Question

Lithium trimers are the star-destroying material of science fiction. Consider the series of tri-atomic species Li₃, Li₃⁺, and Li₃^-. For each species, draw a Lewis dot electron diagram, predict the geometry, identify the Li-Li bond order, and identify the hybridization of the central lithium atom.

Answer 1

Question:

Lithium trimers are the star-destroying material of science fiction. Consider the series of tri-atomic species Li₃, Li₃⁺, and Li₃^-. For each species, draw a Lewis dot electron diagram, predict the geometry, identify the Li-Li bond order, and identify the hybridization of the central lithium atom.

Answers:

Triatomic hydrogen, H, is unstable and breaks up spontaneously. H⁺ , the trihydrogen cation is stable by itself and is symmetric while triatomic hydrogen anion, H^-, is unstable and also breaks up spontaneously. The following answers for the corresponding lithium species are modelled on the basis of triatomic hydrogen species as there is not much information about these species.

Li₃ triatomic cluster:

Lewis dot electron diagram and geometry:

The equilateral triangle geometry is more stable than linear shape as the end atomic orbitals form an antibonding molecular orbital while central atom forms both bonding and non bonding orbitals.

Li-Li bond order:

While calculating bond order lone electron in non bonding orbital is not considered in the calculation of bond order. Only electrons in bonding and antibonding molecular orbital electrons are considered for bond order calculation.

Bond order = ½(number of electrons in bonding MO’s – number of electrons in antibonding MO’s)

= ½ (2 – 0)

= 2/2

Bond order = 1.0

However as there are three lithium atoms and two bonding electrons the bonding order between lithium atoms becomes fractional and the bond order per atom becomes 1/3.

Hybridization of the central lithium atom:

Lithium has one valence electron in 2s orbital. Thus three lithium atoms coming together will form three hybridized 2s orbitals. The molecular orbital with lowest energy is a bonding orbital with all three atomic 2s orbitals having same sign with no nodes among the three atoms. This orbital forms sigma bond among the atoms as there are no nodes. The molecular orbital of next higher energy with a single node on central atom is a non bonding orbital with a single electron in it. The third highest energy molecular orbital is an antibonding orbital with no electrons in it. It has two nodes in it.   

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Li₃⁺ triatomic cluster cation:

The arrangement of the lithium atoms in the molecule is an equilateral triangle. The molecule has a resonance structure which represents a three-center, two-electron bond. The electron pair delocalization contributes to the stability of molecules. The cation is also one of the few known simplest triatomic molecules, since its two electrons are the only valence electrons in the system.

Lewis dot electron diagram and geometry:

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Equilateral triangle

Li-Li bond order:

Bond order = ½(number of electrons in bonding MO’s – number of electrons in antibonding   

MO’s)

number of electrons in bonding MO’s: 2

number of electrons in antibonding MO’s = 0

Bond order = ½ (2-0)

                        = 2/2

Bond order = 1

However as there are three lithium atoms and two bonding electrons the bonding order between lithium atoms becomes fractional and the bond order per atom becomes 1/3.

Hybridization of the central lithium atom:

Lithium has one valence electron in 2s orbital. Thus three lithium atoms coming together will form three 2s orbitals, namely bonding orbital with no nodes, non-bonding orbital with one node and one antibonding orbital with 2 nodes.

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Li₃^- triatomic cluster anion:

Lewis dot electron diagram, geometry, hybridization of the central lithium atom:

The three lithium atoms coming together will form three 2s orbitals, namely bonding orbital with no nodes, non-bonding orbital with one node and one antibonding orbital with 2 nodes. Unlike other lithium species, neutral and cationic Li3, the Li3 anion is expected to be linear in shape since it’s a three atom four electron system. The electrons in the antibonding orbital of end atoms repel with antiboding orbital of other end atom. The central atom has two 2s boding electrons in lower energy bonding orbital.

Li-Li bond order:

Bond order = ½(number of electrons in bonding MO’s – number of electrons in antibonding MO’s)

number of electrons in bonding MO’s: 2

number of electrons in antibonding MO’s = 2

Bond order = ½ (2-2)

                        = 0

Bond order = 0

Since its bond order is zero the existence of the species is doubtful.