Troullier-Martins pseudopotentials

The relaxation of the structure in the KMC-DR method was done using an approach based on the density functional theory and linear combination of atomic orbitals implemented in the Siesta code [97]. The minimum basis set of localized numerical orbitals of Sankey type [98] was used for all atoms except silicon atoms near the interface, for which polarization functions were added to improve the description of the SiOx layer. The core electrons were replaced with norm-conserving Troullier-Martins pseudopotentials [99] (Zr atoms also include 4p electrons in the valence shell). Calculations were done in the local density approximation (LDA) of DFT. The grid in the real space for the calculation of matrix elements has an equivalent cutoff energy of 60 Ry. The standard diagonalization scheme with Pulay mixing was used to get a self-consistent solution. In the framework of the KMC-DR method, it is not necessary to perform an accurate optimization of the structure, since structure relaxation is performed many times. 

Figure 4-3. A comparison of the Car-Parinello and Bom-Oppenheimer molecular dynamics the potential energy (top) and temperature (kinetic energy, bottom) from the CP-MD and BO-MD simulations for ethylene, started from the same geometry and wave function. The results obtained form the simulations with the CPMD program13 (Troullier-Martins pseudopotentials,1415 time step of 4 a.u., fictitious mass 400 a.u., cut-off energy 70 Ry, unit cell 12 A x 12 A xl2 A)...

All na-AIMD calculations reported in this chapter have been performed using the CPMD package [1] employing the BLYP exchange-correlation functional [3,48] and a plane-wave basis set truncated at 70 Ry in conjunction with Troullier-Martins pseudopotentials [93], For further details we refer the reader to the respective original articles. 

A three-layer slab structure was chosen to simulate rutile (110) surface within the periodic model. Unit cells were 5.91 and 6.49 A along the [001] and [-100] directions, respectively. The slabs were shared out with a 20 A gap. Taking into account the experimental data, geometric parameters of two top layers was allowed to relax during the geometry optimization. Calculations were performed within the DFT model with PBE96 exchange-correlation functional [4]. The Troullier-Martins pseudopotentials were chosen to describe Ti and Ag atoms, and the Hamann pseudopotential was used for O atoms. 

Copper atoms are modeled using argon core Troullier-Martins pseudopotentials generated using the utility provided by FHI Berlin [46]. 

All calculations presented here are based on density-functional theory [37] (DFT) within the LDA and LSD approximations. The Kohn-Sham orbitals [38] are expanded in a plane wave (PW) basis set, with a kinetic energy cutoff of 70 Ry. The Ceperley-Alder expression for correlation and gradient corrections of the Becke-Perdew type are used [39]. We employ ah initio pseudopotentials, generated by use of the Troullier-Martins scheme [40], The coreradii used, in au, were 1.23 for the s, p atomic orbitals of carbon, 1.12 for s, p of N, 0.5 for the s of H, and 1.9, 2.0, 1.5, 1.97,... 

Structures of a large amount of different molecules without a chemical Leitmotiv were studied using Troullier-Martins-type pseudopotentials and DFT by Chen et a/.228 For a study using model potentials, see ref. 229. Molecular shapes of metal alkyls and hydrides, ML , were discussed at Valence Bond level by Landis et al.230... 

The method employed was similar to that of Ref. 35, but with several improvements. ab initio, norm-conserving, nonlocal pseudopotential were used to represent the metal ions. This capability enables reliably realistic representation of the metal s electronic structure. Thus the cadmium pseudopotential was able, for example, to reproduce the experimental cadmium-vacuum work function using no adjustable parameters (unlike the procedure followed in Ref. 35). Pseudopotentials of the Troullier and Martins form [53] were used with the Kleinman-Bylander [54] separable form, and a real space... 

In most LDA studies reported in this article, the Ceperley-Alder exchange-correlation formula is used [10,11]. Also the norm-conserving pseudopotentials of Troullier and Martins are used [12]. Therefore, one only has to deal with the valence electrons in solving the self-consistent Kohn-Sham equations in the LDA. As for basis functions, plane waves with the cutoff energy of 50 Ryd are used. 

Troullier N, Martins JL (1991) Efficient pseudopotentials for plane-wave calculations, Phys. Rev. 

A particularly efficient method for the inclusion of relativity in electronic structure calculations is the pseudopotential (PP) approach. In ihe framework of DFT usually norm-conserving PPs (Bachelet etal. 1982 Hamann etal. 1979 Troullier and Martins 1991) are applied for this purpose. The standard form of norm-conserving PPs is given by... 

The way i>f p is generated from the atomic calculation is not unique. Common pseudopotentials are generated following the prescription of, e.g., Bachelet, Hamann and Schlriter [82], Kleinman and Bylander [83], Vanderbilt [84] or Troullier and Martins [85]. Useful reviews are Refs. [86, 87, 88]. The pseudopotential approach is very convenient because it reduces the number of electrons treated explicitly, making it possible to perform density-functional calculations on systems with tens of thousands of electrons. Moreover, the pseudopotentials upp are much smoother than the bare nuclear potentials vext. The remaining valence electrons are thus well described by plane-wave basis sets. 

Total energy calculations (GO) on isolated Si NC have been based on DFT in the local density approximation (LDA), using two different plane wave pseudopotential codes the FHI98md [8] and the CASTEP [9], Both norm conserving Martin-Troullier and ultrasoft pseudopotentials have been used, setting the cut-off energy at... 

Troullier, N., and Martins, J.L. (1991) Efficient pseudopotentials for plane wave calculations II. operators for fast iterative diagonalization, Phys. Rev., B43, 8861-8869. 

Simulations are performed using the ABINIT [1] code within Density Functional Theory (DFT) and Local Density Approximation (LDA). The valence electrons are described by pseudopotentials developed on a plane waves basis set. The generation of the cations pseudopotentials follows the scheme proposed by Haman [12], whereas the oxygen follows the Troullier and Martins scheme [36]. The particular choice of these pseudopotential schemes is detailed elsewhere [34]. During calculations, symmetries are turned off to impose Pi space group. 

N. Troullier, J.L. Martins, 1991, EfEcient pseudopotentials for plane-wave calculation , Phys. Rev. B 43, 1993-2006. 

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