Cumulative coordinates for approximations of high‐order atomic multipole moments in aluminosilicate and aluminophosphate sieves*

Abstract

A scheme to obtain approximate analytical functions for the atomic distributed multipole moments of the crystallographically different atoms within aluminosilicate and aluminophosphate sieves is discussed. Respective atomic multipole moments are derived within the CRYSTAL95 ab initio periodic Hartree-Fock code with different basis sets, from minimal STO-3G to 6-21G * . In order to illustrate the possible applications, distributed analyses are carried out for various structural models from all-siliceous zeolites and aluminophosphates with ratio Al/P = 1 to hydrogen forms of aluminosilicates. Simple approximate forms based on charge and geometry coordinates are proposed for the high-order moments of each atom, which are further required for the calculation of the electrostatic field within the structures. The possibility to use this analytical approach to evaluate the electrostatic field within embedded cluster models is also shortly discussed.

Quick scheme for evaluation of atomic charges in arbitrary aluminophosphate sieves on the basis of electron densities calculated with DFT methods

“…3 static deformation densities calculated at the PHF level 3,43 do not allow a correct representation of the experimental ED maximum along the AlÀ ÀO bond in berlinite, whereas a peak was observed experimentally for the AlO 6 moiety with a smaller bond ED value in AlPO 4 -15. 44 Despite the sharp difference between the ionicities obtained here and in literature, 3,43 6-21G** provides a maximum along AlÀ ÀO for both AlO 4 Together with the relative error ( in Figs. 1-3) in the fitted charges, it is clear that the absolute error values are also important.…”

“…32 A general way to calculate AMMs was already shown starting from the Mulliken charges. 4,5 Herein, simple analytical charge dependences versus the geometries of the nearest atoms were fitted to the calculated charges of seven AlPO models 5 computed with CRYSTAL98 using a series of basis sets from STO-3G, 3-21G, 6-21G** to 8-511*(Al)/8-521*(P)/8-411*(O) at the PDFT level. These basis sets result in extremely different calculated ionicities.…”

“…19 Could the atomic octupoles and hexadecapoles be calculated with, for example, the new version of TOPXD, then one could propagate the high order AMMs on the basis of the Bader charges as developed with the Mulliken scheme 4,5 using the Stone type equation on distributed moments. 20 More precisely, the Bader charges could be used in the CC expression 4,5 to approximate all the Bader type AMMs to achieve a quantitative estimation of the EP/EF as it was realized with the Mulliken partition scheme. [4][5][6] On this basis, the Mulliken partition remains, till now, the unique available practical method for a quantitative evaluation of the EP and EF in crystals in absence of high order AMMs calculated with other schemes.…”

“…3 Therefore, QM/MM approaches should be clearly completed with accurate estimations of the electrostatic part such as proposed with the cumulative coordinate (CC) technique. 4,5 An important initial step in the application of the CC technique 4,5 is the evaluation of the atomic charges on the basis of the electron density (ED). After this step, the CC technique 4 can be considered to calculate high order atomic multipole moments (AMMs) and to evaluate the electrostatic potential (EP).…”

“…4,5 An important initial step in the application of the CC technique 4,5 is the evaluation of the atomic charges on the basis of the electron density (ED). After this step, the CC technique 4 can be considered to calculate high order atomic multipole moments (AMMs) and to evaluate the electrostatic potential (EP). 6 Let us add that the development of fast methods to simulate the EP can, additionally, help the exploration of the structure-dependent potential gradients in the channels and cages of molecular sieves and the assignment of the experimental IR spectra of adsorbed probe molecules.…”