Crystal energy calculation

F. Bole of Crystal Energy Calculations in Refinement of Energy Para-... 

B. van de Graaf and E. de Vos Burchart, Comput. Chem., 17, 81 (1993). Simplification and Acceleration of Crystal Energy Calculations Under Constant Pressure. 

At first sight crystal energy calculations should be relatively simple. In the case of neon, the lattice vibrations are so extensive that a rather elaborate procedure was required, which was similar to a self-consistent field calculation. We started first with the static lattice and found the cell potential, assuming a fixed position for neighboring atoms. This cell potential was then used to calculate the vibratory motion of neighboring atoms, which in turn had a large effect on a recalculation of the cell potential. This procedure was repeated until self-consistency was obtained. 

Many attempts have been performed to calculate the energy of crystals and to predict the crystal structures by Kitaigorodsky [40-42]. However, as Maddox pointed out in 1988 [43], one of the continuing scandals in the physical sciences is that it remains impossible to predict the structure of even the simplest crystalline solids from a knowledge of their chemical composition, this serious problem has not been solved yet. hi the 1990s, the development of computer made it possible to perform full-scale crystal energy calculation and several methods were developed [44] and the crystal structure of benzene was predicted [45]. Further development was reviewed [46 8]. 

NaCl in a gas or crystal. In Txample 20.1 vve calculated the electrostatic interaction energy between Na" and Cl ions in a vacuum at 2.81 A distance. How is this energy related to the crystal energy calculated in Example 20.2 ... 

Microcrystals of SrS04 of 30 A diameter have a solubility product at 25°C which is 6.4 times that for large crystals. Calculate the surface tension of the SrS04-H20 interface. Equating surface tension and surface energy, calculate the increase in heat of solution of this SrS04 powder in joules per mole. 

The electronic energy, as detennined from must be added to tire ion-ion interactions to obtain the structural energies. This is a straightforward calculation for confined systems. For extended systems such as crystals, the calculations can be done using Madelimg summation techniques [2]. 

Feibelman P J 1987 Force and total-energy calculations for a spatially compact adsorbate on an extended, metallic crystal surface Phys. Rev. B 35 2626... 

Catlow C R A and W C Mackrodt 1982. Theory of Simulation Methods for Lattice and Defect Energy Calculations in Crystals. In Lecture Notes in Physics 166 (Comput. Simul. Solids), pp. 3-20. 

Figure 2.Virtual crystal approximation calculations (solid line) compared with coherent potential approximation calculations for Fe-Co (longdashed line), Fe-Ni (dot-dashed line) and Fe-Cu (dashed line). The fcc-bcc energy difference is shown as a function of the atomic number.

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... 

Fig. 20. A. Conformation of the Valinomycin-cation complex derived for solution using a combination of proton magnetic resonance data and conformational energy calculations. This structure agrees within tenths of an Angstrom with the crystal structure subsequently determined (100) and shown in Fig. 21. Reproduced with permission from Ref.99).

Fig. 21. Crystal structure of the Valinomycin-K+ complex. Reproduced with permission from Ref.100). This crystal structure confirmed within tenths of an Angstrom the structure derived previously in solution 97 98) and by means of conformational energy calculations...

The theoretical treatment of the properties of ionic crystals and molecules has been carried farther than that of other types of atomic aggregates. The Bom theory of crystal energy permits the calculation to within... 

The quality of the mean-field approximation can be tested in simulations of the same lattice model [13]. Ideally, direct free-energy calculations of the liquid and solid phases would allow us to locate the point where the two phases coexist. However, in the present studies we followed a less accurate, but simpler approach we observed the onset of freezing in a simulation where the system was slowly cooled. To diminish the effect of supercooling at the freezing point, we introduced a terraced substrate into the system to act as a crystallization seed [14]. We verified that this seed had little effect on the phase coexistence temperature. For details, see Sect. A.3. At freezing, we have... 

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