How we describe bonding is affected strongly by how we describe where/how electrons are held by atoms in molecules.

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1 CHEM 2060 Lecture 8: Atomic Configurations L8-1 Electronic Configurations How we describe bonding is affected strongly by how we describe where/how electrons are held by atoms in molecules. We know that electrons are held in orbitals. (What does this mean?) Let s review these concepts and discuss how electrons affect one another. Atomic Quantum Numbers Each Atomic Orbital (AO) is defined by 3 Quantum Numbers n, l, m l n Principal determines major part of the energy l Angular momentum describes angular dependence; shape m l Magnetic describes orientation in space; subsets of l

2 CHEM 2060 Lecture 8: Atomic Configurations L8-2 [Def] A quantum is the smallest amount of a physical quantity that can exist independently, i.e., a discrete quantity that cannot be further subdivided. Values of these 3 Quantum Numbers n: 1, 2, 3, 4, l : 0, 1,, n-1 l = 0, 1, 2, 3, 4, s p d f g m l : l, l-1, l-2,, -l s orbital: l = 0 m l = 0 (for every value of n, only one s orbital exists) p orbital: l = 1 m l = +1, 0, -1 (three p orbitals exist for each n) d orbital: l = 2 m l = +2, +1, 0, -1, -2 (five d orbitals for each n)

3 CHEM 2060 Lecture 8: Atomic Configurations L8-3 So the number of orbitals in a particular shell is n 2 where n is the principal quantum number. For n = 4, there are 16 atomic orbitals: (1 x 4s) + (3 x 4p) + (5 x 4d) + (7 x 4f) Configurations For Atoms And Ions So we can write down the configuration for any atom or ion (or can we?). In first year, we based this on the building up or AUFBAU principle a method for determining the lowest energy configuration for an atom in its ground state. Pauli exclusion principle: No more than 2 electrons may occupy a single orbital, and if two occupy a single orbital their spins must be paired. However, in multi-electron configurations, it is not quite that simple.

4 CHEM 2060 Lecture 8: Atomic Configurations L8-4 Orbital Energy Levels in the Hydrogen Atom (i.e., the one-electron model) In the one-electron model, the AO energy is solely determined by n. so, for example, all 16 of the n = 4 orbitals are degenerate. This is NOT SO for multielectron systems.

5 Multi-Electron Systems: Penetration And Shielding CHEM 2060 Lecture 8: Atomic Configurations L8-5 In multi-electron systems, orbital energies differ from those in the H atom. WHY? In a one-electron system, no matter which orbital the electron occupies, there are no other electrons in other orbitals that can interfere with how that electron sees the nucleus. In a multi-electron system, the interaction with other electrons also becomes a factor in determining the energy of an atomic orbital. Each electron experiences. 1) coulombic attraction to the nucleus. 2) coulombic repulsion from other electrons. Now the trick is to figure out how to deal with these two contributions. We have to make approximations (can t solve a 3-body problem).

6 We approximate: Electons experience a CENTRAL FIELD CHEM 2060 Lecture 8: Atomic Configurations L8-6 that is the sum of the field from the nucleus and the average field from all the other electrons. The result is that the (postive) nuclear charge felt by each electron is less than the actual nuclear charge because of interference by other (negative) electrons. Reduces nuclear charge from true value (Ze) to effective nuclear charge Z eff e (for a particular electron) Look at the radial probability distribution of the first three s orbitals (think of these like slicing an onion in half and looking at the resulting surface). How does an electron in the 3s orbital see the nucleus?

7 CHEM 2060 Lecture 8: Atomic Configurations L8-7

8 CHEM 2060 Lecture 8: Atomic Configurations L8-8 Obviously, the electrons in the 2s and 1s orbital will shield the electron in the 3s orbital from the nuclear charge to some degree. But it is also clear that there is a non-zero probability that an electron in a 3s orbital is very close to the nucleus (in the previous diagram, there is a fair amount of red near the center, where the nucleus sits). Thus, an electron in a 3s orbital can penetrate to the center remember, orbitals are NOT like planetary orbits! We have at least 2 options for how to deal with this rather complex picture: 1) high-level quantum mechanical calculations that model wavefunctions for each electron even here, approximations are necessary. 2) A very oversimplified, but still useful, back-of-the-envelope approach WE CHOOSE OPTION #2 here we will use a very simple, but useful, model because it is oversimplified, it can be inaccurate!

9 CHEM 2060 Lecture 8: Atomic Configurations L8-9 Shielding Parameter (σ) In this simple approach, we come up with a set of rules to calculate a shielding parameter (σ) that accounts for the difference between the actual nuclear charge Z and the effective nuclear charge Z eff. Z eff = Z - σ Results of this simple calculation are tabulated below Effective nuclear charges Z eff H He Z 1 2 1s Li Be B C N O F Ne Z s s p

10 CHEM 2060 Lecture 8: Atomic Configurations L8-10 Na Mg Al Si P S Cl Ar Z s s p s p NOTE: ns electrons are less shielded than np electrons. WHY?

11 Look at the radial probability distrubtion of the 2s and 2p orbitals pictorially (previous page) or as a plot (right). At a very short radial distance from the nucleus, there is a greater probability of finding an electron in the 2s orbital than in the 2p orbital. In other words, due to penetration, s electrons get closer to the nucleus than p electrons so other electrons shield s electrons from the nuclear charge less effectively than they shield p electrons. s electrons are less shielded than p electrons p electrons are less shielded than d electrons d electrons are less shielded than f electrons CHEM 2060 Lecture 8: Atomic Configurations L8-11 This is why the ns, np, nd and nf orbitals are degenerate in the H atom (one electron system) but non-degenerate in multi-electron systems. In multi-electron systems, the atomic orbital energies: ns < np < nd < nf

12 CHEM 2060 Lecture 8: Atomic Configurations L8-12 NOTE: As the value of the Principal quantum number n increases, the energy differences decrease so there is a greater gap between 1s & 2s than between 2s & 3s, etc. RESULT: For higher values of n, the relative ordering of atomic orbital energies depends on the number electrons present. Example: The 4s and 3d orbitals are very close in energy. In some systems, the 4s is lower and in some systems the 3d is lower. This is entirely a result of electron filling (penetration/shielding) look at K and Ca (right). QUESTION: Why are 2s and 2p at the same energy on the y-axis?

13 CHEM 2060 Lecture 8: Atomic Configurations L8-13 ADVANCED: The relative atomic orbital energies can be so dependent on electron filling that the oxidation state of the atom/ion can change the relative order of the atomic orbitals! Example: atomic vanadium V [Ar]4s 2 3d 3 4s is filled and 3d is partially filled monocation V + [Ar]3d 4 4s is empty and 3d is partially filled Remember this electron-filling mnemonic from high school? This applies to ground state atomic electron configurations. Now you should be able to rationalize it!