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The variational principle is a mathematical technique used in quantum mechanics to build up the coefficients of each atomic orbital basis. A larger coefficient means that the orbital basis is composed more of that particular contributing atomic orbital – hence, the molecular orbital is best characterized by that type.
Quantum mechanics is a fundamental theory that describes the behavior of nature at and below the scale of atoms. [2]: 1.1 It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot.
Atomic orbitals are basic building blocks of the atomic orbital model (or electron cloud or wave mechanics model), a modern framework for visualizing submicroscopic behavior of electrons in matter. In this model, the electron cloud of an atom may be seen as being built up (in approximation) in an electron configuration that is a product of ...
Valence bond theory complements molecular orbital theory, which does not adhere to the valence bond idea that electron pairs are localized between two specific atoms in a molecule but that they are distributed in sets of molecular orbitals which can extend over the entire molecule. Although both theories describe chemical bonding, molecular ...
Quantum mechanics is the study of matter and its interactions with energy on the scale of atomic and subatomic particles.By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the moon.
An initial assumption is that the number of molecular orbitals is equal to the number of atomic orbitals included in the linear expansion. In a sense, n atomic orbitals combine to form n molecular orbitals, which can be numbered i = 1 to n and which may not all be the same. The expression (linear expansion) for the i th molecular orbital would be:
Molecular orbital diagram of dioxygen. Oxygen has a similar setup to H 2, but now we consider 2s and 2p orbitals. When creating the molecular orbitals from the p orbitals, the three atomic orbitals split into three molecular orbitals, a singly degenerate σ and a doubly degenerate π orbital.
This was the first application of quantum mechanics to the diatomic hydrogen molecule, and thus to the phenomenon of the chemical bond. [3] However, prior to this a critical conceptual framework was provided by Gilbert N. Lewis in his 1916 paper The Atom and the Molecule, [4] wherein Lewis developed the first working model of valence electrons.