density functional theory

Quantum mechanical method

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Density functional theory (DFT) is a method to study the electronic structure of multi electron systems. Density functional theory is widely used in physics and chemistry, especially in studying molecules and Condensed matter The nature of is Condensed matter Physics Computational Materials and Computational chemistry One of the most commonly used methods in the field.

Chinese name: density functional theory
Foreign name: Density functional theory

Purpose: Atomic and molecular physics Chemistry
Abbreviations: DFT

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brief introduction

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Electronics Structural theory The classical methods, especially Hartree Fock method and post Hartree Fock method, are based on complex multi electron wave function Of. The main goal of density functional theory is to use electron density Instead of wave function Basic quantity 。 Because the multi electron wave function has 3N variables (N is Number of electrons , each electron contains three spatial variables), while the electron density is only a function of three variables, which is more convenient to handle both conceptually and practically.

Although density functional The concept of theory originated from Thomas Fermi model, but it did not have a solid theoretical basis until Hohenberg Kohn theorem was proposed. The first theorem of Hohenberg Kohn points out that ground-state energy It's just a functional of electron density.

Hohenberg Kohn No. 2 Theorem proof With ground state Density is a variable, and the ground state energy is obtained after minimizing the system energy.

The original HK theory is only applicable to the ground state without magnetic field, although it has been extended. The original Hohenberg Kohn theorem only pointed out that One-to-one correspondence The relationship exists, but does not provide any such precise correspondence. It is precisely in these exact correspondences that approximation exists (this theory can be generalized to Time dependent Domain to calculate excited state Nature).

Approach

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The most common application of density functional theory is realized by Kohn Sham method. In the framework of Kohn Sham DFT, the most difficult multi-body problem (caused by the interaction of electrons in an external electrostatic potential) is reduced to an electron without interaction potential field The problem of movement in. This effective potential field includes the influence of external potential field and Coulomb interaction between electrons, such as exchange correlation. Dealing with exchange related functions is a difficult point in KS DFT. No exact solution for exchange Correlation energy EXC method. The simplest approximate solution is local density Approximation（ LDA Approximate). LDA is used approximately evenly Electron gas To calculate the system's Exchange energy (The exchange energy of the uniform electron gas can be accurately solved), and the relevant energy part adopts Free electron gas It is processed by fitting.

application

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Since 1970, density functional theory has been widely used in the calculation of solid state physics. In most cases, with other solutions quantum mechanics Multibody problem The density functional theory with local density approximation gives very satisfactory results, and the cost of solid-state computing is less than that of experiments. Nevertheless, it is generally believed that quantum chemistry The calculation could not give sufficiently accurate results, until the 1990s, the approximation used in the theory was refined into better Exchange correlation Action model. Density functional theory is an important tool for the study of electron Structural calculation Leading approach. Although the density functional theory has been improved, it is used to properly describe Intermolecular interaction , especially van der Waals force, or calculate the energy gap There are still some difficulties.

For van der Waals force Van der Waals ）, semi empirical dispersion Correction method (DFT-D) can also be realized through some nonlocal newly developed Hybrid switching Associative functional（ Hybrid Exchange correlation functional). For the semiconductor body gap, the GW method considering the Multi body interaction is generally used for calculation. Where G represents Green Function, and W represents shielding parameter. Use different methods to calculate Diamond structure Of Simple substance Semiconductor silicon Of Band gap width (Band Gap), we can see that, Comparative experiment As a result, the GW method provides a very good approximation. stay Condensed matter Domain, according to Fundamental vector and Approximate method The common methods are FP- LCAO (Full Potential Linear Combination of Atomic Originals Atomic orbital FP-LMTO (Full Potential Linear Muffin tin Orbitals), FP-LAPW (Full Potential Linear Augmented Plane wave plane wave Method), Pseudopotential Plane wave (PP-PW, Pseudopotential -Plane wave method). At the same time, the popular software is as follows (in no particular order, please add at any time):