Ab-initio pseudopotentials

In the pseudopotential approach, Vext is replaced by an ionic pseudopotential which combines the nucleus arid the core electrons into one inert entity, and the self-consistent field equations (Eqs. 3 and 4) are carried out only for the valence electrons. 

Several simple schemes have been formulated to extract ab initio ionic pseudopotentials from atomic calculations. The basic procedure is to generate a potential by inversion of the Kohn-Sham equation. Angular-momentum-dependent screened atomic pseudopotentials, V, are first constructed with the constraints that (1) the valence eigenvalues from the all-electron calculation 

Precision requirement cohesive energy lattice constant, bulk modulus phonon frequencies 

Total crystal energy (referred to dissociated entities) all-electron calculation —1000 Ry/atom 

With these constraints, it can be shown that the potentials 

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Figure Al.3.22. Spatial distributions or charge densities for carbon and silicon crystals in the diamond structure. The density is only for the valence electrons the core electrons are omitted. This charge density is from an ab initio pseudopotential calculation [27].

Figure Al.3.23. Phase diagram of silicon in various polymorphs from an ab initio pseudopotential calculation [34], The volume is nonnalized to the experimental volume. The binding energy is the total electronic energy of the valence electrons. The slope of the dashed curve gives the pressure to transfomi silicon in the diamond structure to the p-Sn structure. Otlier polymorphs listed include face-centred cubic (fee), body-centred cubic (bee), simple hexagonal (sh), simple cubic (sc) and hexagonal close-packed (licp) structures.

Figure Al.3.24. Band structure of LiF from ab initio pseudopotentials [39],...

Figure Al.3.27. Energy bands of copper from ab initio pseudopotential calculations [40].

Figure B3.2.1. The band structure of hexagonal GaN, calculated using EHT-TB parameters detemiined by a genetic algorithm [23]. The target energies are indicated by crosses. The target band structure has been calculated with an ab initio pseudopotential method using a quasiparticle approach to include many-particle corrections [194].

Watson S, Jesson B J, Carter E A and Madden P A 1998 Ab initio pseudopotentials for orbital-free density functional Europhys. Lett. 41 37-42... 

It remains to construct an accurate ionic pseudopotential from first principles which will be appropriate for a variety of molecular environments. There have been some very recent developments in the construction of ab initio pseudopotentials and we will only discuss the fundamental strategies [55, 56]. 

Ab initio pseudopotential study of dehydrogenation of methanol on oxygen-modified Ag(llO) surface has been described by Sun et al. [277]. 

Highlights in the chemistry of cyclopentadienyl compounds have been reviewed.65 Trends in the metallation energies of the gas-phase cyclopentadienyl and methyl compounds of the alkali metals have been studied by ab initio pseudopotential calculations. Whereas there is a smooth increase in polarity of M-(C5H5) bonds from Li to Cs, lithium appears to be less electronegative than sodium in methyl derivatives. The difference between C5H5 and CH3 derivatives is attributed to differences in covalent contributions to the M-C bonds. In solution or in the solid state these trends may be masked by the effects of solvation or crystal packing.66 The interaction between the alkali metal ions Li+-K+ and benzene has also been discussed.67... 

Open-shell Pseudohamiltonians.—The majority of atoms do not have valence structures which can be represented by the fully closed-shell wavefunction of equation (14), and consequently ab initio pseudopotentials cannot be derived directly from the theory outlined above. Acceptable wavefunctions for such atoms require either more than one determinant or the use of the symmetry-equivalenced or generalized Hartree-Fock method, and usually include partially filled shells. The total all-electron wavefunction may be symbolically expressed in terms of four subspaces,... 

Energy-Adjusted Ab Initio Pseudopotentials for the Second and Third Row Transition Elements. 

The traditional approach to obtain the electronic structure of a periodic solid with ab initio pseudopotentials has been to solve the Kohn-Sham (KS)... 

The equilibrium geometries of Cp2M (M = Yb, Eu, Sm) were studied by ab initio pseudopotential calculations at the Hartree-Fock (HF), MP2 and CSID levels. In the Hartree-Fock calculations [118] all the metallocenes favoured regular sandwich-type equilibrium structures with increasingly shallow potential energy surfaces for the bending motions along the series, M = Ca, Yb, Sr, Eu, Sm, and Ba. 

G. Igel, and H. PreulS. Int. J. Quantum Chem., 26, 725 (1984). Pseudopotential Calculations Including Core-Valence Correlation Alkali and Noble-Metal Compounds. M. Dolg, U. Wedig, H. Stoll, and H. PreulS, /. Chem. Phys., 86, 866 (1987). Energy-Adjusted Ab Initio Pseudopotentials for the First Row Transition Elements. M. Dolg, H. Stoll, A. Savin, and H. PreulS, Theor. Chim. Acta, 75,173 (1989). Energy-Adjusted Pseudopotentials for the Rare Earth Elements. 

Abstract The ab initio pseudopotential plane wave DPT simulation of the structure and properties of zeolite active sites and elementary catalytic reactions are discussed through the example of the protonation of water and the first step in the protolytic cracking mechanism of saturated hydrocarbons. 

Theoretical modeling of the structure and reactivity of zeolitic materials, with special emphasis on the mechanism of catalytic reactions, has been the subject of several exhaustive review articles in the past decade. Theoretical approaches that have been used to describe such systems range from empirical molecular mechanics calculations to various ab initio methods as well as different variants of the mixed quantum/classical (QM/MM) algorithms. In the present contribution we focus our attention mainly on those studies which were accomplished by ab initio pseudopotential plane wave density functional methods that are able to treat three-dimensional periodic models of the zeolite catalysts. Where appropriate, we attempt a critical comparison of with other theoretical approaches. 

The most obvious improvement of the model was to include the full zeolite structure in ab initio pseudopotential plane wave DPT calculations. However, the attempts to localize proton transferred HSAPO-34.H2O complexes have proved to be unsuccessful the water molecule remained physisorbed. A typical structure, selected from the numerous local minima, is shown in Pig. 6, illustrating that topologically distant framework oxygens participate also in the stabilization of such a complex. A correct account of this feature would neces-... 

The conditions for protonation of the methanol molecule show strong similarities to the case of water. Most of the ab initio pseudopotential or PAW plane wave geometry optimizations and dynamical simulations agree that the proton transfer occurs only at higher methanol coverages. Various framework structures were explored, like CHA, FER, ... 

The delocalized (right-hand) side of Fig. 1.1 involves some form of calculation on the full lattice such as a band-theory calculation. Again, the Hartree-Fock wave function may be employed in an ab initio method or some approximate method such as Huckel band theory, or the local-exchange approximations employed leading to augmented-plane-wave or ab initio pseudopotential (PP) methods. As an alternative to band theory, the development of the ionic approach using pair potentials or modified electron-gas (MEG) theory has proved effective for certain crystalline species. 

Table 3.9. Static structural properties for C, Si, and Ge obtained from the ab initio pseudopotential calculations of density-functional band theory compared with experiment...

Fig. 7.5. Calculated (using ab initio pseudopotentials and a Gaussian basis set) equations of state (expressed in terms of total energy versus cell size in atomic volume) for various binary compounds with the P-Sn, rocksalt, and zincblende structures (a) a III-V compound, namely GaAs (b) a prototypical II-Vl compound (c) a prototypical I-VIl compound (after Chelikowsky and Burdett, 1986 reproduced with the publisher s permission).

In (almost) all the theoretical papers the directions of the calculated relaxations agree with the experimentally determined coordinates. The quantitative agreement is not as good as one could expect from state-of-the art ab initio calculations, however. As Harrison et al. pointed out [2], the extensive experience of calculations on bulk oxides which has been built up in recent years leads one to expect that DFT and HF calculations will reproduce experimental bond lengths to somewhat better than 0.1 A. For example, the bulk structural parameters of Ti02 rutile agree better than 0.06A using softcore ab initio pseudopotentials constructed within the EDA, and a plane-wave basis [44]. 

Vaidehi, N., Wesolowski, T.A. and Warshel, A. (1992) Quantum Mechanical Calculation of Solvent Free Energies. A Combined Ab Initio Pseudopotential Free Energy Perturbation Approach, J. Chem. Phys. 97, 4264 1271. 

Les, A., and Ortega-Blake, I. (1985). Inti. J. Quantum Chem. 27, 567—semiempirical (PCILO.MNDO) and ab initio pseudopotential calculations for relative stabilities of tautomers of 2- and 4-oxopyrimidine. 

From the experimental side, the band-structure parameters are mainly determined from the cyclotron resonance (CR) spectra of electron and holes (see for instance [4]). Some of these parameters can also be obtained from the Zeeman splitting of electronic transitions of shallow impurities involving levels for which the electronic masses can be taken as those of free electrons or holes, or from the magnetoreflectivity of free carriers. Average effective masses can also be deduced from the Hall-effect measurements or from other transport measurements. Calculation methods that have been used to obtain band-structure parameters free from experimental input are the ab-initio pseudopotential method, the k-p method and a combination of both. These theoretical methods are presented in Chap. 2 of [107]. VB parameters at k = 0 including k and q have been calculated for several semiconductors with diamond and zinc-blended structures by Lawaetz [55]. 

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