occupied p-type orbitals (the designations p''x'' p''y'' or p''z'' are meaningless at this point, as they do not fill in any particular order), to form two [[covalent bond]]s with two hydrogen atoms, yielding the "free radical" [[methylene radical|methylene]] CH2, the simplest of the [[carbene]]s. The carbon atom can also bond to four hydrogen atoms by an excitation of an electron from the doubly occupied 2s orbital to the empty 2p orbital, so that there are four singly occupied orbitals.


{| cellpadding=4px align=center
| rowspan=2 |C*||↑↓||↑||↑||↑||↑
|-
|{{overline|1s}}
|{{overline|2s}}
|{{overline|2p''x''}}
|{{overline|2p''y''}}
|{{overline|2p''z''}}
|}

As the energy released by formation of two additional bonds more than compensates for the excitation energy required, the formation of four C-H bonds is energetically favoured.

Quantum mechanically, the lowest energy is obtained if the four bonds are equivalent which requires that they be formed from equivalent orbitals on the carbon. A set of four equivalent orbitals can be obtained which are linear combinations of the valence-shell (core orbitals are almost never involved in bonding) s and p wave functions<ref>McMurray, J. (1995). Chemistry Annotated Instructors Edition (4th ed.). Prentice Hall. p. 272. ISBN 978-0-131-40221-8</ref> which are the four '''sp3 hybrids'''.

{| cellpadding=4px align=center
| rowspan=2 |C*||↑↓||↑||↑||↑||↑
|-
|{{overline|1s}}
|{{overline|sp3}}
|{{overline|sp3}}
|{{overline|sp3}}
|{{overline|sp3}}
|}

In CH4, four sp3 hybrid orbitals are overlapped by [[hydrogen]] 1s orbitals, yielding four [[sigma bond|σ (sigma) bonds]] (that is, four single covalent bonds) of equal length and strength.

[[Image:Ch4 hybridization.svg|A schematic presentation of hybrid orbitals overlapping hydrogen orbitals]] translates into [[Image:Ch4-structure.png|Methane's tetrahedral shape]]

=== sp2 hybrids ===
[[Image:AE3h.svg|thumb|150px|Three sp2 orbitals.]]
[[Image:Ethene-2D-flat.png|thumb|120px|Ethene structure]]

Other carbon based compounds and other molecules may be explained in a similar way as methane. For example, [[ethene]] (C2H4) has a double bond between the carbons.

For this molecule, carbon will sp2 hybridise, because one [[pi bond|π (pi) bond]] is required for the [[covalent bond|double bond]] between the carbons, and only three σ bonds are formed per carbon atom. In '''sp2 hybridisation''' the 2s orbital is mixed with only two of the three available 2p orbitals:

{| cellpadding=4px align=center
| rowspan=2 |C*||↑↓||↑||↑||↑||↑
|-
|{{overline|1s}}
|{{overline|sp2}}
|{{overline|sp2}}
|{{overline|sp2}}
|{{overline|2p}}
|}

forming a total of three sp2 orbitals with one p orbital remaining. In ethylene ([[ethene]]) the two carbon atoms form a σ bond by overlapping two sp2 orbitals and each carbon atom forms two covalent bonds with hydrogen by s–sp2 overlap all with 120° angles. The π bond between the carbon atoms perpendicular to the molecular plane is formed by 2p–2p overlap. The hydrogen–carbon bonds are all of equal strength and length, which agrees with experimental data.

=== sp hybrids ===
[[Image:AE2h.svg|thumb|150px|Two sp orbitals]]
The chemical bonding in compounds such as [[alkyne]]s with triple bonds is explained by '''sp hybridisation'''.

{| cellpadding=4px align=center
| rowspan=2 |C*||↑↓||↑||↑||↑||↑
|-
|{{overline|1s}}
|{{overline|sp}}
|{{overline|sp}}
|{{overline|2p}}
|{{overline|2p}}
|}

In this model, the 2s orbital mixes with only one of the three p orbitals resulting in two sp orbitals and two remaining unchanged p orbitals. The chemical bonding in [[acetylene]] (ethyne) (C2H2) consists of sp–sp overlap between the two carbon atoms forming a σ bond and two additional [[pi bonds|π bonds]] formed by p–p overlap. Each carbon also bonds to hydrogen in a σ s–sp overlap at 180° angles.

== Hybridisation and molecule shape ==
Hybridisation helps to explain [[molecular geometry|molecule shape]] since the angles between bonds are (approximately) equal to the angles between hybrid orbitals, as explained above for the tetrahedral geometry of methane. As another example, the three sp2 hybrid orbitals are at angles of 120° to each other, so this hybridisation favours [[trigonal planar molecular geometry]] with bond angles of 120°. Other examples are given in the table below.

{| class="wikitable"
! Classification
! Main group
! Transition metal<ref>{{cite book |last1=Weinhold |first1= Frank |last2= Landis |first2= Clark R. |title=Valency and bonding: A Natural Bond Orbital Donor-Acceptor Perspective |location=Cambridge |publisher=Cambridge University Press |year=2005 |pages=381–383 |isbn=978-0-521-83128-4}}</ref>
|-----
! AX2
|
* [[linear molecular geometry|Linear]] (180°)
* sp hybridisation
* E.g., CO2
|
* [[bent molecular geometry|Bent]] (90°)
* sd hybridisation
* E.g., VO2+
|-----
! AX3
|
* [[trigonal planar molecular geometry|Trigonal planar]] (120°)
* sp2 hybridisation
* E.g., BCl3
|
* [[trigonal pyramidal molecular geometry|Trigonal pyramidal]] (90°)
* sd2 hybridisation
* E.g., CrO3
|-----
! AX4
|
*[[tetrahedral molecular geometry|Tetrahedral]] (109.5°)
* sp3 hybridisation
* E.g., CCl4
|
*[[tetrahedral molecular geometry|Tetrahedral]] (109.5°)
* sd3 hybridisation
* E.g., MnO4−
|-----
! AX5
| align="center" | -
|
* [[Square pyramidal molecular geometry|Square pyramidal]] (66°, 114°)<ref name=Kaupp>{{cite journal
| title = "Non-VSEPR" Structures and Bonding in d(0) Systems
| first = Martin | last = Kaupp
| journal = Angew Chem Int Ed Engl.
| year = 2001
| volume = 40
| issue = 1
| pages = 3534–3565
| doi = 10.1002/1521-3773(20011001)40:19<3534::AID-ANIE3534>3.0.CO;2-#
}}</ref><ref name=RBKing>{{cite journal |journal= Coordination Chemistry Reviews |volume= 197 |year= 2000 |pages= 141–168 |title= Atomic orbitals, symmetry, and coordination polyhedra |first= R. Bruce |last= King }}</ref>
* sd4 hybridisation
* E.g., Ta(CH3)5
|-----
! AX6
| align="center" | -
|
* [[trigonal prismatic molecular geometry|Trigonal prismatic]] (63°, 117°)<ref name=Kaupp/><ref name=RBKing/>
* sd5 hybridisation
* E.g., W(CH3)6
|}

===Main group compounds with lone pairs===
For main group compounds with lone electron pairs, the s orbital lone pair can be hybridised to a certain extent with the bond pairs.<ref name=Weinhold>{{cite web |url=http://isites.harvard.edu/fs/docs/icb.topic818673.files/Lecture%202%20-%20Weinhold%20et%20al%20-%20Shape%20of%20Oxygen%20Lone%20Pairs.pdf |title=Rabbit Ears Hybrids, VSEPR Sterics, and Other Orbital Absurdities |first=Frank |last=Weinhold |year= |work= |publisher= |location=University of Wisconsin |accessdate=2012-11-11}}</ref> This is analogous to s-p mixing in [[molecular orbital theory]], and maximizes energetic stability according to the [[Walsh diagram]] for the molecule. This rationalisation is applied to explain deviations from ideal bond angles, such as when only p orbitals are used for bonding, most commonly in second and third period elements.

* [[trigonal pyramidal molecular geometry|Trigonal pyramidal]] (AX3E1)
** The s-orbital can be hybridised with the three p-orbital bonds to give bond angles greater than 90°.
** Ex. NH3
* [[bent molecular geometry|Bent]] (AX2E1-2)
** The s-orbital lone pair can be hybridised with the two p-orbital bonds to give bond angles greater than 90°. The out-of-plane p-orbital can either be a lone pair or pi bond. If it is a lone pair, the in-plane and out-of-plane lone pairs are inequivalent, contrary to the common picture depicted by VSEPR theory (see below).
** Exs. SO2, H2O
* Monocoordinate (AX1E1-3)
** The s-orbital lone pair can be hybridised with the p-orbital bond. The two out-of-line p-orbitals can either be lone pairs or pi bonds. The p-orbital lone pairs are not equivalent to the s-rich lone pair.
** Exs. CO, SO, HF

== Hybridisation of [[hypervalent molecule]]s ==

=== Traditional description ===
In general chemistry courses and mainstream textbooks, hybridisation is often presented for main group AX5 and above, as well as for transition metal complexes, using the hybridisation scheme first proposed by Pauling.
{| class="wikitable"
! Classification
! Main group
! Transition metal
|-----
! AX2
| align="center" | -
|
* [[linear molecular geometry|Linear]] (180°)
* sp hybridisation
* E.g., Ag(NH3)2+
|-----
! AX3
| align="center" | -
|
* [[trigonal planar molecular geometry|Trigonal planar]] (120°)
* sp2 hybridisation
* E.g., Cu(CN)32−
|-----
! AX4
| align="center" | -
|
* [[square planar molecular geometry|Square planar]] (90°)
* dsp2 hybridisation
* E.g., PtCl42−
|-----
! AX5
|
*[[trigonal bipyramidal molecular geometry|Trigonal bipyramidal]] (90°, 120°)
* sp3d hybridisation
* E.g., PCl5
|
*[[trigonal bipyramidal molecular geometry|Trigonal bipyramidal]] (90°, 120°)
* dsp3 hybridisation
* E.g., Fe(CO)5
|-----
! AX6
|
*[[octahedral molecular geometry|Octahedral]] (90°)
* sp3d2 hybridisation
* E.g., SF6
|
*[[octahedral molecular geometry|Octahedral]] (90°)
* d2sp3 hybridisation
* E.g., Mo(CO)6
|-----
! AX7
|
*[[pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]] (90°, 72°)
* sp3d3 hybridisation
* E.g., IF7
|
*[[pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]] (90°, 72°)
* d3sp3 hybridisation
* E.g., V(CN)74−
|-----
! AX8
|
*[[square antiprismatic molecular geometry|Square antiprismatic]]
* sp3d4 hybridisation
* E.g., IF8−
|
*[[square antiprismatic molecular geometry|Square antiprismatic]]
* d4sp3 hybridisation
* E.g., Re(CN)83−
|-----
! AX9
| align="center" | -
|
*[[Tricapped trigonal prismatic molecular geometry|Tricapped trigonal prismatic]]
* d5sp3 hybridisation
* E.g., ReH92−
|}

In this notation, d orbitals of main group atoms are listed after the s and p orbitals since they have the same principal quantum number (''n''), while d orbitals of transition metals are listed first since the s and p orbitals have a higher n. Thus for AX5 molecules, sp3d hybridisation in the P atom involves 3s, 3p and 3d orbitals, while dsp3 for Fe involves 3d, 4s and 4p orbitals.

However, hybridisation of s, p and d orbitals together is no longer accepted, as more recent calculations based on molecular orbital theory have shown that in main-group molecules the d component is insignificant, while in transition metal complexes the p component is insignificant (see below).

=== Resonance description ===
As shown by computational chemistry, [[hypervalent molecule]]s can only be stable given strongly polar (and weakened) bonds with electronegative ligands such as fluorine or oxygen to reduce the valence electron occupancy of the central atom to a maximum of 8<ref>{{cite journal
| title = Chemical Bonding to Hypercoordinate Second-Row Atoms: d Orbital Participation versus Democracy
| author = David L. Cooper , Terry P. Cunningham , Joseph Gerratt , Peter B. Karadakov , Mario Raimondi
| journal = [[Journal of the American Chemical Society]]
| year = 1994
| volume = 116
| issue = 10
| pages = 4414–4426
| doi = 10.1021/ja00089a033
}}</ref> (or 12 for transition metals). This requires an explanation that invokes [[sigma bond|sigma]] [[resonance (chemistry)|resonance]] in addition to hybridisation, which implies that each resonance structure has its own hybridisation scheme. As a guideline, all resonance structures have to obey the octet rule for main group compounds and the dodectet (12) rule for transition metal complexes.

{| class="wikitable"
! Classification
! Main group
! Transition metal
|-----
! rowspan="2"| AX2
| align="center" rowspan="2"| -
| align="center"| [[linear molecular geometry|Linear]] (180°)
|-----
| align="center"|[[File:Di silv.svg|300px]]
|-----
! rowspan="2"| AX3
| align="center" rowspan="2"| -
| align="center"| [[trigonal planar molecular geometry|Trigonal planar]] (120°)
|-----
| align="center"|[[File:Tri copp.svg|320px]]
|-----
! rowspan="2"| AX4
| align="center" rowspan="2"| -
| align="center"| [[square planar molecular geometry|Square planar]] (90°)
|-----
| align="center"|[[File:Tetra plat.svg|320px]]
|-----
! rowspan="2"| AX5
| align="center"|[[trigonal bipyramidal molecular geometry|Trigonal bipyramidal]] (90°, 120°)
| align="center"|[[trigonal bipyramidal molecular geometry|Trigonal bipyramidal]] (90°, 120°)
|-----
| align="center"|[[File:Penta phos.png|400px]]
|
* Fractional hybridisation (s and d orbitals)
* E.g., Fe(CO)5
|-----
! rowspan="2"| AX6
| align="center"|[[octahedral molecular geometry|Octahedral]] (90°)
| align="center"|[[octahedral molecular geometry|Octahedral]] (90°)
|-----
| align="center"|[[File:Hexa sulf.png|300px]]
| align="center"|[[File:Hexa moly.svg|300px]]
|-----
! rowspan="2"| AX7
| align="center"|[[pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]] (90°, 72°)
| align="center"|[[pentagonal bipyramidal molecular geometry|Pentagonal bipyramidal]] (90°, 72°)
|-----
| align="center"|[[File:Hepta iodi.svg|420px]]
|
* Fractional hybridisation (s and three d orbitals)
* E.g., V(CN)74−
|-----
! rowspan="2"| AX8
| align="center"| [[square antiprismatic molecular geometry|Square antiprismatic]]
| align="center"|[[square antiprismatic molecular geometry|Square antiprismatic]]
|-----
|
* Fractional hybridisation (s and three p orbitals)
* E.g., IF8−
|
* Fractional hybridisation (s and four d orbitals)
* E.g., Re(CN)83−
|-----
! rowspan="2"| AX9
| align="center" rowspan="2"| -
| align="center"|[[Tricapped trigonal prismatic molecular geometry|Tricapped trigonal prismatic]]
|-----
|
* Fractional hybridisation (s and five d orbitals)
* E.g., ReH92−
|}

==== Main group compounds with lone pairs ====
For hypervalent main group compounds with lone electron pairs, the bonding scheme can be split into two components: the "resonant bonding" component and the "regular bonding" component. The "regular bonding" component has the same description (see above), while the "resonant bonding" component consists of resonating bonds utilizing p orbitals. The table below shows how each shape is related to the two components and their respective descriptions.

{| class="wikitable"
| colspan="2" rowspan="2"|
! colspan="3"| Regular bonding component (marked in red)
|-----
! Bent
! Monocoordinate
! align="center" | -
|-----
! rowspan="6"| Resonant bonding component
! rowspan="2"|Linear axis
| align="center" | [[Seesaw molecular geometry|Seesaw]] (AX4E1) (90°, 180°, >90°)
| align="center" | [[T-shaped molecular geometry|T-shaped]] (AX3E2) (90°, 180°)
| align="center" | [[Linear molecular geometry|Linear]] (AX2E3) (180°)
|-----
| align="center"|[[File:Tetra sulf.svg|160px]]
| align="center"|[[File:Tri chlo.svg|160px]]
| align="center"|[[File:Di xeno.svg|160px]]
|-----
! rowspan="2"|Square planar equator
| align="center" rowspan="2"| -
| align="center" | [[Square pyramidal molecular geometry|Square pyramidal]] (AX5E1) (90°, 90°)
| align="center" | [[Square planar molecular geometry|Square planar]] (AX4E2) (90°)
|-----
| align="center"|[[File:Penta chlo.svg|240px]]
| align="center"|[[File:Tetra xeno.svg|240px]]
|-----
! rowspan="2"|Pentagonal planar equator
| align="center" rowspan="2"| -
| align="center" | [[Pentagonal pyramidal molecular geometry|Pentagonal pyramidal]] (AX6E1) (90°, 72°)
| align="center" | [[Pentagonal planar molecular geometry|Pentagonal planar]] (AX5E2) (72°)
|-----
| align="center"|[[File:Hexa xeno.svg|240px]]
| align="center"|[[File:Penta xeno.svg|240px]]
|}

==Clarifying misconceptions==

===VSEPR electron domains and hybrid orbitals are different===
The simplistic picture of hybridisation taught in conjunction with VSEPR theory does not agree with high-level theoretical calculations<ref name=Weinhold/> despite its widespread usage in many textbooks. For example, following the guidelines of VSEPR, the hybridization of the oxygen in water is described with two equivalent lone electron-pairs.<ref>Petrucci R.H., Harwood W.S. and Herring F.G. "General Chemistry. Principles and Modern Applications" (Prentice-Hall 8th edn 2002) p. 441</ref> However, [[molecular orbital]] calculations give orbitals that reflect the [[Molecular symmetry#Common point groups|C2v symmetry]] of the molecule.<ref name=Levine470>Levine I.N. “Quantum chemistry” (4th edn, Prentice-Hall) p. 470–2</ref> One of the two lone pairs is in a pure p-type orbital, with its electron density perpendicular to the H–O–H framework.<ref name=Laing>[http://dx.doi.org/10.1021/ed064p124 Laing, Michael ''J. Chem. Educ.'' (1987) '''64''', 124–128] "No rabbit ears on water. The structure of the water molecule: What should we tell the students?"</ref> The other lone pair is in an approximately sp0.8 orbital that is in the same plane as the H–O–H bonding.<ref name=Laing/> [[Ultraviolet photoelectron spectroscopy|Photoelectron spectra]] confirm the presence of two different energies for the nonbonded electrons.<ref>Levine p. 475</ref>

=== Non-inclusion of d orbitals in main group compounds ===
{{main|Hypervalent molecule}}

In 1990, Magnusson published a seminal work definitively excluding the role of d-orbital hybridization in bonding in hypervalent compounds of second-row elements. This had long been a point of contention and confusion in describing these molecules using molecular orbital theory. Part of the confusion here originates from the fact that one must include d-functions in the basis sets used to describe these compounds (or else unreasonably high energies and distorted geometries result), and the contribution of the d-function to the molecular wavefunction is large. These facts were historically interpreted to mean that d-orbitals must be involved in bonding. However, Magnusson concludes in his work that d-orbital involvement is not implicated in hypervalency.<ref name="ReferenceA">E. Magnusson. Hypercoordinate molecules of second-row elements: d functions or d orbitals? ''J. Am. Chem. Soc.'' '''1990''', ''112'', 7940-7951. {{doi|10.1021/ja00178a014}}</ref>

=== Non-inclusion of p orbitals in transition metal complexes ===
Similarly, p orbitals have long been thought to be utilized by transition metal centers in bonding with ligands, hence the [[18-electron rule|18-electron]] description; however, recent [[molecular orbital]] calculations have found that such p orbital participation in bonding is insignificant,<ref>{{cite journal
| title = Valence and extra-valence orbitals in main group and transition metal bonding
| author = C. R. Landis, F. Weinhold
| journal = [[Journal of Computational Chemistry]]
| year = 2007
| volume = 28
| issue = 1
| pages = 198–203
| doi = 10.1002/jcc.20492
}}</ref><ref>{{cite web |url=http://www.bowdoin.edu/student-fellowships/pdf/summer-2012/ODonnell%20SRR.pdf |title=Investigating P-Orbital Character In Transition Metal-to-Ligand Bonding |first=Mark |last=O’Donnell |year=2012 |work= |publisher=Bowdoin College |location= Brunswick, ME |accessdate=2012-09-16}}</ref> even though the contribution of the p-function to the molecular wavefunction is calculated to be somewhat larger than that of the d-function in main group compounds.

==Hybridization theory vs. Molecular Orbital theory==

Hybridisation theory is an integral part of [[organic chemistry]] and in general discussed together with [[molecular orbital theory]] in advanced organic chemistry textbooks although for different reasons. One textbook notes that for drawing reaction mechanisms sometimes a classical bonding picture is needed with two atoms sharing two electrons.<ref>{{Clayden|page=105}}</ref> It also comments that predicting bond angles in methane with MO theory is not straightforward. Another textbook treats hybridisation theory when explaining bonding in alkenes<ref>''Organic Chemistry'', Third Edition Marye Anne Fox James K. Whitesell '''2003''' ISBN 978-0-7637-3586-9</ref> and a third<ref>''Organic Chemistry'' 3rd Ed. '''2001''' Paula Yurkanis Bruice ISBN 978-0-130-17858-9</ref> uses MO theory to explain bonding in hydrogen but hybridisation theory for methane.

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 with a closed electron shell in the ground state, this transformation of the orbitals leaves the total many-electron wave function unchanged. The hybrid orbital description of the ground state is therefore ''equivalent'' to the delocalized orbital description for explaining the ground state total energy and electron density, as well as the molecular geometry which corresponds to the minimum value of the total energy.

There is no such equivalence, however, for ionized or excited states with open electron shells. Hybrid orbitals cannot therefore be used to interpret photoelectron spectra, which measure the energies of ionized states, identified with delocalized orbital energies using [[Koopmans' theorem]]. Nor can they be used to interpret UV-visible spectra which correspond to electronic transitions between delocalized orbitals. From a pedagogical perspective, the hybridisation approach tends to over-emphasize localisation of bonding electrons and does not effectively embrace [[molecular symmetry]] as does MO theory.

== See also ==
* [[Linear combination of atomic orbitals molecular orbital method]]
* [[MO diagram]]s
* [[Ligand field theory]]
* [[Crystal field theory]]

== References ==
{{reflist}}

== External links ==
* [http://wps.prenhall.com/wps/media/objects/602/616516/Chapter_07.html Covalent Bonds and Molecular Structure]
* [http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/hybrv18.swf Hybridisation flash movie]
* [http://adomas.org/hopv/ Hybrid orbital 3D preview program in OpenGL]
* [http://college.hmco.com/chemistry/shared/media/zumdahl/dswmedia/undr_dcr/Ch14_u14a.dcr Understanding Concepts: Molecular Orbitals]

{{DEFAULTSORT:Orbital Hybridisation}}
[[Category:Chemical bonding]]
[[Category:Quantum chemistry]]
[[Category:Stereochemistry]]

formulasearchengine - User contributions [en]

Thermal desorption spectroscopy