Ultrasoft pseudopotential

Ultrasoft pseudopotentials have now been constructed for all elements for all elements from H to Bi [10]. It has been shown that without any loss of accuracy even for first-row and transition-elements small PW basis-sets comparable in size to those necessai y for soft normconserving pseudopotentials for A1 or Si can be used. For any further details, see [9,. 37]. 

Kresse, G. and Joubert, D. (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Physical Review B - Condensed Matter, 59, 1758-1775. 

The density functional calculations were performed using the Vienna Ab Initio Simulation Package (VASP). ° The spin-polarized generalized gradient approximation, Perdue—Wang exchange correlation function, and ultrasoft pseudopotentials were used. ... 

G. Kresse and D. Joubert, From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method, Phys. Rev. B 59 (1999), 1758. 

In order to calculate the band structure and the density of states (DOS) of periodic unit cells of a-rhombohedral boron (Fig. la) and of boron nanotubes (Fig. 3a), we applied the VASP package [27], an ab initio density functional code, using plane-waves basis sets and ultrasoft pseudopotentials. The electron-electron interaction was treated within the local density approximation (LDA) with the Geperley-Alder exchange-correlation functional [28]. The kinetic-energy cutoff used for the plane-wave expansion of... 

Also pure density-functional methods combined with plane-wave basis sets and ultrasoft pseudopotentials [58] were used in our studies of extended systems [59]. The computational efficiency of these methods enables larger systems and to some extent dynamical processes to be studied. Generalized-gradient approximation (GGA) or spin-polarized GGA DFT functionals [60, 61] were employed in the electronic structure calculations. 

Hutter J, Tuckerman ME, Parrinello M, Integrating the Car-Parrinello equations III Techniques for ultrasoft pseudopotentials, J Chem Phys, 102, 859 (1995)... 

In the present calculation, we used two ab initio methods to investigate structural stability and the potential for carrier generation of X B6 and X Bi2 clusters in c-Si. Here X is from H to Br in the periodic table. The following two methodsused were (i) plane wave ultrasoft pseudopotential method for the optimization of atomic structures and (ii) discrete variational-Xa (DV-Xa) molecular orbital method for the analysis of the fine electronic structures and activation energies of the clusters. 

Calculations used the CASTEP code with a plane-wave basis set ( cutofr= 340 eV) and Vanderbilt-type ultrasoft pseudopotentials. The surface model as well as the -point mesh was as described in Section IV. 1.//. 

Spontaneous polarisation, that is polarisation in the absence of an electric field, has been calculated using both a Wannier function approach and a Berry s phase approach. Berry s phase involves an adiabatic change around a closed loop which results in a change of phase without change in energy. A recent paper by Ferretti et alP used the PAW method with ultrasoft pseudopotentials and Wannier functions to calculate the spontaneous polarisation of AIN in its wurtzite phase. 

K. Laasonen, A. Pasquarello, R. Car, C. Lee, and D. Vanderbilt, Car-Parrinello molecular dynamics with Vanderbilt ultrasoft pseudopotentials, Phys. Rev. B Condens. Matter, 47 (1993), 10142-10153. 

J. Hotter, M. Tuckerman, and M. Parrinello, Integrating the Car-Parrinello equations. 3. Thechniques for ultrasoft pseudopotentials, J. Chem. Phys., 102(1995), 859-871. 

Most plane wave calculations use ultrasoft pseudopotentials (USPP),15,28 which describe the core electrons of atoms in a mathematically efficient form that greatly reduces the computational cost associated with heavy atoms. An increasing number of calculations used the projector augmented wave (PAW) approach instead.28 In most circumstances where both approaches can be used, the differences between USPP and PAW calculations are minor. Some exceptions to this observation include transition metals with large magnetic moments (e.g., Fe) and alkali metals.28... 

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