The formation of 10,10′(5H,5′H)-spirobiphenophosphazinium chloride by the interaction of diphenylamine and phosphorus trichloride

The Autoionization of [TiF4] by Cation Complexation with [15]Crown‐5 To Give [TiF2([15]crown‐5)][Ti4F18] Containing the Tetrahedral [Ti4F18]2− Ion

“…The energetics in the solid state were estimated by using the equation of Jenkins et al and applying the "volume-based" thermodynamic (VBT) approach. [24,25] [26] To investigate which conditions promote the formation of a stable salt of [Ti 2 F 9 ] À , the DH 298 (s) (% DG 298 (s) ) values of reactions (6) and (7) for salts containing mono-and dications of different sizes were compared (Figure 2). The VBT approach suggests that the monocations generally favor the formation of [cation][Ti 2 F 9 ] (since DH(6) (% DG (6)) is usually > 0), whereas dications favor [cation]-[Ti 4 F 18 ] (since DH(7) (% DG(7)) < 0, i.e., negative and almost independent of the size of the cation).…”

Multiple charge spreading as a generalization of the Bertaut approach to lattice summation of Coulomb series in crystals

“…in agreement with formula (23). The modified electrostatic potential appropriate to (24) is naturally equal tõ…”

“…In particular, this feature results in the fact that the square of the Fourier transform describing the spreading function takes place in the sum over the reciprocal lattice contributing to the Coulomb energy [21,23]. On the other hand, it turns out that a single charge spreading is still sufficient if the electrostatic potential is first considered [24,25,26]. As a result, the Fourier transform of the spreading function, but not its square, arises in the sum over reciprocal lattice vectors contributing to the energy within such a treatment.…”

Convergence peculiarities of lattice summation upon multiple charge spreading generalizing the Bertaut approach

“…Of course, these problems become immaterial if the spreading functions applied to different point charges in a pointcharge lattice do not overlap [12,14]. In this case the sum over direct space is absent and so the error arising upon truncating the summation over reciprocal space is the only subject of interest [15,16,17,18,19].…”