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.

Putting Electrons in the MH3 System

• 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.
• The group orbital configuration developed
for CH3 applies any other MH3, where M = a
main group element.

• Deposit 6, 7 or 8 ē depending on M. 3 H
atoms contribute 3 ē and:
• B contributes 3
• C contributes 4
• N contributes 5
• Even ! systems (M = B or N):
• 6 ! of BH3 occupy MO’s A-C of either planar
or pyramidal form.
• 8 ! of NH3 occupy MO’s A-D of either planar or pyramidal form. D’/D are occupied and influence structure.
Substantial stabilization of D’ in pyramidal form.
• Follow Rule 6: Total energy is the sum of the molecular orbital energies of individual valence ē.

PYRAMIDAL MEHTYL

Walsh Diagram: Pyramidal Methyl

• Can predict how geometric distortions will
affect the MO’s of a fragment (planar CH3).
• Make the orbitals of the pyramidal methyl
group by distorting the planar methyl system
and following Rule 4.
• Rule 4: Start constructing MO’s for structures with
high symmetry, then produce MO’s for related but less
symmetric structures through systematic distortions of
orbitals for higher symmetry.
• Diagram that follows orbital energies as a
function of angular distortions is called a
Walsh diagram. (example to the left)
• Noted changes:
• Energy of A does not change much

• Energy of B and C is raised more than A is
lowered due to their directionality.
• Distortion results in favorable overlap
between H’s and C 2pz lowering energy of D,
resulting in it becoming significantly bonding.
• Rule 7... is then applied: (If the two highest energy MO’s of a given symmetry derive primarily from different
kinds of atomic orbitals, then mix the two MO’s to form hybrid orbitals).
• MO’s D and E have similar symmetry but are based on 28 C 2p and C 2s respectively.
• Group orbitals for methyl: σ(CH3) w/ σ symmetry,
• π(CH3) (a degenerate pair of orbitals) w/ π symmetry.

• σ(out) w/ σ symmetry, pointed away from the hydrogens

PLANAR METHYL

METHYL IS CH3 
valence orbital selected should be 2s and 2p of carbon,1s of hydrogen atom.

Available orbitals: three H 1s orbitals, a C 2s
orbital and three C 2p orbitals.
• Generate delocalized MO’s in accordance to the
rules.
1. Mix C 2s orbital with the three H 1s orbitals. (in
phase forms A & out of phase form E)
2. Mix C 2px and 2py orbitals with the three H 1s
orbitals. (in phase mixing results in MO’s B and C,
out of phase mixing MO’s not shown)

3. C 2pz cannot mix with the H orbitals and thus get
a nonbonding orbital (D)
• Must be a conservation of orbitals...
• Orbitals A-C are bonding orbitals, D is nonbonding
and E is antibonding. The antibonding orbitals
corresponding to B and C are not shown... higher
energy.
• The pair of higher energy orbitals are not typically
occupied or involved in bonding.

WALSH DIAGRAM

A diagram that follows orbital energies as a function of ANGULAR DISTORTIONS is called a Walsh diagram.

A major application of Walsh diagrams is to explain the regularity in structure observed for related molecules having identical numbers of valence electron (i.e. why H₂O and H₂S look similar), and to account for how molecules alter their geometries as their number of electrons or spin state changes.

 Additionally, Walsh diagrams can be used to predict distortions of molecular geometry from knowledge of how the lumo(Lowest Unoccupied Molecular Orbital) affects the homo (Highest Occupied Molecular Orbital) when the molecule experiences geometrical perturbation(change).

Few Terms

Antibonding Molecular Orbital  -  A molecular orbital that results from an out-of-phase overlap of atomic orbitals to produce an orbital that is higher in energy than either of its parent molecular orbitals.

Atomic Orbital  -  A hydrogenic wavefunction, e.g. 1s, 2p, 3d.

Bond  -  That which holds together atoms in molecules and ions in lattices.

Bonding Molecular Orbital  -  A molecular orbital that results from an in-phase overlap of atomic orbitals that has a lower energy than either of its parent atomic orbitals.

Bond Order  -  The difference between the number of bonding electron pairs an the number of antibonding electron pairs in a molecule.

Covalent Bond  -  A bond that results from a sharing of electrons between nuclei.

Hybridization  -  The process by which atomic orbitals are combined to produce a new set of orbitals suitable for use in a discussion of bonding in polynuclear atoms.

Ion  -  A charged species created by the gain or loss of an electron from an atom or neutral molecule.

Ionic Bond  -  A bond that results from electrostatic attraction between oppositely charged ions. The cation is positively charged, while the anion is negatively charged.

Lattice  -  A regularly repeating three-dimensional array of atoms, molecules, or ions.

Lewis Structure  -  A description of a covalent bond whereby electrons are represented by dots and a bond is represented by placing a line between the two atoms in that bond. Only valence electrons are shown in Lewis structures.

Lone Pair  -  A nonbonding pair of electrons.

Molecule  -  A chemical species containing a covalent bond.

Molecular Orbital  -  A combination of atomic orbitals in molecular orbital theory that provides an orbital description of a molecule analogous to the atomic orbital 

RULES OF QMOT

1.Consider valence orbitals only

exp:- these orbitals are the outermost orbitals of a atom and they take part in chemical reaction.

2. Form completely delocalised mos as linear combination of s and p AOS.

exp:- we need to combine i.e add and subtract the atomic orbital.(u will understand this better when we start building molecules).

3. MOS must be either symmetric or antisymmetric with respect to the symmetry operations of the molecule.

4. compose MOS for the structures  of high symmetry and then produce orbitals for related but less symmetric structures by systematic distortion of the orbitals for higher symmetry.

exp:- WALSH DIAGRAM

5.Molecules with similar molecular structures,such as ch3 and nh3 ,have more or less same mos,only difference being the number of electron that occupy mo.

6. the total energy is the sum of the molecular orbitals energies of the individual valence electrons.

7.if the two highest energy mos of a given symmetry derive primarily from different kinds of AOS ,then mix the 2 MOS to form hybrid orbitals.

exp:- you will understand this when i will explain pyramidal methyl

8. when 2 orbitals interact the lower energy orbitals is stabilised and the higher energy orbital is destabilised .the out phase or anti-bonding interaction between the 2 starting orbitals always raise energy more than the corresponding in phase lowers the energy.

9.when two orbitals interact the lower energy orbitals mixes into itself the  higher energy orbital one in bonding way ,while the higher energy orbital mixes itself with lower energy orbitals in anti bonding way

exp:- in phase mixing has greater portion of the lower energy orbital and out phase mixing has higher energy orbital.

10. the smaller energy gap between 2 orbitals the greater the mixing.

11. the more electronegative  elements have lower energy AOS.

12.A change in geometry of a molecule will produce a large change in the energy of a  particular MO if the geometry change results in changes in AO overlap that are large.

exp:- as stated in the earlier rule i.e greater the overlap greater the interaction ,therefore energy changes with change in overlap.

if u have any difficulty in understanding any particular rule comment down below will reply as soon as possible. 

What is MOT?

MOT considers the electrons in molecules to occupy molecular orbitals that are formed by linear combination of all the ATOMIC ORBITALS on all the atoms in the structure.

In MOT ,electrons are not confined  to an individual  atom ,but DELOCALISED over the entire molecule.

Since electrons are delocalised we can easily explain the conjugated pi bonds.Therefore patch like resonance is not necessary.

we will learn more about mot in other post
here the list what all will be covered in other post

1. Terms
2. Rules of QMOT
3. Walsh diagram
4. planar methyl and pyramidal methyl
5. different molecule following mh3 system
6. ch2 group/water molecule
7. making of ethane and ethene
8. effects of hetroatoms 

The three center two electron bond will be covered in the last post 

If u want me to cover anything else other than this comment down below.