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Lecture 2. Placing electrons in orbitals. 5p. E. Approximate order of filling orbitals with electrons. 4d. 5s. 3d. 4s. 4p. 3p. 3s. 2p. 2s. 1s. 5p. E. 4d. 5s. 3d. 4s. 4p. 3p. 3s. 2p. 2s. 1s. Shielding and effective nuclear charge Z* - PowerPoint PPT Presentation
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Lecture 2
Placing electrons in orbitals
Approximate orderof filling orbitalswith electrons
1s
2s2p3s3p
4s
3d4p
5s4d
5pE
1s
2s2p3s3p
4s
3d4p
5s4d
5pE
Shielding and effective nuclear charge Z*
In polyelectronic atoms, each electron is attracted to the nucleusand repelled by the other electrons (both n and l must be taken into account)
Electrons acts as a shieldfor electrons electrons farther away from the nucleus, reducing the attraction between
the nucleus and the distant electrons
Effective nuclear charge: Zeff = Z* = Z –
(Z is the nuclear charge and is the shielding constant)
**
Shielding and effective nuclear charge Z*:
Z* = Z – (a measure of the nuclear attraction for an electron)
To determine s (Slater’s rules):1. Write electronic structure in groups as follows:
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.Note the order does not correspond to filling order. The shielding constant
for each group is formed as the sum of the following contributions:2. Electrons in higher groups (to the right) do not shield those in lower
groups3. An amount of 0.35 from each other electron within the same group except
for the [1s] group where the other electron contributes only 0.30. 4. If the group is of the [s p] type, an amount of 0.85 from each electron with
principal quantum number one less and an amount of 1.00 for each electron with an even smaller principal quantum number
5. If the group is of the [d] or [f], type, an amount of 1.00 for each electron in a lower group (to the left).
Note that (1) as Z increases so does Z* leading to smaller orbitals as we move to right in a period
is the sum of all contributions
Vanadium, Z = 23(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
V V+ V+
Config Z* Config Z* Config Z*
3d3 4.3 4s0 3d2 4.65
4s2 3.3 3d4 3.95 4s2 4.15
For V: 4s
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p)
2 x 1 8 x 1 8 x .85 3 x .85 .35 = 19.7
Z* = 23 -19.7 = 3.3
Vanadium, Z = 23(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
V V+ V+
Config Z* Config Z* Config Z*
3d3 4.3 4s0 3d2 4.65
4s2 3.3 3d4 3.95 4s2 4.15
For V: 3d
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p)
2 x 1 8 x 1 8 x 1 2 x .35 0 = 18.7
Z* = 23 – 18.7 = 4.3
Vanadium, Z = 23(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
V V+ V+
Config Z* Config Z* Config Z*
3d3 4.3 4s0 3d2 4.65
4s2 3.3 3d4 3.95 4s2 4.15
For V+ (4s23d2): 3d
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p)
2 8 x 1 8 x 1 .35 0 18.35
Vanadium, Z = 23(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p) etc.
V V+ V+
Config Z* Config Z* Config Z*
3d3 4.3 4s0 3d2 4.65
4s2 3.3 3d4 3.95 4s2 4.15
For V+: 3d
(1s) (2s, 2p) (3s, 3p) (3d)
2 8 x 1 8 x 1 3 x .35 = 19.05
Z* = 23 – 19.05 = 3.95
Shielding and effective nuclear charge Z*:
There is a particular stabilityassociated with filled and half-filled shells
sdfXeAu
sdKrAg
sdKrMo
sdArCu
sdArCr
654][:
54][:
54][:
43][:
43][:
1014
10
5
10
5
4s electrons are the first ones removed when a 1st row transition metal forms a cation
Spin Multiplicity
Frequently there are several ways of putting electrons into a partially filled subshell. For example, a p2 configuration.
or
or
Both electrons in same orbital. Larger electron-electron repulsion. c, higher energy a positive quantity.
Two electrons of same spin. Energy reduced by exchange energy, e, a negative quantity.
Further Example, p4.
or
or
c + 2e
c + 3e (1-3, 1-4, 3-4)
c + 2e
4s electrons are the first ones removed when a 1st row transition metal forms a cation
Holds maximum of 5
Periodic trends
Generally, atoms with the same outer orbital structureappear in the same column
Ionization Energy (IE):Energy required to remove an electron from a gaseous atom or ion.
Tendency 1: IE1 decreases on going down a group ( n, r increase and Zeff is
constant).
Tendency 2: IE1 increases along a period (Zeff increases, r decreases)
Exception: Half-filled or filled shell are particularly stable
egAgA
egAgA
)()(
)()(2
2
1
IEE
IEE
Tendency 1: IE1 decreases on going down a group ( n, r increase and Zeff is constant).
Tendency 2: IE1 increases along a period (Zeff increases, r decreases)
Maximum for noble gasesMinimum for H and alkali metals
Special “dips”
O: ([He]2s22p4 [He]2s22p3) lower IE than N: ([He]2s22p3 [He]2s22p2) Due to instability of the 4th 2p electron in O
B ([He]2s22p1 [He]2s2) lower IE than Be ([He]2s2 [He]2s1)Due to 2p being further away from nucleus.
Ga: ([Ar]4s2 3d104p1 ([Ar]4s2 3d10 ) lower IE than Zn: ([Ar]4s2 3d10 ([Ar]4s2 3d9 )Due to relative instability of the 4p electron in Ga
Electron affinity (EA) = energy required to remove an electron from a gaseous negatively charged ion (ionization energy of the
anion) to yield neutral atom.
•Maximum for halogens (have maximum of Z*)•Minimum for noble gases (minimum for Z* for elec in next shell)•Much smaller than corresponding IE (working against smaller Z*)
egAgA )()( EAE
Effective atomic radius (covalent radius)
covalent radius =1/2(dAA in the A2 molecule)
Example:
H2: d = 0.74 Å ; so rH = 0.37 Å
To estimate covalent bond distances e.g.:
R----C-H: d C-H = rC + rH = 0.77 + 0.37 =1.14 Å
The size of corresponding orbitals tends to grow with increasing n. As Z increases, orbitals tend to contract, but with increasing number of
electrons shielding keep outer orbitals larger
Tendency 1. Atomic radii increase on going down a group(Zeff ~ constant as n increases because of shielding).
Tendency 2: Atomic radii decrease along a period (Zeff increases .)
Pictorially, here are the trends in radii…..
Ionic radiiCation formation
vacates outermost orbitaland decreases e-e repulsions
(usually decreased shielding)
SIZE DECREASES
Anion formationincreases e-e repulsions
(usually increased shielding)
so they spread out moreSIZE INCREASES
Lewis electron-dot diagrams are very simplified but very useful models for analyzing bonding in molecules
Simple Bonding Theories
Valence electrons are those in the outer shell of an atomand they are the electrons involved in bonding
The Lewis symbol is the element’s symbol plus one dot per valence electron
S......[Ne]3s23p4
Li Be B C N O F Ne
Be .
[He]2s2
.Li .
[He]2s1
B .
[He]2s22p1
..
C .
[He]2s22p2
... N.
[He]2s22p3
.... O.
[He]2s22p4
...
.. F .
[He]2s22p5
..... .
Ne .
[He]2s22p6
...
.. ..
He
Generally, atoms with the same outer orbital structureappear in the same column
The octet rule
Atoms tend to gain, lose or share electronsuntil they are surrounded by eight valence electrons
(i.e., until they resemble a noble gas)
Molecules share pairs of electrons in bondsand may also have lone pairs
: :
O
H HC OO:
:::
Octet Rule, Lewis Structures
Electrons can be stabilized by bond formation.
H atom can stabilize two electrons in the valence shell.
CF can stabilize 8 electrons in the valence shell.
Two electrons around H; Eight electrons complete the octet of CF.
Completing the Octet
Ionic Bonding: Electrons can be transferred to an atom to produce an anion and complete the octet.
Covalent Bonding: Electrons can be shared between atoms providing additional stabilization.
Number of Bonds
H: 1 more electron
H+ 2 more H- 0 more
C: 4 more C2+ 6 more C- 3 more
N: 3 more N+ 4 more N- 2 more
O: 2 more O+ 3 more O- 1 more
F: 1 more F+ 2 more F- 0 more
Additional stabilization that can be provided by some atoms:
Bonds make use of the additional stabilizing capability of the atoms.# Bonds = (Sum of unused stabilizing capability)/2
Formal ChargeFormal charge may begiven to each atom
after all valence shell electrons have been assigned to an atom.– Non-bonding electrons are assigned to the
atom on which they reside.– Bonding electrons are divided equally
between the atoms of the bond.
Formal charge = (# valence shell electrons in neutral atom) - (# nonbonding electrons)
- ½ (# bonded electrons)
Bonding Patterns
Formal
chargeC N O
1
0
-1
C
C
C
N
N
N
O
O
O
Lewis DiagramsTypical Problem: Given a compound of molecular formula CH3CHCH2 draw a Lewis bondingstructure.
How many bonds in the molucule? (3 * 4 + 6 * 1) / 2 = 9 bonds
Draw a bonding structure making use of single bonds to hold the molecule together.
C
C
C
H
H H
H
H
H
How many bonds left to draw? 9 – 8 = 1 bond left
Put remaining bond(s) in any place where the octet rule is not violated.
C
C
C
H
H H
H
H
H
Resonance forms
When several possible Lewis structures with multiple bonds exist,all of them should be drawn (the actual structure is an average)
O
N
O O
O
N
O O
O
N
O O
Expanded shells
When it is impossible to write a structure consistent with the octet ruleincrease the number of electrons around the central atom
Cl P
Cl
Cl
Cl
Cl
10e around P
Only for elements from 3rd row and heavier, which can make use of empty d orbitals
See also: L. Suidan et al. J. Chem. Ed. 1995, 72, 583.
Formal charge
Apparent electronic charge of each atom in a Lewis structure
Formal charge = (# valence e- in free atom) - (# unshared e- on atom) -1/2 (# bonding electrons to atom)
Total charge on molecule or ion = sum of all formal charges
Favored structures•provide minimum formal charges•place negative formal charges on more electronegative atoms•imply smaller separation of charges
Formal charges are helpful in assessing resonance structures and assigning bonding
To calculate formal charges
Assign•All non-bonding electrons to the atom on which they are found•Half of the bonding electrons to each atom in the charge
S C N S C N S C N
- - --1 -1 +1 -2
Favored structure•provides minimum formal charges•places negative formal charges on more electronegative atoms•implies smaller separation of charges
C N-
C: (4 valence electrons) - (2 non bonding + 3 bonding) = -1 N: (5 valence electrons) - (2 non bonding + 3 bonding) = 0
Problem cases- expanded shells- generating charge to satisfy octets
Formal charges and expanded shells
Some molecules have satisfactory Lewis structures with octets but better ones with expanded shells.Expansion allows a atom having a negative charge to donate into a positive atom, reducing the charges.
Charges may generated so as to satisfy the octet.
Cl
B
Cl
Cl
Cl
B
Cl
Cl
Cl Be Cl
+ +2 -
Valence shell electron pair repulsion (VSEPR) theory
(a very approximate but very useful way of predicting molecular shapes)
•Electrons in molecules appear in bonding pairs or lone pairs
•Each pair of electrons repels all other pairs
•Molecules adopt geometries with electron pairs as far from each other as possible
Electron pairs define regions of space where they are likely to be:•Between nuclei for bonding pairs•Close to one nucleus for lone pairs
those regions are called electron domainsthe steric number is the sum of electron domains
Basic molecular shapes
Basic molecular shapes
ABn
Removing atoms from one basic geometry generates other shapes
The geometriesof electron domains
Moleculargeometries
Moleculargeometries
Note that lone pairsadopt equatorial positions
Moleculargeometries
Similar for higher steric numbers
Lone pairs are largerthan bonding pairs
Effect of lone pairs on molecular geometry
Electronegativity Scales
• The ability to attract electrons within a chemical, covalent bond
Pauling: polar bonds have higher bond strengths. Electronegativity assigned to each element such that the difference of electronegativities of the atoms in a bond can predict the bond strength.
Boiling Points and Hydrogen bonding
Hydrogen bonding in ice
The density of water decreases when it freezesand that determines the geology and biology of earth
Hydrogen bonding is crucial in biological systems
Secondary structure of proteins DNA replication
Symmetry and group theory
Natural symmetry in plants
Symmetryin animals
Symmetry in the human body
Symmetry in modern artM. C. Escher
Symmetry in arab architectureLa Alhambra, Granada (Spain)
Symmetry in baroque artGianlorenzo BerniniSaint Peter’s ChurchRome
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Symmetry inNative American crafts
7th grade art projectSilver Star SchoolVernon, Canada
Re2(CO)10
C2F4 C60
Symmetry in chemistry
•Molecular structures•Wave functions•Description of orbitals and bonds•Reaction pathways•Optical activity•Spectral interpretation (electronic, IR, NMR)...
A molecule is said to have symmetry if some parts of it may be interchangedby others without altering the identity or the orientation of the molecule
Molecular structures
Symmetry Operation:
Movement of an object into an equivalent or indistinguishableorientation
Symmetry Elements:
A point, line or plane about which a symmetry operation is carried out
5 types of symmetry operations/elements
Identity: this operation does nothing, symbol: E
Element is entire object
Proper Rotation:Rotation about an axis by an angle of 2/n
How about: NFO2?
H2ONH3
C2 C3
180° (2/2)
C2
The Operation: Proper rotation Cn is the movement (2/n)
The Element: Proper rotation axis Cn is the line
Applying C2 twiceReturns molecule to original oreintation
C22 = E
How about: NFO2?
H2ONH3
C2 180º C3, 120º
Proper rotation axes
Rotation angle Symmetry operation
60º C6
120º C3 (= C62)
180º C2 (= C63)
240º C32(= C6
4)
300º C65
360º E (= C66)
C2
C2
C2, C4
mnC
nnn
nn
CC
EC
1
Rotation 2m/n
PtCl4
Proper Rotation:Rotation about an axis by an angle of 2/n
The highest order rotation axisis the principal axis
and it is chosen as the z axis
2/2 = C2
2/4 = C4
Cnn = E
Reflection and reflection planes(mirrors)
(reflection through a mirror plane)
NH3
Only one ?
H2O
’
H2O
B
F F
F
If the plane containsthe principal axis it is called v
B
F F
F
If the plane is perpendicularto the principal axis
it is called h
n = E (n = even)n = (n = odd)
Inversion: i
Center of inversion or center of symmetry(x,y,z) (-x,-y,-z)
in = E (n is even)in = i (n is odd)
Inversion not the same as C2 rotation !!
Figures with center of inversion
Figures without center of inversion
Improper rotation (and improper rotation axis): Sn
rotation about an axis by an angle 2/nfollowed by reflexion through perpendicular plane
S42 = C2
Also, S44 = E; S2 = i; S1 =
Symmetry operations and elements
Operation Element
proper rotation axis (Cn)
improper rotation axis (Sn)
reflexion plane (s)
inversion center (i)
Identity Molecule (E)
Symmetry point groups
The set of all possible symmetry operations on a moleculeis called the point group (there are 28 point groups)
The mathematical treatment of the properties of groupsis Group Theory
In chemistry, group theory allows the assignment of structures,the definition of orbitals, analysis of vibrations, ...
See: Chemical applications of group theory by F. A. Cotton
To determinethe point groupof a molecule
Groups of low symmetry