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Explore Molecular Orbital Theory: The Key to Chemical Bonding
Dive into the world of molecular orbital theory and revolutionize your understanding of chemical bonding. Learn how electrons behave in molecules, predict molecular properties, and go beyond simple Lewis structures.

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Now Playing:Molecular orbital theory – Example 0a
Intros
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  1. How do atomic orbitals become molecular orbitals?
  2. Linear combination of atomic orbitals (LCAO).
  3. Making molecular orbitals from atomic orbitals.
Atomic orbitals and energy levels
Jump to:NotesConceptExampleFAQsPrerequisites
Notes

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.

Notes:

  • 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' - are wave functions. 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).
  • 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 an antibonding molecular orbital. Here the two wave functions have cancelled each other out, and a node is created.
      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:
    The two MOs created from AOs will be of different energy because of the effects of where the electrons will be 'spending most of their time' in the molecule:
    • 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.
    You can apply MO theory to real molecules to explain their stability – why they exist – and to 'imaginary' molecules to explain their instability – why they don't exist! We will do this for hydrogen and helium as examples when their electrons fill in molecular orbitals.
  • WORKED EXAMPLE: Hydrogen, 1H
    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 H2 molecule is stable and is observed in nature. Individual H atoms on the other hand are unstable; they are not observed in nature.
  • WORKED EXAMPLE: Helium, 2He
    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 an "He2" molecule, there is the same amount of bonding as there is antibonding.
    In short, there is no 'chemical bond' here at all.
    This is supported by the evidence. He2 is not observed in nature; He only exists as single elemental atoms.
  • With higher energy (2s and above) orbitals, because now there are differently-shaped s and p orbitals, we name the types of bonds with MOs based on their symmetry. Despite the s orbitals "2s" and above having nodes, we can still draw MOs with them like we would the 'node-less' 1s orbitals.
    • 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 sigma bond and give them the symbol σ.
      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.
  • With π MOs, drawing energy level diagrams has become more complicated, since π and σ orbitals have different energies.
    Here are some guides for drawing energy level MO diagrams correctly with the O2 molecule as an example:
    • 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.
    A completed molecular orbital diagram for the O2 molecule would look like this:
  • Molecular orbital diagrams help to explain the 'number of bonds' that atoms in a molecule make to each other:
    • Why is the bond in O2 a double bond?
    • Why is the bond in N2 a triple bond?
    We calculate the bond order to find this out.
    Bond  order=(#  bonding  electrons)−(#  antibonding  electrons)2 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 O2 for example, you will see why using MO theory, we say O2 has a double bond. (Note: In bond order calculations, ignore the lower energy levels because they are much lower in energy and do not bond).

    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=(#  bonding  electrons)−(#  antibonding  electrons)2=8−42=2Bond\;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 O2 is a double bond according to MO theory. There is a sigma bond, and a pi bond.
  • Another reason to always look out for symmetry (equal bonding/antibonding MOs) in the MO diagrams is because it will help you predict the number of lone pairs in a molecule or on an atom.
    When bonding MOs and antibonding MOs cancel out, you are left with non-bonding electrons – these are the lone pairs in a molecule.
    • Look at the O2 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!
  • 2nd WORKED EXAMPLE: F2

    F has 9 electrons, so an F2 molecule has 18 electrons in total.
    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=(#  bonding  electrons)−(#  antibonding  electrons)2=8−62=1Bond\;order = \frac{(\#\;bonding\;electrons)-(\#\;antibonding\;electrons)}{2} = \frac{8-6}{2} = 1
    The bond order in F2 is 1 – we say the F-F chemical bond is a single bond!
    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.
    • Concept

    Introduction to Molecular Orbital Theory

    Welcome to the fascinating world of molecular orbital theory! This powerful concept is essential for understanding chemical bonding at a deeper level. Imagine you're building a model of how atoms come together to form molecules. That's exactly what molecular orbital theory helps us do! It explains how electrons are distributed in molecules, giving us insights into their properties and behavior. Our introduction video is a great starting point to grasp these ideas. It breaks down complex concepts into easy-to-understand visuals and explanations. As we explore molecular orbital theory, you'll see how it goes beyond simple Lewis structures, offering a more accurate picture of chemical bonds. This theory is crucial for predicting molecular geometry, reactivity, and even color! Whether you're a chemistry enthusiast or just curious about how the world works at the atomic level, understanding molecular orbital theory will open up a whole new perspective on chemical bonding.

    Example

    How do atomic orbitals become molecular orbitals? Linear combination of atomic orbitals (LCAO).

    Step 1: Understanding Atomic Orbitals

    To understand how atomic orbitals become molecular orbitals, we first need to grasp the concept of atomic orbitals. Atomic orbitals are regions around an atom's nucleus where electrons are likely to be found. These orbitals are defined by quantum numbers and come in different shapes and sizes, such as s, p, d, and f orbitals. Each type of orbital has a specific energy level and spatial distribution.

    Step 2: The Limitation of Atomic Orbitals in Bonding

    While atomic orbitals provide a good understanding of where electrons are located around a single atom, they do not fully explain how atoms bond to form molecules. For instance, the electron configuration of carbon in its ground state is 1s2 2s2 2p2. This configuration suggests that carbon should form only two covalent bonds, as it has two unpaired electrons. However, in reality, carbon forms four covalent bonds, as seen in methane (CH4), where the bond angles and lengths are equal.

    Step 3: Introduction to Hybridization

    To resolve the discrepancy between the predicted and observed bonding behavior of atoms like carbon, the concept of hybridization is introduced. Hybridization involves the mixing of atomic orbitals to form new, equivalent hybrid orbitals. These hybrid orbitals can then overlap with orbitals from other atoms to form covalent bonds. For example, in methane, carbon undergoes sp3 hybridization, where one s orbital and three p orbitals mix to form four equivalent sp3 hybrid orbitals.

    Step 4: Linear Combination of Atomic Orbitals (LCAO)

    The process by which atomic orbitals combine to form molecular orbitals is known as the Linear Combination of Atomic Orbitals (LCAO). In LCAO, atomic orbitals from different atoms combine mathematically to form molecular orbitals. These molecular orbitals can be bonding, anti-bonding, or non-bonding, depending on the phase relationship of the combining atomic orbitals. Bonding molecular orbitals result from constructive interference, where the electron density between the nuclei increases, leading to a stable bond. Anti-bonding molecular orbitals result from destructive interference, where the electron density between the nuclei decreases, leading to an unstable bond.

    Step 5: Application to Simple Molecules

    Let's apply the concept of LCAO to a simple molecule like hydrogen (H2). Each hydrogen atom has one 1s orbital. When two hydrogen atoms approach each other, their 1s orbitals combine to form two molecular orbitals: one bonding (σ1s) and one anti-bonding (σ1s*). The bonding molecular orbital has lower energy and higher electron density between the nuclei, resulting in a stable H2 molecule. The anti-bonding molecular orbital has higher energy and is usually unoccupied in the ground state of H2.

    Step 6: Observing Properties of Molecules

    The formation of molecular orbitals through LCAO explains many observed properties of molecules. For example, the equal bond angles and lengths in methane can be explained by the formation of equivalent sp3 hybrid orbitals. Similarly, the stability of the H2 molecule is explained by the occupation of the bonding molecular orbital. By understanding LCAO, we can predict and explain the bonding behavior and properties of a wide range of molecules.

    FAQs

    Here are some frequently asked questions about molecular orbital theory:

    1. What does molecular orbital theory explain?

    Molecular orbital theory explains how atoms combine to form molecules by describing the behavior of electrons and the nature of chemical bonds. It provides insights into molecular geometry, bond strength, reactivity, and spectroscopic properties of molecules.

    2. What are the principles of molecular orbital theory?

    The key principles include: (1) Atomic orbitals combine to form molecular orbitals, (2) The number of molecular orbitals formed equals the number of atomic orbitals combined, (3) Molecular orbitals can be bonding, antibonding, or non-bonding, and (4) Electrons fill molecular orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

    3. What is bond order in molecular orbital theory?

    Bond order in MO theory is calculated as half the difference between the number of electrons in bonding and antibonding orbitals. It indicates the strength and stability of a chemical bond. A higher bond order generally means a stronger and shorter bond.

    4. Where are electrons most likely to be found in a bonding molecular orbital?

    In a bonding molecular orbital, electrons are most likely to be found in the region between the nuclei of the bonded atoms. This increased electron density between nuclei is what creates the attractive force that holds atoms together in a molecule.

    5. How does molecular orbital theory differ from valence bond theory?

    While valence bond theory focuses on localized bonds between specific atoms, molecular orbital theory considers electrons as delocalized over the entire molecule. MO theory provides a more accurate description of electronic behavior, especially for complex molecules and systems with delocalized electrons.

    Prerequisites

    Molecular orbital theory is a fundamental concept in chemistry that explains the behavior of electrons in molecules. To fully grasp this complex topic, it's crucial to have a solid understanding of certain prerequisite subjects. Two key areas that serve as building blocks for molecular orbital theory are atomic orbitals and energy levels and molecular geometry and VSEPR.

    A strong foundation in atomic orbitals and energy levels is essential for comprehending molecular orbital theory. This prerequisite topic provides the basis for understanding how electrons behave in individual atoms, which is crucial when considering their interactions in molecules. Knowledge of atomic orbitals helps explain the shapes and orientations of molecular orbitals, while familiarity with energy levels is vital for predicting the stability and reactivity of molecular structures.

    The concept of energy levels in molecular orbitals directly builds upon the principles learned in atomic structure. As electrons transition from atomic to molecular orbitals, their energy levels shift, leading to bonding and antibonding orbitals. This understanding is fundamental to explaining molecular stability and predicting chemical reactions.

    Another critical prerequisite is molecular geometry and VSEPR (Valence Shell Electron Pair Repulsion) theory. This topic provides insight into the three-dimensional arrangement of atoms in molecules, which is closely related to the distribution of electrons in molecular orbitals. Understanding molecular geometry is crucial for predicting the overlap of atomic orbitals and the resulting molecular orbital shapes.

    The ability to perform molecular geometry prediction using VSEPR theory complements molecular orbital theory by offering a simpler approach to determining molecular shapes. While molecular orbital theory provides a more detailed electronic picture, VSEPR theory offers quick insights into molecular structure, which can be useful in understanding the overall electron distribution in molecules.

    By mastering these prerequisite topics, students can develop a strong conceptual framework for approaching molecular orbital theory. The knowledge of atomic orbitals provides the foundation for understanding how these orbitals combine to form molecular orbitals. Similarly, familiarity with molecular geometry helps in visualizing the spatial arrangement of these orbitals and predicting molecular properties.

    In conclusion, a thorough understanding of atomic orbitals, energy levels, and molecular geometry is indispensable for students aiming to excel in molecular orbital theory. These prerequisite topics not only provide the necessary background knowledge but also offer complementary perspectives that enhance overall comprehension of molecular behavior and chemical bonding.