Nonlocal Pseudopotential

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... 

Kobayasi, T. and Nara, H. (1993) Properties of nonlocal pseudopotentials of Si and Ge optimized under full interdependence among potential parameters, Bull. Coll. Med. Sci. Tohoku Univ., 2, 7-16. 

Hamiltonian which, in a nonlocal pseudopotential approximation, can be written as... 

Eq. (2). More general nonlocal pseudopotentials (NLPS s) that depend on both r and r require either the DM1 or the full wavelunction for the calculation of V e-We therefore will concentrate on how to construct high-quality LPS s. Before that, however, it is pedagogical to briefly outline the essence of the conventional OB NLPS theory.3 372... 

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... 

As described briefly in Chapter 3, a promising new method of electronic structure calculation utilizing combined molecular-dynamics and density-functional theory has recently been developed by Car and Pari-nello (1985). This approach has recently been applied to cristobalite, yielding equilibrium lattice constants within 1% of experiment (Allan and Teter, 1987), as shown in Table 7.2. New oxygen nonlocal pseudopotentials were also an important part of this study. Such a method is a substantial advance upon density-functional pseudopotential band theory, since it can be efficiently applied both to amorphous systems and to systems at finite temperature. 

Allan, D. A., and M. P. Teter (1987). Nonlocal pseudopotentials in molecular-dynamical density-functional theory application to SiOj. Phys. Rev. Lett. 59, 1136-39. 

They have done calculations for C2H6, Si2H6 and Gc2H6 geometries and internal rotation barriers. They also used the model potential in eqn (2-L-22) for calculation of equilibrium geometries of some homonuclear diatomics," such as O2, Bc2, B2, C2, N2, O2, F2, P2 and CI2. Molecular anisotropy in some diatoms such as H2, O2, C2, N2, O2 (singlet), F2, HF and CO have been evaluated with same model potential. A nonlocal pseudopotential in the FSGO model ... 

Using pseudopotentials has several major beneficial consequences (i) Only the valence electrons must be treated explicitly, thus the number of equations to be solved [Eqs. (13)] can be reduced drastically (ii) the pseudoorbitals are very smooth near the atomic core, and thus Tout can be reduced drastically and (iii) important relativistic effects of the core electrons of heavy elements such as the 5d elements can be included in nonrelativistic calculations. The major downsides are that the potential v(r) in Eq. (3) must be replaced with a more complicated and computationally expensive nonlocal pseudopotential and, more importantly, that the transferability of the pseudopotential, i.e., its accuracy in different bonding environments, may not be perfect. Developing highly transferable pseudopotentials that can be used at as low an cut as possible is a major current topic of research. 

We conclude here that the matrix elements of djdx are constant. This conclusion will follow also from the pseudopotential theory of covalent bonding in Chapter 18, and was found to be true of the matrix elements in the nonlocal pseudopotential calculations of Chelikowsky and Cohen (quoted by Phillips,... 

Theoretical and experimental optical reflectivity based upon empirical calculations of nonlocal pseudopotentials by Chelikowsky and Cohen (1976b). Experimental curves are taken from Philipp and Ehrenreich (1963) for Si and Ge, and from Cardona et al. (1966) for Sn. 

Kobayasi, T. and Nara, H. (1993) Properties of nonlocal pseudopotentials of Si and Ge optimized under full interdependence among potential parameters. Bull. Coll. Med. Set Tohoku Univ., 2, 7-16. Chadi, DJ. and Cohen, M.L. (1973) Special points in the Brillouin zone, Phys. Rev., B8, 5747-5753. Clementi. E. (1965) Tables of atomic functions, in Supplement to the paper Ab initio computations in atoms and molecules . IBMJ. Res. Develop., 9, 2-19. 

C. Nonlocal Pseudopotentials and DMC Excited States Exact Fermion Methods Applications... 

The nonlocal pseudopotential operator W includes pseudopotentials u,( ) for a small number of the lowest symmetry channels, labeled by I (usually spd) ... 

The gap of p-BN increases upon volume compression as in the case of diamond, while in most semiconductors the reverse is true [4]. This is due to the fact that boron and nitrogen atoms have deep and localized pseudopotentials as compared with the atoms of other rows of the periodic table. It can be calculated [5] by the same technique described in [4] that at very high pressures boron nitride should favor the rock salt phase, while the p-BN structure is unstable even at highly compressed volumes [5]. Calculations using a nonlocalized pseudopotential model lead to a band gap of 4.41 eV for p-BN for further details, see [6]. Electronic properties of p-BN have been derived by ab initio, norm-conserving, nonlocal pseudopotential... 

Zunger A, Cohen M (1979) First-principles nonlocal-pseudopotential approach in the density-functional formalism. II. Application to electronic and stmctural properties of sohds. Phys Rev 820 4082-4108... 

S. Fahy, X. W. Wang, and S. G. Louie, Phys. Rev. Lett., 61, 1631 (1988). Variational Quantum Monte Carlo Nonlocal Pseudopotential Approach to Solids Cohesive and Structural Properties of Diamond. 

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