week 2 electron configuration&molecular orbitals

Prepared by:Mrs Faraziehan Senusi

PA-A11-7C

Quantum Theory

Atomic Orbitals

Electronic Configuration

Chapter 1Atoms, Molecules & Chemical bonding

Molecular Orbitals

Bonding and Intermolecular Compounds

David P. White Prentice Hall ©

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Introduction


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Aufbau Principle

Hund’s Rule

Pauli Exclusion Principle

Electron Configuration

Lesson Plan


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At the end of this topic, the students will be able:

To describe atomic orbitals. To write electronic configurations To explain the bonding between different atoms To explain the interactions between molecules


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Pauli’s Exclusions Principle: no two electrons can have the same set of 4 quantum numbers.– Therefore, two electrons in the same orbital must

have opposite spins.• Two electrons can occupy the same orbital only if they have

opposite spins, ms. Two such electrons in the same orbital are paired.

• For simplicity, we shall indicate atomic orbitals as __ and show an unpaired electron as and spin-paired electrons as .

• By “unpaired electron” ,we mean an electron that occupies an orbital singly.

Pauli’s Exclusions Principle


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Aufbau Principle

Each atom is “built up” by (1) adding the appropriate numbers of protons and neutrons as specified by the atomic number and the mass number, and (2) adding the necessary number of electrons into orbitals in the way that gives the lowest total energy for the atom.

• Two general rules help us to predict electron configurations:1. Electrons are assigned to orbitals in order of increasing

value of (n + l).

2. For subshells with the same value of (n + l), electrons are assigned first to the subshell with lower n.

For example:

2s subshell : (n+l=2+0=2),

2p subshell : (n+l=2+1=3),

4s subshell (n+l=4+0=4)

3d subshell (n+l=3+2=5)

2p (n+l=2+1=3)

3s (n+l=3+0=3)

– Orbitals can be ranked in terms of energy to yield an Aufbau diagram.

– As n increases, note that the spacing between energy levels becomes smaller.

Aufbau Principle

(rule 1): fill the 2s subshell before the 2p subshell

(rule 1): fill the 4s subshell before the 3d subshell

(rule 2): fill the 2p subshell before the 3s subshell because 2p has a lower value of n


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Aufbau Principle


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An aid to remembering the usual order of filling of atomic orbitals.


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Hund’s Rule

Hund’s rule: When more than one orbital has the same energy, Electrons occupy all the orbitals of a given subshell singly before pairing begins. These unpaired electrons have parallel spins.

• Electron configurations tell us in which orbitals the electrons for an element are located.

• Electrons fill orbitals starting with lowest n and moving upwards.

Ground-state electron configuration (lowest energy arrangement) of an

atom lists orbitals occupied by its electrons, and is guided by three rules:

1. Lowest-energy orbitals fill first:

1s2s 2p 3s 3p 4s 3d (Aufbau(“build-up”) principle)

2. Electrons act as if they were spinning around an axis. Electron spin can have only two orientations, up ↑ and down ↓. Only two electrons can occupy an orbital, and they must be of opposite spin (Pauli exclusion principle) to have unique wave equations

3. If two or more empty orbitals of equal energy are available, electrons occupy each with spins parallel until all orbitals have one electron (Hund'srule).


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Summary


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Electron Configurations and the Periodic Table

• The periodic table can be used as a guide for electron configurations.

• The period number is the value of n.• Groups 1A and 2A have the s-orbital filled.• Groups 3A - 8A have the p-orbital filled.• Groups 3B - 2B have the d-orbital filled.• The lanthanides and actinides have the f-orbital

filled.

Row 1 (1s)

Row 2 (2p)


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Electron Configurations

n = 2, l = 1, ml = -1, ms = +1/2.

n = 2, l = 1, ml = +1, ms = +1/2.


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Condensed Electron Configurations• Neon completes the 2p subshell.

• Sodium marks the beginning of a new row. So, we write the condensed electron configuration for sodium as Na: [Ne] 3s1. [Ne] represents the electron configuration of neon.

• Inner (core) electrons: electrons in [Noble Gas].They fill all the lower energy levels of an atom.

• Valence electrons: electrons outside of [Noble Gas].


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Transition Metals• After Ar the d orbitals begin to fill.• After the 3d orbitals are full, the 4p orbitals being

to fill.• Transition metals: elements in which the d

electrons are the valence electrons.

Valence Electrons

In chemistry,valence electrons are the electrons of an atom that can participate in the formation of chemical bonds with other atoms.


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Lanthanides and Actinides• From Ce onwards the 4f orbitals begin to fill.• Note: La: [Xe]6s25d14f 0

• Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.

• Elements Th - Lr have the 5f orbitals filled and are called actinides.

• Most actinides are not found in nature.

Na : [Ne] 3s1 Na+ :

[Ne]

Ca : [Ar] 4s2 Ca2+ : [Ar]

Al : [Ne] 3s2 3p1 Al3+ : [Ne]

Electron Configurations of Cations and Anions

Atoms lose electrons so that cation has a noble-gas outer

electron configuration.

H : 1s1 H– : 1s2 or [He]

F : 1s2 2s2 2p5 F – : 1s2 2s2 2p6 or [Ne]

O : 1s2 2s2 2p4 O2– : 1s2 2s2 2p6 or [Ne]

N : 1s2 2s2 2p3 N3– : 1s2 2s2 2p6 or [Ne]

Atoms gain electrons so that anion has a noble-gas outer

electron configuration

Na+, Al3+ , F-, O2-, and N3- are all isoelectronic with Ne

• When a cation is formed from an atom of a transition metal, electrons are always removed first from the ns orbital and then from the (n–1)d orbitals.


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Electron Configurations of Cations of Transition Metals

Fe : [Ar] 4s2 3d6

Fe 2+ : [Ar] 4s0 3d6 or [Ar] 3d6

Fe 3+ : [Ar] 4s0 3d5 or [Ar] 3d5

Mn : [Ar] 4s2 3d5

Mn 2+ : [Ar] 4s0 3d5 or [Ar] 3d5

Molecular Orbital Theory

Bond order

Homonuclear diatomic molecules

Molecular Orbitals

Heteronuclear diatomic molecules

Lesson Plan

At the end of this topic, the students will be able:

To describe atomic orbitals. To write electronic configurations To explain the bonding between different atoms To explain the interactions between molecules


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Molecular OrbitalsMolecular Orbital (MO) Theory.• Just as electrons in atoms are found in atomic

orbitals, electrons in molecules are found in molecular orbitals.

• The combination of atomic orbitals on different atoms forms molecular orbitals (MOs).

• MO theory postulates that:

“the combination of atomic orbitals on different atoms forms molecular orbitals, so that electron in them belong to

the molecule as a whole’’

• When waves are combined, they may interact either constructively or destructively.


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• When they overlap in phase, constructive interaction occurs and a bonding orbital is produced. The energy of the bonding orbital is always lower (more stable) than the energies of the combining orbitals.

• When they overlap out of phase, destructive interaction and an antibonding orbital is produced. This is higher in energy (less stable) than the original atomic orbitals.

Molecular Orbitals

Considered the combination of the 1s atomic orbitals on two different atoms :• In the bonding orbital, the two 1s orbitals have reinforced each other in the

region between the two nuclei by in-phase overlap, or addition of their electron waves.

• In the antibonding orbital, they have canceled each other in this region by out-of-phase overlap, or subtraction of their electron waves.

• We designate both molecular orbitals as sigma (σ) molecular orbitals (which indicates that they are cylindrically symmetrical about the internuclear axis). We indicate with subscripts the atomic orbitals that have been combined. The star () denotes an antibonding orbital. Thus, two 1s orbitals produce a σ1s (“sigma-1s”) bonding orbital and σ

1s (“sigma-1s-star”) antibonding orbital.


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Molecular Orbitals

• In a bonding molecular orbital, the electron density is high between the two atoms, where it stabilizes the arrangement by exerting a strong attraction for both nuclei.

• An antibonding orbital has a node/nodal plane (a region of zero electron density) between the nuclei; this allows for a strong net repulsion between the nuclei, which makes the arrangement less stable.

• Electrons are more stable (have lower energy) in bonding molecular orbitals than in the individual atoms.

• Placing electrons in antibonding orbitals, requires an increase in their energy, which makes them less stable than in the individual atoms.


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Molecular Orbitals


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Molecular Orbitals• The total number of electrons in all atoms are placed in the MOs

starting from lowest energy (1s) and ending when you run out of electrons.• Note that electrons in MOs have opposite spins.

• The Hydrogen Molecule ~ H2 has two bonding electrons.

• The Helium Molecule ~ He2 has two bonding electrons and two antibonding electrons.

Bond Order• Define:

• Bond order = 1 for single bond.• Bond order = 2 for double bond.• Bond order = 3 for triple bond.• Fractional bond orders are possible.

• For H2

Therefore, H2 has a single bond.

• For He2

Therefore He2 is not a stable molecule

electrons gantibondin-electrons bondingorder Bond21

102order Bond21

022order Bond21

The greater the bond order of a diatomic molecule or ion, the more stable we predict it to be. Likewise, for a bond between two given atoms, the greater the bond order, the shorter is the bond length and the greater is the bond energy.

• Bond order = 0 implies there are equal numbers of electrons in bonding and antibonding orbitals.~ same stability as separate atoms.

• Bond order > 0 implies there are more electrons in bonding than antibonding orbitals. ~ Molecule is more stable than separate atoms.


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Bond Order & Bond Stability

• “Homonuclear” means consisting only of atoms of the same element.

• “Diatomic” means consisting of two atoms.

• We look at homonuclear diatomic molecules (e.g. Li2, Be2)

• AOs combine according to the following rules: The number of MOs = number of AOs; AOs of similar energy combine; As overlap increases, the energy of the MO decreases;

• Pauli: each MO has at most two electrons;• Hund: for degenerate orbitals, each MO is first occupied

singly.


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Molecular Orbitals for Li2 and Be2

• Each 1s orbital combines with another 1s orbital to give one 1s and one *

1s orbital, both of which are occupied (since Li and Be have 1s2 electron configurations).

• Each 2s orbital combines with another 2s orbital, two give one 2s and one *

2s orbital.

• The energies of the 1s and 2s orbitals are sufficiently different so that there is no cross-mixing of orbitals (i.e. we do not get 1s + 2s).


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Molecular Orbitals for Li2

• There are a total of 6 electrons in Li2:• 2 electrons in 1s;

• 2 electrons in *1s;

• 2 electrons in 2s; and

• 0 electrons in *2s.

• Since the 1s AOs are completely filled, the 1s and *1s are filled. We generally ignore core electrons in MO diagrams.

124order Bond21


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Molecular Orbitals for Be2

• There are a total of 8 electrons in Be2:• 2 electrons in 1s;

• 2 electrons in *1s;

• 2 electrons in 2s; and

• 2 electrons in *2s.

• Since the bond order is zero, Be2 does not exist.

044order Bond21


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Molecular Orbitals from 2p Atomic Orbitals• There are two ways in which two p orbitals overlap:

• end-on so that the resulting MO has electron density on the axis between nuclei (i.e. type orbital);

• sideways so that the resulting MO has electron density above and below the axis between nuclei (i.e. type orbital).

• The six p-orbitals (two sets of 3) must give rise to 6 MOs:• , *, , *, , and *.• Therefore there is a maximum of 2 bonds that can come from p-

orbitals.

• The relative energies of these six orbitals can change.


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Molecular Orbitals from

2p Atomic Orbitals

Configurations for B2 Through Ne2

• As the atomic number decreases, it becomes more likely that a 2s orbital on one atom can interact with the 2p orbital on the other.• As the 2s-2p interaction increases, the 2s MO lowers in energy and

the 2p orbital increases in energy.

• For B2, C2 and N2 the 2p orbital is higher in energy than the 2p.

• For O2, F2 and Ne2 the 2p orbital is lower in energy than the 2p.


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MOLECULAR ORBITAL ENERGY LEVEL DIAGRAMS

(a) For B2,C2,and N2 molecules,the two 2p orbitals are lower in energy than the σ2p orbital. (b) However, for O2, F2, and Ne2 molecules, the σ2p orbital is lower in energy than the 2p orbitals.


• Once the relative orbital energies are known, we add the required number of electrons to the MOs, taking into account Pauli’s exclusion principle and Hund’s rule.• As bond order increases, bond length decreases.

• As bond order increases, bond energy increases. • The bond energy is the amount of energy necessary to

break a mole of bonds, therefore, bond energy is a measure of bond strength.


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Electron Configurations and Molecular Properties

• Paramagnetic ~ it has unpaired electrons.

~ substances that are attracted by a magnet

• Diamagnetic ~ no unpaired electrons.

~ substances that repelled by a magnet


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• Atomic orbitals of the more electronegative element are lower in energy than the corresponding orbitals of the less electronegative element.

• Atomic orbitals of two different elements, such as the 2s orbitals of nitrogen and oxygen atoms, have different energies because their nuclei have different charges and therefore different attractions for electrons.


The atomic orbitals of oxygen, the more electronegative element, are a little lower in energy than the atomic orbitals of nitrogen, the less electronegative element.


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Formation of σsp and σ*sp molecular orbitals in HF by overlap of the 1s orbital of H with a 2p orbital of F.


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Pop Quiz!!

Try draw MO diagram and electron configuration for N2 and O2 molecules.

Determine the bond order for both molecules.

Hint:

N : 1s2 2s2 2p3

O : 1s2 2s2 2p4

week 2 electron configuration&molecular orbitals

Technology

p orbitals

unpaired electrons

d orbitals

f orbitals

s subshell n

electron spin

lowestenergy orbitals

electron configurations