According to molecular orbital theory, the species among the following that does not exist is
(a) O2

Q: Why does a bond order of zero mean the molecule doesn't exist?

A bond order of zero means that the number of electrons trying to pull the atoms together (bonding) is exactly equal to the number of electrons trying to push them apart (anti-bonding). With no net attractive force, the atoms simply drift apart.

Q: Can a bond order be a fraction like 0.5?

Absolutely! A fractional bond order like 0.5 or 1.5 indicates that there is an odd number of electrons involved in bonding. These species are often radicals and might be highly reactive, but they do exist!

Q: Do I need to count the inner shell electrons for bond order?

Technically, no. The inner shell electrons (like the 1s electrons in Beryllium) always form an equal number of bonding and anti-bonding pairs, canceling each other out. You can save time by only calculating the bond order using valence electrons!

Q: Why is $He_2^+$ stable but $He_2$ is not?

$He_2$ has 4 electrons, filling both the bonding and anti-bonding 1s orbitals, resulting in a bond order of 0. However, removing one electron to form $He_2^+$ leaves only 1 anti-bonding electron against 2 bonding electrons, giving a net positive bond order of 0.5.

Q: How do I remember the filling order of molecular orbitals?

For molecules with 14 or fewer electrons (like $N_2$ or $C_2$), the $\pi 2p$ orbitals are lower in energy than the $\sigma 2p_z$ orbital. For molecules with more than 14 electrons (like $O_2$ or $F_2$), the $\sigma 2p_z$ drops below the $\pi 2p$ orbitals.

Question

According to molecular orbital theory, the species among the following that does not exist is

Options:

(A) $O_2^{2-}$

(B) $He_2^-$

(C) $Be_2$

(D) $He_2^+$

Sigma Percentile · Accepted Answer

### The Mythical Molecules

Have you ever wondered why some molecules exist in nature while others are completely impossible? The answer lies deep within the quantum realm, specifically in **Molecular Orbital Theory (MOT)**.

According to this theory, when atoms come together, their atomic orbitals merge to form molecular orbitals. Some of these new orbitals are bonding, which pull the atoms together, while others are anti-bonding, which push them apart.

The ultimate test of a molecule's survival is its **Bond Order**. If the bond order is zero or negative, the anti-bonding forces overpower or cancel the bonding forces, meaning the molecule simply cannot exist!

### The Master Equation

To find out if a molecule is real or a myth, we use a very simple formula. We count the number of electrons in bonding orbitals and subtract the number of electrons in anti-bonding orbitals.

$$ 	ext{Bond Order} = \frac{N_b - N_a}{2} $$

Here, $N_b$ represents the bonding electrons, and $N_a$ represents the anti-bonding electrons. A positive bond order means the molecule is stable. Let's put our suspects to the test!

### Testing the Suspects

First, let's look at the peroxide ion, $O_2^{2-}$. It has a total of 18 electrons. When we fill its molecular orbitals, we find 10 bonding electrons and 8 anti-bonding electrons.

$$ 	ext{B.O.} = \frac{10 - 8}{2} = 1 $$

Since the bond order is 1, this ion definitely exists! Next up is the $He_2^-$ ion, which has 5 electrons.

$$ 	ext{B.O.} = \frac{3 - 2}{2} = 0.5 $$

With a bond order of 0.5, it's a bit fragile, but it can exist under the right conditions.

### The Case of Beryllium

Now, let's investigate $Be_2$. A single Beryllium atom has 4 electrons, so a $Be_2$ molecule would have 8 electrons in total. Let's fill the molecular orbitals from the ground up.

$$ \sigma 1s^2, \sigma^* 1s^2, \sigma 2s^2, \sigma^* 2s^2 $$

If we count them up, we have exactly 4 bonding electrons and 4 anti-bonding electrons. Let's plug this into our master equation.

$$ 	ext{B.O.} = \frac{4 - 4}{2} = 0 $$

**The bond order is exactly zero!** This means there is absolutely no net force holding the two Beryllium atoms together. Therefore, the $Be_2$ molecule does not exist.

### The Final Verdict

Just to be thorough, let's check $He_2^+$. With 3 electrons, it has 2 bonding and 1 anti-bonding electron, giving a bond order of 0.5. It survives the test!

So, our investigation concludes that $Be_2$ is the only species on the list that cannot exist. This is a common pattern for elements with fully filled s-subshells, like Beryllium and the noble gases. Their bonding and anti-bonding electrons perfectly cancel out!

Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: According to molecular orbital theory, the species among the following that does not exist is

Select Answer:

Visualized Solution

Condition for Existence

Bond Order Formula

Checking $O_{2}^{2 -}$ and $H e_{2}^{-}$

Checking $B e_{2}$

Conclusion

The Way Forward

The Sigma Insight: Molecular Orbital Theory

The Mythical Molecules

The Master Equation

Testing the Suspects

The Case of Beryllium

The Final Verdict

Similar Questions

According to molecular orbital theory, which of the following will not be a viable molecule?

According to molecular orbital theory, the number of unpaired electron(s) in $O_{2}^{2 -}$ is ....... .

In which of the following pairs of molecules/ions both the species are not likely to exist?

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