Vanderbilt pseudopotential

We employed density functional calculations using the ultrasoft pseudopotential plane wave method to investigate the CHQ nanotubes and the encapsulated silver nanowires. The local density approximation (LDA) of Ceperley and Alder and Vanderbilt pseudopotential was employed and the cutoff energy of the plane wave basis set was 20 Ry [27,182-185]. Full-potential linearized augmented plane wave method calculations were also carried out on the isolated silver nanowire [195-197]. To check the reliability of our... 

Reference [73] Cl scheme LDA soft-core Vanderbilt pseudopotentials [269] simple cubic cell with a = 25.9 a.u. cutoff of 15 Ry, and augmentation density with a cutoff of 130 Ry. 

Density functional theory calculations are carried out using the CPMD code, which allows to simulate systems with periodic boundary conditions [31]. The BP exchange correlation functional [32] is used with ultrasoft Vanderbilt pseudopotentials [33], especially designed to work with a... 

In all of the simulations discussed in this chapter the TDDFT FSSH theory was implemented with the VASP" DFT package. The simulations were performed with either Perdew and Wang or PBE exchange-correlation fimctions, Vanderbilt pseudopotentials" and a converged plane wave basis. The simulations were carried out in a cubic cell periodically replicated in three dimensions, as stipulated by the plane wave basis. To prevent spurious interactions between periodic images of the QD, the cell was constructed to have at least 8 A of vacuum between the QD replicas. 

Vanderbilt D 1990 Soft self-consistent pseudopotentials in a generalized eigenvalue formalism Phys. Rev. B 41 7892-5... 

Each pseudopotential is defined within a cut-off radius from the atom center. At the cut-off, the potential and wavefunctions of the core region must join smoothly to the all-electron-like valence states. Early functional forms for pseudopotentials also enforced the norm-conserving condition so that the integral of the charge density below the cut-off equals that of the aU-electron calculation [42, 43]. However, smoother, and so computationally cheaper, functions can be defined if this condition is relaxed. This idea leads to the so called soft and ultra-soft pseudopotentials defined by Vanderbilt [44] and others. The Unk between the pseudo and real potentials was formaUzed more clearly by Blochl [45] and the resulting... 

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.//. 

Much effort has been put to improve the pseudopotentials. [71,72] The most successful pseudopotential model is the so called ultra-soft pseudopotentials, proposed by Vanderbilt. [73] The model allows one to work with optimally smooth pseudopotentials. Thus the number of plane waves needed to express the pseudo-wavefunctions can be greatly reduced. In the model, pseudo-wavefunctions ipiif match the true orbitals outside a given core radius re, within Tc, are al-... 

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. 

D. Vanderbilt (1985) Optimally smooth norm-conserving pseudopotentials. Phys. Rev. B 32, p. 8412... 

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. 

The relatively few QM studies of these materials reflect both the structural complexity (including low symmetry) and also the strong scattering associated with the oxygen potential, which makes the generation of reliable and efficient pseudopotentials for PW-LDA calculations difficult. There has been a concerted effort to solve this problem over the last few years which has yielded a new family of ultra-soft pseudopotentials with which oxygen has been described with plane wave cut-offs as low as 500 eV (Vanderbilt, 1990). In the all electron LCAO-HF method the major approximation is associated with the choice of basis set. This has been studied in some detail and reliable basis sets developed (Nada et al., 1990). In the absence of analytic forces, the use of this method to optimize fully the geometry of such complex structures is rare. 

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