9. Consider the cyclic cation C,H,*. a. How many electrons are in the n system? Circle your answer. [2 pts] 8 9 10 b. Use the appropriate polygon (below) to complete the Hückel analysis of this π system by drawing in the energy levels of the MOs and filling them with the number of electrons you answered in part a. Only one of the four polygons is correct for the analysis in both ring size and- orientation. [6 pts] 8 8 9 9 c. Is the cyclic cation C,H,* aromatic, antiaromatic, or nonaromatic? Circle your answer. [2 pts] aromatic antiaromatic nonaromatic

Consider a ring system made up of 8 atoms (each one contributing a p atomic orbital to make 8 pi molecular orbitals). If the system is filled with 6 orbitals containing single, electrons, there will 6 orbitals containing pairs of electrons and 1 unpaired electrons. Hint: Use a Frost Circle. Use numbers rather than text for your answers.

3. The molecule BF has such a large energy difference between B and F that the 2s orbital of boron combines with the 2pz orbital on F. The remaining 2p orbitals on fluorine combine with two of the 2p orbitals on boron to form pi orbitals. The third 2p orbital on boron is nonbonding. The energy ordering of the molecular orbitals is (2sF) < 4(2sg + 2pf) < Þ(2pg - 2pf) < y(2sg-2pf) < (2pg + 2pf) < (2pB) a. Draw the molecular orbital energy diagram for BF. b. Determine the bond order of BF. Is it paramagnetic?

1. Derive the following expression for the bonding and antibonding orbitals of a heteronuclear diatomic molecule consisting of two electrons in a molecular orbital of the form y = CAA + CBB with atomic orbitals A and B. Let aa=HAA, aB=HBB, B=HAB=HBA, SAA-SBB=1, and, as a simplification, let SAB=SBA=S=0 (zero-overlap approximation). Note that the assumption of SAB=SBA=S=0 is used simply to get a more transparent expression. Show that the secular determinant is given by a,-E - E and energies are given by 1/2 2B E̟ = }(a, +a,)±(a,-a,) For B<0, E+ is the lower energy solution.

Given that the following MO-energy-level diagram applies to the the diatomic molecular cation BO+, match the letter label of each energy level with the corresponding orbital descriptor. (See attached image!) O2pσ2pσ2s*π2pσ2p*B+2sπ2p*σ2sO2sB+2p Does this diagram display the effect of s-p orbital mixing? YES or NO? Which kind of magnetism would be observed for this cation? paramagnetism diamagnetism What is the bond order for this cation? 0.0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 2.0

44. The molecule H3* has long been speculated to exist. The interest here is that the addition of the smallest bit of nuclear matter, a proton, now introduces additional nuclear repulsion over the H₂ problem. The issue was whether electron distributions could lead to a stable configuration. a) Draw what you think would be the most stable structure for H3* and show all the Coulombic terms (write out the potential needed for the corresponding Schroedinger equation). b) Draw what you think is the least stable configure of the 3 protons and 2 electrons. c) It is found that the structure involves the rotation of one proton around the other two, and interchange of which proton is rotating. Offer a potential explanation (think tunneling).

For the O2, O2+, O2-,           Draw the molecular orbital electron configuration (1sσ2, 1sσ*2, 2sσ2,             2sσ*, 2pσ2, 2pπ2,,,, ) for O2-.

An energy level scheme for the orbitals of second row diatomic molecules O, through Ne2 , lists the molecular orbitals in the following order of increasing energy 02 < o'2s < Ozp(z) < T2p(y)- 7T2P(x) < T*2p(y), 7T* 2p(x) < o*2plz) Based on this energy level scheme, how many electrons are there in all of the antibonding molecular orbitals of the F2* ion in its ground state?

The MO of the ground state of a heteronuclear diatomic molecule AB is Vmol = CA4A + CB4B If a bonding electron spends 90% of its time in an orbital pA on atom A and 10% of its time in øB on atom B, what are the values of CA and Cg? (Neglect the overlap of the two orbitals.)

6. For heteronuclear diatomic molecules, the energy-level diagrams of the molecular orbitals need to be modified via calculation. For both NO and CN', the order of molecular orbitals are similar to that of O,. Write electron configurations of NO and CN including core electrons, starting with o1,'01,*². Which bond is stronger? (hint: bond order)