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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 3-, [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 semi- empirical 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)3 4- is 180° 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-Oπ 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°, 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 2.079Å, 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 (PαO2) and 2.358Å (PβO2), showing a significant lengthening for Ca-OPα, 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 2.251Å and 2.525 (PαO2), 2.407 and 2.338 (PβO2), and 2.251 and 2.228Å (PγO2), showing a shortening for the Ca-OPγ bond upon methylation. The (Pβ)O-Pγ bond length increases significantly (0.09 Å) 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 PγO3 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-. Therefore the linear methyltriphosphates (and reasonably nucleoside triphosphates) are predicted to form metal complexes which are less stable than diphosphonate or inorganic diphosphate ligands, at least in the case the organic moiety does not have any appreciable coordination ability toward the metal. The energy of complex formation for [Ca{O(PO3)3}]3- is much higher than that for [Ca{O(PO3)2}]2- and [Ca(PO3)3}]− (some 116 and 345 kcal, respectively). This is in part a rationale for the high dissolving ability (DA) toward CPPD crystals, shown by solutions of pentasodium tripolyphosphate. DA values of 65.4±3.0 μg Ca/mL were detected, via atomic absorption spectroscopy, in solutions of Na5{O(PO3)3} 0.06 M after digestion (1.00 h, 37°C, pH 7.4) in the presence of CPPD crystals. Efficient non-toxic dissolving agents for CPPD crystals are needed to cure chondrocal-cinosis desease. The semi-empirical computations gave correct overall optimized structures and conformations for, at least, the free not-substituted ligands and the relevant Mg(II)-com- plexes. The optimized structure for [Mg{O(PO3)2}]2- has computed P-O(t) and P-O(d) bond distances of 1.503 and 1.598Å, in perfect agreement with the results from DFT calculations.
