Derive that vibrational partition

26. Let U = {arithmetic, algebra, calculus, geometry, trig- onometry, analysis, topology, statistics), B = {analysis, topology, calculus}, C = {algebra, calculus, trigonom- etry, analysis}, D = {arithmetic, algebra, calculus, topology, statistics), E = {algebra, calculus, geometry, trigonometry, analysis}. In each of the following, repre- sent the given set by an array of zeros and ones. (a) BUC (b) CnD (c) BO(DnE) (d) BUE (e) Cn(BUE)15. Derive the vibrational partition function at the high-temperature limit (T - co). 16. Use the particle in the 3-D box model to calculate the translational energy difference (AE = E2 - 81) for the molecular nitrogen (N2) and compare it with the available thermal energy at 298 K (take the length of the box to be I cm). 17. Using statistical mechanics, derive the molar entropy of monoatomic ideal gas.4. One of the computational chemical methods used to determine the energy of a compound is Molecular Mechanics. Molecular mechanical equations are stated as follows: E= [ko(T-To)? + [ko(0-8.)? + 41+ cos(nt - ] lori + EET 919 1 + + (a) Explain the meaning of each term in the equation above so that it can be explained the contribution of each component determining the amount of energy. (b) Describe the strengths and weaknesses of molecular mechanics methods in determining the properties of compounds.3. Metal coordination compounds are difficult system for molecular mechanics methods. Why is this? (Please discuss this in detail.) 4. What are the advantages and disadvantages of semi-empirical methods in term of transferability from one set of compounds to another, and in term of comparing chemically disparate system? 5. Name and explain six energy terms included in molecular mechanics