Lecture 2

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