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Stage of chemical reactions: Why is the linear combination atomic orbital technique so critical?
In the interdisciplinary field of chemistry and physics, linear combination atomic orbital (LCAO) technology has always been an important tool for understanding molecular structures and chemical reaction processes. This technique is a fundamental method in quantum chemistry, allowing scientists to calculate the properties of molecular orbitals from the superpositions of atomic orbitals. Since it was first proposed by Sir John Leonard-Jones in 1929, LCAO technology has been deeply involved in the study of various chemical reactions, and with the advancement of computational chemistry, this technology has become increasingly important.
The wave function of electron configuration describes the behavior and distribution of electrons inside an atom.
In quantum mechanics, the electron configuration of an atom is viewed as a wave function. These wave functions are the basis set functions that describe the electrons in the atom. When a chemical reaction occurs, these wave functions change depending on the types of atoms participating in the chemical bond. This means that the shape of the electron cloud changes as the atoms change, so we can use the LCAO technique to understand these changes and their impact on chemical reactions.
It is assumed that the number of molecular orbitals (MO) is equal to the number of atomic orbitals (AO) included in the linear expansion. In other words, n atomic orbitals can be combined into n molecular orbitals. For each molecular orbital i, it can be written as:
ϕ_i = c_1i χ_1 + c_2i χ_2 + c_3i χ_3 + ... + c_ni χ_n
Among them, φ_i is the molecular orbital, χ_r represents the atomic orbital, and c_{ri} represents the contribution weighting coefficient. These coefficients can reflect the contribution of different atomic orbitals to molecular orbitals. Using the Hartley-Fokke method, we can calculate the values of these coefficients and derive the total energy of the molecular system.
Using LCAO methods can help researchers predict and explain the properties of molecules and the mechanisms of their chemical reactions.
With the development of computational chemistry, the LCAO method is not only a simple wave function optimization, but also a qualitative discussion method that can provide a prediction and rationalization background for the results obtained by modern methods. This method relies on comparing the atomic orbital energies of individual atoms (or molecular fragments) and applying some known rules such as "energy level repulsion" to deduce the shape of molecular orbitals and their energies.
In this process, molecular symmetry plays an important role. Through symmetry, we can use the so-called "symmetry adaptive linear combination (SALC)" to explore molecular geometry. For example, a molecule must first be classified into a certain point group. The result of each operation affects the number of bonds that do not move. This characteristic is called a character. In further analysis, it can be decomposed into irreducible representations using reducible representations, and these irreducible representations correspond to the orbital symmetries in the participating processes.
Molecular orbital diagram provides a simple qualitative processing method of LCAO to help us understand the reactivity and structural characteristics of molecules.
In practice, the Hückel method, the extended Hückel method and the Pariser–Parr–Pople method provide some quantitative theories to help further research. These methods provide strong support for LCAO technology and enable a deeper understanding of chemical bonds and chemical reactions. How will future research further apply this technology to elucidate more complex molecular systems and their reaction mechanisms?
