Density functional geometry optimization and energy calculations of calcium(II)-triphosphate complexes. Polyphosphates as possible dissolving agents for calcium pyrophosphate dihydrate crystals in chondrocalcinosis disease

Abstract

Geometry optimizations and energy calculations have been carried out via molecular orbital methods at the density functional B3LYP/LANL2DZ level on the molecules PO3-, OPO3(3-), HOPO3(2-), CH3OPO3(2-), H(CH3OPO3)-, O(PO3)2(4-), HO(PO3)2(3-), CH2(PO3)2(4-), (CH3OPO2)O(PO3)3-, O(PO3)3(5-), HO(PO3)3(4-), (PO3)3(3-), (CH3OPO2)O(PO3)2(4-), [Mg[O(PO3)2)]]2-, [Ca[O(PO3)2]]2-, [Ca[CH2(PO3)2]]2-, [Ca[CH3OPO2)O(PO3)]]-, [Ca(PO3)3]-, [Ca[O(PO3)3]]3-, and [Ca[CH3OPO2)O(PO3)2]]2- with the aim to find reliable and easily accessible computational methods to simulate some phosphate-containing molecules of importance for the living cells and to study the energetics for protonation and metal-complex formation reactions. The analysis is part of a general investigation on phosphate-containing molecules as potential dissolving agents for calcium pyrophosphate dihydrate (CPPD) crystals which deposit in certain articular diseases. The basis set was expanded to 6-31G** for the P atoms for all the molecules investigated and to 6-31G* for the O atoms for OPO3(3-). Calculations at the semiempirical MNDO/d level were also carried out for comparison purposes on the free ligand molecules and on [Mg[O(PO3)2]]2-. The density functional analysis reproduced well the geometry found at the solid state via X-ray diffraction. The analyses of the geometrical parameters and the total electronic energy of the molecules shows that O(PO3)2(4-) and other di- and tri-phosphates are versatile ligands for divalent metal ions like Ca2+. The computed P-O-P bond angle for free O(PO3)2(4-) is 180 degrees and the conformation of the two PO3- groupings is staggered along the P...P vector. The linear arrangement for P-O-P is assisted by P-O pi interactions. The bending of the P-O-P angle when accompanied by a slight P-O(b) elongation requires a very small amount of energy; 4.65 kcal/mol to pass from 180 to 140 degrees , as calculated at the DFT level. The computed Ca-O and Mg-O bond distances for [M[O(PO3)2]]2- are 2.378 and 2.079A, when the metal ions link two oxygen atoms from each PO3 group. The computed Ca-O bond lengths for [Ca[CH3OPO2)O(PO3)]]- are 2.482 (PalphaO2) and 2.358A (PbetaO2), showing a significant lengthening for Ca-OPalpha, when compared to the pyrophosphate derivative. The Ca-O bond lengths for [Ca[O(PO3)3]]3- and [Ca[CH3OPO2)O(PO3)2]]2- are 2.251A and 2.525 (PalphaO2), 2.407 and 2.338 (PbetaO2), and 2.251 and 2.228A (PgammaO2), showing a shortening for the Ca-OPgamma bond upon methylation. The (Pbeta)O-Pgamma bond length increases significantly (0.09 A) upon Ca(II) coordination to (CH3OPO2)O(PO3)2(4-) via all the three PO3 groups. This latter result suggests that metal complexes of linear organic-triphosphates have a larger tendency to release the PgammaO3 group when compared to the free ligand molecules. The electronic contribution to the energy of the complex formation reaction for [Ca[CH2(PO3)2]]2- is only slightly higher (some 1.8 kcal) than that for [Ca[O(PO3)2]]2-; but is much higher (some 63 kcal) than that relevant to the formation of [Ca[CH3OPO2)O(PO3)2]]2-. (ABSTRACT TRUNCATED)