Molecular orbital theory
Intros
Lessons
- How do atomic orbitals become molecular orbitals?
- Linear combination of atomic orbitals (LCAO).
- Making molecular orbitals from atomic orbitals.
- Using MO theory to predict: Hydrogen
- Using MO theory to predict: Helium
- Sigma and pi MOs
- Drawing correct MO diagrams: example.
- Bond order and lone pairs.
- Worked example: F2
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Topic Notes
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.
Fundamentals of Molecular Orbital Theory
Molecular orbital theory is a fundamental concept in chemistry that explains how atoms combine to form molecules. At its core, this theory revolves around the idea that atomic orbitals merge to create molecular orbitals. To understand this process, let's first revisit the concept of atomic orbitals.
Atomic orbitals merge are regions in an atom where electrons are most likely to be found. They come in various shapes, such as spherical (s-orbitals), dumbbell-shaped (p-orbitals), and more complex forms. When atoms come together to form molecules, these individual atomic orbitals interact and combine to form molecular orbitals.
Think of atomic orbitals as musical notes. Just as individual notes can combine to create harmonious chords, atomic orbitals merge to form molecular orbitals. This combination process is not simply additive; it involves a complex interplay of electron energies and wave functions.
One of the key principles of molecular orbital theory is that the number of molecular orbitals formed equals the number of atomic orbitals that combine. For instance, if two hydrogen atoms, each with one 1s orbital, come together, they will form two molecular orbitals.
These molecular orbitals can be classified into two main types: bonding orbitals and antibonding orbitals. Bonding orbitals are lower in energy than the original atomic orbitals and contribute to holding the atoms together in a molecule. They are formed when atomic orbitals overlap in a way that increases electron density between the nuclei.
Imagine two children on a seesaw. When they sit close to each other near the center, they create a stable, low-energy configuration. This is analogous to a bonding orbital, where electron density is concentrated between the nuclei, creating a strong bond.
On the other hand, antibonding orbitals are higher in energy than the original atomic orbitals and tend to weaken or break bonds. They occur when atomic orbitals combine in a way that creates regions of low electron density between the nuclei. Continuing our seesaw analogy, this would be like the children sitting at opposite ends, creating an unstable, high-energy situation.
The difference between bonding and antibonding orbitals is crucial in determining molecular stability and reactivity. Molecules with more electrons in bonding orbitals than in antibonding orbitals are generally more stable. This concept helps explain why some molecules exist while others do not.
Molecular orbital theory also introduces the idea of delocalized electrons. Unlike in valence bond theory, where electrons are considered to be localized between specific atoms, molecular orbital theory allows for electrons to be spread out over the entire molecule. This concept is particularly useful in explaining phenomena like resonance in organic molecules and conductivity in metals.
To better grasp this, think of electrons in a molecule as commuters in a city. Valence bond theory would have them always taking the same route between two specific locations, while molecular orbital theory allows them to use any available path throughout the city.
While molecular orbital theory provides a powerful framework for understanding molecular structure and behavior, it's worth comparing it briefly with valence bond theory. Valence bond theory focuses on how individual atomic orbitals overlap to form localized bonds between specific atoms. It's like looking at a molecule as a collection of individual bonds.
Molecular orbital theory, in contrast, considers the molecule as a whole, with electrons occupying orbitals that extend over the entire molecule. This approach is particularly useful for explaining concepts like aromaticity and the electronic properties of conjugated systems.
Both theories have their strengths and are often used complementarily. Valence bond theory is often more intuitive and aligns well with how chemists visualize and draw molecules. Molecular orbital theory, while sometimes more mathematically complex, provides a more accurate description of electronic behavior in molecules, especially for more complex systems.
In conclusion, molecular orbital theory offers a sophisticated yet elegant explanation for how atoms combine to form molecules. By understanding the interplay between atomic orbitals, bonding and antibonding molecular orbitals, and the concept of delocalized electrons, we gain powerful insights into molecular structure, stability, and reactivity. This theory, alongside valence bond theory, forms
Electron Distribution in Molecular Orbitals
Understanding how electrons are distributed in molecular orbitals is crucial for grasping the nature of chemical bonding. In molecular orbitals, electrons are not confined to specific atoms but are spread out across the entire molecule. This distribution plays a vital role in determining the properties and behavior of molecules.
When atoms come together to form molecules, their atomic orbitals combine to create molecular orbitals. These molecular orbitals can be classified as bonding, antibonding, or non-bonding. In bonding orbitals, electrons are most probably located in the region between the nuclei of the bonded atoms. This concentration of electrons between nuclei is what holds the atoms together, forming a chemical bond.
To visualize this concept, imagine two balloons being squeezed together. The area where they touch and deform represents the region of highest electron probability in a bonding orbital. This analogy helps illustrate how electrons in bonding orbitals are concentrated between the nuclei, effectively "gluing" the atoms together.
The concept of electron density is closely related to the distribution of electrons in molecular orbitals. Electron density refers to the probability of finding an electron in a particular region of space around a molecule. In bonding orbitals, the electron density is highest in the internuclear region. This increased electron density between atoms is what gives rise to the attractive forces that hold molecules together.
We can think of electron density as a cloud surrounding the molecule, with varying thickness. The thicker parts of the cloud represent areas of higher electron density, which typically correspond to bonding regions. In contrast, areas of lower electron density are found farther from the nuclei or in antibonding regions.
The relationship between electron density and bond strength is direct and significant. Generally, the higher the electron density in the bonding region between two atoms, the stronger the bond. This is because a higher concentration of electrons between nuclei leads to stronger electrostatic attraction between the positively charged nuclei and the negatively charged electron cloud.
To illustrate this relationship, consider a simple diatomic molecule like hydrogen (H). The molecular orbital diagram for H shows a single bonding orbital occupied by two electrons. The high electron density between the two hydrogen nuclei results in a strong covalent bond. In contrast, if we look at a molecule with a weaker bond, such as the van der Waals interaction in a noble gas dimer, we would see a much lower electron density between the atoms, corresponding to the weaker attractive forces.
The distribution of electrons in molecular orbitals also explains why some bonds are stronger than others. For example, double and triple bonds are stronger than single bonds because they involve more electrons concentrated in the bonding region. This increased electron density leads to stronger attractive forces between the nuclei.
It's important to note that the electron distribution in molecular orbitals is not static. Electrons are constantly in motion, and their distribution is best described by probability. The areas of highest electron density represent the regions where electrons are most likely to be found at any given moment.
In more complex molecules, the distribution of electrons becomes more intricate. Molecular orbital theory allows us to understand how electrons are shared across entire molecular systems, leading to delocalized bonding in structures like benzene rings or conjugated systems. In these cases, electrons are spread out over multiple atoms, resulting in unique properties and reactivity.
Understanding electron distribution in molecular orbitals is not just a theoretical exercise; it has practical applications in various fields. In materials science, knowledge of electron distribution helps in designing new materials with specific properties. In biochemistry, it aids in understanding enzyme-substrate interactions and drug design. Even in the field of nanotechnology, manipulating electron distribution at the molecular level is key to developing novel devices and materials.
In conclusion, the distribution of electrons in molecular orbitals, particularly in bonding orbitals, is fundamental to understanding chemical bonding. The concept of electron density provides a quantitative measure of this distribution, directly correlating with bond strength. By visualizing these concepts through diagrams and analogies, we can better grasp the invisible world of electrons that governs the behavior of molecules and materials around us. This understanding forms the basis for much of modern chemistry and continues to drive innovations
Molecular Orbital Diagrams
Molecular orbital (MO) diagrams are powerful tools in chemistry that help us understand the electronic structure and properties of molecules. These diagrams provide a visual representation of how atomic orbitals combine to form molecular orbitals, offering insights into bond formation, stability, and reactivity. In this guide, we'll walk you through the process of constructing and interpreting molecular orbital diagrams, with a focus on the oxygen molecule (O2) as an example.
To begin constructing a molecular orbital diagram, we start by identifying the atomic orbitals of the constituent atoms. For diatomic molecules like O2, we consider the valence orbitals of each oxygen atom. The next step involves combining these atomic orbitals to form molecular orbitals. This combination follows specific rules based on symmetry and energy considerations.
Energy levels play a crucial role in molecular orbital diagrams. As atomic orbitals combine, they form bonding and antibonding molecular orbitals. Bonding orbitals have lower energy than the original atomic orbitals and contribute to the stability of the molecule. Conversely, antibonding orbitals have higher energy and can destabilize the molecule if occupied. The energy difference between bonding and antibonding orbitals determines the strength of the chemical bond.
When constructing the diagram, we arrange the molecular orbitals in order of increasing energy. This arrangement is essential for understanding electron filling and predicting molecular properties. Electrons fill these orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. Starting from the lowest energy level, electrons occupy orbitals in pairs until all valence electrons are accounted for.
Let's apply this knowledge to the oxygen molecule (O2) as an example. Oxygen atoms have the electron configuration 1s²2s²2p. In the molecular orbital diagram for O2, we combine the 2s and 2p orbitals of both oxygen atoms. The 1s orbitals are too low in energy to participate significantly in bonding.
The resulting molecular orbital diagram for O2 shows the following orbitals in order of increasing energy: σ2s (bonding), σ*2s (antibonding), σ2p (bonding), π2p (two degenerate bonding orbitals), π*2p (two degenerate antibonding orbitals), and σ*2p (antibonding). The oxygen molecule has 16 valence electrons in total, which fill these orbitals from bottom to top.
Interpreting this diagram reveals important information about O2. The bond order, which indicates the strength of the bond, can be calculated as half the difference between the number of electrons in bonding and antibonding orbitals. For O2, this calculation yields a bond order of 2, indicating a double bond. This aligns with the known strength and reactivity of the oxygen-oxygen bond.
The molecular orbital diagram also helps predict the magnetic properties of O2. In this case, the highest occupied molecular orbitals (HOMOs) are the π*2p orbitals, which contain two unpaired electrons. This electronic configuration makes O2 paramagnetic, meaning it is attracted to magnetic fields a property that can be observed experimentally and has significant implications for oxygen's behavior in biological systems.
Understanding how to construct and interpret molecular orbital diagrams is invaluable for chemists and materials scientists. These diagrams provide insights into bond strengths, molecular stability, and reactivity. They help explain phenomena such as why some molecules are colorless while others absorb light, or why certain compounds exhibit unexpected magnetic properties.
As you become more familiar with molecular orbital theory, you'll find that it can be applied to more complex molecules and even extended systems like solids. The principles remain the same: combine atomic orbitals, arrange molecular orbitals by energy, fill with electrons, and interpret the results to predict molecular properties.
In conclusion, molecular orbital diagrams are powerful tools for visualizing and understanding the electronic structure of molecules. By mastering the process of constructing these diagrams and interpreting energy levels and electron filling patterns, chemists can predict and explain a wide range of molecular properties. The example of the oxygen molecule demonstrates how MO theory can be applied to real-world systems
Sigma and Pi Bonds in MO Theory
Molecular orbital (MO) theory provides a comprehensive framework for understanding chemical bonding, particularly the formation of sigma (σ) and pi (π) bonds. These two types of covalent bonds play crucial roles in determining molecular structure, reactivity, and properties. In this discussion, we'll explore how sigma and pi bonds form, their differences in electron distribution and strength, and use the example of ethene (C2H4) to illustrate pi bonding.
Sigma bonds are the most common type of covalent bond and form through the head-on overlap of atomic orbitals. In MO theory, this overlap results in the formation of a bonding molecular orbital that is symmetrical around the internuclear axis. The electron density in a sigma bond is concentrated between the nuclei of the bonded atoms. This direct overlap leads to strong, stable bonds that form the backbone of molecular structures.
Pi bonds, on the other hand, form through the side-by-side overlap of p orbitals. Unlike sigma bonds, pi bonds have electron density distributed above and below the internuclear axis. This unique electron distribution gives pi bonds some distinct characteristics and reactivity. Pi bonds are generally weaker than sigma bonds due to less effective orbital overlap, but they play a crucial role in many chemical reactions and molecular properties.
The electron distribution in sigma and pi bonds significantly affects their strength and reactivity. Sigma bonds, with their concentrated electron density between nuclei, are stronger and more resistant to breaking. This strength contributes to the stability of single bonds in molecules. Pi bonds, with their more diffuse electron distribution, are weaker and more susceptible to reactions. This reactivity is why double and triple bonds (which include pi bonds) are often sites of chemical activity in molecules.
To illustrate the concept of pi bonding, let's consider the example of ethene (C2H4). Ethene is the simplest alkene, featuring a carbon-carbon double bond. In ethene, the carbon atoms are sp2 hybridized, meaning each carbon has three sp2 hybrid orbitals and one unhybridized p orbital. The sigma bond between the carbon atoms forms through the overlap of two sp2 orbitals. The remaining p orbitals on each carbon, which are perpendicular to the plane of the molecule, overlap sideways to form a pi bond.
This pi bond in ethene results in electron density above and below the plane of the molecule, creating regions of high electron probability. This electron distribution gives ethene its planar structure and contributes to its reactivity. The presence of the pi bond makes ethene more reactive than ethane (C2H6), which only has sigma bonds. This increased reactivity is why ethene can undergo addition reactions, a characteristic property of alkenes.
The strength difference between sigma and pi bonds is evident in bond dissociation energies. In ethene, breaking the pi bond requires less energy than breaking the sigma bond. This difference in bond strength explains why, in many reactions involving double bonds, the pi bond is broken while the sigma bond remains intact.
Understanding the formation and characteristics of sigma and pi bonds through MO theory is crucial in predicting and explaining molecular behavior. For instance, the presence of pi bonds in molecules like benzene leads to the concept of aromaticity, which profoundly affects the molecule's stability and reactivity. In more complex molecules, the interplay between sigma and pi bonds can influence everything from molecular shape to spectroscopic properties.
In conclusion, sigma and pi bonds, as described by molecular orbital theory, are fundamental to our understanding of chemical bonding. Sigma bonds, formed by head-on orbital overlap, provide structural stability with their concentrated electron density. Pi bonds, resulting from side-by-side p orbital overlap, contribute to molecular reactivity with their more diffuse electron distribution. The example of ethene perfectly illustrates how these bonds coexist in molecules, influencing their properties and reactivity. As we continue to explore more complex molecular systems, the principles of sigma and pi bonding remain essential tools for chemists in predicting and explaining molecular behavior.
Applications of Molecular Orbital Theory
Molecular Orbital (MO) theory is a powerful tool in chemistry that provides invaluable insights into the behavior and properties of molecules. Its practical applications extend across various fields, from fundamental chemistry to materials science and beyond. One of the most significant uses of MO theory is in predicting molecular geometry. By analyzing the distribution and interactions of electrons in molecular orbitals, scientists can accurately determine the three-dimensional structure of molecules. This capability is crucial in understanding how molecules will behave in different environments and react with other substances.
In terms of reactivity, MO theory offers a detailed explanation of chemical bonding and helps predict how molecules will interact in chemical reactions. By examining the energy levels and symmetry of molecular orbitals, chemists can anticipate which reactions are likely to occur and under what conditions. This predictive power is especially valuable in designing new synthetic pathways and in understanding complex reaction mechanisms. For instance, in organic chemistry, MO theory helps explain the regioselectivity and stereoselectivity of various reactions, guiding chemists in their synthetic strategies.
Spectroscopic properties of molecules are another area where MO theory proves indispensable. The theory provides a framework for interpreting spectroscopic data, such as UV-visible, infrared, and NMR spectra. By understanding the energy levels and transitions between molecular orbitals, scientists can predict and analyze spectral patterns. This application is crucial in fields like analytical chemistry and materials characterization. For example, in UV-visible spectroscopy, MO theory explains why certain molecules absorb light at specific wavelengths, relating these absorptions to electronic transitions between orbitals.
When it comes to understanding complex molecules, MO theory is particularly powerful. It can explain the unique properties of transition metal complexes, including their color, magnetism, and catalytic activity. In organometallic chemistry, MO theory helps rationalize the bonding in metal-carbon compounds, which is essential for developing new catalysts for industrial processes. The theory also sheds light on the electronic structure of large biological molecules like proteins and DNA, aiding in the understanding of their function and interactions.
In materials science, MO theory plays a crucial role in designing and understanding advanced materials. It helps explain the electronic properties of semiconductors, which are fundamental to modern electronics. By applying MO concepts, scientists can predict and manipulate the band structure of materials, leading to innovations in solar cells, LEDs, and other electronic devices. In the field of nanotechnology, MO theory is used to understand the unique properties of nanomaterials, such as quantum dots and carbon nanotubes, which exhibit quantum confinement effects.
MO theory also contributes significantly to computational chemistry. It forms the basis for many quantum chemical calculations used to model molecular systems. These computational methods allow scientists to predict properties of molecules before they are synthesized, saving time and resources in research and development. In drug discovery, for instance, MO-based calculations help in predicting how potential drug molecules might interact with target proteins, guiding the design of new pharmaceuticals.
The applications of MO theory extend to environmental chemistry as well. It helps in understanding the behavior of pollutants in the atmosphere and their interactions with ozone and other atmospheric components. This knowledge is crucial for developing strategies to combat air pollution and climate change. In photochemistry, MO theory explains the light-induced reactions in the atmosphere and in photosynthesis, contributing to our understanding of these vital processes.
In conclusion, molecular orbital theory is a versatile and powerful tool with wide-ranging applications in chemistry and related fields. Its ability to predict molecular geometry, reactivity, and spectroscopic properties makes it invaluable in both theoretical and practical aspects of chemical research. From understanding complex molecules to designing new materials and drugs, MO theory continues to be a cornerstone of modern chemical science, driving innovation and discovery across multiple disciplines.
Conclusion
Molecular orbital theory provides a powerful framework for understanding chemical bonding at the quantum level. The key points discussed include the formation of molecular orbitals through linear combinations of atomic orbitals, the concept of bonding and antibonding orbitals, and the importance of electron configuration in determining molecular properties. The introduction video serves as a crucial foundation for grasping these complex concepts, offering visual representations and clear explanations. As you delve deeper into molecular orbital theory, you'll discover its wide-ranging applications in chemistry, materials science, and even biochemistry. We encourage readers to explore further resources, such as advanced textbooks, scientific papers, and online courses, to expand their knowledge of this fundamental theory. By mastering molecular orbital theory, you'll gain invaluable insights into the nature of chemical bonds, reactivity, and spectroscopic properties of molecules, opening doors to exciting research and practical applications in various scientific fields.
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.
Prerequisite Topics for Understanding Molecular Orbital Theory
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.
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:
- 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, 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.
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.
- 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.
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.
- Why is the bond in O2 a double bond?
- Why is the bond in N2 a triple bond?
Bondorder=2(#bondingelectrons)−(#antibondingelectrons)
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:
Bondorder=2(#bondingelectrons)−(#antibondingelectrons)=28−4=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.
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!
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).
Bondorder=2(#bondingelectrons)−(#antibondingelectrons)=28−6=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.
remaining today
remaining today