Quantum Chemistry

Quantum chemistry is a branch of theoretical chemistry and a basic science that applies the basic principles and methods of quantum mechanics to study chemical problems. The research scope includes the structure and performance of stable and unstable molecules and the relationship between structure and performance; the interaction between molecules; the collision and interaction between molecules and other issues.

Classification

  1. Molecular orbital method (referred to as MO method, see molecular orbital theory).
  2. Valent bond method (referred to as VB method, see valence bond theory).

The following only introduces the molecular orbital method, which is a generalization of the atomic orbital to the molecule. In the physical model, it is assumed that each electron in the molecule moves in the average potential field generated by all atomic nuclei and electrons, that is, each electron can be formed by a single electron. The electronic function (a function of the coordinates of the electron) is used to express its state of motion, and this single-electron function is called the molecular orbital, and the motion state of the entire molecule is composed of the molecular orbitals of all the electrons in the molecule (linear combination of products). It is the origin of the name of the molecular orbital law.

RHF equation

A closed shell system means that all electrons in the system are paired to fill certain shells in a way that their spins are reversed (shell refers to a molecular energy level or two molecular energy levels with the same energy that are degenerate). The characteristic of this system is that the single-slater determinant can be used to express the multi-electron wave function (the state of the molecule). The HFR equation describing this system is called the restrictive HFR equation. The so-called restriction requires each pair of spins. Opposite electrons have the same spatial function. The restrictive HFR equation is abbreviated as the RHF equation.

UHF equation

Unrestricted Hartree–Fock (UHF) theory is the most common molecular orbital method for open shell molecules where the number of electrons of each spin are not equal. While restricted Hartree–Fock theory uses a single molecular orbital twice, one multiplied by the α spin function and the other multiplied by the β spin function in the Slater determinant, unrestricted Hartree–Fock theory uses different molecular orbitals for the α and β electrons. This has been called a different orbital for different spins (DODS) method.

Ab initio calculation

In principle, with the HFR equation (whether it is the RHF equation or the UHF equation), you can calculate the electronic structure and properties of any polyatomic system. Really strict calculations are called ab initio calculations. The difference between the limit energy of the RHF equation and the exact solution of the non-relativistic Schrodinger equation is called the correlation energy. For some purposes, the relevant capabilities of the system also need to be considered. The UHF equation considers a small part of the correlation energy, and a more precise approach is to take the wave function of the linear combination of the Doslet determinant, and obtain the combination coefficients of these Slater determinants by the variational method. The electronic structure of these molecules described by a Slater determinant or a combination of several Slater determinants in a certain way is called a configuration, so this method of taking the Doslater wave function is called a configuration interaction law.

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