9A Valence Bond Theory

What is the wavefunction for two weakly spaced atoms?

Ψ(1,2)=ΨA​(1)ΨB​(2)+ΨA​(2)ΨB​(1)

What does the linear combination without a negative sign result in?

It results in constructive interference, enhancing the probability density of sss-orbitals in the internuclear region.

What kind of symmetry does a sigma (σ\sigmaσ) bond exhibit?

Cylindrical symmetry around the internuclear axis.

How is a sigma bond formed between two atoms with 2pz​ orbitals?

By spin pairing of electrons in the 2pz​ orbitals along the internuclear axis.

Why can't 2px​ and 2py​ orbitals form sigma bonds?

They cannot merge along the internuclear axis and thus form π bonds.

How are π bonds formed?

From the spin pairing of electrons in 2px or 2py​ orbitals, which approach side by side.

What does a sigma (σ) bond resemble?

It resembles s-orbitals.

What does a pi (π) bond resemble?

It resembles a pair of p-orbitals.

What is the overall bonding pattern of N2​?

N2​ has a bonding pattern of 1 σ bond and 2 π bonds, represented as N≡N

What can a Valence Bond (VB) wavefunction be a superposition of?

Wavefunctions that correspond to different descriptions of bonding.

What does the general VB wavefunction consist of?

A combination of Ψcovalent+λΨionic

What are the two extremes in an ionic-covalent resonance structure?

One is purely covalent, and the other is purely ionic

What is a resonance hybrid?

The unnormalized wavefunction that blends pure covalent and pure ionic structures.

What does the probability of finding an ionic structure depend on?

It is proportional to λ²

What happens if λ² < < 1?

The covalent description dominates.

What happens if λ² > > 1?

The ionic description dominates

What is resonance in Valence Bond Theory?

A blending of characteristics from covalent and ionic structures.

What does the variation principle state?

The calculated energy using an arbitrary wavefunction will always be greater than or equal to the true energy.

What is a trial wavefunction?

An arbitrary wavefunction used in the variation principle to estimate energy.

How do you find the best value of λ\lambdaλ in resonance theory?

It is the value that results in the lowest energy when calculating the expectation value of the Hamiltonian.

What is the ionic contribution to resonance proportional to?

It is proportional to λ²

How does resonance affect the bond character in benzene?

It distributes bond character evenly around the ring, making all C-C bond lengths and strengths identical.

What is resonance stabilization?

The allowance of electrons to adjust into a lower-energy distribution, responsible for the stability of aromatic rings

When does resonance lower the energy the most?

When the contributing structures have similar energies

What is promotion in the context of electrons?

The excitation of an electron to an orbital of higher energy.

Why is the promotion of carbon a characteristic feature?

The promotion energy is small, and the promoted electron relieves electron-electron repulsion in the valence 2p orbital.

What is the configuration of sp³ hybrid orbitals?

sp^3= s + px + py + pz

What is the configuration of sp²hybrid orbitals?

sp^2=s+px+py

What is a lone pair of electrons?

A pair of electrons not participating directly in bond formation but potentially influencing the shape of the molecule.

What is the first sp² hybrid orbital configuration?

h1​=s+ 2^1/2py

What is the second sp² hybrid orbital configuration?

h2=s+(3/2)^1/2px − (1/2)^1/2py

What is the third sp² hybrid orbital configuration?

h3​=s−(3/2)^1/2px + (1/2)^1/2py

What is the first sp hybrid orbital configuration?

h1​= s + pz

What is the second sp hybrid orbital configuration?

h2​= s− pz

What are the two principal theories of molecular electronic structure?

Valence-bond (VB) theory and molecular orbital (MO) theory.

What is the key idea behind Valence Bond Theory?

A bond forms when an electron pairs its spin with that of another electron in an atomic orbital on a different atom.

What does the Born-Oppenheimer approximation state?

The nuclei can be treated as stationary while the electrons move around them.

What does the molecular potential energy curve show?

The variation of potential energy with bond length

What happens to the electron probability when two atoms in a diatomic molecule approach each other?

It's equally likely for either electron to be found on either atom.

How is a sigma bond formed in diatomic molecules like H2​?

Through orbital overlap and spin pairing of two s-orbitals.

How is a sigma bond formed in N2​?

By orbital overlap and spin pairing of two pz​ orbitals along the internuclear axis.

How are pi bonds formed?

Through the side-by-side overlap of p-orbitals perpendicular to the internuclear axis

What is resonance in the context of bonding?

The superposition of structures with different electron distributions but the same nuclear arrangement.

What is resonance stabilization?

The lowering of energy due to resonance

What is promotion in the context of bonding?

The excitation of an electron to an empty orbital to enable the formation of additional bonds

What is hybridization?

The blending of atomic orbitals to form hybrid orbitals.

What is the bond angle predicted by VB theory for H2O?

90 degrees (although the actual bond angle is 104.5 degrees).

What is the hybridization of carbon in methane?

sp3 hybridization

What is the bond angle in molecules with sp² hybridization?

120 degrees

What is the bond angle in molecules with spspsp hybridization?

180 degrees

What is the hybridization in acetylene (HC≡CH)?

sp hybridization.