Chemistry Physical CHEM3504 Fall 2008 Practice-final 2008 (Note that these problems refer only to the new material covered after Test 2. For the comprehensive part, refer to the practice, quiz and homework problems). 1. The O2 molecule is paramagnetic, i.e. it has a net magnetic moment. Explain this fact on the basis of molecular orbital theory.
2. The formaldehyde molecule is isoelectronic with O2, since both the O atom and the CH2 group have 6 valence electrons. Do you expect formaldehyde to be paramagnetic as O2 is? Base your arguments on the calculated valence orbital energies. These are, for O2, (in increasing order and in atomic units (Eh): -1.287(), -0.795(), -0.533(), -0.517(), -0.517(), -0.215(), -0.215(), +0.219(),..., and for formaldehyde: -1.069(a1), -0.638(a1), -0.500(a1), -0.456(a1), -0.407(a1), -0.273(a1), -0.049(a1), +0.048(a1) ,...
3. The normalized 1s atomic orbital in the H2 molecule are A (on the first nucleus) and B (on the second nucleus). Their overlap is S=ABd=0.63 . (a) Determine the correct normalization factor N for the linear combination =N(0.5A+0.8B) (b) Are the two functions 1=A+2B and 2=1.1637A-B orthogonal?
B
Solution: N=0.8470; yes within the precision of the data. 4. Let us place a hydrogen 1s atomic orbital on a nucleus situated at A=(Ax,Ay,Az)= (0,0,2ao) (i.e. the center of is at A). The 1s hydrogen wave function is -1/2a0-3/2exp(-r/ao) where r is the distance from its center. What is the value of this atomic orbital at the point r=(4ao,0,-1ao), in units of a0-3/2, and what is the electron density provided by this orbital? Value=0.00380 a0-3/2, Electron density=1.444E-5 a0-3 5. According to a Hckel MO calculation, the orbital energies of anthracene and phenanthrene are, in increasing order (in eV units) Anth. -1.931 -1.600 -1.131 -1.131 -0.800 -0.800 -0.331 +0.331 +0.800 ..... Phen. -1.948 -1.561 -1.213 -1.045 -0.914 -0.615 -0.484 +0.484 +0.615 ..... Based on this, which molecule is more stable in the Hckel approximation, and by how much in kJ/mol? Which has a higher ionization energy? Which has a higher first excitation energy? (1 eV=1.602E-19 J; Avogadro's number is NA=6.022E+23 mol-1).
Phenanthrene is more stable by 9.86 kJ/mol according to the (generally very poor) Huckel calculation. Phenanthrene also has the higher ionization energy. 6. Describe the main features of molecular mechanics, semiempirical and ab initio (including density functional theory) electronic structure calculations by accuracy and computational expense.
7. What is a basis set in ab initio calculations? Describe 3 basis sets in order of increasing accuracy.
8. The electronic states of a C2v molecule can belong to four possible symmetry species (irreducible representation): A1, A2, B1 or B2. Which dipole transitions are allowed from a state with B2 symmetry? (Answer: to A1, A2 and B2; transitions to B1 are forbidden).
9. What is the symmetry point group of allene, H2C=C=CH2 ? (Note: the 2 methylene groups lie in perpendicular planes!!!). Does this symmetry group degenerate have representations? (If you cannot find its character table in the book, look it up on the Internet). D2d; yes, it does have a degenerate symmetry species. 10. How do the 5 degenerate d orbitals split under the symmetry group D3? They split into 3 groups. The first group has z2 (A1);. The second group contains the degenerate pair (xz,yz)(E), and the third group contains (xy,x2-y2)(another E). Which is lowest, which is highest cannot be predicted from group theory.
11. Describe the degeneracy and the behavior under the symmetry operations of a wavefunction belonging to the A2 symmetry species in the group D3. This wavefunction is non-degenerate. It is symmetrical (unchanged) under the C3 operation, and is antisymmetric (changes sign) under the C2 operations. Its notation
corresponds to this: it is A (symmetrical under the main operation) and it has the subscript 2 (antisymmetric under the secondary operation C2).
12. Describe and sketch the Michelson interferometer.
13. What is an optical grating?
14. The transmittance of a 0.2 M potassium bichromate solution in a 2 mm cell at 488 nm is 0.3 (30%). What is the transmittance of a 0.4 M solution? 9%
15. The rotational constant B for a linear molecule is 1.95 cm-1. What are the wavenumbers of its pure rotational transitions? 3.90 cm-1, 7.80 cm-1, 11.70 cm-1, 15.60 cm-1 etc. 16. A lowest rotational Raman transition (J=0 to 2) of 35Cl2 is at a Raman shift of 5.851 cm-1. Predict the corresponding Raman shift for 35Cl37Cl. 5.686 cm-1
17. The fundamental vibrational wavenumber of 35Cl2 is 560 cm-1. What is its force constant in SI units? The atomic mass of 35Cl=34.9688 amu. 322.8 N/m= 322.8 kg s-2. 18. What is the difference between d-d and charge transfer transitions? Which is, in general, more intense?
19. Describe the ...