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Unformatted text preview: Chem 3502/5502 Physical Chemistry II (Quantum Mechanics) 3 Credits Fall Semester 2009 Laura Gagliardi Lecture 31, November 30, 2009 (Some material in this lecture has been adapted from Cramer, C. J. Essentials of Computational Chemistry , Wiley, Chichester: 2002; pp. 275-281.) Solved Homework An extra electron would be expected to localize in the lowest-energy unoccupied molecular orbital (LUMO). In water, that is orbital 6. The appearance of orbital 6 is This orbital is antibonding between oxygen and the two hydrogen atoms, so filling it would be expected to lengthen the O–H bonds. A good way to think about the quantum mechanical rationale behind the lengthening of the bonds is that this decreases the curvature of the orbital wave function associated with the nodes (by moving the nodes further from one another) and thereby lowers the kinetic energy. The same argument (the decrease in kinetic energy associated with moving the nodes further from one another) suggests that one would expect the bond angle at oxygen to open up to be wider. The geometry of the water radical anion (from an independent computation) has bond lengths of 1.274 Å and an HOH angle of 135.4 deg. This agrees with our analysis based on the LUMO. 31-2 Other Computed Properties—Partial Atomic Charges An enormous amount of chemical reactivity can ultimately be rationalized by a rather simple observation: positively charged things like to associate with negatively charged things and vice versa, but charges of like sign repel one another. This simple precept explains most acid/base reactions, bimolecular nucleophilic substitution (as we'll see in more detail below), ester hydrolysis, and many other reactions at a mechanistic level. As such, a key property about which chemists like to think is the so-called partial charge associated with an atom. Thus, for example, in formaldehyde, H 2 C=O, we know that the C=O double bond is polarized in a way that makes the oxygen end more negative and the carbon end more positive, and that's why nucleophilic reagents add to the carbon atom of carbonyl groups. In principle, we might try to quantify that polarization by assigning partial charges to each atom (typically being fractional in magnitude, e.g., +0.25 for C and –0.25 for O, ignoring the H atoms for the moment). Part of the driving force for this conceit is that it allows one to conveniently ignore the wave character of the electrons and deal only with the pleasantly more particulate atoms, these atoms reflecting electronic distribution by the degree to which they carry positive or negative charge. From quantum mechanics, at least as associated with Hartree-Fock calculations, we have a natural way to come up with quantitative charges on atoms because we have occupied orbitals that are made up of basis functions on different atoms. So, if basis functions on oxygen are used more than basis functions on carbon for the occupied orbitals, we'd see more charge on the oxygen than the carbon. Let's look at this in a bit orbitals, we'd see more charge on the oxygen than the carbon....
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This note was uploaded on 12/14/2010 for the course CHEM 3502 taught by Professor Staff during the Spring '08 term at Minnesota.
- Spring '08