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- 3. How many vibrational modes do each of the following have? a) Azulene, C₁0H8: b) Ammonia, NH3:2. Explainthefollowing,relatedtophysicalinsighttointernalenergy(i)Translationenergy(ii)rotational kinetic energy (iii) vibrational kinetic energy (iv) Internal energy (v) spin energy (vi) sensible energy (vii) latent energy (viii) chemical energy (ix) nuclear energy (x) thermal energy2. We can form a group of symmetry operations, with our operation being do one operation and do another. For a molecule with an isosceles triangle molecule like water, we talked about the 4 symmetry operations as E (do nothing), C2 (rotation by 180°), σv (the reflection of one hydrogen to the other), and σv’ (the reflection from front to back). By putting coordinates on each of the three atoms (z points along the C2 rotation axis, x points from one hydrogen to the other, and y points out of the plane of the molecule) find the “multiplication” table for this group.
- a.) Write down for yourself the secular determinant for the hypothetical molecule linear H3 making the Huckel approximation, using the 1s atomic orbitals from each atom as the basis set. Given that α=-2.00 eV and β= -3 eV, what is the total electronic energy in eV? b.) Write down the secular determinant for the hypothetical molecule cyclic H3 making the Huckel approximation, using the 1s atomic orbitals from each atom as the basis set. Given that α=-2.00 eV and β= -2 eV, what is the total electronic energy in eV?TOPIC: QUANTUM, ATOMIC AND MOLECULAR PHYSICIS (a) Using Hückel's method, describe the energy of the molecular orbitals T of cyclobutadiene C4H4, which is a flat molecule made up of a square ring of carbons, as shown in the figure; (b) Do the same for 1,3-butadiene C4H6, which is an elongated planar molecule, as shown in the figure. (c) In both cases, draw an energy diagram indicating the filling of the orbitals and identifying the HOMO and the LUMO. Sketch by hand schematically (using two colors to distinguish the lobes from the 2pz orbitals) the result obtained for the orbitals, identifying them with the corresponding energy. If possible, you can use the Orbital Viewer program to plot the orbitals.Inversion is not a symmetry operation of methane.Explain.
- 1. For the molecules hexatriene (A) and cyclopentadienyl radical (B) shown below, use the Hückel approximation to obtain the following: (a) Secular determinant (b) Energy levels (c) Molecular orbitals (d) Delocalization energy (A) (B)6) This question is concerned with vibrational spectra (Infrared and Raman). a) How many normal modes of vibration are expected in these molecules? (Show calculations) i) Theobromine (the caffeine-like stimulant that is found in chocolate) b) In the molecular vibration shown here for trans-1,4-dichlorocyclohexane, both chlorine atoms stretch away from the carbon to which they are bonded (arrows). Will this mode be IR active? Will this mode be Raman active? In each case, why or why not? ii) Cyanopolyyne (an organic molecular wire that has been detected spectroscopically in interstellar space, and is postulated to be a precursor to biomolecules: HC=C-C=C-C=N c) Why are CH4 and CO₂ considered greenhouse gases, but O₂ and N₂ are not? d) Are the vibrations shown here a degenerate pair (Yes/No)? Why or why not? HN CI CH3 ci↑ ∙H -F CH3 -F(b) Calculate the bond order in the peroXiue lon 0) (c) Which of these species has the stronger bond? Og (superokide) is Stronger 8) Draw three canonical Lewis structures for ozone. it 9) In a quantum mechanical calculation on ethene, 116 atomic orbital basis functions were used. After symmetry adapting these functions, there were 23 functions of a, symmetry, 7 functions of b, symmetry, 11 functions of b2, symmetry, 17 functions of b3g symmetry, 7 of a, symmetry, 23 of bu symmetry, 17 functions of b2u symmetry, and 11 of b3u symmetry. (a) How many molecular orbitals will be formed in the calculation? (b) How many of these molecular orbitals will be occupied in the ground state? (c) How many of the molecular orbitals will be of ungerade symmetry?
- Q4) What two types of orbitals are interacting here (just use letter designations) and what would the symmetry relationship for an interaction between the following two orbitals be?6. Which symmetry elements are lost on going from (a) BC13 to BCl2F and (b) BC12F to BBRCIF. Which symmetry elements are common to all these molecules?Give the ground state electron configurations of(a) Li2 (b) Be2 (c) C2 .Use the symmetry-specific nomenclature appropriate for homonuclear diatomics. Example, Sg would stand for σg. Enclose each MO in parenthesis followed by the number of electrons in that MO, e.g., the entry (1Sg)2 would represent 1σg2. Letter P then is used to represent a pair of π MO's.