How can the formation of a covalent bond be described from a quantum perspective, and what implications does it have for traditional chemical bonding theory?

Specifically, in the context of many-electron systems where electron correlation becomes significant, how do modern quantum chemical methodologies, such as Hartree-Fock theory and Density Functional Theory, contribute to our refined understanding of covalent interactions? Furthermore, how does this quantum perspective challenge, extend, or complement classical notions of bonding, as represented by Lewis structures, valence bond theory, and molecular orbital theory?

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    $\begingroup$ chemistry.stackexchange.com/questions/710/… $\endgroup$
    – Mithoron
    Commented Sep 1, 2023 at 13:55
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    $\begingroup$ What is a covalent bond outside of a quantum perspective? How do you explain electronic structure outside of a QM perspective? You can't. $\endgroup$
    – Buck Thorn
    Commented Sep 1, 2023 at 14:13
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    $\begingroup$ If there is anything like traditional chemical bonding theory, it is likely wrong and obsolete. Lewis structures are rooted in quantum theory. Valence bond theory and molecular orbital theory are approaches to solving for the wave function. Hartree-Fock is basically just an implementation of MO Theory. I don't understand this question. $\endgroup$ Commented Sep 1, 2023 at 22:31
  • $\begingroup$ @Martin-マーチン Agree, not sure what is being asked. If I had votes I would vote to close for lack of focus $\endgroup$
    – Ian Bush
    Commented Sep 3, 2023 at 6:01

1 Answer 1


Quantum Chemistry and Covalent Bonding:

Quantum chemistry, a nexus between quantum mechanics and molecular science, furnishes an in-depth framework for comprehending and predicting the nuances of chemical bonding. By incorporating quantum principles, this domain offers a granular look into electron behaviors in atoms and molecules, surpassing the sometimes oversimplified interpretations of classical models.

Atomic and Molecular Orbitals:

Atoms are characterized by wave functions or atomic orbitals, which are mathematical representations of the probability density of an electron, indicating the likelihood of finding an electron at a given location. As two atoms approach each other, their atomic orbitals begin to overlap. This overlap can result in the formation of molecular orbitals — either bonding (when the overlap is constructive) or antibonding (when the overlap is destructive). It's crucial to note that this phenomenon isn't driven by "intent" but by the intrinsic properties and behaviors of electrons in the atomic orbitals.

Wave Function and Superposition:

At its core, quantum mechanics presents the notion of the wave function, which encapsulates the probabilistic nature of electron positions. Electrons in a bond don't reside in a fixed location; they exist in a state of superposition. This means they have a probability of being in multiple locations simultaneously. The Schrödinger equation provides a time-dependent wave function, representing the state of the system, encapsulating this electron behavior.

Electron Correlation and Many-Electron Systems:

A particularly challenging aspect in quantum chemistry is addressing electron correlation, especially in systems with multiple electrons. Electrons, being fermions, adhere to the Pauli exclusion principle and also repel each other due to their like charges. Capturing the behavior of one electron influenced by all others is a computational challenge. This is where methods like Hartree-Fock theory, which offers an approximation by treating electrons as moving independently in an average field created by others, and Density Functional Theory (DFT), which considers the electron density rather than the wave function, come into play.

Quantitative Approaches in Theoretical Chemistry:

Delving deeper into bonding characterizations, there are quantitative methodologies in theoretical chemistry. Atoms in Molecules (AIM) theory provides a method to study chemical systems using the electron density, allowing for the analysis of bond critical points and bond paths. Electron Localization Function (ELF) helps in visualizing areas where electrons are likely localized.Then, Natural Bond Orbitals (NBO) analysis provides insight into bonding and antibonding interactions, giving a clearer definition and quantification to the concept of covalent bonds.

Implications for Traditional Chemical Bonding Theory:

Quantum chemistry refines our understanding from traditional bonding theories. Lewis structures and valence bond theory provide intuitive visual models, but they don't capture the nuanced electron behaviors that quantum mechanics does. Molecular orbital theory, rooted in quantum principles, offers a more accurate depiction, especially for molecules exhibiting resonance or delocalized electrons.

In essence, while classical theories provide a foundational understanding, quantum chemistry and its myriad of methodologies grant us a more intricate, quantitative, and comprehensive insight into the fascinating world of molecular interactions and electron behaviors.

This answer now addresses the criticisms and integrates the suggested improvements.

I hope this provides a comprehensive dive into the topic!

For further information I recommend to read Ira.N.Levine "Quantum Chemistry".

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    $\begingroup$ "When two atoms come close together with the intent of forming a bond." QM does not ascribe electrons with "intent". They just are what they are. $\endgroup$
    – Buck Thorn
    Commented Sep 1, 2023 at 14:11
  • $\begingroup$ I downvoted, for such a long answer its lacking quantitative content. This could be improved by mentioning quantitative approaches(AIM, ELF, ELI-D, NBO's, etc.) that exist in theoretical chemistry to characterize bonding and to give the conceptual idea of covalent bonds a clear definition. $\endgroup$
    – Hans Wurst
    Commented Sep 1, 2023 at 14:55
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    $\begingroup$ I updated the answer, I always try to do my best.... $\endgroup$ Commented Sep 1, 2023 at 16:17
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    $\begingroup$ This is informative, sure. I'm not sure it answers the question. But as I've stated above, I'm not even sure what the question is. | More to the topic though: I disagree that Lewis structures are traditional bonding theory. And given that VB and MO theory are congruent when used within the same framework, one cannot be more accurate then the other. I'm sure you mean the right thing, but it reads like there is resonance in MO theory. $\endgroup$ Commented Sep 1, 2023 at 22:40

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