chem f244: physical chemistry – iii
TRANSCRIPT
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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 ******