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- Intro to Atomic and Molecular Structure

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Get Started Now- Intro Lesson: a4:40
- Intro Lesson: b6:55
- Intro Lesson: c3:31
- Intro Lesson: d2:41
- Intro Lesson: e10:29
- Intro Lesson: f9:16
- Intro Lesson: g7:24
- Intro Lesson: h7:26

In this lesson, we will learn:

- To understand the forming of molecular orbitals using the LCAO method.
- To understand the bonding and antibonding nature of molecular orbitals.
- To apply MO theory when explaining the existence and nonexistence of chemical substances.
- To use molecular orbital diagrams and bond order to explain the type of bonding observed in molecules.

- We now know how electrons are held in atomic orbitals of different energy levels and shape. In the same way that atoms combine to make molecules,
__atomic orbitals (AOs) combine to form molecular orbitals (MOs).__

This is called the*linear combination of atomic orbitals (LCAO)*and when applied, it predicts the stability of molecules that we know exist, and the instability of molecules that we don't know exist. - Before we go further with electrons in atomic orbitals (AOs) making MOs, remember that
__atomic orbitals__– the electron 'houses' that show where electrons 'probably are' -They mathematically describe how likely it is an electron will be in a certain place at a certain time. These atomic orbitals can combine like waves can combine, either constructively (mathematically adding them together) and destructively (subtracting them and just cancelling each other out).*are wave functions.* __Whenever two different atomic orbitals combine, two different molecular orbitals are made.__- One is made when
__atomic orbitals overlap__(think mathematically + and +, wave functions combining, or waves in the same phase) and is called a__bonding molecular orbital.__ - One is when the
__atomic orbitals cancel out__(think mathematically + and –, or waves in opposite phases) and is called anHere the two wave functions have cancelled each other out, and a node is created.*antibonding molecular orbital.*

Just like with atomic orbitals, molecular orbitals can be drawn using an energy level diagram and in terms of energy, these MOs are positive and negative versions of each other – the energy level diagram should look symmetrical.

Drawing MOs when 1s orbitals combine looks like this:

__In the bonding molecular orbital__, the constructive overlap means in this MO any electrons will most likely be found between the two nuclei of the atoms involved.

Between the two nuclei, any electrons have more nuclear charge to be attracted to than in one individual atom with just one of those nuclei. Also, with both atoms providing electrons in forming the MO, there will be more electrons for the nuclei to be attracted to as well. This is what a chemical bond is.

In short, using the wave analogy, two in-phase waves combine to create a larger sum than as individual waves.__Therefore this MO is of lower energy than the individual AOs__that combine to make it.__In the antibonding molecular orbital__, the destructive overlap (cancelling out of the wave functions) means there is zero probability that any electrons occupying this MO will be found between the two nuclei – it is a node. This leaves the two positive nuclei exposed to each other with no mutual negative charge to be attracted to; the nuclei will just repel one another in a destabilizing interaction.__Therefore this MO is of higher energy than the individual AOs__that combine to make it, where individually in the AO, no such repulsion occurs.- WORKED EXAMPLE: Hydrogen,
^{1}H

A hydrogen atom has only one electron occupying the 1s orbital. Using MO theory, we can show that a diatomic hydrogen molecule would be of lower energy than an individual atom of hydrogen:

If two hydrogen atoms interact, their combined two electrons (one each) fill up the bonding MO, which is lower energy (more stable) than their individual AO as a lone hydrogen atom.

Since hydrogen atoms only carry one electron each and orbitals can hold up to two electrons, the bonding MO is full and the antibonding MO is empty. The H-H interaction is a stabilizing, attractive interaction (a chemical bond) with no destabilizing interactions.

This is supported by empirical evidence; the H_{2}molecule is stable and is observed in nature. Individual H atoms on the other hand are unstable; they are not observed in nature.

A helium atom has two electrons both occupying its 1s atomic orbital. If two atoms of helium were to try and form a chemical bond, then the following molecular orbitals would be made:

Since an orbital can only hold two electrons maximum, the four electrons from the two helium atoms fill up both the bonding MO and the antibonding MO.

This results in the bonding and antibonding MOs cancelling out completely –

In short,

This is supported by the evidence. He

- When s orbitals (and p orbitals, when head-on) combine, they make
__cylindrical MOs with symmetry around an axis.__These are*sigma molecular orbitals*and__when electrons fill MOs with this symmetry, we call it a__and give them the symbol σ.*sigma bond*

This is true for antibonding MOs too – if it is symmetrical when rotating on an axis, it is a sigma MO! Antibonding sigma MOs are given the symbol σ*, the * to show antibonding nature. - σ orbitals from s orbitals can be drawn like in the energy-level diagrams of hydrogen and helium above.
- σ molecular orbitals can be made from p orbitals too. See below:
- When other p atomic orbitals combine, they can form MOs with symmetry through a plane because the p AOs are planar too.
__MOs with planar symmetry are called pi molecular orbitals__(given the symbol π) and__when electrons fill pi MOs we call it a pi (π) bond__, as we do with the antibonding pi orbitals, π*. - These two pi MOs are orthogonal and of equal energy to each other.
- Because these orbitals are out at a plane perpendicular to the two nuclei and not in line with them, there is less interaction with the nuclei so
__π bonding orbitals are slightly higher energy than their counterpart σ bonding MOs.__ - As bonding and antibonding MOs are symmetrical in energy,
__π antibonding orbitals are slightly lower energy than their counterpart σ antibonding MOs.__ - Drawing pi molecular orbitals (especially antibonding orbitals) is quite hard to do accurately so they are normally left drawn as if they were still their lone atomic orbitals.

- Two MOs are made of two AOs coming together, so you need to
__draw the AOs of the two atoms making the MOs on either side of the diagram. The MOs form in the 'middle'__which you can show on your diagram.

See the green "1" marks on the diagram below. __Atomic orbitals of identical atoms will have identical energy – so draw them level__with each other!

See the green "2" marks on the diagram below.__For any MO, the bonding and antibonding forms are symmetrical in energy;__compared to their AOs, the bonding MO will be as low as the antibonding MO is high. You should see SYMMETRY! (We will get to exceptions later…)

See the green "3" marks on the diagram below.- Just like s atomic orbitals are lower in energy than p atomic orbitals, MOs made from s atomic orbitals will be lower in energy than MOs made from p atomic orbitals.
__Fill in electrons using the lowest energy MO first__(this is the Aufbau principle). Fill in the electrons in the AOs too; this should help you avoid any mistakes in the number of electrons you put in the MOs.__When filling incomplete π orbitals, place electrons in separate orbitals first__, only pairing them up when they have to be – this is obeying the Pauli principle.

See the green "4" mark on the diagram below.

- Why is the bond in O
_{2}a double bond? - Why is the bond in N
_{2}a triple bond?

$Bond\;order = \frac{(\#\;bonding\;electrons) - (\#\;antibonding\;electrons)}{2}$

Bond order is found by subtracting electrons in bonding MOs ('bonding electrons') by electrons in antibonding MOs ('antibonding electrons') and then dividing by two because you need two electrons make a covalent bond. If we apply this to O

Counting from 2s and above, we can see that there are eight bonding electrons (two in the 2s σ bonding MO, two in the 2p σ bonding MO and four in the 2p π bonding MO) and only four antibonding electrons (two in the 2s σ* antibonding MO and two in the 2p π* antibonding MO). Putting these into the equation we get:

$Bond\;order = \frac{(\#\;bonding\;electrons) - (\#\;antibonding\;electrons)}{2} = \frac{8-4}{2} = 2$

A bond order of 2 is found – this is why we say the O-O bond in O

When bonding MOs and antibonding MOs cancel out, you are left with

- Look at the O
_{2}MO diagram above. The full 2s σ and σ* MOs cancel four electrons, and two π electrons cancel with two π* electrons. This is eight electrons cancelling out, or four lone pairs over two oxygen atoms – two lone pairs for each atom!

F has 9 electrons, so an F

Filling the molecular orbitals from the lowest energy level first gives us the setup above.

Note that the π bonding and antibonding MOs completely cancel each other out – always try and look for symmetry in these MO diagrams to see what is not cancelled out. What do you think the bond order will be?

We can calculate it using the formula – remember you don't need to add the 1s electrons to this.

We have eight bonding electrons (two in the 2s σ bonding MO, two in the 2p σ bonding MO, four in the two π bonding MOs) and six antibonding electrons (two in the 2s σ* antibonding MO, four in the 2p &pi* antibonding MO).

$Bond\;order = \frac{(\#\;bonding\;electrons)-(\#\;antibonding\;electrons)}{2} = \frac{8-6}{2} = 1$

The bond order in F

We can also show the number of lone pairs as the bonding/antibonding MOs cancel out for non-bonding electrons – the 2s σ and σ* MOs cancel for four electrons, as do all of the π and π* electrons, eight electrons in total. We are just left with a σ bonding MO with the 2p electrons and twelve electrons, or six lone pairs over two atoms – three each.

- Introduction
__How do atomic orbitals become molecular orbitals?__a)Linear combination of atomic orbitals (LCAO).b)Making molecular orbitals from atomic orbitals.c)Using MO theory to predict: Hydrogend)Using MO theory to predict: Heliume)Sigma and pi MOsf)Drawing correct MO diagrams: example.g)Bond order and lone pairs.h)Worked example: F_{2}

2.

Intro to Atomic and Molecular Structure

2.1

Atomic orbitals and energy levels

2.2

Molecular orbital theory

2.3

Atomic orbital hybridization