Pseudopotential first-principles calculations

Experimental data supported by first-principles calculations. Static data collected at 14.1 T at 292 and 150 K, which showed significant deviation from the CASTEP calculations attributed to the limitations of the pseudopotentials used. 

Results of a first principles calculation shows that the antiferromagnetic state is more stable than the ferromagnetic state, and that the energy gap decreases with the Mn composition (Zhao, Y.-J. et al. 2001b). The reason for the discrepancies between theoretical expectations and experimental results is not clear it may stem from the substitution of Ge for Mn in surface-doped samples. More recent plane-wave pseudopotential and KKR-CPA calculations show that the intrinsic defects are responsible for the stabilization of the ferromagnetic state (Mahadevan and Zunger 2002 Kamatani and Akai 2001b). 

The question of methanol protonation was revisited by Shah et al. (237, 238), who used first-principles calculations to study the adsorption of methanol in chabazite and sodalite. The computational demands of this technique are such that only the most symmetrical zeolite lattices are accessible at present, but this limitation is sure to change in the future. Pseudopotentials were used to model the core electrons, verified by reproduction of the lattice parameter of a-quartz and the gas-phase geometry of methanol. In chabazite, methanol was found to be adsorbed in the 8-ring channel of the structure. The optimized structure corresponds to the ion-paired complex, previously designated as a saddle point on the basis of cluster calculations. No stable minimum was found corresponding to the neutral complex. Shah et al. (237) concluded that any barrier to protonation is more than compensated for by the electrostatic potential within the 8-ring. 

The positions of hydrogen in hydrides are sometimes difficult to be determined experimentally. So, in this study, the crystal structures of hydrides are optimized by the total energy minimization using the plane-wave pseudopotentital method. For this purpose, the first-principle calculations based on the DFT are performed with a generalized gradient approximation (GGA) by Perdew et al. [5]. The implementation of DFT employed here combines a plane-wave basis set with the total energy pseudopotential method, as is embodied in the CASTEP code [6]. 

To calculate the eigenvalue spectra of nanocrystals, we need to know the e s for the various orbitals and the t s for the interactions. These are evaluated by performing a TB-fit, with a prudent choice of the basis orbitals and the interactions, to the band structure of the bulk solid obtained from first principle calculations such as LAPW, LMTO or the pseudopotential methods. 

First principles calculations, minimizing the energy with respect to atomic positions as in sect. 5, give results for surface relaxations in reasonable agreement with experiment, for example a pseudopotential study of Al(110) gives (Ho and Bohnen, 1985) ... 

The greatest shortcoming of quantum mechanical calculations on metal complexes and mineral surfaces is an inadequate description of solvation. To that end, dielectric continuum models are still of use, but only to describe the long-range solvation effect. With increasing computational power, moreover, the application of plane-wave pseudopotential based ab initio molecular dynamics will allow us to explicitly treat bulk solution effects from first-principles calculations on large systems. 

One of the successes of first-principles methods in studying new materials is the prediction of superhard C3N4. Using first-principles calculation based on pseudopotential and plane-wave method, Liu and Cohen predicted that the bulk modulus of C3N4 could be comparable to that of diamond which stimulated wide interests in this material. Films consisting of a-C3N4 and P-C3N4 with bulk moduli of up to 349 GPa have reportedly been synthesized. ... 

The methods of the preceding sections involve, at the outset, few necessary approximations. Even the muffin tin approximation can be dispensed with in the APW method. In practice, of course, all kinds of approximations are involved in the practical application of such schemes, especially when they are used in a semiempirical manner. This is not simply for reasons of convenience but also because one may find that a theory which has all the elements of a first principles calculation has too many free parameters in semiempirical work. For instance, if one chooses to use the parameters v(g) in pseudopotential theory as fitting parameters, one is forced to neglect (or fix the values of) the higher components g > 2kp entirely (Ref. 51, pp. 83-86), otherwise the number of fitting parameters would be too great and they would be undetermined by the available data. ... 

A further simplication often used in density-functional calculations is the use of pseudopotentials. Most properties of molecules and solids are indeed determined by the valence electrons, i.e., those electrons in outer shells that take part in the bonding between atoms. The core electrons can be removed from the problem by representing the ionic core (i.e., nucleus plus inner shells of electrons) by a pseudopotential. State-of-the-art calculations employ nonlocal, norm-conserving pseudopotentials that are generated from atomic calculations and do not contain any fitting to experiment (Hamann et al., 1979). Such calculations can therefore be called ab initio, or first-principles. ... 

Some of the major areas of activity in this field have been the application of the method to more complex materials, molecular dynamics, [28] and the treatment of excited states. [29] We will deal with some of the new materials in the next section. Two major goals of the molecular dynamics calculations are to determine crystal structures from first principles and to include finite temperature effects. By combining molecular dynamics techniques and ah initio pseudopotentials within the local density approximation, it becomes possible to consider complex, large, and disordered solids. 

Recent GGA first principles pseudopotential calculations conclude that Aun clusters adopt planar structures up to larger sizes than silver and copper, particularly the anionic species, due to relativistic effects. Specifically, Fernandez and coworkers obtain planar structures for the ground state of anionic v=l), neutral v=0), and cationic (z/=+l) species of Au(( clusters... 

As an example we consider the system Si/Si(00 1). Over the years there have been several first principles DFT calculations aimed at establishing the relative stability of these structures [75, 77-80] the results are collected in Table 1. All of these DFT calculations make use of a supercell technique, pseudopotentials to represent the Si ion cores, and a basis set that consists of plane waves to expand the valence wave functions. Car-Parrinello techniques are used to simultaneously optimize the electronic... 

The theoretical calculations of the band structure of InN can be grouped into semi-empirical (pseudopotential [10-12] or tight binding [13,14]) ones and first principles ones [15-22], In the former, form factors or matrix elements are adjusted to reproduce the energy of some critical points of the band structure. In the work of Jenkins et al [14], the matrix elements for InN are not adjusted, but deduced from those of InP, InAs and InSb. The bandgap obtained for InN is 2.2 eV, not far from the experimentally measured value. Interestingly, these authors have calculated the band structure of zincblende InN, and have found the same bandgap value [14]. 

Accurate energy bands obtained from first principles by computer calculation are available for most covalent solids. A display of the bands obtained by the Empirical Pseudopotential Method for Si, Ge, and Sn and for the compounds of groups 3-5 and 2-6 that are isoclec-tronic with Ge and Sn shows the principal trends with mctallicity and polarity. The interpretation of trends is refined and extended on the basis of the LCAO fitting of the bands, which provides bands of almost equal accuracy in the form of analytic formulae. This fitting is the basis of the parameters of the Solid State Table, and a plot of the values provides the test of the d dependence of interatomic matrix elements. 

Recently, Zunger and coworkers [18, 58-63] employed the semi-empirical pseudopotential method to calculate the electronic structure of Si, CdSe [60] and InP [59] quantum dots. Unlike EMA approaches, this method, based on screened pseudopotentials, allows the treatment of the atomistic character of the nanostructure as well as the surface effects, while permitting multiband and intervalley coupling. The atomic pseudopotentials are extracted from first principles LDA calculations on bulk solids. The single particle LDA equation,... 

First-principles simulations of one- or few-electron systems involve quantum systems of the lowest dimensionality we will consider in this section. These might entail the smallest error intrinsic in the calculation of the wave function. However, the blessing of small dimensionality is compensated by the tendency of systems in this class usually involve electrons in highly irregular potentials. Furthermore, the potential is usually a pseudopotential which describes the effect of atomic cores and/or solvent molecules on the quantum system of interest. Unfortunately, pseudopotentials introduce errors which are difficult to calibrate. 

Our aim in the present section is to examine the nature of vibrations in several exotic carbon structures, and we begin with the Ceo itself. The calculations to be described here were based on first-principles techniques in which the electron-ion interaction was handled using pseudopotentials in conjunction with a mixed basis including both plane wave states and localized s- and p-orbitals associated with the carbon atoms (Bohnen et al. 1995). As has already been made clear, to... 

According to past investigations into the structure of oxyapatite, there exists a linear chain of O2- ions parallel to the c-axis, each one followed by a vacancy (Alberius Henning et al., 1999) (Figure 6.9b). Calculations by density-functional theory with local-density approximation (DFT-LDA) and first-principles pseudopotentials (Calderin, Stott and Rubio, 2003) postulated a hexagonal "c empty ... 

A review of First Principles simulation of oxide surhices is presented, focussing on the interplay between atomic-scale structure and reactivity. Practical aspects of the First Principles method are outlined choice of functional, role of pseudopotential, size of basis, estimation of bulk and surface energies and inclusion of the chemical potential of an ambient. The suitability of various surface models is discussed in terms of planarity, polarity, lateral reconstruction and vertical thickness. These density functional calculations can aid in the interpretation of STM images, as the simulated images for the rutile (110) surface illustrate. Non-stoichiometric reconstructions of this titanium oxide surface are discussed, as well as those of ruthenium oxide, vanadium oxide, silver oxide and alumina (corundum). This demonstrates the link between structure and reactivity in vacuum versus an oxygen-rich atmosphere. This link is also evident for interaction with water, where a survey of relevant ab initio computational work on the reactivity of oxide surfaces is presented. 

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