Total Lattice Energy Research Articles

Hydrogen Bond Strength and Charge Distribution in the Bifluoride Ion, HF2−. Lattice Energies of LiHF2, NaHF2, KHF2, RbHF2, and CsHF2

Electrostatic energies and Madelung parameters for LiHF2, NaHF2, KHF2, RbHF2, and CsHF2 are reported together with a term-by-term calculation of the total cohesive lattice energy, all expressed as single-parameter quadratic functions of the charge Q(F) on the terminal fluorine atoms of the linear HF2− ion. An assessment of the charge distribution in this ion is made in conjunction with a calculation of the enthalpy change, Δ H1, of the reaction, HF2−(g)→ HF(g) + F−(g),thus measuring the strength of the hydrogen bond. The intersections of the curves for Δ H1 as a function of Q(F) are used to assign values of −0.73 e.u. to Q(F) and 252 kJ mol−1 to Δ H1 and the following values for the total potential lattice energies: Epot(LiHF2)=820.6 kJ mol−1; Epot(NaHF2)=755.3 kJ mol−1; Epot(KHF2)=648.2 kJ mol−1; Epot(RbHF2)=626.9 kJ mol−1, and Epot(CsHF2)=607.4 kJ mol−1.

Berechnung der Gitterenergie der Alkalihydrogenfluoride KHF2, RbHF2 und CsHF2

Abstract In the paper of Neckel , Kuzmany , and Vinek5 a procedure was proposed for the calculation of the electrostatic interaction energy of a crystal lattice provided the multipole moments of the particles are known. In the present paper a method for calculating multipole moments using LCAO-MO-wave functions is discussed. The multipole moments for the [FHF]--ion and the Madelung energy of KHF2 , RbHF2 and CsHF2 are evaluated. The results are com pared with calculations obtained by using a point charge model. For KHF2 , RbHF2 and CsHF2, the total lattice energies are evaluated.

Binding forces in crystals having the sphalerite lattice

A check is made of the applicability of an interpolation equation proposed for the binding energy in mixed ionic-covalent crystals having the sphalerite structure. It is shown that the parameters of the equation can be adjusted for most such crystals to match the physical properties. The equation reveals that the covalent interaction makes a large contribution to the total lattice energy.

Distribution of the lattice energy in cubic crystals and its variation with compression or expansion

The total lattice energy of face-centred and body-centred cubic crystals has been calculated on the assumption of a pair-wise interaction potential, for a variety of such potentials. These were either of Morse or Mie (Lennard-Jones) type, with the parameters adjusted to minimize the total lattice energy for an ideal unstrained crystal at 0°K. The same potentials were used to compute the variation in lattice energy when the lattice is allowed to expand or contract by up to 2.5 per cent. The relative contributions of different interactions to the total energy are given. For face-centred cubic crystals, most potentials predict a major contribution from nearest-neighbour interactions, although the contributions of second and higher neighbours are still significant. For body-centred cubic crystals, the dominant contribution usually comes from the second neighbour interactions. Some typical variations in these contributions with changes in lattice parameter are given.

On the equilibrium shape of cubic crystals

The equilibrium shapes of face-centred and body-centred cubic crystals have been calculated from theoretical calculations of surface energy based on the broken-bond model with a variety of interaction potentials. The potentials used were of either Morse or Mie (Lennard-Jones) type with a range of parameter values adjusted in each case to minimize the total lattice energy of an ideal unstrained crystal at 0°K. These potentials were used to calculate the surface energy not only for the unstrained crystal but also for crystals where the lattice is expanded, e.g. thermally, or contracted, e.g. by external pressure, by up to 2.5 per cent. The calculations take account of the interactions between all neighbours and cover about 50 different orientations. The equilibrium shapes are compared with the experimental shapes found in well-annealed field-emitter tips. Quantitative agreement is found with (5, 7) or (5, 8) Mie potentials for Mo, W, V, and α-Fe, with a Mie potential between (4.5, 8) and (4.5, 14) for Ta and Nb, and with a (4.5, 7) potential for Ni, and possibly for Ir, Pt, and Nb.

Forces in the benzene crystal

The total lattice energy of benzene is evaluated by summation of pair interactions in the crystal. The relative contributions of the σ and π electrons to the attractive part of the energy are separated out explicitly: the π electrons contribute 40 per cent of this energy (although they represent only 20 per cent of the valence electrons). However the three component σ-σ, σ-π, and π-π dispersion energies are of the same order of magnitude. The effect of σ-π and π-π electron correlation is also investigated. The total lattice energy agrees well with the available experimental heat of sublimation data.

Madelung Constants

AbstractMadelung constants are simple numbers which depend on the type of structure investigated. They are needed for the calculation (using the Born‐Haber cycle) of lattice energies and enthalpies of formation of ionic compounds. Each Madelung constant is the sum of partial Madelung constants which represent the contributions of the individual ions to the total lattice energy. The partial Madelung constants depend on the ionic charge and, clearly though not stringently, on the coordination number. On the other hand, each Madelung constant can be represented by a sum of Madelung constants for related simple primitive AB structures. Surprisingly, these Madelung constants are numerically interrelated in a simple manner, and are related to the partial Madelung constants of interstitial sites. – Madelung constants of parameter‐dependent structures (e.g. of the rutile or anatase type) and their variations with the structure‐determining quantities are of particular interest. Madelung constants also yield information in the case of complex compounds and – surprisingly – of non‐metal compounds (e.g. XeF2, XeF4, XeF2·XeF4).

A model for the rationalization of saline and metallic hydride formation

The exothermic, reversible formation of solid hydrides from the elements is rationalized on the basis of a model in which the hydride consists of hydrogen anions and metal cations, the latter likewise engaging in metal-metal bonding in the metallic hydrides. The lattice energy is evaluated as the sum of the Madelung energy and this metal-metal interaction energy. Two empirical methods of estimating the latter are suggested, one involving crystal field stabilization. The total lattice energy so calculated is compared semi-quantitatively with the sum of the endothermic factors in a Born-Haber cycle. The energy balance is favourable with few exceptions for hydrides known to form directly, and unfavourable for hydrides which evidently do not form directly from the elements.

The Lattice Energies of the Silver and Thallium Halides

The lattice energies and lattice constants of the silver and thallium halides are calculated assuming ionic crystals with a van der Waals potential. The latter term, which is large, accounts for the low solubilities (high lattice energies) of the salts. The calculations appear to be quantitatively satisfactory for the thallium halides, TlCl, TlBr and TlI, and for the three silver halides AgF, AgCl and AgBr. Definite evidence is found for assuming the existence of a homopolar potential in AgI of about 10 percent of the total lattice energy. One reason for believing this, is the stability of the zincblend instead of the rocksalt lattice, which latter should be stable were the compound purely ionic. There is presumably some homopolar binding in AgBr but it cannot be large. The thallium salts probably are entirely ionic. The theoretically calculated and experimental (chemical) lattice energies are, respectively, in K cal., AgF, 219, 217.7; AgCl, 203, 205.7; AgBr, 197, 201.8; AgI, 190, 199.2; TlCl, 167, 170.1; TlBr, 164, 165.6; TlI, 159, 160.8.