M polyelectronic atoms need another quantum number, m s it is found that atoms, substances with unpaired electrons have a magnetic moment, 2 s(s+1) where {s = m s } Pauli Exclusion Principle no two electrons may have all 4 quantum numbers the same Aufbau (building up) Principle M Today Send me your e-mail address for HW 1.. (wtikkan@exchange.calstatela.edu) Read 47-64 for next class
M the spin quantum number a fourth quantum number is required to completely specify the electronic state of a hydrogenic atom, the spin quantum number, m s, which two allowed values, +1/2 and -1/2. The angular momentum associated with this quantum mechanical property (the electron does not spin in the classical sense) is given by: h/2 {s(s+1)} 1/2. (s = m s ). We represent the two values of m s with arrows, pointing up ( ) denotes m s = 1/2 and pointing down ( ) denotes m s = -1/2 M why can we use orbitals from H-like atoms in polyelectronic systems? self consistant field calculations show that orbitals in polyelectronic atoms look much like those in H-like atoms. it is easier to utilize these familiar orbitals than starting completely from first principles
M orbital filling in polyelectron atoms follow this order and Hund s 1st rule and you are rarely wrong 1st rule: add electrons to degenerate orbitals to maximize unpaired electrons 2nd rule: in degenerate orbitals, maximize spin before pairing electrons M Shielding and Slater s Rules a valence electron does not experience the full nuclear charge since there is significant electron density between that electron and the nucleus: it is shielded or screened from the nucleus full positive charge. e Ze+ e e e
M how to estimate shielding: Slater s Rules 1. Write down electronic configuration in groups by the following scheme: (1s), (2s2p), (3s3p), (3d), (4s4p), (4d) (4f),, (5s5p), etc. 2. Electrons in a group to the right of an electron with principle qn n for which is being determined contribute 0 to. 3. electrons in the ns,np shells or in that group each contribute 0.35 to (if 1s, 0.30) 4. all electrons in the n-1 shell contribute 0.85 to 5. All electrons in shells with principle quantum number n-2 are completely efficient in shielding and contribute 1 to. 6. If the electron is in an nf or nd shell, rules 4 and 5 should be changed to read: all electrons in groups to left contribute 1 to. M shielding for valence electrons in F and i F:(1s 2 )(2s 2 2p 4 p) = 0.35*6 + 0.85*2= 5.2 Z*(2p) = Z- = 9-5.2 = 3.8 i:(1s 2 )(2s) = 0.85*2= 1.7 Z*(2s) = Z- = 3-1.7= 1.3
M Use this table for real numerical Z*! M Periodic Properties- Shielding in action atomic radius ionization energies electron affinities All of the above can think of in terms of electrostatics and shielding. electronegativity hardness/softness Not your simple electrostatic arguments
M Ionization energies describe the general trend observed in ionization energies for consecutive ionizations of an atom, that is A A + + e A + A 2+ + e etc. M In class Q. How could you estimate the ionization energy of sodium using the information provided so far in this course?
M Periodic Properties atomic radius ionization energies electron affinities electronegativity hardness/softness M atomic size/radius Measuring atomic size is like measuring a really ripe grapefruit the size you get depends on how hard you squeeze
M atomic radius as a function of Z M today Rest of chapt 2 Next time read 47-60 2nd ed\ Today s q- why do you expect that the first electron affintiy should be exothermic?
M trends??????? steady decrease in size as one proceeds across a period note peak size begins when the first electron in the new n shell is added!! M Ionic radii
M Any trends? Note that for a given electron configuration, size decreases with increasing +ve charge. M ionization energy defined as H for the following reaction: A n+ A (n+1)+ + e -
M first ionization energies vs. Z M Successive ionization energies
M Calc ionization energy? Use slater s rules to estimate the effective nuclear charge and treat system as a hydrogenic atom. M electron affinity defined as - H of the following reaction A + e - A - To add to confusion, some texts use the opposite sign convention
M electron affinities of some metals M Some EA s representative elements
M M Electronegativity This property quantitates the ability of an element to attract electron density when in compounds Halogens have high electronegativity Alkali metals have low electronegativity
M Several definitions Pauling used a definition based on bond energies Mulliken: m = 1/2 (I +E a ) Other new scales being developed (uo, Y.; Pacey, P. D. J. Am. Chem. Soc. 1991, 113, 1465-1466) M Pauling Electronegativity vs. Z
M Hardness/Softness A new-ish property- related to several other properties, but is somewhat periodic It s related to the polarizability of an atom (or molecule or molecular fragment) M polarizability Describes how easily the electron cloud is distorted To distort, there must be low energy orbitals to accept the electron density in its new location
M Polarization of s orbital + M Today More Hard/Soft talk Beginnings of bonding Next time 42-62
M What facilitates mixing? the highest occupied orbital (HOMO) and the lowest unoccupied orbital (UMO) must mix- The closer the participating orbitals are in energy, the more mixing occurs So, the closer in E the HOMO and UMO, the greater the polarizability M Energy diagrams from the past E E Small gap, mixing arge gap, little mixing
M ow polarizability Highly charged cations Al 3+, Zn 2+, Be 2+ Group 1 cations Highly electronegative, small elements O, F Anions of O, F M High polarizability Metal ions with small charges Fe 2+, Co -1, Cu + 3rd row bases (SR 2, PR 3 ) Anions of S, Br, P easily distorted electron clouds- larger radius for the same charge will be more polarizable
M hardness Absolute hardness,, is related to polarizability IE EA 2 M Relevance? ow difference, high polarizability and low hardness E EA IE 0 Big difference, low polarizability, high hardness
M Importance? Important in bonding later on However, electronegativity shows periodicity