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BITS Pilani, Pilani Campus; Semester-II, 2016-17 CHEM F244: Physical Chemistry – III

Thursday, July 28, 2017 Comprehensive Examination Duration: 1.5 (+1.5) hours

Part A: Closed-book Quiz Maximum Marks for Part A: 60 out of 120

Instructions: This examination has two parts. This part, (Part A) is a closed-book. Part B is open-book. Part A is to

be solved on the question paper only. No supplements will be provided for solving Part A. Part-A is having 15 questions

over three pages.

Constant values: charge of electron: 1.602 × 10-19 C, Mass of electron: 9.11 × 10-31 kg

Name: ______________________________________ ID: ___________________ Marks obtained ____

1. A HF calculation for HeH+ is carried out with minimal basis function and with 6-31G* basis set. How the

nuclear repulsion energy and number of occupied orbital will vary? [2]

Nuclear repulsion energy: ........................................................................................................

Number of occupied orbital: ...................................................................................................

2. Assume ψ be the complete wave function of a molecule which follows Born-Oppenheimer approximation.

Is the following relation holds true? 2⟨𝜓|𝑇�̂� + 𝑇�̂�|𝜓⟩ = − ⟨𝜓|�̂�|𝜓⟩. Justify your answer. [4]

3. Given that De=4.75 eV and Re=0.741 Å for the ground electronic state of H2. Find, [5]

U(Re) =

⟨𝑉⟩|𝑅𝑒 =

⟨𝑇𝑒𝑙⟩|𝑅𝑒 =

⟨𝑉𝑁𝑁⟩ =

⟨𝑉𝑒𝑙⟩ =

4. Fill in the blanks [12]

(i) The permanent dipole moment of a molecule which is having inversion center of symmetry is

always ..............................

(ii) Under Møller-Plesset perturbation theory: 𝐸0(0)

+ 𝐸0(1)

= .................................................

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5. The gross populations (N) of the basis functions on each atom of H2S are, NS = (2.00 + 1.83+ 2 + 1.12 +

1.50), NH1 = 0.77 = NH2. Calculate the net charges on S-atom (qS) and H-atom (qH). [2]

qS = ................................................ and qH = .....................................................

6. For NaCl, Re= 2.36 Å. The ionization energy of Na is 5.14 eV and the electron affinity of Cl is 3.61 eV.

Use the simple model of NaCl as a pair of spherical ions in contact to estimate De in eV. [3]

7. Write down the expression of the one electron Fock operator for electron m in a n electron molecule which

is having nuclei. [4]

𝑓(m) =

8. State whether following statements are True or False [Write down True or False] [15]

(i) Two external potentials va (ri) and vb (ri) will always give rise to the different ground-state electron density

ρ0 ...................

(ii) The spatial parts of the wave function of He atom in the ground and lowest excited state are, symmetric

and antisymmetric respectively. ...................................

(iii) Consider overlap population contribution: nr-s, i for which r and s lie on different atoms. Thus, nr-s, i is

always negative for non-bonding molecular orbital .......................................

(iv) H-atom 1s atomic orbitals of H2O don’t transform according to any symmetry species of the

molecule .........................................................

(v) For a diatomic molecule, the equilibrium dissociation energy (De) is equal in magnitude to that obtained

by experiment ………………………

9. Write down the expression for RHF and UHF wave functions for Li atom in ground electronic state: [4]

RHF =

UHF =

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10. Apply Hellmann-Feynman theorem to one-dimensional simple harmonic oscillator. Consider to be the

force constant. [4]

11. How can we predict mixing of atomic states under external perturbation using the concept of molecular

symmetry and group theory. [4]

12. For non-linear polyatomic molecules, angular momentum classification of electronic terms can not be

used. Explain briefly. What are the basis of classification of electronic terms and why? [4]

13. What are the terms for a molecule having 2 non-equivalent electrons in ππ configuration. [4]

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14. In Raman spectroscopy Stokes lines are in general more intense compared to anti-Stokes lines. Explain

the reason(s) in brief. Propose an experimental parameter which can be tuned to obtain more intense anti-

Stokes lines compared to Stokes lines. Justify your answer. [5]

15. (i) Determine all the symmetry elements in trans-hydroquinone. (ii) How many classes are present in the

point group to which the molecule belongs? Represent all those classes. (iii) Construct the character table.

(iv) Assign Mulliken symbol to each of the representations. [2+2+2+2]

--- END OF PART A

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Birla Institute of Technology & Science, Pilani, Rajasthan - 333 031

Second Semester 2016-2017

CHEM F244 Physical Chemistry - III

Comprehensive Examination Make-up (Open Book)

Part II Time: 90 minutes Date: 28.07.2017 (10.00 - 13.00 hrs.) Marks: 60 out of 120

Don't scribble on the question paper

Instructions: Irrelevant writing for a question would not be considered for evaluation and may lead to

deduction of marks

1 (i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

Determine the symmetry of p-dichlorobenzene molecule.

Determine the symmetry of ground state and lowest electronic excited state.

What would be the lowest energy spin allowed transition in this molecule? Represent the transition

using symmetry representations.

Is the lowest energy spin allowed pure electronic transition of p-dichlorobenzene is orbitally

allowed? Justify your answer.

Determine the polarization of the 0-0 transition in case this transition is allowed?

Normal mode of vibration, ν8, is having b2g symmetry. Determine the polarization of 801 transition

in case this is allowed.

Normal mode of vibration, ν10, is having b1g symmetry. Are the transitions 1001 𝑎𝑛𝑑 101

0 allowed?

Determine the polarization in case these transitions are allowed?

Propose an experimental parameter through which you can differentiate the transitions

1001 𝑎𝑛𝑑 101

0.

[3]

[8]

[3]

[6]

[3]

[3]

[6]

[3]

2 (i) Calculate the number of molecular orbitals for the given molecules and the basis sets:

[Tabulate you answer in the following way]

Molecule Basis set Number of molecular orbitals

C2H2 6-311G

NH4OH 6-31+G

C6H12 6-31G**

[23]

(ii) A HF calculation was carried out followed by Full CI for LiH+2 molecule. 6-31G* basis set was

used for this calculation. Only singlet spin states (S=0) are used. Consider the full CI configuration.

Calculate,

a) the number of singly-excited configurations;

b) the number of doubly-excited configurations; and

c) the total number of configurations.

[3]

[2]

[4]

(iii) A phosphane molecule is perturbed by the application of an electric field in the x-direction. Which

orbitals of P atom in phosphane molecule would mix with a d-orbital under this perturbation? [6]

(iv) Consider a molecule is in an external electric field of strength 𝐹 ⃗⃗ ⃗. The Hamiltonian of the system is

given by Ĥ = 𝐻𝑜 − 𝜇 ⃗⃗⃗ . 𝐹 ⃗⃗ ⃗, where the unperturbed Hamiltonian corresponds to the system when no

external electric field acts on it. Compare this system with the non-degenerate perturbation method

and recognize that polarizability is change in the dipole moment with respect to the change in the

external field, write the expressions for the ground-state permanent dipole moment

[4]

****** End ******