Bulk total energy

Structure Lattice Density Atomic Bulk Total energy Bond Bond... 

Also the bulk basis set can still be improved by the addition of polarization functions, which do not contribute to the energy of atoms and ions in the gas phase because of AO orthogonality, but they can be important in the expansion of the bulk wave function. However, in this particular case, the contribution from polarization functions to the bulk total energy (Case 5) is minimal, because of high symmetry and the nearly spherical shape of the closed-shell ions. 

Weinert M, Wimmer E and Freeman A J 1982 Total-energy all-electron density functional method for bulk solids and surfaces Phys. Rev. B 26 4571-8... 

Jansen H J F and Freeman A J 1984 Total-energy full-potential linearized augmented plane-wave method for bulk solids electronic and structural properties of tungsten Phys. Rev. B 30 561-9... 

The tenn represents an externally applied potential field or the effects of the container walls it is usually dropped for fiilly periodic simulations of bulk systems. Also, it is usual to neglect v - and higher tenns (which m reality might be of order 10% of the total energy in condensed phases) and concentrate on For brevity henceforth we will just call this v(r). There is an extensive literature on the way these potentials are detennined experimentally, or modelled... 

The precursor of such atomistic studies is a description of atomic interactions or, generally, knowledge of the dependence of the total energy of the system on the positions of the atoms. In principle, this is available in ab-initio total energy calculations based on the loc density functional theory (see, for example, Pettifor and Cottrell 1992). However, for extended defects, such as dislocations and interfaces, such calculations are only feasible when the number of atoms included into the calculation is well below one hundred. Hence, only very special cases can be treated in this framework and, indeed, the bulk of the dislocation and interfacial... 

In crystals with the LI2 structure (the fcc-based ordered structure), there exist three independent elastic constants-in the contracted notation, Cn, C12 and 044. A set of three independent ab initio total-energy calculations (i.e. total energy as a function of strain) is required to determine these elastic constants. We have determined the bulk modulus, Cii, and C44 from distortion energies associated with uniform hydrostatic pressure, uniaxial strain and pure shear strain, respectively. The shear moduli for the 001 plane along the [100] direction and for the 110 plane along the [110] direction, are G ooi = G44 and G no = (Cu — G12), respectively. The shear anisotropy factor, A = provides a measure of the degree of anisotropy of the electronic charge... 

The most difficult part of the theory lies in obtaining actual values for AF and v. For a large cluster of N molecules the extra surface tension due to the incremental surface area, edA, contributes an increase to the total free energy, whilst the bulk free energy per volume summed over the incremental volume, AF dV, gives a decrease to the total free energy. Hence, AF can be estimated as the maximum value of ad A — AF dV as a function of N. It is found that AF is proportional... 

Fig.l. Total energy (lmRy=0.314 kcal/mole) per unit cell for a five-layer W(OOl) slab as a function of lateral displacement, 5, and spacing between the surface and sub-surface layers, A the latter is given relative to the bulk spacing of 1.581 A (after Ref. 26). 

This mechanism may account for the stability, in the absence of any external stabilising agent, of amphiphilic homopolymers in the fully collapsed/glo-bular state. The total free energy of a collapsed macromolecule includes a surface energy contribution in addition to the bulk free energy. Obviously, to form a stable particle, the outer shell of the particle should be hydrophilic enough. 

The total energy of this adsorption reaction can be found experimentally from the microscopic activity quotient, and separated theoretically into the following components (1) transfer of the ion to be adsorbed from the bulk of solution to the oxide surface plane, at which the mean electrostatic potential is t/>q with respect to the bulk of solution (2) reaction of the adsorbate in the surface plane with a functional group at the surface (3) transfer of a fraction of the counter charge from solution into the solution part of the double layer by attraction of counter ions and (4) transfer of the remainder of the counter charge by expulsion of co-ions from the solution part of the double layer to the solution. 

For liquids, Stefan26 long ago advanced the hypothesis that, when a molecule is transferred from the bulk to the interface with the saturated vapor, its total energy changes just as much as when the molecule moves on from this interface into the vapor. Consequently,... 

The most important ZnS surface is the (110), which is the most common growth surface and is also the perfect cleavage surface. Therefore, the calculation is based on the ZnS (110) surface. The surfaces are cleaved from the bulk ZnS with the optimtun tinit cell volume determined using the GGA with CASTER The Cu and Fe doped surfaces are built by the substitution of Cu or Fe for Zn atom on the cleaved surface. A vacuum spacing of 1.5 nm is inserted in the z-direction to form a slab and mimic a 2D surface. In order to eliminate the interactions between mirror images in the z-direction due to the periodic boimdary conditions, in test calculations, we have done some total energy calculation to find a proper thickness of slab. The result shows that 1.5 run is a desirable thickness. 

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