A molecular orbital diagram , or MO diagram , is a qualitative descriptive tool explaining chemical bonds in molecules in terms of molecular orbital theory in general and linear combination of atomic orbitals (LCAO) orbital method molecules in particular. The basic principle of these theories is that when atoms bind to form molecules, a number of atomic orbitals combine to form the same molecular orbitals, although the involved electrons can be redistributed among orbitals. This tool is particularly suited for simple diatomic molecules such as dihydrogen, dioxygen, and carbon monoxide but becomes more complex when discussing even relatively simple polyatomic molecules, such as methane. The MO diagram can explain why some molecules exist and others do not. They can also predict bond strength, as well as an electronic transition that can occur.
Video Molecular orbital diagram
Histori
The qualitative MO theory was introduced in 1928 by Robert S. Mulliken and Friedrich Hund. The mathematical descriptions are given by contributions of Douglas Hartree in 1928 and Vladimir Fock in 1930.
Maps Molecular orbital diagram
Basics
The molecular orbital diagram is a diagram of the molecular orbital energy level (MO), which is shown as a short horizontal line in the center, flanked by the atomic orbitals constituent (AO) energy level for comparison, with the energy level rising from the bottom up. The lines, often cut the diagonal lines, connect MO levels with their constituent AO levels. The degenerate energy level is usually shown side by side. The corresponding AO and MO levels are filled with electrons by the Pauli Exclusion Principle, denoted by a small vertical arrow whose direction indicates the spin of an electron. The form of AO or MO itself is often not shown in this diagram. For diatomic molecules, MO diagrams effectively show the energetic bonds between two atoms, whose unbound AO energy is shown on the sides. For simple polyatomic molecules with "central atoms" such as methane ( CH
4 ) or carbon dioxide ( CO
2 ), the MO diagram can show one of the identical bonds to the central atom. For other poliatomic molecules, MO diagrams may show one or more interesting bonds in the molecule, leaving the other for simplicity. Often even for simple molecules, the levels of AO and MO internal orbitals and their electrons can be removed from the diagram for simplicity.
In theory MO molecular orbitals are formed by overlapping atomic orbitals. Because bonds have more overlapping than? bond,? and? * bonding and antibonding orbitals have a greater separation of energy (separation) than? and? * Orbital. The energy of atomic orbitals is correlated with electronegativity because the electronegative atoms hold their electrons more tightly, lowering their energy. Sharing molecular orbitals between atoms is more important when atomic orbitals have comparable energy; when energy is very different, orbital tends to be localized to one atom and bond mode becomes ionic. The second condition for overlapping atomic orbitals is that they have the same symmetry.
Two atomic orbitals can overlap in two ways depending on their phase relationship. The orbital phase is a direct consequence of the wave-like nature of electrons. In orbital graphical representation, the orbital phase is represented either with a plus or minus sign (which has no relation to the electrical charge) or with a shadow of one lobe. The phase signals themselves have no physical significance except when mixing orbitals to form molecular orbitals.
Two orbitals with the same sign have constructive overlap that make up the molecular orbital with most of the electron density between the two nuclei. This MO is called bonding orbital and its energy is lower than the original atomic orbitals. Bonds involving symmetrical molecular orbitals with regard to rotation around the bond axis are called sigma bonds (? -bond). If the phase changes, the bond becomes a pi bond (? -bond). The later symmetry label is determined by whether the orbital retains its original character after the inversion of its center; if yes, it is a defined gerade, g . If the orbital does not retain its original character, it is ungerade, u .
The atomic orbitals can also interact with each other outside the phase leading to destructive cancellation and there is no electron density between the two cores on so-called nodal plane described as a vertical dotted line. In this anti-bond MO with a much higher energy than the original AO, every available electron is located in the lobe that leads away from the central central axis. For related orbital ? , such orbital will be symmetrical but distinguished from it by asterisks as in ? * . For a ? -bound, the corresponding bonding and bonding orbital will not have symmetry around the bond axis and set ? and ? * , respectively.
The next step in building a MO diagram is to fill a newly formed molecular orbital with electrons. Three general rules apply:
- The Aufbau principle states that the filled orbits begin with the lowest energy
- The Pauli exclusion principle states that the maximum number of electrons occupying the orbital is two, with the opposite spin
- The Hund rule states that when there are multiple MOs with the same energy, an electron occupies one MO at a time before two electrons occupy the same MO.
The highest MO content in energy is called the Highest Molecular Orbital of the High or the HOMO and the MO is empty just above it is the Lowest Orbital Molecular Terleher or LUMO. Electrons in a MO bond are called binding electrons and each electron in an antibonding orbital will be called an anti-bonding electron. This reduction of electron energy is the driving force for the formation of chemical bonds. Anytime mixing for atomic orbitals is not possible for reasons of symmetry or energy, non-bonded MOs are made, which are often very similar to and have the same energy levels or are close to their AO constituents, thus not contributing to energetic bonding. The resulting electron configuration can be described in terms of bonding, parity and occupancy types such as dihydrogen 1? g 2 . Or it can also be written as a symbol of the term molek, eg. 1 ? g for dihydrogen. Sometimes, the letter n is used to designate a non-bonding orbital.
For a stable bond, the bond sequence, defined as
should be positive.
The relative sequence in MO energy and occupancy corresponds to the electronic transitions found in photoelectron spectroscopy (PES). In this way it is possible to experimentally verify the MO theory. In general, the sharp PES transition shows non-bonding electrons and broad bands are indicative of delocalized bonds and electrons. The band can be transformed into a fine structure with a distance corresponding to the vibration mode of the molecular cations (see Franck-Condon's principle). The PES energy is different from the ionization energy associated with the energy required to release the electron n after the first span of electron n - 1 has been removed. MO diagram with energy value can be obtained mathematically using Hartree-Fock method. The starting point for each MO diagram is the molecular geometry that has been determined for the intended molecule. The exact relationship between geometry and orbital energy is given in the Walsh diagram.
mixing s-p
The phenomenon of s-p mixing occurs when the molecular orbitals of the same symmetry formed from a combination of 2s and 2p atomic orbitals are close enough in energy to interact further, which can cause changes in the desired orbital sequence. When molecular orbitals are formed, they are mathematically derived from a linear combination of the early atomic orbitals. Generally, to predict their relative energy, it is sufficient to consider only one atomic orbitals of each atom to form a pair of molecular orbitals, since contributions from others can be ignored. For example, in dioxygen, 3? g MO can be roughly thought to be formed from the oxygen interaction 2p z AO only. This energy is found to be lower than 1? u MO, both experimentally and from a more sophisticated computational model, so that the expected fill order is 3? g before 1? u . Then the approach to ignore the effect of further interaction is valid. However, experimental and computational results for homonuclear diatomics from Li 2 to N 2 and certain heteronuclear combinations such as CO and NO show that 3? g MO is higher in energy than (and therefore filled after) 1? u MO. Can this be rationalized because of the first 3 approach? g has symmetry suitable for interacting with bond 2? g MO formed from 2s AOs. As a result, 2? g is lowered in energy, while 3? g is raised. For the above mentioned molecule, this yields 3? g is higher in energy than 1? u MO, which is the most obvious mixing of s-p. Likewise, the interaction between 2? u * and 3? u * MOs lead to a decrease in energy from the previous and the last energy increase. This however is less significant than the binding interaction of MO.
Diatomic MO diagram
A diatomic molecular orbital diagram is used to understand the bonds of a diatomic molecule. MO diagrams can be used to deduce the magnetic properties of a molecule and how they change with ionization. They also provide insight into the sequence of molecular bonds, how many bonds are split between two atoms.
The energy of the electrons is further understood by applying the Schrödinger equation to a molecule. Quantum Mechanics is able to describe energy appropriately for a single electron system but can be approximated appropriately for some electron systems using the Born-Oppenheimer approach, so the nuclei are assumed to be stationary. The LCAO-MO method is used together to further explain the molecular state.
The diatomic molecule consists of bonds between only two atoms. They can be divided into two categories: homonuclear and heteronuclear. A homonuclear diatomic molecule is a molecule consisting of two atoms of the same element. Examples are H 2 , O 2 , and N 2 . A heteronuclear diatomic molecule consists of two atoms of two different elements. Examples include CO, HCl, and NO.
Dihydrogen
The smallest molecule, hydrogen gas exists as dihydrogen (H-H) with a single covalent bond between two hydrogen atoms. Since each hydrogen atom has a single atomic orbital atom for its electron, the bond is formed by the overlap of these two atomic orbitals. In the picture two atomic orbitals are drawn on the left and on the right. The vertical axis always represents the orbital energy. Each atomic orbitals are singly occupied with up or down arrows representing electrons.
Application of MO theory for dihydrogen yield has two electrons in MO bond with electron 1 configuration? g 2 . The bond order for dihydrogen is (2-0)/2 = 1. The photoelectron spectrum of hydrogen shows a set of multiplets between 16 and 18 eV (electron volts).
The dihydrogen MO diagram helps explain how the bond breaks. When applying energy to dihydrogen, the electronic transition of molecules occurs when one electron in a MO bond is promoted to the MO antibody. The result is no more net energy gain.
Superposition of two 1s atomic orbital leads to formation? and? * molecular orbitals. Two atomic orbitals in phase create a larger electron density, which leads to? orbital. If two 1s orbitals are not in phase, the vertices between them cause an energy jump, orbital *. From the diagram you can deduce the bond sequence, how many bonds are formed between the two atoms. For this molecule is equal to one. The bond sequence can also provide insight into how close or stretched the bonds are if the molecules are ionized.
Dihelium and Dubbedli
Dihelium (He-He) is a hypothetical molecule and MO theory helps explain why helium does not exist in nature. MO diagrams for helium look very similar to hydrogen, but each helium has two electrons in a 1s atomic orbital rather than one for hydrogen, so now there are four electrons to be placed in the newly formed molecular orbital.
The only way to achieve this is to occupy bonding and bonding orbital with two electrons, which reduces the bonding sequence ((2-2)/2) to zero and nullifies clean energy stabilization. However, by removing one electron from the dihelium, the stable gas phase species He > 2 ions formed with the 1/2 bond command.
Another molecule blocked under this principle is dipyllium . Beryllium has a 1s 2 2s 2 electron configuration, so there are two more electrons at the valence level. However, 2s can mix with the 2p orbital in the beryllium, whereas there is no p orbitals at the hydrogen or helium valence level. This mixing makes anti bond 1? u orbital is slightly less than bond bond 1? g orbital is a bond, with the net effect that the whole configuration has a few bonding properties. Therefore enzyme molecules exist (and have been observed in the gas phase). Nevertheless still have low dissociation energy of only 59 kJ Â · mol -1 .
Dilithium
The MO theory precisely predicts that dilithium is a stable molecule with a bond sequence 1 (configuration 1 < g 2 1 < 2 2 g 2 ). The 1s MOs are completely filled and do not participate in the bond.
Dilithium is a gas phase molecule with a bond that is much lower than dihydrogen because 2s electrons are further removed from the nucleus. In more detailed analysis, both 1? Orbital has higher energy than 1s AO and 2 occupied? also higher in energy than 2s AO (see table 1).
Diboron
MO diagram for diboron (BB, electron configuration 1? g 2 1? u 2 2 g 2 2 u > 2 2 ) requires the introduction of an overlapping atomic orbital model for p orbitals. Three dumbbell-shaped p orbitals have the same energy and are oriented perpendicularly (or orthogonally). X-oriented p orbital (p x ) can overlap at the end form a bond (symmetric)? orbital and anti-bonding? * molecular orbitals. Unlike the 1s sigma MO, is it? 2p has a non-bonding electron density on both sides of the nuclei and? * 2p has an electron density between nuclei.
Two other p orbitals, p y and p z , may overlap on the side. The resulting bonding orbital has its electron density in the form of two lobes above and below the molecular plane. Orbitals are not symmetrical around the molecular axis and therefore are pi orbitals. The pi anti-bonding orbital (also asymmetric) has four lobes pointing away from the nucleus. Both p y and p z orbital form the same pair of pi orbitals in energy (degenerate) and can have higher or lower energy than sigma orbital.
In diboron the 1s and 2s electrons do not participate in the bond but a single electron in 2p orbital occupies 2? P y and 2? P z MO produces sequence 1 bonds. Because electrons have the same energy (they degenerate) diboron is diradical and because the spins are parallel, the compound is paramagnetic.
In certain diborynes a boron atom is eager and the order of bonding is 3.
Dicarbon
Like diboron, dicarbon (electron configuration CC: 1 < g 2 1 < u 2 2 < g 2 2 u 2 1 u 4 ) is a reactive gas phase molecule. The molecule can be described as having two pi bonds but no sigma bonds.
Dinitrogen
With nitrogen, we see two molecular orbitals mixing and repulsion of energy. This is the reason for the rearrangement of the more familiar diagrams. Notice how? of 2p behave more non-bond like because of mixing, equal to 2s ?. This also causes a large spike of energy in the 2p * orbital. The diatomic nitrogen bond sequence is three, and it is a diamagnetic molecule.
The bond order for dinitrogen (1 < g 2 1 < u 2 2 < g 2 2 u 2 u 4 3 < g 2 ) is three because two electrons are now also added in 3? MO. The MO diagram correlates with the experimental photoelectron spectrum for nitrogen. 1? electrons can be matched with peaks at 410 eV (area), 2? g electrons at 37 eV (area), 2? u electron at 19 eV (doublet), electron 1? u 4 at 17 eV (multiplet), and finally 3? g 2 at 15.5 eV (sharp). Dioxygen
Oxygen has an arrangement similar to H 2 , but now we consider the 2s and 2p orbitals. When creating the molecular orbitals of the p orbitals, consider three atomic orbitals divided into three molecular orbitals, which are single degenerate? and double degenerate? orbital. Another property that we can observe by examining the molecular orbital diagram is the magnetic properties of diamagnetic or paramagnetic. If all electrons are paired, there is little repulsion and is classified as diamagnetic. If an unpaired electron is present, it is attracted to the magnetic field, and is therefore paramagnetic. Oxygen is an example of paramagnetic diatomics. Also note the sequence of diatomic oxygen bonds is two.
MO dioxygen treatment differs from previous diatomic molecule because p? MO is now lower in energy than 2? orbital. This is associated with the interaction between 2s MO and 2p z MO. Distributing 8 electrons over 6 molecular orbitals leaving the last two electrons as a pair of degenerations in a 2p/2b bonding orbital produces a bonding sequence 2. As in the diboron, these two unpaired electrons have the same spin in the ground state, the triplet oxygen assembled paramagnetically. The first excited state has both HOMO electrons paired in one orbital with the opposite spin, and is known as single oxygen.
Urutan ikatan menurun dan panjang ikatan meningkat dalam urutan O
2 (112.2 pm), O
2 (121 pm), O < span> -
2 (128 pm) dan O 2 -
2 (149 pm).
Pencampuran
Mixing occurs when the energy gap between the 2s and 2p orbitals is not very large. This leads to the mixing of two orbitals that end in repulsion. This expulsion causes a large enough energy shift so that the 2s * energy is lowered and 2p? energy is increasing rapidly. This is just a trend with the initial elements, once the oxygen mixing stops. The underlying cause of mixing is the similarity in the energy of the 2s and 2p orbital along with the same symmetry (gerade/ungerade). Initial elements have low effective nuclear charges so they are susceptible to mixing. Oxygen is the first diatomic where the energy difference between the 2s and 2p orbitals is significant enough to ignore the mixing. Next, we look at the molecular orbital diagram of N 2 and observe this mixing of nature.
Difluorine and dineon
In difluorin, two additional electrons occupy 2p? * In binding order 1. In dineon Ne
2 (as with dihelium) the number of bonding electrons is equal to the number of antibonding electrons and this compound does not exist.
Dimolybdenum and ditungsten
Dimolybdenum (Mo 2 ) is famous for having sextuple bonds. This involves two sigma bonds (4d z 2 and 5s), two pi bonds (using 4d xz and 4d yz ), and two delta bonds (4d x 2 Ã,-y 2 and 4d xy ). Ditungsten (W 2 ) has a similar structure.
Energy MO summary
Table 1 gives an overview of MO energy for first line diatomic molecules calculated by the Hartree-Fock-Roothaan method, together with the energy of the atomic orbitals.
Heteronuclear Diatomics
In heteronuclear diatomic molecules, mixing of atomic orbitals only occurs when the value of electronegativity is the same. In carbon monoxide (CO, isoelectric with dinitrogen) the oxygen 2s orbitals are much lower in energy than the carbon 2s orbital and therefore the mixing rate is low. Electron Configuration 1? 2 1? * 2 2? 2 2? * 2 1? 4 3? 2 is identical to nitrogen. The g and u subsectors are no longer valid because the molecule has no central symmetry.
In hydrogen fluoride (HF), the hydrogen 1s orbitals can mix with the 2p > fluorine orbital to form sigma bonds because experimentally the energy of 1s hydrogen is proportional to 2p of fluorine. HF 1 electron configuration? 2 2? 2 3? 2 1? 4 reflects that the other electrons remain in three independent pairs and that the bond order is 1.
The more electronegative the atoms are more excited because they are more like energy to their atomic orbitals. It also accounts for the majority of electron negativity that surrounds more electronegative molecules. Applying the LCAO-MO method allows us to move away from a more static Lewis type approach and actually take into account the periodic trends affecting the movement of electrons. The non-bonding orbital refers to the independent pair seen on certain atoms in a molecule. A further understanding of the increase in energy levels can be obtained by investigating quantum chemistry; Schrödinger equations can be applied to predict movement and describe the state of electrons in a molecule.
NO
Nitric oxide is a heteronuclear molecule that shows mixing. The MO diagram construction is the same as the homonuclear molecule. It has a bond order of 2.5 and is a paramagnetic molecule. The difference in 2s orbital energy is quite different so that each produces its own non-bonding? orbital. Note this is a good example to make NO ionization stabilize the bonds and produce triplicate bonds, also convert magnetic properties to diamagnets.
HF
Hydrofluoric acid is another example of a homogeneous molecule. Is this a little different because of that? unbound orbital, as well as 2s ?. From hydrogen, 1s valence electrons interact with 2p fluor electrons. The molecule is diamagnetic and has a one-bonded sequence.
Triatomic molecule
Carbon dioxide
Carbon dioxide, CO
2 , is a linear molecule with a total of sixteen bond electrons in the valence shell. Carbon is the central atom of the molecule and the main axis, the z axis, is visualized as a single axis passing through the center of carbon and two oxygen atoms. For conventions, the lobes of the blue atomic orbitals are positive, the red atomic orbitals are negative phases, with respect to the wave function of the Schrödinger equation solution. In carbon dioxide carbon energy 2s (-19.4 eV), 2p carbon (-10.7 eV), and 2p oxygen (-15.9 eV)) associated with atomic orbitals are in proximity whereas 2 -s oxygen energy -32.4 eV) is different.
Carbon and every oxygen atom will have 2s atomic orbitals and 2p atomic orbitals, where the p orbitals are divided into p x , p y , and p z . With this inherited atomic orbitals, the symmetry label is deduced by paying attention to the rotation about the major axis that produces a phase change, pi bond (? ) or produces no phase change, known as sigma bond (? ). The symmetry label is further determined by whether the atomic orbitals retain their original characters after the inversion of the central atom; if the atomic orbital retains its original character, it is defined gerade, g , or if the atomic orbitals do not retain its original character, ungerade, u . The atomic orbitals labeled this final symmetry are now known as non-minimized representations.
The molecular orbital of carbon dioxide is made by a linear combination of atomic orbitals of the same irreducible representation which is also similar in the energy of the atomic orbitals. The significant overlap of atomic orbitals explains why sp bonding can occur. The strong mixing of the oxygen 2s atomic orbitals is not expected and is a non-bonding degeneration molecular orbital. The combination of similar orbital/atomic wave functions and combinations of orbital inversion functions creates a special energy associated with non-bonding (unchanged), bonds (lower than the parent orbital energy) and anti-bond (higher energy than the atomic orbitals orbital energy) molecular orbitals.
- MO model carbon dioxide
Water
Water ( H
2 O ) is a cyclic molecule (105 °) with a molecular symmetry C 2v . The oxygen atomic orbital is labeled as its symmetry as 1 for orbitals 2s and b 1 (2p x > (2p y ) and a 1 (2p z ) for three 2p orbital. Two 1-hydrogen orbital equivalents are matched to form 1 (?) And b 2 (? *) MO.
Mixing occurs between the same symmetry orbitals of comparable energy resulting in a new MO set for water:
- 2a 1 MO from mixing oxygen 2s AO and hydrogen? MO. Small oxygen 2p z AO mixture strengthens the bond and lowers the orbital energy.
- 1b 2 MO from mixing oxygen 2p y AO and hydrogen? * MO.
- 3a 1 MO from mixing oxygen 2p z AO and hydrogen? MO. The small oxygen 2s AO admixture weakens the bond and increases the orbital energy.
- 1b 1 nonbonding MO from oxygen 2p x AO (p-orbital perpendicular to the molecular plane).
According to this description the photoelectron spectrum for water shows a sharp peak for nonbonding 1b 1 MO (12.6 eV) and three broad peaks for 3a 1 MO (14.7 eV) ), 1b 2 MO (18.5 eV) and 2a 1 MO (32.2 eV). The 1b 1 MO is a free pair, whereas 3a 1 , 1b 2 and 2a 1 MO's can be localized to give two OH bonds and an in-plane free pair. MO water treatment does not have two electronic pairs that are equal to rabbit ears .
Hydrogen sulfide (H 2 S) also has a symmetry of C 2v with 8 valence electrons but a bend angle of only 92 Â °. As reflected in the photoelectron spectrum compared with water 5a 1 MO (corresponding to 3a 1 MO in water) stabilized (increase in overlap) and 2b 2 MO (corresponding to 1b 2 MO in water) is unstable (worse overlap).
References
External links
- MO diagram in meta-synthesis.com Link
- MO diagram at chem1.com link
- Molecular orbitals at winter.group.shef.ac.uk Links
Source of the article : Wikipedia
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