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Pseudo-wavefunction

The pseudo-wavefunction within this frame work is guaranteed to be nodeless. The parameters (a, p, y, 8) are... [Pg.111]

This ensures that (]) (r) = for r> after the wavefiinctions have been nomialized. (2) The pseudo-wavefunction should be continuous and have continuous first and second derivatives at r An example of a... [Pg.111]

One of the simplest variational methods in density functional theory was already mentioned in Section I define the pseudo-wavefunction... [Pg.470]

Much effort has been put to improve the pseudopotentials. [71,72] The most successful pseudopotential model is the so called ultra-soft pseudopotentials, proposed by Vanderbilt. [73] The model allows one to work with optimally smooth pseudopotentials. Thus the number of plane waves needed to express the pseudo-wavefunctions can be greatly reduced. In the model, pseudo-wavefunctions ipiif match the true orbitals outside a given core radius re, within Tc, are al-... [Pg.114]

In the pseudopotential construction, the atomic waveflmctions for the valence electrons are taken to be nodeless. The pseudo-wavefunction is taken to be identical to the appropriate all-electron wavefunction in the regions of interest for solid-state effects. For the core region, the wavefunction is extrapolated back to the... [Pg.110]

With the density functional theory, the first step in the construction of a pseudopotential is to consider the solution for an isolated atom [27]. If the atomic wavefunctions are known, the pseudo-wavefunction can be constructed by removing the nodal structure of the wavefimction. For example, if one considers a valence wavefunction for the isolated atom, then a pseudo-wavefunction, ( ) (r), might have the properties... [Pg.111]

Once the eigenvalue and pseudo-wavefunction are known for the atom, the Kohn-Sham equation can be inverted to yield the ionic pseudopotential ... [Pg.111]

Since and depend only on the valence charge densities, they can be determined once the valence pseudo- wavefunctions are known. Because the pseudo-wavefiuictions are nodeless, the resulting pseudopotential is well defined despite the last term in equation Al.3.78. Once the pseudopotential has been constructed from the atom, it can be transferred to the condensed matter system of interest. For example, the ionic pseudopotential defined by equation Al.3.78 from an atomistic calculation can be transferred to condensed matter phases without any significant loss of accuracy. [Pg.112]

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT techniques [81]. PAW, however, provides all-electron one-particle waveflmctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in terms of a pseudo-wavefunction (easily expanded in plane waves) term that describes interstitial contributions well, and one-centre corrections expanded in terms of atom-centred functions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential formalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [82. 83]. PAW is also formulated to carry out DFT dynamics, where the forces on nuclei and wavefunctions are calculated from the PAW wavefunctions. (Another all-electron DFT molecular dynamics technique using a mixed-basis approach is applied in [84]. )... [Pg.2214]

In the case of two or more valence electrons we have to make a choice which is absent from the single-electron case we must choose a model for the electronic structure. We have to decide if we shall use a single determinant for the pseudo-wavefunction (using an obvious generalisation of the term pseudo-orbital) or a more accurate model containing electron correlation. Obviously the detailed form of the pseudopotential and of the pseudo-wavefu notion will depend on this choice of model and the development will become too complex to be useful. Let us make the opposite choice look at the formal equations independent of model and see if there are some general decisions to be made which will enable us to use the theory developed so far for a single electron. [Pg.304]

The pseudopotential and pseudo-wavefunction resulting from this transformation have some interesting properties which enable the effect of the Pauli principle to be simulated by a pseudopotential. [Pg.689]

Fig. A1.2 Ga and As atoms and pseudo-atoms radial parts of the wavefunctions (solid lines) ane pseudo-wavefunctions (broken lines), as calculated for valence electrons from the self-consistent potentials and pseudopotentials of Fig. Al.l. [Pg.306]

A crucial development in pseudopotential theory is the formulation of normconserving pseudopotentials (Hamann et al., 1979 Kerker, 1980). From a local-density calculation of the allelectron free atom, the relatively weak pseudopotentials which bind only the valence electrons are constructed. The valence pseudo-wavefunctions do not contain the oscillations necessary to orthogonalize to the core, but are instead smooth functions which are much easier to handle in calculations on real solids. The features of such potentials are discussed in detail by, e.g., Bachelet et al. (1982), who also present pseudopotentials for all atoms from H to Pu. [Pg.316]

The normconserving pseudopotentials have proven to work well for many systems, notably semiconductors (see, e.g., Kune, this volume) and their surfaces (see, e.g., Morthrup and Cohen, 1982), ionic compounds (Froyen and Cohen, 1984), and simple metals (see, e.g., Lam and Cohen, 1981). Applications to transition metals also exist (see, e.g., Greenside and Schluter, 1983). The pseudopotential approximation becomes less satisfactory when valence and core electrons begin to have large overlap, both because of the pseudo-wavefunctions lacking nodes, and because the x-c potential ih the core region should also account for the presence of the core electrons. The latter problem can in many cases be treated well by "nonlinear" pseudopotentials (Louie et al., 1982). [Pg.316]

This example demonstrates practically independent development of ECPs for molecules and crystals when for the same ECP property different terms are used. The work by PhiUips and Kleinman (PK) [473] is an important step in the ECP apphcations for sohds. PK developed the pseudopotential formalism as a rigorous formulation of the earher empirical potential approach. They showed that ECP that has the plane-wave pseudo wavefunctions as its eigenstates could be derived from the all-electron potential and the core-state wavefunctions and energies. Thus a nonempirical approach to finding ECP was introduced. [Pg.300]

From calculations of the pseudo-wavefunctions, Schliiter et al [393, 394] have derived the charge densities of the valence electrons in GaSe. These densities are in fair agreement with what one would expect from a simple chemical picture though we were somewhat deceived to find no hint of the s pair of the anion. The lowest energy bands are formed by Se 4s states only. They are obviously non-bonding and the electrons occupying them behave like core electrons. [Pg.149]

Why is this a useful approach First, consider the definition of the pseudo-wavefunctions through Eq. (2.114) what this definition amounts to is projecting out of the valence wavefunctions any overlap they have with the core wavefunctions. In fact, the quantity... [Pg.74]


See other pages where Pseudo-wavefunction is mentioned: [Pg.108]    [Pg.111]    [Pg.14]    [Pg.14]    [Pg.134]    [Pg.331]    [Pg.460]    [Pg.134]    [Pg.114]    [Pg.114]    [Pg.114]    [Pg.115]    [Pg.73]    [Pg.108]    [Pg.256]    [Pg.259]    [Pg.215]    [Pg.5]    [Pg.326]    [Pg.189]    [Pg.307]    [Pg.308]    [Pg.309]    [Pg.40]    [Pg.41]    [Pg.41]    [Pg.183]    [Pg.149]    [Pg.500]    [Pg.74]   
See also in sourсe #XX -- [ Pg.470 ]




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