Several tricks (“Z-effective” and “Self Consistent Field”) allow one to correct approximately for the error in using orbitals when there is electron-electron repulsion. Residual error is hidden by naming it “Correlation energy.” J.J. Thomson’s Plum-Pudding model of the atom can be modified to visualize the form of molecular orbitals. There is a close analogy in form between the molecular orbitals of CH 4 and NH 3 and the atomic orbitals of neon, which has the same number of protons and electrons. The underlying form, dictated by kinetic energy, is distorted by pulling protons out of the Ne nucleus to play the role of H atoms. Synchronize when the speaker finishes saying “we’ve been looking at atoms.” Synchrony can be adjusted by using the pause(||) and run(>) controls. Chemistry 125: Lecture 11 Orbital Correction and Plum-Pudding Molecules For copyright notice see final page of this file

What's Coming for Next Exam? Molecules Plum-Pudding Molecules (the "United Atom" Limit) Understanding Bonds (Pairwise LCAO) "Energy-Match & Overlap" Reality: Structure (and Dynamics) of XH 3 Molecules Atoms Orbitals for Many-Electron Atoms (Wrong!) Recovering from the Orbital Approximation Payoff for Organic Chemistry! Reactivity HOMOs and LUMOs Recognizing Functional Groups How Organic Chemistry Really Developed (Intro)

2-e 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 2 22 No way can electrons be independent! They repel one another.

Tricks for Salvaging Orbitals

Pretend that the other electron(s) just reduce the nuclear charge for the orbital of interest. "Clementi-Raimondi" values for Z eff (best fit to better calculations) Atom Z Z eff 1s He s 2p Z - effective Z eff 2s Z eff 2p C Z eff 3s Na ! ! 2s slightly less screened than 2p vice versa for Na Pretty Crude  r 2Z2Z na o 1s = K e -  /2 (subtle) 1s

Self-Consistent Field (SCF) 1. Find approximate orbitals for all electrons (e.g. using Z eff ) 2. Calculate potential from nuclei and... fixed clouds for all electrons but one. 3. Use this new potential to calculate an. an..improved orbital for that one electron. 4. Repeat steps 2 and 3 to improve the orbital for another electron.... Improve all orbitals one by one. Quit When orbital shapes stop changing Cycle back to improve 1 st orbital further, etc. etc.

Still Wrong! because real electrons are not fixed clouds. They keep out of each other’s way by correlating their motions. True Energy < SCF Energy

"Correlation Energy" Hide the residual error after full SCF calculation to the “Hartree-Fock” limit by giving it a fancy name: Where to get correct energy (& total electron density)? by experiment or by a whopping calculation: e.g. “Configuration Interaction” (CI) or “Density Functional Theory” (DFT)

If we’re really lucky, "Correlation Energy" might be Negligible.

"Non-bonded" Contacts (1-20) C Energy Magnitudes Should Chemists care about the error in Orbital Theory? -2 log (Energy Change kcal / mole C Core (2  10 4 ) 1/2  4 Single Bonds (2  10 2 ) 52Å! (2  ) Changes in "correlation energy" can be ~10-15% of Bond Energy. Orbital Theory is fine for Qualitative Understanding of Bonding. C "Correlation Energy" (10 2 ) - C C 12 C Nucleus (2  10 9 ) Loses 0.1 amu (E = mc 2 ) Fortunately nuclear energy is totally unchanged during chemistry! 0.001% change in nuclear energy would overwhelm all of Coulomb. correlation error ≈ bond ~ C Atom (3  10 3 ) 

Orbitals can't be “true” for >1 electron, because of e-e repulsion but we'll use them to understand bonding, structure, energy, and reactivity

What gives Atomic Orbitals their Shape? Potential Energy scales r (via  ) Kinetic Energy creates nodes 4d 2s double the nuclear charge

If we use orbitals, how should we reckon total electron density? Density of electron 1 =  1 2 (x 1,y 1,z 1 ) Density of electron 2 =  2 2 (x 2,y 2,z 2 ) Total density (x,y,z) =  1 2 (x,y,z) +  2 2 (x,y,z) (Sum, not Product. Not a question of joint probability)

How Lumpy is the N Atom? Total = K(r 2 ) e -  (2p x ) 2 = K x 2 e -  (2p y ) 2 = K y 2 e -  (2p z ) 2 = K z 2 e -  Total = K(x 2 + y 2 + z 2 ) e -  Spherical ! [from an Organic Text]

TFDCB C CC C F N is round not clover-leaf nor diamond! C N Triple Bond 2p x 2 + 2p y 2 depends on (x 2 +y 2 ) It is thus symmetrical about the z axis cross section ?

Molecules Plum-Pudding MOs (the "United Atom" Limit) Understanding Bonds (Pairwise LCAO-MOs) “Overlap & Energy-Match" Atoms 3-Dimensional Reality (H-like Atoms) Hybridization Orbitals for Many-Electron Atoms (Wrong!) Recovering from the Orbital Approximation

Ways of Looking at an Elephant

Set of atoms Atoms with small bonding distortion Single “United Atom” Ways of Looking at a Molecule (or a Molecular Orbital) e-density contours of H 2 Which contour should we use? Molecule from set of atoms Molecule as one atom distorted by a fragmented nucleus Nuclei embedded in a cloud of electrons dispersed and “noded” by kinetic energy J. J. Thomson's Plum Pudding! (backwards) Molecule as atoms

How the Plums Distort Electronic Puddings

Methane & Ammonia Spartan 6-31G* calculates good SCF MOs (on my laptop!) We want to understand them visually.

4 Pairs of Valence Electrons H CHH H NHH H Compare MOs to AOs of Ne (4 electron pairs with n=2)

1s CH 4 NH 3 "Core" Orbitals Like 1s of C/N Tightly Held Little Distortion Contour Level e/Å 3 We'll focus on Valence Orbitals Boring!.. 8 valence e -  4 MOs 8 valence e -  4 MOs energy Three “degenerate” Molecular Orbitals

2s..

2s.. “Spherical” node

2p x.. CH 4 NH 3..

CH 4 NH 3 2p y.. CH 4 NH 3..

CH 4 NH 3 2p y.. CH 4 NH 3..

CH 4 NH 3 2p z HOMO Lewis's "unshared pair".. CH 4 NH 3.. +Unoccupied Orbitals

CH 4 NH 3 3s LUMO "HUMO?"..

2s CH 4 NH 3 3s LUMO "HUMO"..

CH 4 NH 3 3d x 2 -y 2..

CH 4 NH 3 3d x 2 -y 2..

CH 4 NH 3 3d xy..

CH 4 NH 3 3d xy..

CH 4 3d z 2..

End of Lecture 11 Sept. 29, 2008 Copyright © J. M. McBride Some rights reserved. Except for cited third-party materials, and those used by visiting speakers, all content is licensed under a Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0).Creative Commons License (Attribution-NonCommercial-ShareAlike 3.0) Use of this content constitutes your acceptance of the noted license and the terms and conditions of use. Materials from Wikimedia Commons are denoted by the symbol. Third party materials may be subject to additional intellectual property notices, information, or restrictions. The following attribution may be used when reusing material that is not identified as third-party content: J. M. McBride, Chem 125. License: Creative Commons BY-NC-SA 3.0