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09.23.2011 - Lecture 08 Today in Chemistry 260/261 Chem...

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Lecture 08 9/23/11 1 Chem 260/261 Lecture 8 9/23/2011 1 Today in Chemistry 260/261 • Multi electron systems orbitals •Aufbau exceptions/oddities Periodic trends: • Atomic/ionic radii • Ionization energy • Electron affinity • Electronegativity Start Quantum view of bonding, Valence bond model Next in Chemistry 260/261 • Reading: 6.1, 6.4 • Quantum view of bonding, Valence bond model 2 The Hartree Self-Consistent Field (SCF) Method Assumptions: 1. Assign electrons to one-electron orbitals 2. Combine effects of all other electrons as an effective field ( ) ( ) ( ) ( ) k k k k k i i i r r r r ! " # ! " # ! " # # $ , , , , , , % % % = = & = ! 2 2 2 2 1 1 1 1 1 First guess: Use guess to find J ( r 1 ), …, J ( r k ) Refine wavefunction, find J ( r 1 ), …, J ( r k ) again Repeat until no more change 3 Hartree many-electron wave functions The many electron ( k ) wave function consists of a product of one-electron (hydrogenic) wave functions. The angular portions of the wave functions are identical to the hydrogenic wave functions. The radial part is different: Hartree wave functions for argon ( ) ( ) ( ) ( ) k k k k k i i i r r r r ! " # ! " # ! " # # $ , , , , , , % % % = = & = ! 2 2 2 2 1 1 1 1 1 ( ) ( ) ( ) , , eff j n l l m m R r ϕ θ ϕ = ×Θ ×Φ ( ) [ ] 2 2 n n Z eff n ! " E 4 ( ) ! " # $ % & ' ( ) * + , + - + . 2 0 2 1 1 2 1 1 n l l n Z a n r eff nl ) ( Comparing Hydrogen & Hartree wave functions ! " # $ % & ' ( ) * + , + - + = 2 0 2 1 1 2 1 1 n l l Z a n r nl ) ( For the hydrogen atom: For multi-electron atoms: ( ) [ ] 2 2 n n Z eff n ! " E Average distance from nucleus Orbital Energy (in rydbergs) 2 2 n Z E n ! = 08_14 50 100 150 66 Distance from the nucleus (pm) Electron distribution n=3 n=2 n=1 8_15 5 Z eff is not #electrons- #protons. Z eff is obtained by Hartree approximation method calculations. Shielding Effects Energies are shifted and become dependent on l Model assuming each electron experiences a net reduced nuclear charge (Z eff (n)), due to the other electrons. The Z eff experienced by s and p electrons are different because of the different wave functions and therefore different distributions around the nucleus. The individual orbitals of a given subshell (s,p or d…) remain degenerate because they have the same radial characteristics and so experience the same Z eff . ( ) 2 , 2 , eff n l Z n l n ≈ − E 6
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Lecture 08 9/23/11 2 Hartree orbitals Corresponding energy levels are dependent on Z eff : multiple electrons lift degeneracy from the subshells energy depends on quantum numbers n and l , unlike hydrogenic orbitals s electrons penetrate the
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