One of the three HMO molecular orbitals (MOs) for allyl radical is given below:

ψ = ½ χ₁ – (1/√2) χ₂ + ½ χ₃

Find out all three MOs of allyl radical and arrange them in order of increasing energy. Justify your answer. 

One of the three HMO molecular orbitals (MOs) for allyl radical is given below:

ψ = ½ χ₁ – (1/√2) χ₂ + ½ χ₃

Find out all three MOs of allyl radical and arrange them in order of increasing energy. Justify your answer. 

Write down the wave function for the nonbonding molecular orbital for a heteronuclear diatomic molecule AB assuming that the electron on an average spend 90% of its time on nucleus A and 10% of its time on nucleus B. 

Write down the molecular orbital configuration of B₂⁺ ion. 

Formulate the spatial wavefunction for hydrogen molecule using the ground state wavefunction of hydrogen molecule ion. 

Draw a schematic diagram of the variation of E⁺ and E⁻ for hydrogen molecule as a function of internuclear distance. 

Write the complete Hamiltonian for the Hydrogen Molecule and specify different terms involved. 

Define mathematical groups and outline their characteristics. 

Deduce the point group of all the isomers of difluoroethane. 

Deduce the point group of all the isomers of difluoroethane. 

Formulate the matrix representation for reflection of a vector through xy plane. 

Consider the following trial wavefunction for a particle of mass m confined to move in a one-dimensional box of length, L.

ψ = ax(L – x)²
Determine the corresponding energy by using variation theorem. 

Why the approximation methods are necessary in quantum chemistry? Give the difference between variation method and the Perturbation theory. 

Write the Slater determinant for the ground state for lithium atom. 

What is Hückel's assumption for an exchange integral?

What are the factors that determine the energy of molecular orbitals?

What are the factors that determine the energy of molecular orbitals?

Give the difference between symmetry element and symmetry operation.

Give the difference between symmetry element and symmetry operation.

Which of the perturbation methods used gives a better estimate of the ground state energy of helium atom?