CHAPTER 9 QUANTUM MECHANICS OF MULTIELECTRON SYSTEMS AND THE LINK BETWEEN ORBITAL STRUCTURE AND CHEMICAL REACTIVITY Quantum mechanics first developed to quantitatively describe the structure of the hydrogen atom Multielectron Atoms Silver atoms fired through magnetic field exhibit spatial quantization of angular momentum two dots appeared instead of the predicted single large spot Pauli Exclusion Principle no two electrons can share the same set of quantum numbers o Means that as we move from a single electron system to multiple electrons those electrons must sequentially pair up o One will have spin number while the other will have spin quantum number ms Electrons will be inserted sequentially into shells and subshells in order of increasing energy with a max of two electrons one spin up one spin down adds up to total of electrons possessed by that element in periodic table Electrons enter orbitals with different values of ml before pairing up pairs of one up one down Hund s Rule o Electron electron repulsion dominates the interaction energy of the system within a given set of quantum numbers must maximize distance between electrons Penetration and Shielding Balance of electron electron e e repulsions against electron proton e p attraction o This balance determine the size of the atom ability of atom to retain its own electrons and ability of atom to draw other electrons to itself chemical behavior of atom Two ideas o Penetration A measure of how close an electron comes to the nucleus Coulomb force between a single electron and the proton s in the nucleus Fe p Ze2 r2 Z atomic number of atom e charge of electron r distance between electrons and protons in atom As Z increases the force between the electron and the nucleus increases decreases r and in turn makes its potential energy more negative Larger atoms more stable harder to remove electrons Orbital is more stable o Shielding Measure of how electrons that occupy a spatial domain closer to the nucleus serve to reduce the attraction between the nucleus and electrons at greater distances from the nucleus Inner electron shields the nuclear charge from and outer electron Each e makes the other e easier to remove Outer electron will see a reduced attraction to the nucleus because of the shielding by the inner electron and will move to a larger distance from the nucleus easier to remove o Penetration implies reaching closer to the nucleus greater stability by virtue of a greater negative energy binding the electron to the nucleus o Outer electron that is shielded is less stable and more easily removed Penetration and shielding come together in a single variable Zeff S orbitals most strongly penetrating o Always have the lowest energy b c it dominates the most deeply penetrating domain close to the nucleus P d f orbitals angular momentum radial distances Zeff Energy ordered as such o Es Ep Ed Ef Building Up Period 3 4s electron is better able to penetrate than the more strongly shielded 3d orbitals o Zeff ins greater for the 4s than the 3d o 4s lower in energy more stable than 3d Group 7A halogens highly reactive non metals p5 electrons penetrate effectively remove electrons from other elements Group 8A noble gasses unreactive monoatomic gases Building Up Period 4 Enter 4s orbital before 3d But with Cr and Cu take out of 4s to complete 3d more stable o Organization of the Periodic Table Divide periodic table into blocks s p d f P block remarkable variability in chemical behavior o Move across row of p block Effective nuclear charge Zeff increases and the orbital energies decrease become more stable with the valence e more strongly attracted by the increasing Zeff Greater tendency to attract electrons towards the right of the row o Going down column larger atoms with less tightly bound electrons greater chance to delocalize electron density in bonding with other atoms o Far right of p block noble gases very high Zeff D block F block o First 3 rows transition metals o Two 14 element rows o Less thoroughly studied o Least diverse Summary of Principles Linking Electron Configuration with Chemical Principles 4 main points 1 Elements w in a group have similar chemical properties similar e outer 2 Sequence of elements in periodic table built up by filling orbitals 3 Chemical behavior or elements is based upon 3 categories of electrons configurations Core Outer Valence 4 Distinction between group number and period number Group column Period row Atomic Size Two broad patterns Zeff and Size Zeff increases left to right in a period Zeff increases in going from top to bottom in group Size increases top to bottom Ionization Energy Energy require to remove an electron o Depends upon the structure of atom and orbital of electron Ionization Energy energy required to move an electron from a specific orbital and move it to a position that the binding energy drops to zero First Ionization Energy minimum energy required to remove from the atom the most weakly bound valence electron Second Ionization Energy remove next electron typically considerably greater than the first ionization energy Atoms w low IE tend to donate electrons forming cations High IE extract electrons forming anions Electron Affinity energy released when a neutral atom acquires an electron Electron affinity increases as you move from left to right across the periodic table Electron Affinity Halogens have highest Electron Affinity decreases as atomic size increases o Entry of additional electron to valence shell results in attractive force reduced by the large diameter not a strong enough pull from protons in nucleus Trends in the Chemical Behavior of Metals Tend to reflect light excellent conductors or electricity and heat ductile malleable donate electrons to non metals Low ionization energy of metals Lattice position of ions cations in metal o Sea of electrons Tendency to lose electrons in chemical reaction Increased metallic behavior and tendency to lose electrons occurs as you move down a group