Transcript Slide 1

Lecture 4
THE ELEMENTS’ VALENCE SHELL
1) Electron Shielding. Slater’s rules
If inner-sphere electrons in atoms were concentrated in thin inner layers near nucleus (“onion-like” structure), an outersphere electron would interact with nucleus, as it would in the hydrogen atom (Z = 1), according to laws of electrostatics.
In fact, the interaction is stronger and can be described by an effective nuclear charge Z*>1.
Z* = Z – S,
here S is a shielding constant specific for each element subshell
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In the series of orbitals s, p, d, f the ability of electrons occupying them to shield outer sphere electrons decreases,
while vulnerability to the shielding effect of inner sphere electrons increases. This trends result from the decreasing
number of radial nodes for ns > np > nd > nf orbitals which is equal to n-l-1 and their decreasing penetration through
inner sphere electron shield.
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The approximate value of the shielding constant S(ns, np) for electrons occupying ns or np orbitals can be estimated
by applying Slater rules. Electrons occupying orbitals to the right of a subshell in the row below are considered to
contribute nothing to the shielding of the electrons on that subshell:
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
S(ns, np) = 0.35[N(ns, np) – 1] + 0.85N(n-1) + 1N(all other inner shells)
here N(x) is the number of electrons occupying the shell (x)
Example of the oxygen atom:
the electronic configuration is 1s22s22p4;
for oxygen 2p electrons S(2p) = 0.355+0.852 = 3.45
so that Z* = 8 - 3.45 = 4.55
Effective nuclear charges of elements by Clementi and Raimondi (more precise calculation of Z *):
http://www.webelements.com/webelements/properties/text/image-flash/eff-nucl-charge-clem-1s.html
1s
14.00
12.00
10.00
8.00
1000*[r*R(r)]2
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2p
6.00
2s
4.00
r
2.00
0.00
According to Clementi, for O S(2p)= 3.58 and Z*=4.42
0
2
4
6
8
2) Slater effective nuclear charge
• Z* increases rapidly in periods (but there are gaps immediately after inert gases and the last
of the d-elements).
• Z* increases also in groups but more slowly.
16
14
12
10
8
6
4
2
0
H He Li Be Be C
N
O
F Ne Na Mg Al Si P
S
Cl Ar
K Ca Sc Ti
• Atomic radii and Z*’s form a base for understanding
of a number of important atomic properties
V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
3) Some important properties of atoms. Ionization energy (IE)
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The IE is the energy necessary to remove an electron from an isolated atom in the gas
phase:
A  A + + eThe first IE characterizes the energy of the highest occupied atomic orbital.
Its value is affected by both the effective atomic nuclear charge Z* and atomic radius R
(http://www.webelements.com/webelements/properties/text/image-flash/atomic-radiusemp.html ).
Within a given family of non-transition elements heavier analogues have lower IE (Z*
changes slightly while atomic radius R increases significantly).
Within a given series of non-transition elements IE increases (Z* increases while
atomic radius R decreases). Some local maxima are observed for the elements with
half- or completely filled subshells. These maxima reflect the enhanced stability of
such subshells.
4) Electron affinity (EA)
This is the energy released when an electron is added to an isolated atom in the gas
phase, taken with the opposite sign: A + e-  A•
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The EA characterizes the energy of the lowest unoccupied atomic orbital.
Within a given family heavier elements have lower EA mainly because of the
increasing atomic radius (exception: elements of the 2nd row).
Within a given series of non-transition elements EA tends to increase because of the
increasing Z* and decreasing R. The effects of (half)filled subshell are responsible for
the non-continuous character of this trend.
EA, eV
4.00
3.50
3.00
Cl
F
Br
I
At
Au
2.50
Se
S
C
1.50
1.00
H
0.50
Li
B
O
Si
Na
Cu Ge
Ni
P
Al
Cr
Pt
Te
2.00
Ag
Os
W
Nb
As
K
Z
Pb
Tc
Ga
Po
Ir
0.00
Rn
0
20
40
60
80
100
5) Electronegativity
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According to Pauling, electronegativity is the power of an atom in a molecule to attract
electrons to itself.
There are several scales of electronegativity, they correlate one with another:
c(A)-c(B) = [(E(A-B) – 0.5{E(A-A)+E(B-B)})1/2, eV],
Pauling’s thermochemical
Here E(A-B), E(A-A) and E(B-B) are energies of A-B, A-A and B-B bonds respectively
c = [0.118·(IE+EA)-0.207, eV],
Mulliken-Jaffe
Here IE is ionization energy and EA is electron affinity of an atom
c = [(mep+nes)/(m+n)],
Allen’s spectroscopical
Here ep is the energy of p-electrons and es is the energy of s-electrons; m and n are populations of p- and s-orbitals respectively.
Allred-Rochow’s semi-empirical c = [0.744+3590·Z*/r2] etc.
Here Z* is effective nuclear charge and r is atomic radius.
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Electronegativity increases in series of non-transition elements and decreases in a given
family as atomic number increases (see a fragment of the Pauling scale below):
Li
Na
0.98
0.93
Be
1.57
B
2.04
C
2.55
N
3.04
O
3.44
F
Mg
1.31
Al
1.61
Si
1.90
P
2.19
S
2.58
Cl
Electronegativity, various scales:
http://www.chm.davidson.edu/ronutt/che115/electroneg.htm
http://www.webelements.com/webelements/properties/text/image-flash/electroneg-mulliken.html
3.98
3.16