|
|
| Line 1: |
Line 1: |
| A '''molecular orbital diagram''', or '''MO diagram''', is a qualitative descriptive tool explaining [[chemical bonding]] in [[molecule]]s in terms of [[molecular orbital theory]] in general and the [[linear combination of atomic orbitals]] (LCAO) molecular orbital method in particular.<ref>{{Clayden|pages=96–103}}</ref><ref>''Organic Chemistry'', Third Edition, Marye Anne Fox, James K. Whitesell, '''2003''', ISBN 978-0-7637-3586-9</ref><ref>''Organic Chemistry'' 3rd Ed. '''2001''', Paula Yurkanis Bruice, ISBN 0-13-017858-6</ref> A fundamental principle of these theories is that as atoms bond to form molecules, a certain number of [[atomic orbital]]s combine to form the same number of [[molecular orbital]]s, although the [[electron]]s involved may be redistributed among the orbitals. This tool is very well suited for simple [[diatomic molecule]]s such as [[dihydrogen]], [[dioxygen]], and [[carbon monoxide]] but becomes more complex when discussing even comparatively simple polyatomic molecules, such as [[methane]]. MO diagrams can explain why some molecules exist and others do not. They can also predict bond strength, the [[electronic transition]]s that can take place.
| | Company Secretary Crochet from Yellowknife, really likes beatboxing, como ganhar dinheiro na internet and tool collecting. Of late took some time to make a vacation in Chaco Culture.<br><br>my site ... [http://ganhedinheironainternet.comoganhardinheiro101.com/ ganhando dinheiro na internet] |
| ==History==
| |
| | |
| Qualitative MO theory was introduced in 1928 by [[Robert S. Mulliken]] <ref>{{cite DOI|10.1103/PhysRev.32.186}}</ref><ref>{{cite DOI|10.1103/PhysRev.32.388}}</ref> and [[Friedrich Hund]].<ref>Hund, F. Z. Physik 1928, 51, 759.</ref> A mathematical description was provided by contributions from [[Douglas Hartree]] in 1928 <ref>Hartree, D. R. Proc. Cambridge. Phil. Soc. 1928, 24, 89</ref> and [[Vladimir Fock]] in 1930.<ref>Fock, V. Z. Physik 1930, 61, 126</ref>
| |
| | |
| ==Basics==
| |
| | |
| Molecular orbital diagrams are diagrams of molecular orbital (MO) [[energy level]]s, shown as short horizontal lines in the center, flanked by constituent atomic orbital (AO) energy levels for comparison, with the energy levels increasing from the bottom to the top. Lines, often dashed diagonal lines, connect MO levels with their constituent AO levels. [[Degenerate energy levels]] are commonly shown side by side. Appropriate AO and MO levels are filled with electrons symbolized by small vertical arrows, whose directions indicate the [[electron spin]]s. The AO or MO shapes themselves are often not shown on these diagrams. For a [[diatomic molecule]], an MO diagram effectively shows the energetics of the bond between the two atoms, whose AO unbonded energies are shown on the sides. For simple polyatomic molecules with a "central atom" such as [[methane]] ({{chem|CH|4}}) or [[carbon dioxide]] ({{chem|CO|2}}), a MO diagram may show one of the identical bonds to the central atom. For other polyatomic molecules, an MO diagram may show one or more bonds of interest in the molecules, leaving others out for simplicity. Often even for simple molecules, AO and MO levels of inner orbitals and their electrons may be omitted from a diagram for simplicity.
| |
| | |
| In MO theory molecular orbitals form by the overlap of atomic orbitals. The atomic orbital energy correlates with [[electronegativity]] as more electronegative atoms hold an electrons more tightly, lowering their energies. MO modelling is only valid when the atomic orbitals have comparable energy; when the energies differ greatly the mode of bonding becomes [[ionic bond|ionic]]. A second condition for overlapping atomic orbitals is that they have the same symmetry.
| |
| | |
| {| class="wikitable"
| |
| |- align="center"
| |
| ||
| |
| [[File:Dihydrogen-MO-Diagram.svg|center|400px|MO diagram hydrogen]]
| |
| |- align="center"
| |
| ! MO diagram for dihydrogen. Here electrons are shown by dots.
| |
| |}
| |
| | |
| Two atomic orbitals can overlap in two ways depending on their phase relationship. The phase of an orbital is a direct consequence of the wave-like properties of electrons. In graphical representations of orbitals, orbital phase is depicted either by a plus or minus sign (which has no relationship to [[electric charge]]) or by shading one lobe. The sign of the phase itself does not have physical meaning except when mixing orbitals to form molecular orbitals.
| |
| | |
| Two same-sign orbitals have a constructive overlap forming a molecular orbital with the bulk of the [[electron density]] located between the two nuclei. This MO is called the bonding orbital and its energy is lower than that of the original atomic orbitals. A bond involving molecular orbitals which are symmetric with respect to rotation around the bond axis is called a [[sigma bond]] ('''σ'''-bond). If the phase changes, the bond becomes a [[pi bond]] ('''π'''-bond). Symmetry labels are further defined by whether the orbital maintains its original character after an inversion about its center; if it does, it is defined [[molecular term symbol|gerade]], ''g''. If the orbital does not maintain its original character, it is [[molecular term symbol|ungerade]], ''u''.
| |
| | |
| Atomic orbitals can also interact with each other out-of-phase which leads to destructive cancellation and no electron density between the two nuclei at the so-called nodal plane depicted as a perpendicular dashed line. In this [[anti-bonding]] MO with energy much higher than the original AO's, any electrons present are located in lobes pointing away from the central internuclear axis. For a corresponding '''σ'''-bonding orbital, such an orbital would be symmetrical but differentiated from it by an [[asterisk]] as in '''σ<sup>*</sup>'''. For a '''π'''-bond, corresponding bonding and antibonding orbitals would not have such symmetry around the bond axis and be designated '''π''' and '''π*''', respectively.
| |
| | |
| The next step in constructing an MO diagram is filling the newly formed molecular orbitals with electrons. Three general rules apply:
| |
| *The [[Aufbau principle]] states that orbitals are filled starting with the lowest energy
| |
| *The [[Pauli exclusion principle]] states that the maximum number of electrons occupying an orbital is two, with opposite spins
| |
| *[[Hund's rule]] states that when there are several MO's with equal energy, the electrons occupy the MO's one at a time before two electrons occupy the same MO.
| |
| | |
| The filled MO highest in energy is called the [[HOMO/LUMO|Highest Occupied Molecular Orbital]] or HOMO and the empty MO just above it is then the [[HOMO/LUMO|Lowest Unoccupied Molecular Orbital]] or LUMO. The electrons in the bonding MO's are called [[bonding electron]]s and any electrons in the antibonding orbital would be called [[antibonding electron]]s. The reduction in energy of these electrons is the driving force for chemical bond formation. Whenever mixing for an atomic orbital is not possible for reasons of symmetry or energy, a [[non-bonding orbital|non-bonding MO]] is created, which is often quite similar to and has energy level equal or close to its constituent AO, thus not contributing to bonding energetics. The resulting electron configuration can be described in terms of bond type, parity and occupancy for example dihydrogen 1σ<sub>''g''</sub><sup>2</sup>. Alternatively it can be written as a [[molecular term symbol]] e.g. <sup>1</sup>[[Sigma|Σ]]<sub>g</sub><sup>+</sup> for dihydrogen. Sometimes, the letter '''n''' is used to designate a non-bonding orbital.
| |
| | |
| For a stable bond, the [[bond order]], defined as
| |
| | |
| <math>\ \mbox{Bond Order} = \frac{(\mbox{No. of electrons in bonding MOs}) - (\mbox{No. of electrons in anti-bonding MOs})}{2} </math>
| |
| | |
| must be positive.
| |
| | |
| The relative order in MO energies and occupancy corresponds with electronic transitions found in [[photoelectron spectroscopy]] (PES). In this way it is possible to experimentally verify MO theory. In general, sharp PES transitions indicate nonbonding electrons and broad bands are indicative of bonding and antibonding delocalized electrons. Bands can resolve into fine structure with spacings corresponding to vibrational modes of the molecular cation (see [[Franck–Condon principle]]). PES energies are different from [[Ionization energy|ionisation energies]] which relates to the energy required to strip off the {{math|n}}th electron after the first {{math|n − 1}} electrons have been removed. MO diagrams with energy values can be obtained mathematically using the [[Hartree–Fock method]]. The starting point for any MO diagram is a predefined [[molecular geometry]] for the molecule in question. An exact relationship between geometry and orbital energies is given in [[Walsh diagram]]s.
| |
| | |
| ==s-p mixing==
| |
| In molecules, orbitals of the same symmetry are able to mix. As the s-p gap increases (C<N<O<F), such mixing loses its importance, leading to the inversion of 3σ<sub>g</sub> and 1π<sub>u</sub> MO levels in homonuclear diatomics between N<sub>2</sub> and O<sub>2</sub>.
| |
| | |
| ==Diatomic MO diagrams==<!-- This section is linked from [[Molecular orbital]] -->
| |
| | |
| ===Dihydrogen MO diagram===
| |
| The smallest molecule, [[hydrogen]] gas exists as dihydrogen (H-H) with a single [[covalent bond]] between two hydrogen atoms. As each hydrogen atom has a single 1s [[atomic orbital]] for its [[electron]], the bond forms by overlap of these two atomic orbitals. In figure 1 the two atomic orbitals are depicted on the left and on the right. The vertical axis always represents the [[Atomic orbital#Orbital energy|orbital energies]]. Each atomic orbital is singly occupied with an up or down arrow representing an electron.
| |
| | |
| [[Image:MO diagram dihydrogen.png|thumb|center|300px|MO diagram of dihydrogen]]
| |
| | |
| Application of MO theory for dihydrogen results in having both electrons in the bonding MO with electron configuration 1σ<sub>''g''</sub><sup>2</sup>. The bond order for dihydrogen is (2-0)/2 = 1. The [[photoelectron spectrum]] of dihydrogen shows a single set of multiplets between 16 and 18 [[Electronvolt|eV]] (electron volts).<ref>.[http://www.pes.arizona.edu/facility/PESdatabase/hydrogen.jpg hydrogen @ PES database arizona.edu]</ref>
| |
| | |
| The dihydrogen MO diagram helps explain how a bond breaks. When applying energy to dihydrogen, a [[molecular electronic transition]] takes place when one electron in the bonding MO is promoted to the antibonding MO. The result is that there is no longer a net gain in energy.
| |
| | |
| [[Image:MO diagram dihydrogen bond break.png|thumb|center|300px|Bond breaking in MO diagram]]
| |
| | |
| ===Dihelium MO diagram===
| |
| '''Dihelium''' (He-He) is a hypothetical molecule and MO theory helps to explain why dihelium does not exist in nature. The MO diagram for dihelium (2 electrons in each 1s AO) looks very similar to that of dihydrogen but instead of two electrons there are now four electrons to place in the newly formed molecular orbitals.
| |
| [[Image:MO diagram dihelium.png|thumb|center|300px|MO diagram of dihelium]]
| |
| | |
| The only way to accomplish this is by occupying the both the bonding and antibonding orbitals with two electrons, which reduces the bond order ((2-2)/2) to zero and cancels the net energy stabilization.However, by removing one electron from dihelium, the stable gas-phase species {{chem|He|2|+}} ion is formed with bond order 1/2.
| |
| | |
| | |
| Another molecule that is precluded based on this principle is '''diberyllium''' ([[beryllium]] with [[electron configuration]] 1s<sup>2</sup>2s<sup>2</sup>).
| |
| | |
| ===Dilithium MO diagram===
| |
| MO theory correctly predicts that [[dilithium]] is a stable molecule with bond order 1 (configuration 1σ<sub>''g''</sub><sup>2</sup>1σ<sub>''u''</sub><sup>2</sup>2σ<sub>''g''</sub><sup>2</sup>). The 1s MOs are completely filled and do not participate in bonding.
| |
| | |
| [[Image:MO diagram dilithium molecule.png|thumb|center|300px|MO diagram of dilithium]]
| |
| | |
| Dilithium is a gas-phase molecule with a much lower [[bond strength]] than dihydrogen because the 2s electrons are further removed from the nucleus. In a more detailed analysis both the 1σ orbitals have higher energies than the 1s AO and the occupied 2σ is also higher in energy than the 2s AO (see table 1).
| |
| | |
| ===Diboron MO diagram===
| |
| The MO diagram for [[diboron]] (B-B [[electron configuration]] [[boron]]: 1s<sup>2</sup>2s<sup>2</sup>2p<sup>1</sup>) requires the introduction of an atomic orbital overlap model for [[p orbital]]s. The three [[dumbbell]]-shaped p-orbitals have equal energy and are oriented mutually perpendicularly (or [[orthogonal]]ly). The p-orbitals oriented in the x-direction (p<sub>x</sub>) can overlap end-on forming a bonding (symmetrical) sigma orbital and an antibonding sigma<sup>*</sup> molecular orbital. In contrast to the sigma 1s MO's, the sigma 2p has some non-bonding electron density at either side of the nuclei and the sigma<sup>*</sup> 2p has some electron density between the nuclei.
| |
| | |
| The other two p-orbitals, p<sub>y</sub> and p<sub>z</sub>, can overlap side-on. The resulting bonding orbital has its electron density in the shape of two lobes above and below the plane of the molecule. The orbital is not symmetric around the molecular axis and is therefore a [[pi orbital]]. The antibonding pi orbital (also asymmetrical) has four lobes pointing away from the nuclei. Both p<sub>y</sub> and p<sub>z</sub> orbitals form a pair of pi orbitals equal in energy ([[Degenerate energy level|degenerate]]) and can have higher or lower energies than that of the sigma orbital.
| |
| | |
| In diboron the 1s and 2s electrons do not participate in bonding but the single electrons in the 2p orbitals occupy the 2πp<sub>y</sub> and the 2πp<sub>z</sub> MO's resulting in bond order 1. Because the electrons have equal energy (they are degenerate) diboron is a [[diradical]] and since the spins are parallel the compound is [[paramagnetic]].
| |
| | |
| [[Image:MO diagram diboron.png|thumb|center|400px|MO diagram of diboron]]
| |
| | |
| In certain [[diboryne]]s the boron atoms are excited and the bond order is 3.
| |
| | |
| ===Dicarbon MO diagram===
| |
| Like diboron, [[dicarbon]] (C-C [[electron configuration]]:1s<sup>2</sup>2s<sup>2</sup>2p<sup>2</sup> MO's 2σ<sub>g</sub><sup>2</sup>2σ<sub>u</sub><sup>2</sup>1π<sub>u</sub><sup>4</sup>) is a reactive gas-phase molecule. The molecule can be described as having two pi bonds but without a sigma bond. <ref>Shaik, S., Rzepa, H. S. and Hoffmann, R. (2013), ''One Molecule, Two Atoms, Three Views, Four Bonds?'' . Angew. Chem. Int. Ed., 52: 3020–3033. {{doi|10.1002/anie.201208206}}</ref>
| |
| | |
| ===Dinitrogen MO diagram===
| |
| The bond order for [[dinitrogen]] (2σ<sub>g</sub><sup>2</sup>2σ<sub>u</sub><sup>2</sup>1π<sub>u</sub><sup>4</sup>3σ<sub>g</sub><sup>2</sup>) is three because two electrons are now also added in the 3σ MO. The MO diagram correlates with the experimental [[photoelectron spectroscopy|photoelectron spectrum]] for nitrogen.<ref>{{cite DOI|10.1021/ed051p506}}</ref> The 1σ electrons can be matched to a peak at 410 [[Electronvolt|eV]] (broad), the 2σ<sub>g</sub> electrons at 37 eV (broad), the 2σ<sub>u</sub> electrons at 19 eV (doublet), the 1π<sub>u</sub><sup>4</sup> electrons at 17 eV (multiplets), and finally the 3σ<sub>g</sub><sup>2</sup> at 15.5 eV (sharp).
| |
| | |
| ===Dioxygen MO diagram===
| |
| MO treatment of [[dioxygen]] is different from that of the previous diatomic molecules because the pσ MO is now lower in energy than the 2π orbitals. This is attributed to interaction between the 2s MO and the 2p<sub>z</sub> MO.<ref name=Jolly>''Modern Inorganic Chemistry'' William L. Jolly '''1985''' ISBN 0-07-032760-2</ref> Distributing 8 electrons over 6 molecular orbitals leaves the final two electrons as a degenerate pair in the 2pπ<sup>*</sup> [[antibonding orbital]]s resulting in a [[bond order]] of 2. As in diboron, when these unpaired electrons have the same spin, this type of dioxygen called [[triplet oxygen]] is a [[paramagnetic]] [[diradical]]. When both HOMO electrons pair with opposite spins in one orbital, this other oxygen type is called [[singlet oxygen]].
| |
| | |
| [[Image:MO diagram dioxygen.png|thumb|center|400px|MO diagram of dioxygen]]
| |
| | |
| The bond order decreases and the [[bond length]] increases in the order {{chem|O|2||+}} (112.2 pm), {{chem|O|2}} (121 pm), {{chem|O|2||-}} (128 pm) and {{chem|O|2||2-}} (149 pm).<ref name=Jolly/>
| |
| | |
| ===Difluorine and dineon MO diagrams===
| |
| In [[fluorine|difluorine]] two additional electrons occupy the 2pπ<sup>*</sup> with a bond order of 1. In '''dineon''' {{chem|Ne|2}} (as with dihelium) the number of bonding electrons equals the number of antibonding electrons and this compound does not exist.
| |
| | |
| ==MO energies overview==
| |
| Table 1 gives an overview of MO energies for first row diatomic molecules together with atomic orbital energies.
| |
| {| align="center" class="wikitable"
| |
| !colspan="100%" | Table 1. Calculated MO energies for diatomic molecules in [[Hartree]]s <ref>{{cite DOI|10.1021/ed082p1205}}</ref>
| |
| |-
| |
| ! || H<sub>2</sub> || Li<sub>2</sub> || B<sub>2</sub> || C<sub>2</sub> || N<sub>2</sub> || O<sub>2</sub> || F<sub>2</sub>
| |
|
| |
| |-
| |
| | 1σ<sub>g</sub> || -0.5969 || -2.4523 || -7.7040 || - 11.3598 || - 15.6820|| - 20.7296 || -26.4289
| |
| |-
| |
| | 1σ<sub>u</sub> || || -2.4520 || -7.7032|| -11.3575|| -15.6783|| -20.7286|| -26.4286
| |
| |-
| |
| | 2σ<sub>g</sub> || || -0.1816 || -0.7057 ||-1.0613||-1.4736 || -1.6488|| -1.7620
| |
| |-
| |
| | 2σ<sub>u</sub> || || ||-0.3637|| -0.5172|| -0.7780|| -1.0987|| -1.4997
| |
| |-
| |
| | 3σ<sub>g</sub> || || || || || -0.6350 || -0.7358 || -0.7504
| |
| |-
| |
| | 1π<sub>u</sub> || || ||-0.3594 || -0.4579||-0.6154 ||-0.7052 ||-0.8097
| |
| |-
| |
| | 1π<sub>g</sub> || || || || || ||-0.5319 || -0.6682
| |
| |-
| |
| | 1s (AO) || -0.5 || -2.4778 || -7.6953|| -11.3255|| -15.6289|| -20.6686 || -26.3829
| |
| |-
| |
| | 2s (AO) || || -0.1963 ||-0.4947 || -0.7056||-0.9452 || -1.2443|| -1.5726
| |
| |-
| |
| | 2p (AO) || || || -0.3099|| -0.4333|| -0.5677|| -0.6319||-0.7300
| |
| |}
| |
| | |
| ==Heteronuclear diatomics==
| |
| In heteronuclear diatomic molecules, mixing of atomic orbitals only occurs when the [[electronegativity]] values are similar. In [[carbon monoxide]] (CO, [[isoelectronic]] with dinitrogen) the oxygen 2s orbital is much lower in energy than the carbon 2s orbital and therefore the degree of mixing is low. The electron configuration 1σ<sup>2</sup>1σ<sup>*2</sup>2σ<sup>2</sup>2σ<sup>*2</sup>1π<sup>4</sup>3σ<sup>2</sup> is identical to that of nitrogen. The g and u subscripts no longer apply because the molecule lacks a center of symmetry.
| |
| | |
| In [[hydrogen fluoride]] (HF), the hydrogen 1s orbital can mix with fluorine 2p<sub>z</sub> orbital to form a sigma bond because experimentally the energy of 1s of hydrogen is comparable with 2p of fluorine. The HF electron configuration 1σ<sup>2</sup>2σ<sup>2</sup>3σ<sup>2</sup>1π<sup>4</sup> reflects that the other electrons remain in three [[lone pair]]s and that the bond order is 1.
| |
| | |
| ==Multinuclear molecules==
| |
| ===Carbon dioxide MO Diagram===
| |
| [[Carbon dioxide]], {{chem|CO|2}}, is a [[Linear molecular geometry|linear molecule]] with a total of sixteen [[Valence electron|bonding electrons]] in its [[valence shell]]. Carbon is the central atom of the molecule and a principal axis, the z-axis, is visualized as a single axis that goes through the center of carbon and the two oxygens atoms.
| |
| For convention, blue atomic orbital lobes are positive phases, red atomic orbitals are negative phases, with respect to the wave function from the solution of the [[Schrödinger equation]].<ref>{{Housecroft3rd|page=9}}</ref> In carbon dioxide the carbon 2s (−19.4 eV), carbon 2p (−10.7 eV), and oxygen 2p (−15.9 eV)) energies associated with the atomic orbitals are in proximity whereas the oxygen 2s energy (−32.4 eV) is different.<ref>"An Introduction to Molecular Orbitals". Jean & volatron. ""1993"" ISBN 0-19-506918-8. p.192</ref>
| |
| | |
| Carbon and each oxygen atom will have a 2s atomic orbital and a 2p atomic orbital, where the p orbital is divided into p<sub>x</sub>, p<sub>y</sub>, and p<sub>z</sub>. With these derived atomic orbitals, symmetry labels are deduced with respect to rotation about the principal axis which generates a phase change, [[pi bond]] (''π'')<ref>{{Housecroft3rd|page=38}}</ref> or generates no phase change, known as a [[sigma bond]] (''σ'').<ref>{{Housecroft3rd|page=34}}</ref> Symmetry labels are further defined by whether the atomic orbital maintains its original character after an inversion about its center atom; if the atomic orbital does retain its original character it is defined [[molecular term symbol|gerade]],''g'', or if the atomic orbital does not maintain its original character, [[molecular term symbol|ungerade]], ''u''. The final symmetry-labeled atomic orbital is now known as an irreducible representation.
| |
| | |
| Carbon dioxide’s molecular orbitals are made by the [[linear combination of atomic orbitals]] of the same irreducible representation that are also similar in atomic orbital energy. Significant atomic orbital overlap explains why sp bonding may occur.<ref>{{Housecroft3rd|page=33}}</ref> Strong mixing of the oxygen 2s atomic orbital is not to be expected and are [[Non-bonding orbital|non-bonding]] [[Degenerate energy levels|degenerate]] molecular orbitals. The combination of similar atomic orbital/wave functions and the combinations of atomic orbital/wave function inverses create particular energies associated with the [[Non-bonding orbital|nonbonding]] (no change), bonding (lower than either parent orbital energy) and [[antibonding]] (higher energy than either parent atomic orbital energy) molecular orbitals.
| |
| | |
| <gallery caption="MO model carbon dioxide" widths="250px" heights="300px" perrow="3">
| |
| Image:Atomic Orbitals CO2.svg| Atomic orbitals of carbon dioxide
| |
| Image:Molecular Orbitals CO2.svg| Molecular orbitals of carbon dioxide
| |
| Image:MO Diagram CO2.svg| MO Diagram of carbon dioxide
| |
| </gallery>
| |
| | |
| ===Water MO diagram===
| |
| Water ({{chem|H|2|O}}) is a bent molecule (105°) with C<sub>2v</sub> [[molecular symmetry]]. The oxygen atomic orbitals are labeled according to their symmetry as a<sub>1</sub> for the 2s<sup>2</sup> orbital and b<sub>2</sub> (2p<sub>x</sub>), b<sub>1</sub> (2p<sub>y</sub>) and a<sub>1</sub> (2p<sub>z</sub>) for 4 electrons in the 2p orbital. The two hydrogen 1s orbitals are premixed to form a A<sub>1</sub> (bonding) and B<sub>2</sub> (antibonding) MO.
| |
| | |
| {| class="wikitable"
| |
| ! C<sub>2v</sub> || E || C<sub>2</sub> || σ<sub>v</sub>(xz) || σ<sub>v</sub>'(yz) || ||
| |
| |-
| |
| | A<sub>1</sub> || 1 || 1 || 1 || 1 || ''z''
| |
| | ''x''<sup>2</sup>, ''y''<sup>2</sup>, ''z''<sup>2</sup>
| |
| |-
| |
| | A<sub>2</sub> || 1 || 1 || −1 || −1 || R<sub>z</sub> || ''xy''
| |
| |-
| |
| | B<sub>1</sub> || 1 || −1 || 1 || −1 || ''x'', R<sub>y</sub> || ''xz''
| |
| |-
| |
| | B<sub>2</sub> || 1 || −1 || −1 || 1 || ''y'', R<sub>x</sub> || ''yz''
| |
| |}
| |
| | |
| Mixing takes place between same-symmetry orbitals of comparable energy resulting a new set of MO's for water. The lowest-energy MO, 1a<sub>1</sub> resembles the oxygen 2s AO with some mixing with the hydrogen A<sub>1</sub> AO. Next is the 1b<sub>1</sub> MO resulting from mixing of the oxygen b<sub>1</sub> AO and the hydrogen B<sub>1</sub> AO followed by the 2a<sub>1</sub> MO created by mixing the a<sub>1</sub> orbitals. Both MO's form the oxygen to hydrogen sigma bonds. The oxygen b<sub>2</sub> AO (the p-orbital perpendicular to the molecular plane) alone forms the 1b<sub>2</sub> MO as it is unable to mix. This MO is nonbonding. In agreement with this description the photoelectron spectrum for water shows two broad peaks for the 1b<sub>2</sub> MO (18.5 eV) and the 2a<sub>1</sub> MO (14.5 eV) and a sharp peak for the nonbonding 1b<sub>1</sub> MO at 12.5 eV. This MO treatment of water differs from the [[orbital hybridisation]] picture because now the oxygen atom has just one lone pair instead of two and contrary to the oversimplified [[VSEPR]] picture, water does not have two equivalent lone electron pairs resembling ''rabbit ears''.<ref>{{cite journal|doi = 10.1021/ed064p124|title = No rabbit ears on water. The structure of the water molecule: What should we tell the students?|year = 1987|last1 = Laing|first1 = Michael|journal = Journal of Chemical Education|volume = 64|pages = 124|bibcode = 1987JChEd..64..124L }}</ref>
| |
| | |
| [[Hydrogen sulfide]] (H<sub>2</sub>S) too has a C<sub>2v</sub> symmetry with 8 valence electrons but the bending angle is only 92°. As reflected in its PE spectrum as compared to water the 2a<sub>1</sub> MO is stabilised (improved overlap) and the 1b<sub>2</sub> MO is destabilized (poorer overlap).
| |
| | |
| ==See also==
| |
| <!--*Difluorine MO diagram: [[Fluorine#Atomic and molecular properties]] Diagram no longer on this page-->
| |
| *Dimolybdenum MO diagram: [[Sextuple bond]]
| |
| | |
| ==References==
| |
| {{Reflist|2}}
| |
| | |
| ==External links==
| |
| *MO diagrams at meta-synthesis.com [http://www.meta-synthesis.com/webbook/39_diatomics/diatomics.html Link]
| |
| *MO diagrams at usm. Maine.edu [http://www.usm.maine.edu/~newton/Chy251_253/Lectures/MO%20Theory/MOTheory.html Link]
| |
| *MO diagrams at chem1.com [http://www.chem1.com/acad/webtext/chembond/cb08.html Link]
| |
| *Molecular orbitals at winter.group.shef.ac.uk [http://www.winter.group.shef.ac.uk/orbitron/MOs/N2/2px2px-pi/index.html Link]
| |
| | |
| [[Category:Chemical bonding]]
| |