CHEM 1310 A/B Fall 2006CHAPTER 17: Many-Electron Atoms and Chemical Bonding•Many-Electron Atoms and the Periodic Table•Experimental Measures of Orbital Energies•Sizes of Atoms and Ions•Peoperties of the Chemical Bond•Ionic and Covalent Bonds•Oxidation States and Chemical BondingCHEM 1310 A/B Fall 2006Many-electron atoms• We can solve HΨ=EΨ exactly for H atom to get energies and orbitals• For more than one electron, can no longer solve exactly (“many-body” problem)• Approximation: assume each electron moves around in the electrostatic field of the nuclei and the average charge distribution of the other electrons. Mean field or self-consistent-field or Hartree-Fock theory. For >1 atom, this is also molecular orbital theory• In Hartree-Fock theory, each pair of electrons (one α, one β) move in their own orbital φi(xi, yi, zi)CHEM 1310 A/B Fall 2006Electronic structure of atoms• Just as H atom orbitals have quantum numbers (n, l, ml, ms), the approximate orbitals for other atoms do also• Problem: which orbitals do the electrons prefer to occupy?• Answer: lower energy ones filled first. Aufbau (“filling up”) principleCHEM 1310 A/B Fall 2006Aufbau principle• Fill lowest-energy orbitals first• H atom energy levels are not valid for larger atoms; however, general idea (energy increases with n) is roughly true• For non-H atoms, energy also depends on L (e.g., s orbitals usually lower than p)• Usual order1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p• Recalling that there’s 1 s orbital, 3 p orbitals; 5 d orbitals, 7 f orbitals, we see how the periodic table matches this order!CHEM 1310 A/B Fall 2006Aufbau and Periodic TableCHEM 1310 A/B Fall 2006Experimental “orbital energies”Energy required to remove an electron from various orbitals for the first 97 elements based on photoelectron spectroscopyCHEM 1310 A/B Fall 2006Hund’s rules• (Simplified version): When adding electrons to orbitals with equal energy, a single electron enters each orbital before a second electron enters any orbital• Allows us to predict diamagnetic or paramagnetic. Diamagnetic atoms/molecules have all electrons paired and are repelled by a magnetic field. Paramagnetic atoms/molecules have 1 or more unpaired electrons and are attracted to magnetic fields.• Is C atom diamagnetic or paramagnetic? How about Ne atom?CHEM 1310 A/B Fall 2006Aufbau/Hund for atomsCHEM 1310 A/B Fall 2006Exceptions to Aufbau principle• Sometimes filling or half-filling a subshellis preferred over regular rules (subshell: all orbitals for a given n and l, e.g., 2p)• Cu: should be [Ar] 4s23d9by Aufbau, but instead it’s [Ar] 4s13d10• Ag: [Kr] 5s14d10• Cr: [Ar] 4s13d5• Mo: [Kr] 5s14d5• Au: [Xe] 6s15d10CHEM 1310 A/B Fall 2006Valence electrons and Periodicity• Only the electrons added in the lowest available row of the periodic table for a given atom are “valence” electrons. Electrons from higher rows are “core.”• Mg is 1s22s22p63s2… the 3rdrow is lowest, so only 3s2is valence• What are the valence electrons for Zr?CHEM 1310 A/B Fall 2006Valence electrons and Periodicity• Notice: any 2 elements in the same column of the periodic table have the same type and number of valence electrons (just different values for n)• This explains why elements in the same column react the same way! Quantum mechanics explains periodicity!• E.g., Mg is [Ne] 3s2and Ca is [Ar] 4s2… both have 2 valence s electrons, and they react similarly!• The core electrons are lower in energy and usually do not affect chemistryCHEM 1310 A/B Fall 2006Periodic Trends in Ionization Energies• Ionization energy: the minimum amount of energy needed to detach an electron from an atom/molecule• Going across a row to the right, IE increases because the nuclear charge is increasing and holds electrons tighter• Does this mean IE always increases for larger atoms? No, because core electrons are held close to nucleus and effectively screen (cancel out) part of the nuclear charge. The IE “resets” to low value at each row.• Elements on left have low IE, elements on right have high IE. QM explains origin of electropositivity and electronegativity!CHEM 1310 A/B Fall 2006Periodicity of IE’sCHEM 1310 A/B Fall 2006First ionization energiesCHEM 1310 A/B Fall 2006Electron affinity• Electron affinity is the energy change when an atom gains an electron:X (g) + e-→ X-(g) - ∆E = EA• A positive ∆E (unfavorable reaction) gives a negative EA, and a negative ∆E (favorable reaction) gives a positive EA• Based on arguments for IE, expect EA to increase across a row (except for noble gases; they have filled shells and won’t want electrons)• Basically true but EA has more variation with filled subshells --- the atom is happy and doesn’t really want electrons. Alkaline earth elements and Zn/Cd/Hg don’t care for electrons (low or negative EA). Mn/Tc/Re low EA because half-filled d subshell also fairly stableCHEM 1310 A/B Fall 2006Electron affinitiesCHEM 1310 A/B Fall 2006Sizes of Atoms & Ions• Can determine sizes by theory or experiment (see how close atoms/ions get to each other in crystals, etc)• Cations usually slightly smaller, anions slightly larger than their parent atoms• Higher effective nuclear charge as go across a row because nuclear charge Z increases, but the added electrons all into the same shell and are not very effective at screening each other. Atoms get smaller because electrons held closer in• As go down a column, size gets bigger (electrons take more room); effective nuclear charge felt by valence electrons is constant going down a row because of screeningCHEM 1310 A/B Fall 2006Periodic trends in atomic radiusCHEM 1310 A/B Fall 2006Bond length, bond enthalpy, bond order• We already mentioned that the more bonds between two atoms, the stronger that bond (higher bond enthalpy) and the shorter that bond• See book for more detailsCHEM 1310 A/B Fall 2006Ionic and Covalent Bonds• Can tell the difference between these two types of bonding using concept of electronegativity• Mulliken’s definition: electronegativity is proportional to (IE + EA) / 2• Halogens: high IE and EA, so high electronegativity• Alkali metals: low IE and EA, so low electronegativity• Electronegativity increases across a row, decreases going down a column [as go down, bigger size of atom means easier to take off electrons]CHEM 1310 A/B Fall