Hamann Potential

One of the most used parameterizations for the pseudo wave-functions is the one proposed in 1979 by Hamann, Schliiter, and Chiang [59] and later improved by Bachelet, Hamann and Schliiter [60] and Hamann [61]. 

The method proposed consists of using an intermediate pseudo-potential, wi r), given by 

In the method proposed by Hamann [61], the parameters c are adjusted so that 

To impose norm-conservation, the final pseudo wave-functions, i f (r), are defined as a correction to the intermediate wave-functions 

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Kihara20 used a core model in which the Lennard-Jones potential is assumed to hold for the shortest distance between the molecular cores instead of molecular centers. By use of linear, tetrahedral, and other shapes of cores, various molecules can be approximated. Thomaes,41 Rowlinson,35 Hamann, McManamey, and Pearse,14 Atoji and Lipscomb,1 Pitzer,30 and Balescu,4 have used other models of attracting centers and other mathemtical methods, but obtain similar conclusions. The primary effect is to steepen the potential curve so that in terms of inverse powers of the inter-... 

Local-density potentials greatly simplify the computational problems associated with defect calculations. In practice, however, such calculations still are very computer-intensive, especially when repeated cycles for different atomic positions are treated. In most cases the cores are eliminated from the calculation by the use of pseudopotentials, and considerable effort has gone into the development of suitable pseudopotentials for atoms of interest (see Hamann et al., 1979). 

Shilabin AG Kasanah N, Tekwani BL, Hamann MT. (2008) Kinetic studies and bioactivity of potential manzamine prodrugs. JNat Prod 71 1218-1221. 

In the s-wave-tip model (Tersoff and Hamann, 1983, 1985), the tip was also modeled as a protruded piece of Sommerfeld metal, with a radius of curvature R, see Fig. 1.25. The solutions of the Schrodinger equation for a spherical potential well of radius R were taken as tip wavefunctions. Among the numerous solutions of this macroscopic quantum-mechanical problem, Tersoff and Hamann assumed that only the s-wave solution was important. Under such assumptions, the tunneling current has an extremely simple form. At low bias, the tunneling current is proportional to the Fermi-level LDOS at the center of curvature of the tip Pq. 

Fig. 1.25. The s-wave-tip model. The tip was modeled as a spherical potential well of radius R. The distance of nearest approach is d. The center of curvature of tip is To, at a distance (R + d) from the sample surface. Only the 5-wave solution of the spherical-potential-well problem is taken as the tip wavefunction. In the interpretation of the images of the reconstructions on Au(llO), the parameters used are R = 9 A, d = 6 A. The center of curvature of the tip is 15 A from the Au surface. (After Tersoff and Hamann, 1983.)...

Fig. 4.3. Position of the image plane in the jellium model. The surface potential of an electron in the jellium model is calculated using the local-density approximation. By fitting the numerically calculated surface potential with the classical image potential, Eq. (4.7), the position of the image plane is obtained as a function of r, and z. The results show that the classical image potential is accurate down to about 3 bohrs from the boundary of the uniform positive charge background. For metals used in STM, r, 2 — 3 bohr, zo 0.9 bohr. (Reproduced from Appelbaum and Hamann, 1972, with permission.

Appelbaum, J. A., and Hamann, D. R. (1973a). Surface potential, charge density, and ionization potential of Si(lll) - a self-consistent calculation. Phys. Rev. Lett. 32, 225-228. 

The shape-consistent (or norm-conserving ) RECP approaches are most widely employed in calculations of heavy-atom molecules though ener-gy-adjusted/consistent pseudopotentials [58] by Stuttgart team are also actively used as well as the Huzinaga-type ab initio model potentials [66]. In plane wave calculations of many-atom systems and in molecular dynamics, the separable pseudopotentials [61, 62, 63] are more popular now because they provide linear scaling of computational effort with the basis set size in contrast to the radially-local RECPs. The nonrelativistic shape-consistent effective core potential was first proposed by Durand Barthelat [71] and then a modified scheme of the pseudoorbital construction was suggested by Christiansen et al. [72] and by Hamann et al. [73]. 

Donia M, Hamann MT (2003) Marine Natural Products and Their Potential Applications as Anti-Infective Agents. Lancet 3 338... 

Refs. [i]KahlertH(2002) Potentiometry. In ScholzF(ed)Electroanalytical methods. Springer, Berlin, pp 227-228 [ii] Oldham KB, Myland IC (1994) Fundamentals of electrochemical science. Academic Press, San Diego, p 135 [iii] Damaskin BB, Petrii OA (1978) Fundamentals of theoretical electrochemistry. (In Russian), Vysshaya Shkola, Moscow, p 118 [iv] Brett CMA, Oliveira Brett AM (1993) Electrochemistry. Oxford University Press, p 21 [v] Petrii OA, Tsirlina GA (2002) Electrode potentials. In Bard AJ, Stratman M, Gileadi E, Urbakh M (eds) Thermodynamics and electrified interfaces. Encyclopedia of electrochemistry, vol 1. Wiley-VCH, Weinheim, pp 1-23 [vi] Erdey-Gruz T (1972) Kinetics of electrode processes, p 149 [vii] Hamann CH, Hammett A, Vielstich W (1998) Electrochemistry. Wiley-VCH, Weinheim, p 86... 

Donia M, Hamann MT. Marine natural products and their potential applications as anti-infective agents. Lancet Infect. Dis. 2003 3 338-348. 

Several empirical and semiempirical interatomic potentials have been developed for the Si H systembased on extensions and modifications of well-known potentials for Si including up to three-body interactions (StilUnger and Weber, 1985 Biswas and Hamann, 1985 Biswas et al., 1987 Mousseau and Lewis, 1991 Baskes, 1992). Recent atomic-scale simulation work of plasma-surface interactions in the PECVD of Si thin films has been based on an empirical description of interatomic interactions in the Si H system according to Tersoff s (1986, 1988, 1989) potential for Si, as extended by Ohira and co-workers (1994, 1995, 1996) to incorporate Si-H, H-H, and the corresponding three-body interactions. The extension of the potential to include the presence of hydrogen adopted the Tersoff parametrization to fit results of ab initio calculations for the structure and energetics of Sil 1., x <4, species in the gas phase (Ohira et al., 1994,1995,1996). A similar form of... 

Hamann (1987) employed a potentiometric urea electrode in an enzyme difference analyzer for urea determination in serum. The difference between the potential changes of a urease-covered and a bare pH glass electrode is evaluated 30 s after sample injection. This fixed-time regime provides a measuring frequency of 20-25/h the linear range for 1 120 diluted samples is 1-20 mmol/l. These results are better than those of common potentiometric enzyme sensors. 

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. 

In principle, surface atomic and electronic structures are both available from self-consistent calculations of the electronic energy and surface potential. Until recently, however, such calculations were rather unrealistic, being based on a one-dimensional model using a square well crystal potential, with a semi-infinite lattice of pseudo-ions added by first-order perturbation theory. This treatment could not adequately describe dangling bond surface bands. Fortunately, the situation has improved enormously as the result of an approach due to Appelbaum and Hamann (see ref. 70 and references cited therein), which is based on the following concepts. 

Appelbaum and Hamann [209] produced a fully self-consistent first principles calculation for the chemisorption of H on Si lll, which showed that the Si—H bond potential is considerably greater than that for Si—Si. The force on the H atom is small and inward, with a bond length of 2.73 0.02 a.u. The Si-H bond force constant is 0.175a.u. compared with the measured value of 0.173 a.u. for SiH4. The corresponding surface phonon, as mentioned previously, has been observed by ELS [214]. In the calculated electronic structure of the Si—H surface, the most notable feature is the disappearance of states in the fundamental band gap and the corresponding appearance of a band of states, clearly connected with the Si- H bond, in the gap between the second and third valence bands. 

Hamann et al. were among the first to use the apertureless near-field approach to greatly enhance optical processes in the near-field region. One important result of this investigation is that the spatial resolution of this approach is correlated with the radius of the tip apex, while the high cross section arises from an anteima enhancement provided by the tip volume [118]. This illustrates the high potential of this approach for local spectroscopy and optical imaging on the nanometer scale. 

Many other functional forms exist for semiconductor potentials, but most derive from SW and Tersoff formulations. Examples include those of Pearson et i. [84Peal], Biswas-Hamann [85Bisl], Bolding-Anderson [90Boll], Wang-Rockett [91Wanl]. 

Schnipper, J.L., Hamann, C., Ndumele, C.D. et al. (2009) Effect of an electronic medication reconciliation apphcation and process redesign on potential adverse drug events a cluster-randomized trial. Archives of Internal Medicine, 169(8), 771-780. 

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