Chem 125 Lecture 13 10/6/2006 Projected material This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed.

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Presentation transcript:

Chem 125 Lecture 13 10/6/2006 Projected material This material is for the exclusive use of Chem 125 students at Yale and may not be copied or distributed further. It is not readily understood without reference to notes from the lecture.

Which shell (1 or 2) has higher density? 1 2 Which shell contains more stuff (probability) ? 2 has ~ 3  the radius ~9  the volume of 1.

Multiplying and Adding Wave Functions Multiply “pieces” to create 1-electron wave function for atom:   ( , ,  ) = R(r)   (   )   (   ) “ORBITAL” Add orbitals of an atom to create a “hybrid” atomic orbital: 2p y + 2p z = hybrid orbital Function of what? Position of one electron!

Change Orientation by Hybridization a 2p y + b 2p z (a weighted sum) 2pz2pz 2py2py 25%50% 75% 50:50 mixture of p z and p y ? Other mixtures of p z and p y ?

Change Shape by Hybridization sp n = a 2  + b 2p x (sp n ) 2 = a 2 2  2 + b 2 2p x 2 + 2ab 2  2p x b2b2 a2a2 n n  (a weighted sum) Maximum extension for sp 1 hybrid (see Web & A-i-B) E

1.00 Change Shape by Hybridization sp n = a 2  + b 2p x (sp n ) 2 = a 2 2  2 + b 2 2p x 2 + 2ab 2  2p x b2b2 a2a2 n n  (a weighted sum) E  (Pure 2p)

Two (or more) Electrons Joint Probability Prob (A and B) = Prob (A)  Prob (B) Tossing two coins for two heads IF the events are independent

2 22 No way the electrons can be independent! 2-e Wave Function “An Orbital is a One-Electron Wave Function” (r1,1,1,r2,2,2)(r1,1,1,r2,2,2)  a (r 1,  1,  1 )   b (r 2,  2,  2 ) = ? Multiply 1-e Wave Functions function of what?

Tricks to Salvage Orbitals

Approximate e-Repulsion for He H Z = 1

Approximate e-Repulsion for He He Z = 2

Approximate e-Repulsion for He "He" Z = 1.69

Z effective "Clementi-Raimondi" values for Z eff Atom Z Z eff 1s He Z eff 2s Z eff 2p C Z eff 3s Na Let other electron(s) "screen" nuclear charge ! ?

Self-Consistent Field (SCF)

"Correlation Energy" Error after full SCF calculation Get correct energy by experiment or by a whopping calculation: e.g. “Configuration Interaction” (CI) or “Density Functional Theory” (DFT)

Might "Correlation Energy" be Negligible?

End