(a) Determine the contributions of the 2s and 2p AOs in this hybrid and compare them with the respective contributions in the spn (n=1,2,3) hybrids. (b) Calculate ? and write down the hybrid AO as proper combination of hydrogen-like 2s and 2p AOs for the C atom (use 2p oriented in the direction of hybrid), with numerical coefficients. (c) Show that average distance from the nucleus for electron in the hybrid AO can be written as ?r? = (?2/(1+ ?2)) ?r?2s + (1/(1+ ?2)) ?r?2p in terms of the ?r? values for the 2s and 2p AOs.Document Preview:1. Consider the boron-nitride, BN, molecule (basic unit of the boron-nitride nanotubes) in the ground state. Using Chem3D (with RORestricted open shell if calculating open-shell species) (a) Calculate total energies separately for each of B and N atoms (in the ground state). (b) Optimize the molecule and obtain total energy and equilibrium distance Refor each of the singlet (S=0) and triplet (S=1) states. Conclude which is the ground state, and calculate its dissociation energy De. Draw the MO energy diagram for this molecule accordingly and conclude which MO is HOMO and if the s-p mixing switches the relevant s and p MOs. (c) Calculate total energies separately for each of the atomic cations (B+ and N+). (d) Optimize the molecular cation BN+ and obtain its total energy, Re and De, and compare them with respective valus for BN. (e) Calculate and compare the ionization energies for B, N, and BN. 2. For the C atom consider the s2p3 hybrid (occurs for anionic carbon in some molecules). (a) Determine the contributions of the 2s and 2p AOs in this hybrid and compare them with the respective contributions in the spn (n=1,2,3) hybrids. (b) Calculate ? and write down the hybrid AO as proper combination of hydrogen-like 2s and 2p AOs for the C atom (use 2p oriented in the direction of hybrid), with numerical coefficients. (c) Show that average distance from the nucleus for electron in the hybrid AO can be written as r = (?2/(1+ ?2)) r2s + (1/(1+ ?2)) r2p in terms of the r values for the 2s and 2p AOs. (d) Use Maple to calculate this average r value for the hybrid AO (using hydrogen-like AO with proper Z). What are the nearest longer and nearest shorter spn hybrids? (e) Draw the s2p3 hybrid using Orbital Viewer. Attachments: structure-and.docx
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