Density general letter theory
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Description of the density general letter theory
As a quantum mechanics method for studying the electronic structure of a multielectronic system, the density general communication theory is widely applied both physically and chemically, especially in terms of molecular and condensate properties, and is one of the methods commonly used in the field of z in condensation physics and chemistry。
Although the concept of the density generalist theory originated in the thomas-fermi model, it was not until the hohenberg-kohn theorem was introduced that there was a solid theoretical basis. The hohenberg-kohndiyi theorem states that the system's base-state energy is simply a general message of electron density. Hohenberg-kohn's second theorem proves that the base-state energy is obtained after the system z has been downsized with the base-state density variable。
The initial hk theory of z only applies to the underlying state, which does not exist in a magnetic field, although it has now been extended. The hohenberg-kohn theorem of z in the beginning merely pointed to the existence of a correspondence, but did not provide any such precise correspondence. It is in these precise counterparty relationships that there is a approximation (a theory that can be extended to time-related areas and thus be used to calculate the nature of the triggering state。
The general application of the density general communication theory z was achieved through the kohn-sham method. In the framework of kohn-sham dft, the difficult multi-body problem of z (as a result of electronic interactions in an external static dynamic) has been simplified into a problem of electronic motion in an effective field without interaction. This effective field includes the influence of external dynamics and the interaction between the electronic cologne, for example, exchanges and related roles. The handling of exchange-related effects is a difficult point in ks dft. There is no precise solution to exchange excs. Z's simple approximation solver is the local density approximation (lda approximation). Lda uses almost even electronic gas to calculate the exchange power of the system (the exchange of even electronic gas can be solved with precision), while the relevant energy elements are treated by the method of collating free electronic air。
The main principles of the density general communication theory and the steps of implementation
Wave functions do not directly correspond to physics, and it is difficult to guess what a wave function should look like on the basis of physical intuition or physical experiments. This reminds us of heisenberg's starting point in z's initial construction of quantum mechanics, which is that a theory z can be constructed from a visible physical mass。
The wave function is not exactly a physical amount that can be directly observed, which suggests that the scherdingian equation hψe=e= is not actually useful for a multielectronic system. Density letter theoryThis is where the point of departure is, together with our understanding of hydrogen molecule ion, is that the density of the electron n(r) varies from space to space, but the n(r) is mainly distributed between two protons and leads to two protons being bound together. Can we develop a new theory that seeks to solve the problem of polyelectronics through electron densityn rather than wave function
First, the wave function of a n-electronic corresponds to the density distribution of an electronic:
This means giving a base-state electron density distribution of n0, and we can calculate its base-state wave function, in other words, the base-state wave function is a generic function of n0。
The basic energy e0 is also a general letter of n0:
Assuming the electron density distribution is n(r), we can change n(r) to make the energy ez small, the corresponding electron density is the base electron density n0. Let's think first of all about a multi-electronic system that does not have electronic-electronic interaction, or if we assume that the effects of electronic-electronic interaction are included in a valid single-body interaction, which means a single-electronic scholten equation
The electron density n, effective monomer interaction, the equation diyi item v is external, the second is the interaction of the electron in the cologne field formed by the electronic distribution of the density n, and the third is the “exchange-connectivity” effect, which can be associated with “exchange-connectivity”。
The mediocre multibody correlation effect in quantum mechanics is included in the third, which is also a function of electron density n。
Here it is defined n, n will change veff and decide, so it is a process of self-harmonic resolution. We usually guess an electron density distribution n(r) and then repeat the process of “n-> veff->-n ...” until the results of the calculations are agreed。
Application of the density general communication theory
Since 1970, the density general communication theory has been widely applied in solid physics calculations. In most cases, the use of a broad message theory of local density of close density gives very satisfactory results compared to other solutions to the problem of quantum mechanics, while solid-state calculations cost less than experiments. Nevertheless, it is generally accepted that quantum chemistry cannot produce sufficiently precise results until the 1990s, when the approximation used in the theory was re-compiled into better exchange-related role models. The density general communication theory is the current lingxian method of computation of electronic structures in various fields. Despite improvements in the density general communication theory, it is difficult to properly describe molecular interactions, especially van der waals, or to calculate the energy gap of the semiconductor。
For van der waalsley, a half-experienced color-dip. The positive method (dft-d) can also be achieved in a similar way (vdw-df) through a number of newly developed non-local hybrid exchange general letters (hybrid exchange-correlation operations). For semiconductor energy faults, the gw method, which takes into account multibody (many-body), is generally used. Of these, g indicates green faction, while w indicates shield parameters. The figure below shows the use of different methods to calculate a single semiconductor silicon (band gap) width of the diamond structure. It can be seen that the gw method provides a very good approximation against the results of the experiment。
In the field of condensation, depending on the orientation and approximation approach, the methods that are now more commonly used are: fp-lcao (full popular-linear company of atomic atomic orbitals, full linetial-linear muffin-tin orbitals, whole-lapw (full potential-linearied plane-wave, whole-line-line-linearized plane-wave, pan-linematically-swave-shot-shot-shot-shot) and p72entian-plane-wave (pp-pw, spectane-shot-shot-w)。
