Molecular Orbital Theory Explained in 11 Minutes

To understand molecular orbital theory

deeply, we will cover these topics in

this video. Main postulates of molecular

orbital theory, difference between

bonding molecular orbitals and

antib-bonding molecular orbitals, what

is bond order and how we can find it.

How to check paramagnetic and

diamagnetic behavior and how to

determine the energy order of molecular

orbitals. First, let's start with the

main postulates of molecular orbital

theory. The first postulate says that

atomic orbitals intermix to form

molecular orbitals. For example, in the

case of a hydrogen molecule, when its

two atomic orbitals intermix with each

other, they result in the formation of

molecular orbitals. And we will discuss

this in detail. According to the second

postulate, the number of molecular

orbitals formed will always be equal to

the number of atomic orbitals that

intermix. This means that if two atomic

orbitals are involved in mixing, it will

always form two molecular orbitals.

According to the third postulate, only

those atomic orbitals will intermix with

each other that have comparable

energies. This means that the 1s orbital

will overlap with the 1s orbital of

another atom. And similarly, the 2s

orbital will overlap with the 2s orbital

of another atom. It is not possible that

the 1s orbital of one atom can overlap

with the 2s orbital of another atom.

Now, we will move towards bonding

molecular orbitals and antib-bonding

molecular orbitals. To understand this,

we will draw the molecular orbital

diagram of a hydrogen molecule. As we

know, a hydrogen atom has one electron

and it is present in the 1s orbital. So,

it means that in order to form a bond,

these atomic orbitals should intermix.

Here we can see that two atomic orbitals

are taking part in mixing. So, it means

that two molecular orbitals will be

obtained. But we need to keep in mind

that half of the molecular orbitals will

have lower energy than the parent atoms

and half will have higher energy than

the parent atoms. So it simply means

that the two molecular orbitals which

will be formed in this case, one will

have lower energy and the other one will

have higher energy than the parent atom.

Now it's time to see what actually is

the difference between bonding molecular

orbitals and antib-bonding molecular

orbitals. Keep in mind that molecular

orbitals that have lower energy than

their parent atomic orbitals will be

called bonding molecular orbitals and

those having higher energy than their

parent atomic orbitals will be

antib-bonding molecular orbitals. We

need to understand one more important

point. Since anti-bonding molecular

orbitals are higher in energy than

bonding molecular orbitals, they will be

denoted by placing a star on them. For

example, sigma star and pi star. Bonding

molecular orbitals due to their lower

energy will be denoted without a star

and they will be called sigma and pi

bonds. Now, we need to understand how we

should place electrons in molecular

orbitals. Keep in mind we need to follow

the rules of electronic configuration

such as Pauliey's exclusion principle,

offbal principle and Hun's rule. For

example, in the case of a hydrogen

molecule since there are a total of two

electrons in the atomic orbitals of

hydrogen, we need to place them in

molecular orbitals. Both electrons will

be placed in the sigma 1s orbital which

is actually a bonding molecular orbital

and no electron will be available for

antib-bonding molecular orbitals. This

happens due to the offbell principle

which states that electrons must be

filled according to their increasing

energy levels. So first we need to

complete the sigma 1s orbital and both

electrons will be filled in it. Now we

will discuss what bond order is and how

we can find it. Actually bond order

refers to the total number of bonds

formed between two atoms when their

atomic orbitals overlap. We can find the

bond order of any molecule with this

formula. Bond order is equal to total

number of electrons in bonding molecular

orbitals subtracting total number of

electrons in anti-bonding molecular

orbitals and divided by two. We can

understand this with the example of a

helium molecule. As we know the atomic

number of helium is 2. So its veence

electrons will be present in the 1s

orbital and its electronic configuration

will be 1 s2. To draw its molecular

orbital diagram, the 1s orbital of one

helium atom should intermix with the 1s

orbital of the other helium atom.

According to the postulates, two

molecular orbitals should be formed. One

will have lower energy than the parent

atom and will be called a bonding

molecular orbital while the other will

have higher energy than the parent atom

and will be called an anti-bonding

molecular orbital. As we can see, there

are a total of four electrons present in

the atomic orbitals of helium. So now we

need to place them in molecular

orbitals. According to the rules, two

electrons should be placed in the sigma

1s orbital and two will be placed in the

sigma star 1s orbital. Now to find the

bond order, we will apply the formula.

As we can see, two electrons are present

in bonding molecular orbitals and two

electrons are present in anti-bonding

molecular orbitals. So it will be 2

subtraction 2 and divided by two and its

answer will be equal to zero. This means

that the bond order of helium is zero.

From this we can conclude that helium

will never form a bond since its bond

order is zero. You can also check this

for a hydrogen molecule and its bond

order will be one which shows that

hydrogen will always form one bond. Now

we will understand the difference

between paramagnetic and diamagnetic

behavior. We need to remember that if

there is any unpaired electron present

in molecular orbitals then that molecule

will always be paramagnetic in nature.

But if all the electrons are paired and

no unpaired electron is present in

molecular orbitals then we should say

that it is diamagnetic in nature. To

understand this deeply and also to

understand the main concepts of

molecular orbital theory. Now we will

take the example of a nitrogen molecule.

As we know the atomic number of nitrogen

is 7. From the electronic configuration

of nitrogen, we can see that in this

case, first of all, the 2s orbital of

the first nitrogen atom should overlap

with the 2s orbital of the second

nitrogen atom and will form two

molecular orbitals of nitrogen. And as

mentioned earlier, electrons will be

placed in them. But here we need to

deeply understand how 2 p orbitals will

overlap and how electrons will be placed

in them. First of all, remember that 3 2

p orbitals of one nitrogen will overlap

with 32 p orbitals of the second

nitrogen. It means that a total of six

orbitals are intermixing in this case.

So according to the postulate, six

molecular orbitals should be formed. But

we need to understand that half will

have lower energy and half will have

higher energy than their parent

orbitals. This means that out of six

molecular orbitals, three will be

bonding molecular orbitals and three

will be anti-bonding molecular orbitals.

In the next step, we need to place

electrons of 2 p orbitals into molecular

orbitals that are being formed. In this

case, as we can see, there are a total

of six electrons present in atomic

orbitals. So, we have to place them in

molecular orbitals. All these six

electrons will be placed in bonding

molecular orbitals and no electron will

go towards anti-bonding molecular

orbitals. Now, if we move towards the

bond order of this molecule again, we

need to apply the formula which shows

that there are six electrons in bonding

molecular orbitals and no electrons are

present in anti-bonding molecular

orbitals. So it will be 6 subtracting 0

and divided by two and its answer will

be three. This shows that the bond order

of nitrogen is three and it will form

three bonds. Now if we look at its

magnetic behavior as we can see all

electrons in molecular orbitals are

paired and no unpaired electrons are

present here. So we can say that

nitrogen is diiamagnetic in nature. Now

we'll discuss how to write the relative

energy order for molecular orbitals.

Keep in mind that molecular orbitals

formed are different in energy from each

other. So in order to assign them an

energy order, we simply need to start

writing their energy levels in ascending

order. For example, in the case of

hydrogen, as mentioned above, sigma 1s

will have lower energy than sigma star 1

s. Similarly, if a molecule also has 2 s

orbitals involved in mixing, we can say

that the energy of sigma 2s will be

lower than sigma star 2s. But one thing

we need to keep in mind is that the

energy of pi^ 2 py and 2pz will always

be equal. So by following this simple

concept we can write the energy order

for any molecule. Now we will discuss

how molecular orbital theory explains

ions such as hydrogen ion, nitrogen ion

and oxygen ion. First let's start with

hydrogen ion. As we know a neutral

hydrogen atom has one electron in its 1

s orbital. When two hydrogen atoms

combine their atomic orbitals intermix

to form molecular orbitals resulting in

bonding and antib-bonding molecular

orbitals. Now if we consider hydrogen

molecular ion we can see that only one

electron is available. According to the

offbound principle this electron will be

placed in the lower energy bonding

molecular orbital which is sigma 1s.

Since there is no electron present in

the anti-bonding molecular orbital which

is sigma star 1 s. The bond order can be

found using the formula. So we can see

bond order will be equal to 1

subtracting 0 and divided by 2 which

will be equal to 0.5. Since the bond

order is not zero, it means that

hydrogen molecular ion is capable of

existing as a weakly bonded species but

it will be less stable than hydrogen

molecule. Now let's move to nitrogen

ion. For a neutral nitrogen molecule, we

know that nitrogen has an atomic number

of 7. Meaning its electronic

configuration is 1 s2 2 s2 2 p3. Now

let's consider nitrogen ion. Since

nitrogen negative ion has one extra

electron, it will be placed in the next

available molecular orbital which is a

pi star 2p orbital. Now the bond order

will also change. Bond order will be

equal to 8 subtracting 3 and divided by

2 which will be equal to 2.5. This means

that when an extra electron is added the

bond order decreases making nitrogen

negative ion less stable than a neutral

nitrogen molecule. Now we will discuss

oxygen ion. Molecular orbital

explanation for O negative ion. Now if

we consider oxygen negative ion, it has

one extra electron which will enter the

pi star 2p orbital. This changes the

bond order as follows. Bond order will

be equal to 8 subtracting 5 and divided

by 2 which will be equal to 1.5. This

means that oxygen negative ion has a

lower bond order than a neutral oxygen

molecule making it less stable and

weaker in bonding strength. Effect of

charge on bond order and stability. From

these examples, we can conclude that

adding an electron as in nitrogen

negative ion and oxygen negative ion

decreases bond order making the molecule

weaker. Removing an electron as in

hydrogen molecular ion reduces bond

order but does not completely eliminate

bonding. More charge generally results

in a weaker molecular bond due to

increased electron repulsion in

antib-bonding orbitals. Now moving

towards limitations of molecular

orbitals theory. It has several

important limitations. Number one, no

clear molecular shape. It does not

explain the exact shapes of molecules

unlike VR theory. Number two, complex

mathematical calculations. The theory

relies on advanced math making it

difficult to apply. Number three, fails

for some molecules. It does not

correctly predict bonding in certain

molecules such as oxygen where

experimental results show differences in

magnetic properties. Number four, weak

explanation of bond strength. It does

not always explain why some bonds are

stronger or weaker in certain molecules.

Number five, contradictions with other

theories. It sometimes disagrees with

valance bond theory, which explains

bonding in a different way.