The energy levels of N atoms in the tight-binding Hückel approximation are the roots of a tridiagonal determinant (eqn 15C.1):
\(E_{k}=\alpha+2 \beta \cos \frac{k \pi}{N+1}\) \quad \(k=1,2, \ldots, N\)
If the atoms are arranged in a ring, the solutions are the roots of a ‘cyclic’ determinant:
\(E_{k}=\alpha+2 \beta \cos \frac{2 k \pi}{N}\) \quad \(k=0, \pm 1, \pm 2, \ldots, \pm \frac{1}{2} N\)
(for N even). Discuss the consequences, if any, of joining the ends of an initially straight length of material.
Text Transcription:
E_k=alpha+2 beta cos k pi/N+1
k=1,2, ldots, N
E_k=alpha+2 beta cos 2k pi/N
k=0, pm 1, pm 2, ldots, pm1/2 N
Chemistry 107001 (M,T,W,TH) Dr. Mentele Week 1: 2/5 – 2/8 Nomenclature: “the naming game” *remember: ionic = metal + nonmetal; molecular = nonmetal + nonmetal 1. Naming Ionic Compounds: (type I & type II) Polyatomic ions in a compound i. Cations (+): name stays the same ii. Anion (): ending in the prefix ide Metal NonMetal Chemical Formula Name Calcium Bromine CaBr 2 calcium bromide Magnesium Oxygen MgO magnesium oxide Aluminum Nitrogen AlN aluminum nitride Ionic Compounds Type I (+1) Type II (+2) One ion More than one ion Al3+, Zn2+, Ag1+ All other metals Ionic compounds: w/ type II metals o Same rules: cation + anion o Use roman numerals for charge of metal that can have more that one charge Ex. iron(III) Fe3+ Ex. iron(II) chloride Cl 2 o Common names: Ion with lower charge = “ous” Ion with higher charge = “ic” Ex. iron(II) chloride = ferrous chloride Ex. iron(II
