Chapter 17 Many-Electron Atoms and Chemical Bonding

17.1 Many-Electron Atoms and the Periodic Table

17.2 Experimental Measures of Orbital Energies17.3 Sizes of Atoms and Ions17.4 Properties of the Chemical Bond17.5 Ionic and Covalent Bonds17.6 Oxidation States and Chemical

Bonding

17.1 Many-Electron Atoms

Many electron atoms and the periodic table

Building up electron configurations

Building up from H to Ar

Building from K to Kr: Transition elements and d orbitalsElectron shells and the periodic table

Hund’s rule, paramagnetism and diamagnetism.

1a

2a

3a 4a 5a 6a 7a 8 8 8 1b 2b

3a 4a 5a 6a 7a

8a

Building up the table from electron configurations

Electronic structure of atoms of the elements:

(1)Atoms of the various elements differ from each other in their values of Z and electrons.

(2)Electrons in atoms are arranged in orbitals and shells.

(3)Orbitals are characterized by the quantum numbers n, l and ml.

(4)Orbitals having the same value of n are said to be in the same shell. Orbitals having the same values of n and l are said to be in the same subshell.

Many electron atoms and the periodic table

Comparison of the electron densities of the H atom orbitals and many electron atoms.

The quantum numbers n, l and ml still have an approximate validity

Every electron in an atom has a set of four quantum numbers that describe its spatial distribution and

spin state.

This means that every electron in a multielectron atom occupies an atomic orbital with a characteristic

size, shape, energy and spin direction.

Building up electron configurations

An electron configuration is a list of the occupied orbitals and the number of electrons in each.

The electron configuration of lowest energy is termed the ground state electronic

configuration.

Aufbau Principle: The ground state electron configuration is built by filling the lowest energy orbitals first obeying the Pauli principle and Hund’s rule

The orbital approximation: The electron density of an isolated many-electron atom is approximately the sum of the electron densities of each of the

individual electrons taken separately.

For atoms with more than one electron, approximations are required in order to make

quantitative quantum mechanical approximations.

The approximation amounts to treat each electron as if it were moving in a field o charge that is the net result of the nuclear attraction and the average

repulsions of all the other electrons.

Determining a ground state electronic configuration

(1) Use the n + l rule to determine the relative energies of the atomic orbitals from 1s to …..

(2) Imagine a bare nucleus of charge +Z surrounded by empty atomic orbitals.

(3) Add Z electrons to the empty orbitals starting with the lowest energy orbital first, obeying the Pauli principle at all times.

(4) Electrons are placed in orbitals of lowest ener

Effective nuclear charge (Zeff) on the outer electrons

Maintain hydrogen atom like orbitals as an approximation, but subshell energies are not equal: Ens < Enp < End < Enf

A s electron penetrates to the nucleus more than a p electron: a p electron penetrates to the nucleus more

than a d electron: more penetration, more stable, lower energy.

Subshell energies: E3s < E3p < E3d

Electron shielding of the nuclear charge by other electrons

Why is the energy of a 3s orbital lower than than of a 3p orbital? Why is the energy of a 3p orbital

lower than the energy of a 3d orbital?

Effective charge, Zeff, see by valence electrons*

*Note x-axis is incorrect. What should it be?

Are the following two states allowed for N by the Pauli principle?

1s22s22px12py

12pz1 or 1s22s22px

22py12pz

0

Hund’s rule refers to the lowest energy of electron configurations allowed by the Pauli exclusions principle. It does not forbid the existence of any of the Pauli allowed

configurations. If there are more than electron configurations one allowed Pauli configuration, the lower energy on will be

predicted by Hund’s rule and the others will be excited states.

Which is more stable?

1s22s22px()2py()2pz() is more stable than 1s22s22px()2py()2pz()

The presence of two orbitally and spin unpaired electrons in the ground state of carbon makes the

atom paramagnetic.

A paramagnetic substance is attracted to a magnetic field. A diamagnetic substance is

repelled from a magnetic field.

All substances which possess one or more orbitally unpaired electrons are paramagnetic.

All substances which possess only spin paired electrons are diamagnetic.

Paramagnetic and diamagnetic substances

Examples of diamagnetic and paramagnetic atoms

Which of the following atoms are paramagnetic?

1H, 2He, 3Li, 4Be, 5B, 6C, 7N, 8O, 9F, 10Ne

1H, 3L, 5B, 7N, 9F must be paramagnetic since they possess an odd number of electrons.

6C and 8O are paramagnetic because of Hund’s rule:6C: 1s22s2px

1py1

8O: 1s22s2px2py

1pz1

2He, 4Be and 10Ne are diamagnetic.

The energy of an orbital of a hydrogen atom or any one electron atom only depends on the value of n

shell = all orbitals with the same value of nsubshell = all orbitals with the same value of n and l

an orbital is fully defined by three quantum numbers, n, l, and ml

The energy of subshells increase with l for a given value of n

The (n + l) rule of orbital energies in a multielectron atom.

Electrons fill orbitals of different energies by filling the lowest energy first. The energies of orbitals of multielectron atoms follow the (n + l) rule: the lowest value of (n + l) has the lowest energy.

Examples with (n + l)1s (1 + 0) < 2s (2 + 0) < 3s (3 + 0) < 3p (3+1) ,< 4s (4 + 0) < 3d (3 + 2) < 4p (4 + 1)

When n + l is the same for two orbitals, the orbital with the higher value of n has the

higher energy.

Shell and SubshellStructure

Atomic Energy Levelsaccording to the

(n + l) rule

Buildup (aufbau) Principle

Relative orbital energies for the multielectron atom.

The energy of an orbital of a multielectron atom depends on n and l (but not ml)

2s < 2p

3s < 3p < 3d ~ 4s (may switch with Z)

Note energy levels are getting closer together for n = 3 as expected from the Bohr atom.This means that factors ignored may have to be considered

Classification of orbitals of a many electron atom according to their energies.

A group of orbitals with exactly equal energies comprise a subshell.

Example: 2px, 2py and 2pz

Orbitals with same value of n and different value of l comprise a shell.

Example: 2s and 2p comprise a shell.

The orbital approximation ignores electron-electron repulsion, but takes into account Hund’s rule:

electrons with parallel spins () tend to stay apart compared to electrons with antiparallel spins ().

Orbital shells and the building up of the periodic

tableA shell is a set of orbitals with the same value of n

and l for a H atom.

The Ar atom has shells as shown (left) in the profile of electron density as a

function of distance from the nucleus

The last shell are the valence electrons of our

Lewis structures!

Electronic structure and the periodic table

Electrons in the outermost shell of an atom are the most important in determining chemical properties. Chemical reactions involve only the outer (valence) electrons. The

inner (core) electrons are not involved in chemical reactions.

Elements in a given vertical column (families) of the periodic table have similar outer-shell electron configurations and similar properties. They are

isoelectronic with respect to the number of valence electrons.

Elements in a row show regular trends in their properties due to the continuing increase in the

number of valence electrons until a shell is filled.

The Pauli exclusion principle and magic number of electrons.

Two equivalent statements of the exclusion principle:

(1)No two electrons may have the same set of four quantum numbers;

(2)No more than two electrons may occupy the same orbital.

Because of the Pauli exclusion principle, outer electrons do not “fall” into the inner shell. Thus,

the atom is stable.

The Pauli principle imposes structure on the many electron atom.

Without it, all the electrons might be expected to crowd into the low energy orbitals. With it the electrons are organized, filled orbitals with no

more than two electrons.

The ground state is the lowest energy organization of electrons around the nucleus. The

electron organization is described by electron configurations.

The ground state of an atom corresponds to the lowest energy electron configuration.

Ground state electron configuration of a many electron atom: Governs reactivity

of atoms under normal condition

Imagine a bare nucleus of charge +ZImagine empty orbitals surrounding the nucleus

Fill the orbitals with Z electrons for the neutral atom following two principles:

Aufbau principle: fill lowest energy orbitals firstPauli exclusion principle: each electron must have four different quantum numbers (maximum of 2 electrons in an orbital).

Constructing the periodic table by filling orbitals with electrons (electron configurations).

Aufbau: Fill 1s orbital firstPauli: no more than two

electrons in the 1s orbitalThe basis of the duet rule:

filling a shell1s subshell filled with 2He

= stable electron core given symbol [He].

Construction of the first row of the periodic table.Electron configurations: 1H and 2He.

Filling the orbitals of 3Li, 4Be and 5B

Aufbau: Fill 1s orbital first, then 2s, then 2p.

Pauli: no more than two electrons in the 1s orbital.

2s subshell filled with 4Be.

For carbon, how do the two 2p electrons distribute themselves in the three 2p orbitals?

For nitrogen, how do the three 2 p electrons distribute themselves in the three 2p orbitals?

Filling the orbitals of 6C and 7N. The need for a third rule (Hund’s rule):

Hund’s rule: Applies when filling the orbitals of a subshell with electrons (np or nd or nf subshells). Or

more generally when filling orbitals of identical energy

When adding electrons to a subshell, the ground state electronic configuration is formed by maximizing the number of electrons with parallel spins ()() before

pairing two electrons in one orbital ()().

Example: 6C = [He]2s22px()2py()2pz() = ground stateExample: 6C = [He]2s22px()2py()2pz() = excited state

Filling the orbitals of 6C and 7N. The need for a third rule (Hund’s rule):

Hund’s Rule: When electrons occupy orbitals of the same

energy, the lowest energy state corresponds to the configuration with the greatest number of orbitally and spin unpaired

electrons.

When the configuration is written as 1s22s22p2 it is understood that two different p orbitals are

occupied.

Filling the orbitals of 8O, 9F and 10Ne

Filling the 2p subshell produces another stable configuration of electrons which serves as the core shell of the third row: symbol [Ne]

Summary: Electron configurations from 1H to 10Ne.

No new features for the electron configurations from 11Na to 18Ar.

The third full row of the periodic table: 19K-36Kr

The 4s orbital is slightly more stable than the 3d orbital at the beginning of the third full period of the periodic table:

19K = [Ar]4s13d0 20Ca = [Ar]4s23d0

The reason is that the 4s orbital has a higher probability of being closer to the nucleus and see a greater effective Zeff than a 3d orbital.

The 4s and 3d orbitals are close in energy in the one electron atom. Difficult to predict stability for multielectron atom.

Electron configuration of the transition elements:

21Sc through 30Zn

21Sc, 22Ti, 23V, 24Cr, 25Mn, 26Fe, 27Co, 28Ni, 29Cu, 30Zn

19K = [Ar]4s3d0

20Ca = [Ar]4s23d0

What would you expect for 21Sc?

21Sc = [Ar]4s23d1. Not quite correct….

The 3d electron is lower in energy than the 4s electron in 21Sc from experiment: 21Sc = [Ar] 3d14s2

d orbitals raise their ugly heads!

Ground State Electron Configurations

ORBITALS and Hund’s Rule

Element “Expected” Found Comment 21Sc [Ar]3d14s2 [Ar]3d14s2 22Ti [Ar]3d24s2 [Ar]3d24s2 23V [Ar]3d34s2 [Ar]3d34s2 24Cr [Ar]3d44s2 [Ar]3d54s1 Half-filled shell 25Mn [Ar]3d54s2 [Ar]3d54s2 26Fe [Ar]3d64s2 [Ar]3d64s2 27Co [Ar]3d74s2 [Ar]3d74s2 28Ni [Ar]3d84s2 [Ar]3d84s2 29Cu [Ar]3d94s2 [Ar]3d104s1 Full and half-filled shell 30Zn [Ar]3d104s2 [Ar]3d104s2

“Expected” and found electron configurations of the d block elements from Z = 21 to Z = 30

Atomic Electronic Configurations

1H to 36KrGroup I: ns1

Group II: ns2

Group III: ns2p1

Group IV: ns2p2

Group V: ns2p3

Group VI: ns2p4

Group VII: ns2p5

Group VIII: ns2p6

17.2 Experimental Measures of Orbital Energies

Photoelectron spectroscopy

Periodic trends in ionization energies

Periodic trends in electron affinities

Ionization Energy

• Measure of the effort needed to remove electron(s) from a ground state atom:– Values are positive– Obtained by photoelectron spectroscopy

X + h X+ + e- E = IE1

– Second ionization energy always exceeds first

X X+ + e- E = IE1

X+ X2+ + e- E = IE2

Reactivity increases with the number of shells shielding the electrons in the outer (valence) shell. DEMONSTRATION

lA Family Volts Valence Shell Li 5.39 2s1 Na 5.14 3s1

K 4.34 4s1

Rb 4.18 5s1

Cs 3.89 6s1

Ionization EnergyThe Alkali Metal (IA) Family of Elements

Reactivity increases with the number of shells shielding the electrons in the outer (valence) shell. DEMONSTRATION

lA Family Volts Valence Shell Li 5.39 2s1 Na 5.14 3s1

K 4.34 4s1

Rb 4.18 5s1

Cs 3.89 6s1

Ionization Energy: The Alkali Metal (IA) Family of Elements

Ionization energies (ionization potentials):

The ionization energy (IE) of an atom is the minimun energy required to remove an electron from a gaseous atom.

X(g) X+(g) + e-

The first ionization energy IE1 is the energy required to remove the first electron from the atom, the second ionization energy IE2, is the energy required to remove the second electron from

the +1 positive ion of the atom and so on.

Conclusions from experimental IE values:An abrupt change in IE in going along a row or column of the

periodic table indicates a change in the valence electron shell or subshell. Let’s take a look:

Experimental data and theoretical ideas

Explain the “two slopes” for the ionization energies of carbon.

6C 1s22s22p2

6C+5 1s12s02p0

6C+4 1s22s02p0

6C+3 1s22s12p0

6C+2 1s22s22p0

6C+1 1s22s22p1

It gets more and more energy to remove an electron from an increasingly positively charged atom.

The first smaller slope is due to removal of n = 2 electrons, the second larger slope is due to removal of n = 1 electrons.

Ionization energies in tabular form

Ionization energies in graphical form

Periodic trends of the first ionization energies of the representative elements: What are the correlations

across and down?

The electron affinity (EA) of an atom is the energy change which occurs when an atom gains an electron.

X(g) + e- Xe- (g)

Electron affinities of the representative elements:What are the correlations across and down?

Ionization energies in tabular form

Ionization energies in graphical form

Periodic trends of the first ionization energies of the representative elements: What are the correlations

across and down?

The electron affinity (EA) of an atom is the energy change which occurs when an atom gains an electron.

X(g) + e- Xe- (g)

Electron affinities of the representative elements:What are the correlations across and down?

17.3 Sizes of Atoms and Ions

The radii of atoms and ions

Covalent radius, atomic radius and ionic radius

Periodic trends in the radius of atoms and ions

Radii generally increase down a group (n of outer shell increases) and decrease (Zeff decreases for same shell) from left to right across a period. Cations are generally smaller than their parent

atoms and anions are larger.

Atomic Volume

Covalent Radii from Experiment

• The covalent radius is defined as half the distance between two atoms bound by a single bond in a molecule.

Periodic properties of atomic radius:What are the correlations?

General Rule: The size of an atom decreases in a row as the nuclear charge increases and the size of

an atom increases in a column as the nuclear charge increases

17.4 Properties of the Chemical Bond

Bond length:

Bond enthalpy:

Bond order:

The distance between the nuclei of two bonded atoms.

The energy required to break a bond between two atoms.

The number of shared electron pairs (not electrons) in a covalent bond.

Bond LengthsH2 = 0.74Å

• F2 1.42• Cl2 1.99• Br2 2.28• I2 2.67• ClF 1.09• BrCl 2.14• BrF 1.76• ICl 2.32

• HF 0.92• HCl 1.27• HBr 1.41• HI 1.61• N2 1.09• O2 1.21• NO 1.15• CO 1.13

The Nature of the Chemical Bond

•Pose the question:“Why do atoms sometimes form stable molecules and compounds…. and sometimes not?”

•Or perhaps reducing the general question to more limited questions for which there is a higher probability of getting answers:

–“What is the energy in bonds?”–“What is the distance between atoms?”–“What is the shape and geometry that results?”

• Li2 105

• Na2 71

• K2 50

• Rb2 46

• Cs2 44

• F2 154

• Cl2 247

• Br2 192

• I2 151

• N2 946

• O2 498

Bond EnergiesH2 = 400 kJ/mol

Bond Energy (Enthalpy)

17.5 Ionic and Covalent Bonds

Ionic bonds:

Electron density is mainly transferred from one atom to another atom to create a bond between two atoms.

Covalent bonds:

Electron density is shared by two bonded atoms.

Electronegativity:

A measure of the ability of an atom in a bond to attract electrons from other atoms.

Percent covalent (ionic) character:

A measure of the polarity of a bond between two atoms.

Electronegativity (EN): a measure of the ability of an atom to attract electrons

to itself in competition with other atoms