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The secret of the electron cloud: How does LCAO change our understanding of chemical bonding?
In the field of quantum chemistry, linear combination atomic orbital (LCAO) technology provides a new perspective on understanding the nature of chemical bonds. As a technology for quantum super-stacking of atomic orbitals, LCAO allows us to gain an in-depth understanding of the electron distribution in molecules through the calculation of molecular orbitals.
According to quantum mechanics, the electron configuration of an atom is described as a wave function. These wave functions are essentially the basis functions that describe the electrons of a given atom. During a chemical reaction, the orbital wave function between atoms changes, and with it the shape of the electron cloud. Sir John Leonard-Jones first introduced the method as early as 1929 to describe the bonding of diatomic molecules in the first main group of the periodic table, but earlier in history, Linus Paul Lin has also applied this approach to hydrogen molecules (H2+).
This technology not only calculates molecular orbitals, but also helps us understand the formation process of chemical bonds.
Mathematically, LCAO is based on the assumption that the number of molecular orbitals is equal to the number of atomic orbitals contained in the linear expansion. Specifically, n atomic orbitals combine to form n molecular orbitals. For the i-th molecular orbital, its expression is in the form:
ϕi = c1iχ1 + c2iχ2 + ... + cniχn
Among them, ϕi represents the molecular orbital, and χr is the atomic orbital, c ri is the coefficient associated with these atomic orbitals. These coefficients reflect the contribution of each atomic orbital to the molecular orbital. The Hartree-Fock method is specifically used to obtain these expansion coefficients and thereby determine the total energy of the system.
This quantitative method is now widely used in computational chemistry to find optimal energy configurations.
With the development of computational chemistry, the significance of the LCAO method has gradually expanded. It is now often used to conduct qualitative discussions that are important for predicting and interpreting results obtained through modern methods. In this process, the shape of the molecular orbitals and their energies are approximately derived by comparing the atomic orbital energies of individual atoms or molecular fragments and applying rules such as hierarchical repulsion. To aid understanding, scientists often display these relationships using so-called correlation diagrams.
These graphics fully reflect the changes in energy between atomic orbitals and key steps in the formation of molecules.
In this process, another important concept is symmetry adaptive linear combination (SALC). This requires us to first assign a point group to the molecule and then perform calculations on each operation to ultimately obtain the symmetry of the orbitals involved. These techniques not only help understand molecular structure but also provide tools for in-depth analysis of chemical bonding properties.
Molecular orbital diagrams are a simple qualitative tool for LCAO processing, while many other methods such as the Hückel method, the extended Hückel method, and the Pariser-Pal-Popper method provide some quantitative theory.
Through the combination of these methods, LCAO not only reveals the fascinating world of chemical bonds, but also encourages scientists to continue to explore deeper chemical phenomena. These techniques not only allow us to understand existing chemical bonding models, but also lay a solid foundation for future research. So, in the face of the ever-evolving world of chemistry, can we uncover more scientific mysteries through these new technologies?
