THE THREE CENTERED TWO ELECTRON BOND

A three centered two electron bond as name suggest speaks about three centres sharing two electrons to make one  bond.
These type of bonding is possible only in electron deficient species
eg:- bh3 dimerises  to form b2h6.

The stability of  B2H6 is well established.

In the above structure a,b,c,d represent conventional 2 centered two electron bond ,but e and f represent three center 2 electron bond .

B2H6 has 12 electron out of which 8 electron are used in forming B-H bonds and remaining 4 electron is used in 3 center 2 electron bond.Thus we have two B-H-B bridging structure.

let us understand the stability of these structure considering mot.

So we consider group orbitals of BH3 system.

If we consider BH3  it has six electrons thus the d orbital would be the one which is vacant.

So we need to mix d orbitals which are basically pure p orbital .

So now we have  P+P AND P-P ORBITAL .

THESE orbital mix with the 1s orbital of hydrogen and give us P+P-S ,P-P+S,P+P+S.

BUILDING Formaldehyde

• Oxygen p orbitals are lower energy than the CH2 p orbital.
• MO’s analogous to key orbitals in ethylene are formed including both the σ and π orbitals of the double bond.
• However, Rule 9 predicts polarization in all of the orbitals.
• Rule 9: When two orbitals interact, the lower energy orbital mixes into itself the higher energy one in a bonding way, while the higher energy orbital mixes into itself the lower energy orbital in an antibonding way.

• In the case of the π and π* orbitals, the oxygen p orbital is lower in energy than the CH2 p.
• In the case of the π and π* orbitals, the oxygen p orbital is lower in energy than the CH2 p.
• The lower energy π MO that is formed i s polarized towards the O, and the higher energy π* orbital is polarized towards the C. Corroborated by ab initial models.
• 12 ē valence electrons between O and CH2.
• LUMO is the π* [p – py] MO
• HOMO is [π(CH2) – px] MO
• MOT does not always lead to simple correspondence with
classical views.
• The MO’s of O-containing molecules predict the existence of lone pairs of ē.
• The MO diagram for this prototype carbonyl has significant
ramifications for predicting and rationalizing reactivity patterns.
• Nucleophiles will preferentially interact with the LUMO at the
atom/group with the larger coefficient. (in this case C)
• Polarization of the HOMO towards O has implications for reactivity as well. (protonation at O not C)
• The simple QMOT model of a carbonyl (formaldehyde) is completely compatible with more conventional (VBT) bonding
models.
• Group orbitals for an olefin would be those derived for
ethylene.
• Group orbitals for an aldehyde or ketone would be those derived
for formaldehyde. 

Effects of Heteroatoms - Formaldehyde

• Rule 5: Molecules with similar structures will have qualitatively similar
MO’s, with the major difference being the number of valence ē
occupying the common MO system.
• Essentially true, but situation is frequently more complicated.
• Formaldehyde and ethylene are isoelectroni; same number of
valence ē and the same types of valence orbitals.
• Can expect formaldehyde and ethylene to have similar MO’s, with some perturbations introduced by the O of formaldehyde.

• The primary consequence of introducing heteroatoms into
hydrocarbon systems is to alter orbital energies:
• Rule 12: More electronegative elements have lower energy atomic
orbitals.
• In generating mixing diagrams, valence state ionization energies
provide a convenient guideline for orbital energies. The higher
the ionization energy the harder it is to an electron... energy of
the orbital is lower.
• Electronegative elements have relatively low lying-atomic orbitals.
• Thus, must consider second order perturbation rules for orbital
mixing

Ethylene

• Standard bonding picture for
ethylene is viewed as being made
from 2 sp2 hybridized C atoms, and
consists of a C-C double bond.
• MOT does not employ hybridization
and does not assume bonding
arrangements.
• Build ethylene from two CH2 groups
without preconceived bonding
arrangements.

• As with ethane earlier, the MO’s
derived from σ(CH2) and π(CH2)
make four MO’s that are primarily C-H
bonding - do not change much with
mixing in forming C-C bond.
• [σ(out)+ σ(out)] is the major σ bond
component, while (p+p) mixing
produces the π bond.
• Each CH2 group brings 6 valence ē
(total of 12 ē).
• The π orbital is the HOMO, and the
LUMO is the out-of-phase combination
of the p orbitals (which is antibonding).

Ethane

• As molecules get bigger constructing the molecular orbitals
becomes more challenging.
• Insights into bonding of larger molecules can be attained by
combining fragments with well defined MO’s... through orbital
mixing.
• In this manner, ethane can be constructed from MO’s of two
pyramidal CH3 groups.

• Only consider the first-order mixings:
• σ(CH3) and π(CH3) orbitals are primarily C-H bonding - do not
change much with mixing in forming C-C bond.
• σ(out) is directed away from hydrogens and towards the C-C bond
being formed... they overlap well and result in strong mixing
interaction. Significant lowering of energy of the σ(out)+ σ(out) MO.
• Each CH3 brings 7 valence ē (combine for 14 ē). MO filling
lowest to highest in energy.
• The highest occupied molecular orbital (HOMO) consists
of a degenerate pair of orbitals, π(CH3)-π(CH3).
• σ(out)+ σ(out) = C-C σ bonding translates well for alkane fragments
in general.

Orbital Mixing - Building Larger Molecules

• Essence of orbital mixing is stated in Rules 8 and 9.
• Rule 8: When two orbitals interact, the lower energy orbital is stabilized
and the higher energy orbital is destabilized. The out-of-phase
(antibonding) interaction always raises in energy to a greater degree than
the corresponding in-phase (bonding) interaction is lowered in energy.
• Rule 9: When two orbitals interact, the lower energy orbital mixes into
itself the higher energy one in a bonding way, while the higher energy
orbital mixes into itself the lower energy orbital in an antibonding way.
• Key aspect of orbital mixing is that the antibonding combination is
raised in energy more than the bonding combination is lowered in
energy.
• If both of the original orbitals are doubly occupied so too shall be the
resulting two orbitals.... net interaction is destabilizing.
• If only electrons are involved, then they end up in the lower energy
mixed orbital... which is favorable.
• Nondegenerate mixing of orbitals results in polarization of the
resulting MO orbitals.
• Perturbation theory:
• First-order perturbation = mixing of degenerate orbitals.
• Second-order perturbation = mixing of nondegenerate orbitals

The CH2/MH2 Group

THEORY FOR CH2 IS SAME AS CH3 SO I HAVE EXPLAINED IT IN SHORT IF U STILL HAVE DOUBT COMMENT BELOW.

• Generate group orbitals for CH2 group.
• Compare linear vs. bent orientation of the two
H atoms relative to C.
• Linear configuration
• Angled/bent configuration
• Expect secondary mixing between C and E
producing C’ and E’.
• σ(CH2) w/ σ symmetry,
• π(CH2) (a degenerate pair of orbitals) w/ π
symmetry.
• σout(CH2) w/ σ symmetry, pointed away from the
hydrogens.

• As with CH3 = MH3... there is an MH2.
How do shifts in positioning of H atoms impact the energetics of the group orbitals?
• Water 􀀁 M = O, brings 6 valence σ(CH3) w/ each H atom contributing 1 ē. (total of 8 valence ē) . Fill
starting with lowest energy group orbital, σ(CH2).
• Water prefers bent geometry because of energy gains from lowering the energy of C/C’, which is
occupied. Oxygen lone pairs of ē are not equivalent and are best thought of as being in C’ and D
MO’s.