phosphate hydrate complexes of singly and doubly charged magnesium ions: Structure,energies, and spin states

For mixed magnesium phosphate hydrate complexes containing Mg²⁺ and Mg⁺ cations and HPO₄²⁻, HPO₄⁻, and H₂P₂O₇²⁻ anions, theoretical analysis of the electronic structure and energies has been performed at the model level in order to predict the actual role of these systems in various reactions that occur in the catalytic sites of ATP synthesizing enzymes. The calculations (DFT/B3LYP, MP2 with the 6–31G* basis set) of isolated aqua complexes Mg(H₂O) _n ^p (n = 1−6, p = 0, +1, +2) show that their relative stability monotonically increases with increasing n in each series and sharply decreases at a given n in going from the charged systems of Mg²⁺ (4–16 eV) and Mg⁺ (2–7 eV) to the neutral systems of Mg (<2 eV). An even higher stability is predicted for mixed magnesium complexes. The energies of fragmentation of mixed Mg²⁺ complexes into singlet phosphate and Mg²⁺-containing fragments at n = 0–4 are within 6–27 eV, and the energies of fragmentation into the corresponding radical ions are within 3–10 eV; for the Mg⁺ complexes, the fragmentation energies are also high (6–14 eV). The reasons for the enhanced stability of the complexes of both types have been analyzed with allowance for the predicted specific features of the electron density redistribution upon complex formation. Typical changes in the geometry of the P- and Mg-containing fragments caused by formation of mixed complexes have been discussed in the framework of the vibronic model of heteroligand systems. The high stability of all mixed magnesium complexes relative to various fragmentation products presumably rules out any dissociative processes in them in the course of ATP synthesis with the participation of phosphorylating enzymes.     

Effect of the Hydrostatic Pressure on the Thermodynamics of Structural Phase Transition in Quasi-One-Dimensional Ferroelectrics Pb(H/D)PO<Subscript>4</Subscript>: Quantum Chemical Analysis

The change in the structural phase transition thermodynamics of lead hydrogen phosphate (LHP) and lead deuterium phosphate (LDP) depending on the external hydrostatic pressure was studied using the Ising pseudo-spin model taking account of tunneling and long-range effects. The same simplified version of the quantum chemical approach that we proposed for studying these systems at atmospheric pressure was used. The critical transition temperatures T_c were estimated for both systems and the considerable decrease in T_c observed experimentally was explained in each case. The calculations gave an estimate for the width of the barrier in LHP (≈0.35 Å); no experimental neutron diffraction value for this barrier is available from the literature.     

Magnesium isotope effects in enzymatic phosphorylation

Recent discovery of magnesium isotope effect in the rate of enzymatic synthesis of adenosine triphosphate (ATP) offers a new insight into the mechanochemistry of enzymes as the molecular machines. The activity of phosphorylating enzymes (ATP-synthase, phosphocreatine, and phosphoglycerate kinases) in which Mg(2+) ion has a magnetic isotopic nucleus 25Mg was found to be 2-3 times higher than that of enzymes in which Mg(2+) ion has spinless, nonmagnetic isotopic nuclei 24Mg or 26Mg. This isotope effect demonstrates unambiguously that the ATP synthesis is a spin-dependent ion-radical process. The reaction schemes, suggested to explain the effect, imply a reversible electron transfer from the terminal phosphate anion of ADP to Mg(2+) ion as a first step, generating ion-radical pair with singlet and triplet spin states. The yields of ATP along the singlet and triplet channels are controlled by hyperfine coupling of unpaired electron in 25Mg+ ion with magnetic nucleus 25Mg. There is no difference in the ATP yield for enzymes with 24Mg and 26Mg; it gives evidence that in this reaction magnetic isotope effect (MIE) operates rather than classical, mass-dependent one. Similar effects have been also found for the pyruvate kinase. Magnetic field dependence of enzymatic phosphorylation is in agreement with suggested ion-radical mechanism.     

Chemical bond inside endohedral complexes H@C59B and H@C59P

The geometries, electronic structures, and spin densities on the atoms of paramagnetic heterofullerenes C₅₉X (X = B, P) and their endohedral derivatives H@C₅₉X were obtained from B3LYP/6-31G* density functional calculations. The encapsulated hydrogen atom can form a C-H bond inside the fullerene sphere. The energies of the C-H(endo) bonds are 40–50 kcal mol⁻¹ lower than those of the corresponding exo-bonds. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1239–1243, July, 2007.     

Anomalous values of 〈Ŝ2〉 before and after annihilation of the first spin contaminant in UHF wave function

We present a number of molecular systems for which the average values 〈?²〉 before and after annihilation of the first spin contaminant in the wave function of the unrestricted Hartree-Fock method are anomalously large (they substantially exceed the expected value S (S + 1)). An example of such systems is N@C₂₀, for the doublet state of which the 〈?²〉 values are equal to 4.2595 before and 13.1390 after annihilation, respectively (calculated by UHF/6-31G* method). We show that four, at the least, spin multiplets (S′ = S, S + 1, S + 2, S + 3) contribute comparatively to the wave function of such systems. The relations are derived allowing one to estimate the contributions of the highest multiplets basing on the average values of 〈?²〉 before and after annihilation of the first spin contaminant.     

Spin density distribution in paramagnetic azafullerene

Hyperfine coupling (HFC) constants for ¹⁴N and ¹³C nuclei in azafullerene C₅₉N (1) were calculated. The HFC constants for the ¹H and ¹³C nuclei in the ^·CH₃ radical were calculated as functions of the pyramidal distortion of the angles at the carbon atom. Using this angular dependence, the spin density distribution of the unpaired -electron in 1 was determined. The spin density of the unpaired -electron in 1 is mainly localized around the nitrogen atom.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 2372–2374, November, 2004.     

Endofullerenes: size effects on structure and energy

The geometric and energy characteristics of endohedrals X@C _n (X = He, Ne, Ar; n = 20, 24, 30, 32, 40, 50, 60) were calculated by the density functional theory. The insertion of the helium atom leads to only a slight change in the geometry of the fullerene cage of the endohedrals. As the size of the trapped atom increases, the average C—C bond length increases in proportion to the radii of these atoms (by 0.05 for Ne@C₂₀ and 0.12 for Ar@C₂₀). The inclusion energies of endofullerenes and the pressure of the cage exerted on the endo atom were calculated for all the above-mentioned endohedrals.     

Quantum-chemical simulation of unit process for the oxidation reactions of ethylene and its derivatives invoving <Superscript>1</Superscript>O<Subscript>2</Subscript> (<Superscript>1</Superscript>Δg)

The results of simulation of oxidation reactions of ethylene derivatives with different substituents (F atoms, CH₃O and CH₃ groups) and butadiene molecule with participation of ¹O₂ (¹Δg) have shown the possibility to realize different routes for the majority of the considered reactions. The largest product variety is obtained for butadiene and CH₃ derivatives of ethylene. For butadiene, along with 1,2-cycloaddition reactions resulting in four-membered dioxetane (which is realized in all cases), the possibility to form six-membered cyclic epidioxides (1,4-addition) and diepoxide products with two three-membered rings (epoxidation) has been found. The formation of hydroperoxide forms along with 1,2-addition reactions is also possible for all CH₃ derivatives of ethylene. Formation conditions and relative stability of the noted products have been analyzed for each case and certain features of the revealed reaction pathways with the transfer of two oxygen atoms have been discussed.     

Quantum chemical calculations of N@Cn endofullerenes (n ≤ 60)

The geometric parameters and energy characteristics of small endofullerenes N@C_n (n = 20, 24, 30, 32, 40, 50) and N@C₆₀ in the quartet ground state were calculated by the B3LYP/6-31G* method. The N atom is located at the center of the carbon cage in all molecules except N@C₃₀, where it is bound to the cage wall. Encapsulation of nitrogen atom has little effect on the fullerene cage geometry for n = 40, 50, and 60. No significant charge transfer from the N endo-atom to the cage was revealed for all the N@C_n endofullerenes studied. The calculated spin density on the nitrogen endo-atom increases as the size (n) of the carbon cage increases. The relative stabilities of C_n fullerenes and corresponding endofullerenes N@C_n are discussed. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 15–20, January, 2006.