Energy pseudopotential

G.P. Francis and M.C. Payne, Finite basis set corrections to total energy pseudopotential calculations, J. 

We have performed calculations using ab initio total energy pseudopotential methods [13]. A Car-Parrinello-like scheme has been used for energy minimization [14]. Specifically, we made use of the fhi96md program, written by... 

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]. 

The term within the brackets in (8.23) is the Hamiltonian. If an approximate expression for the exchange-correlation energy V r) is given the bulk of the work involved in a total-energy pseudopotential calculation is the solution of the eigenvalue problem. 

In this subsection, we describe several examples of applications of the total energy pseudopotential method to structural phase transformations induced either by pressure or temperature. 

Figure 1 Band structures of BP by (a) total-energy pseudopotential technique within the local density approximation (18), and (b) GW approximation (21).

Table 9. Calculated surface free energy y of metals for various orientations. The subscripts A and B refer to the two possible surface terminations of (1010) surfaces of hep crystals [910ve], where the termination with the smaller lattice spacing is denoted A [98Vit]. Calculations were performed for T = 0 K. The method of calculation is indicated FS empirical n-body Finnis-Sinclair potential, PSP total energy pseudopotential, EAM embedded atom method, DFT density functional theory, FPLAPW full potential linear combination of augmented waves, FPLMTO full potential linear combination of muffin tin orbitals.

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... 

There are complicating issues in defmmg pseudopotentials, e.g. the pseudopotential in equation Al.3.78 is state dependent, orbitally dependent and the energy and spatial separations between valence and core electrons are sometimes not transparent. These are not insunnoimtable issues. The state dependence is usually weak and can be ignored. The orbital dependence requires different potentials for different angular momentum components. This can be incorporated via non-local operators. The distinction between valence and core states can be addressed by incorporating the core level in question as part of the valence shell. For... 

It is possible to identify particular spectral features in the modulated reflectivity spectra to band structure features. For example, in a direct band gap the joint density of states must resemble that of critical point. One of the first applications of the empirical pseudopotential method was to calculate reflectivity spectra for a given energy band. Differences between the calculated and measured reflectivity spectra could be assigned to errors in the energy band... 

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.3.27. 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].

The pseudopotential is derived from an all-electron SIC-LDA atomic potential. The relaxation correction takes into account the relaxation of the electronic system upon the excitation of an electron [44]- The authors speculate that ... the ability of the SIRC potential to produce considerably better band structures than DFT-LDA may reflect an extra nonlocality in the SIRC pseudopotential, related to the nonlocality or orbital dependence in the SIC all-electron potential. In addition, it may mimic some of the energy and the non-local space dependence of the self-energy operator occurring in the GW approximation of the electronic many body problem [45]. 

Flere we distinguish between nuclear coordinates R and electronic coordinates r is the single-particle kinetic energy operator, and Vp is the total pseudopotential operator for the interaction between the valence electrons and the combined nucleus + frozen core electrons. The electron-electron and micleus-micleus Coulomb interactions are easily recognized, and the remaining tenu electronic exchange and correlation... 

In practice, therefore, a pseudopotential is invariably employed and only plane waves with a kinetic energy (= /2m) k -t Gp) less than some cutoff are included in the calculation. The... 

The pseudopotential density-functional technique is used to calculate total energies, forces on atoms and stress tensors as described in Ref. 13 and implemented in the computer code CASTEP. CASTEP uses a plane-wave basis set to expand wave-functions and a preconditioned conjugate gradient scheme to solve the density-functional theory (DFT) equations iteratively. Brillouin zone integration is carried out via the special points scheme by Monkhorst and Pack. The nonlocal pseudopotentials in Kleynman-Bylander form were optimized in order to achieve the best convergence with respect to the basis set size. 5... 

DZ double-zeta STO HF Hartree-Fock limit STO AE all electrons PP pseudopotential, this calculation. Energies are in a.u., and DZ and HF results are from Reference 4. 

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