Troullier

Troullier, A., Reinstadler, D., Dupont, Y, Naumann, D., and Forge, V. (2000). Transient non-native secondary structures during the refolding of alpha-lactalbumin detected by infrared spectroscopy. Nat. Struct. Biol. 7, 78-86. 

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,... 

In this work we recalculate the structures of Au clusters with 6scalar relativistic Troullier-Martins pseudo-potentials , respectively, and within the SIESTA code" . In Fig 2 we present our results for the structures and relative binding energies. We see that GGA leads to planar structures whereas LDA favors 3D structures for n>7 clusters. Thus, in addition to relativistic effects, the observed planarity of Au clusters is accounted for using only the GGA level of theory. 

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... 

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. 

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. 

Figure 4-2. Energy conservation in CP-MD the potential energy (Ee, main axis), temperature (kinetic energy, T, auxiliary, right-hand side axis), physical energy (T + Ee, auxiliary axis), and conserved energy (Econs). The difference between Ec0 s and T + Ee is the fictitious kinetic energy of the wavefunction. The data from the simulation for the ethylene molecule with the CPMD program13 (Troullier-Martins pseudopotentials1415, time step of 4 a.u., fictitious mass 400 a.u., cut-off energy 70 Ry, unit cell 12 Ax 12 A xl2 A)...

Figure 4-6. Plane wave convergence of the carbon-carbon bond length in the ethylene and butadiene molecules, from the simulations with the CPMD program13 (Troullier-Martins pseudopotentials,1415 time step 4 a.u., fictitious mass 400 a.u., unit cell 12 A x 12 A x 12 A)...

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

Troullier A, Girardet JL, Dupont Y (1992) J Biol Chem 267 22821 (and references cited therein)... 

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. 

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