Electron-Pair Distribution in Chemical Bond Formation.

The chemical formation process has been studied from relaxation holes, Δh(u), resulting from the difference between the radial intracule density and the nonrelaxed counterpart, which is obtained from atomic radial intracule densities and the pair density constructed from the overlap of the atomic densities. Δh(u) plots show that the internal reorganization of electron pairs prior to bond formation and the covalent bond formation from electrons in separate atoms are completely recognizable processes from the shape of the relaxation hole, Δh(u). The magnitude of Δh(u), the shape of Δh(u) ∀ u < Req, and the distance between the minimum and the maximum in Δh(u) provide further information about the nature of the chemical bond formed. A computational affordable approach to calculate the radial intracule density from approximate pair densities has been also suggested, paving the way to study electron-pair distributions in larger systems.

The trans Effect in Palladium Phosphine Sulfonate Complexes.

Palladium phosphine sulfonate complexes constitute an efficient family of catalysts for both homopolymerization of ethylene and copolymerization of ethylene with a number of polar monomers. Their catalytic mechanisms have been extensively studied but not fully understood at the electronic structure level. The energy decomposition analysis, complemented with the inspection of the natural orbitals for chemical valence, reveals that their catalytic activity can be rationalized in terms of the so-called trans effect. Furthermore, our analysis shows that the competition for the σ donation of the two ligands PMe3 and L, of the palladium phosphine sulfonate complexes, to the same orbital of Pd in the trans isomer and to different orbitals in the cis isomer is the origin of the trans effect. Although the dominance of the phosphine group prevents an efficient interaction of the ligand L with the Pd atom, the large stabilization gained by the phosphine group renders a very stable trans complex.

Aluminum interaction with glutamate and α-ketoglutarate: a computational study.

Aluminum, although a nonessential element in the human body, has been found to be involved in a variety of diseases. Thus, it has recently been reported that aluminum interferes with the metabolic tricarboxylic acid cycle, in which α-ketoglutarate (α-KG) is involved. α-KG is transformed to glutamate (or vice versa) by glutamate dehydrogenase (GDH). Al(III) inhibits the normal function of GDH, and it was speculated that the reason for this inhibition is triggered by the Al(III)-assisted tautomerization of α-KG from keto to enol. In the present study, we investigate the interaction of both tautomers of α-KG with Al(III) as well the complexation of glutamate to the metal. The results confirm that Al(III) indeed displaces the tautomerization reaction and favors the enol form of α-KG by 28 kcal/mol. However, when citrate is included in the system, the stabilization of the enol tautomer decreases, as this tautomer is only 1.5 kcal/mol more stable than the keto form of α-KG. Finally, possible routes for the complexation of these molecules to Al(III) in a biological environment are discussed; we propose that the ternary complexes formed by Al(III), citrate, and α-KG or glutamate can be the more likely species.

The natural orbital functional theory of the bonding in Cr2, Mo2 and W2.

In this paper, we present for the first time a description based on the natural orbital functional theory (NOFT) of the group VI dimers, namely, Cr(2), Mo(2) and W(2). The PNOF5, Piris Natural Orbital Functional, has been used throughout this work, and the results are compared to multireferential perturbation theory (CASPT2) results. Both methods have been combined with effective core potentials to take into account the scalar relativistic effects. In addition, for Cr(2), an all-electron TZVP quality basis set has also been used to recover the core-valence dynamical correlation. In all cases, PNOF5 shows better behavior than CASPT2, which needs a larger basis set to recover comparable amounts of dynamical correlation. PNOF5 is able to account for the non-dynamical electron correlation, which is responsible for the multireferential nature of these dimers. However, it does not fully recover the dynamical correlation, which is crucial for the accurate description of these challenging potential energy curves. Consequently, PNOF5 predicts longer equilibrium distances and lower dissociation energies than the experimental values. Unlike CASPT2, the PNOF5 results do not significantly improve by using larger basis sets. These new findings represent a major step in the NOFT development, since PNOF5 is the first functional of the natural orbitals reported to yield a chemically balanced and accurate description of these challenging transition metal dimers.

Quantum chemical study of the catalytic activation of methane by copper oxide and copper hydroxide cations.

The activation of methane and its subsequent conversion into more valuable feedstocks under ambient conditions are regarded as one of the major challenges in contemporary catalysis, due to its thermodynamically strong and kinetically inert C-H bond. Several enzymes and synthetic bioinorganic systems perform the activation of C-H bonds in methane and small hydrocarbons, mediated by transition metal mononuclear centers. Among them, monocopper cores and, in particular, CuO(+) and CuOH(+) have been suggested as efficient catalytic centers; this activity has not been experimentally proven until very recently, mainly due to the difficulty to produce sufficient amounts of active species to demonstrate the bond activation processes. The theoretical study presented here provides a thorough quantum chemical description of the activity of both species, together with molecular level insight into the elementary steps of the experimentally observed reactions. Post-HF (CCSD(T), CASPT2) and Density Functional Theory (DFT) methods have been used to unravel detailed electronic and mechanistic aspects of the reaction paths. Our study reveals the decisive role of the oxygen-centered radical in the reactivity of both species, and the improvement of the reactivity as a result of the protonation of the active species.

Pro-oxidant activity of aluminum: promoting the Fenton reaction by reducing Fe(III) to Fe(II).

The possibility for an Al-superoxide complex to reduce Fe(III) to Fe(II), promoting oxidative damage through the Fenton reaction, is investigated using highly accurate ab initio methods and density functional theory in conjunction with solvation continuum methods to simulate bulk solvent effects. It is found that the redox reaction between Al-superoxide and Fe(III) to produce Fe(II) is exothermic. Moreover, the loss of an electron from the superoxide radical ion in the Al-superoxide complex leads to a spontaneous dissociation of molecular oxygen from aluminum, recovering therefore an Al(3+) hexahydrated complex. As demonstrated in previous studies, this complex is again prone to stabilize another superoxide molecule, suggesting a catalytic cycle that augments the concentration of Fe(II) in the presence of Al(III). Similar results are found for Al(OH)(2+) and Al(OH)(2)(+) hydrolytic species. Our work reinforces the idea that the presence of aluminum in biological systems could lead to an important pro-oxidant activity through a superoxide formation mechanism.

Molecular dynamics simulations of iron- and aluminum-loaded serum transferrin: protonation of Tyr188 is necessary to prompt metal release.

Serum transferrin (sTf) carries iron in blood serum and delivers it into cells by receptor-mediated endocytosis. The protein can also bind other metals, including aluminum. The crystal structures of the metal-free and metal-loaded protein indicate that the metal release process involves an opening of the protein. In this process, Lys206 and Lys296 lying in the proximity of each other form the dilysine pair or, so-called, dilysine trigger. It was suggested that the conformational change takes place due to variations of the protonation state of the dilysine trigger at the acidic endosomal pH. In 2003, Rinaldo and Field (Biophys. J. 85, 3485-3501) proposed that the dilysine trigger alone can not explain the opening and that the protonation of Tyr188 is required to prompt the conformational change. However, no evidence was supplied to support this hypothesis. Here, we present several 60 ns molecular dynamics simulations considering various protonation states to investigate the complexes formed by sTf with Fe(III) and Al(III). The calculations demonstrate that only in those systems where Tyr188 has been protonated does the protein undergo the conformational change and that the dilysine trigger alone does not lead to the opening. The simulations also indicate that the metal release process is a stepwise mechanism, where the hinge-bending motion is followed by the hinge-twisting step. Therefore, the study demonstrates for the first time that the protonation of Tyr188 is required for the release of metal from the metal loaded sTf and provides valuable information about the whole process.

Aluminum speciation in biological environments. The deprotonation of free and aluminum bound citrate in aqueous solution.

Citrate is the main low mass molecule chelator of aluminum in serum, and knowledge of the interaction mode of this organic molecule with this cation is necessary to understand aluminum speciation in biosystems. However, the 1:1 complexation of citric acid to Al(III) is a complex process due to the myriad of coordination sites and protonation states of this molecule. Moreover, due to the acidic character of the complex, its entire experimental characterization is elusive. The system is also challenging from a computational point of view, due to the difficulties in getting a balanced estimation of the large range of solvation free energies encountered for the different protonation states of a multiprotic acid in both situations, complexed and uncomplexed with a trivalent cation. Herein, the deprotonation process of the free citric acid in solution and that interacting with Al(III) have been investigated considering all possible coordination modes and protonation states of the citric acid. All the structures were optimized in solution combining the B3LYP density function method with the polarizable continuum IEFPCM model. In addition, different schemes have been employed to obtain reliable solvation energies. Taking into account the most stable isomer of each protonation state, the pK(a) values were computationally estimated for the free citric acid and that interacting with Al(III), showing a good agreement with the experimental data. All these results shed light on how the deprotonation process of the citric acid takes place, and show that Al(III) not only increases the acidity of the molecule, but also changes qualitatively the deprotonation pattern of the citric acid. This information is highly relevant to understand aluminum speciation in biological environments, for which citrate is the main low molecular weight chelator, and responsible for its cellular in-take.

Non-Born-Oppenheimer electronic and nuclear densities for a Hooke-Calogero three-particle model: non-uniqueness of density-derived molecular structure.

We consider the calculation of non-Born-Oppenheimer, nBO, one-particle densities for both electrons and nuclei. We show that the nBO one-particle densities evaluated in terms of translationally invariant coordinates are independent of the wavefunction describing the motion of center of mass of the whole system. We show that they depend, however, on an arbitrary reference point from which the positions of the vectors labeling the particles are determined. We examine the effect that this arbitrary choice has on the topology of the one-particle density by selecting the Hooke-Calogero model of a three-body system for which expressions for the one-particle densities can be readily obtained in analytic form. We extend this analysis to the one-particle densities obtained from full Coulomb interaction wavefunctions for three-body systems. We conclude, in view of the fact that there is a close link between the choice of the reference point and the topology of one-particle densities that the molecular structure inferred from the topology of these densities is not unique. We analyze the behavior of one-particle densities for the Hooke-Calogero Born-Oppenheimer, BO, wavefunction and show that topological transitions are also present in this case for a particular mass value of the light particles even though in the BO regime the nuclear masses are infinite. In this vein, we argue that the change in topology caused by variation of the mass ratio between light and heavy particles does not constitute a true indication in the nBO regime of the emergence of molecular structure.

A computational study on the intriguing mechanisms of the gas-phase thermal activation of methane by bare [Ni(H)(OH)]+.

A detailed computational study on the reaction mechanisms of the thermal activation of methane by the bare complex [Ni(H)(OH)](+) has been conducted. The experimentally observed reaction features, i.e. the ligand exchange Ni(H) → Ni(CH(3)), the H/D scrambling between the incoming methane and the hydrido ligand of the nickel complex, the spectator-like behavior of the OH ligand, and the relatively moderate reaction efficiency of 6% relative to the collision rate of the ion/molecule reaction, can be explained by considering three competing mechanisms, and a satisfactory agreement between experiment and theory has been found.

A QM/MM study of the complexes formed by aluminum and iron with serum transferrin at neutral and acidic pH.

Serum transferrin (sTf) transports iron in serum and internalizes in cells via receptor mediated endocytosis. Additionally, sTf has been identified as the predominant aluminum carrier in serum. Some questions remain unclear about the exact mechanism for the metal release or whether the aluminum and iron show the same binding mode during the entire process. In the present work, simulation techniques at quantum and atomic levels have been employed in order to gain access into a molecular level understanding of the metal-bound sTf complex, and to describe the binding of Al(III) and Fe(III) ions to sTf. First, hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations were carried out in order to analyze the dynamics of the aluminum-loaded complex, taking into account the different pH conditions in blood and into the cell. Moreover, the complexes formed by transferrin with Al(III) and Fe(III) were optimized with high level density functional theory (DFT)/MM methods. All these results indicate that the interaction mode of Al(III) and Fe(III) with sTf change upon different pH conditions, and that the coordination of Al(III) and Fe(III) is not equivalent during the metal intake, transport and release processes. Our results emphasize the importance of the pH on the metal binding and release mechanism and suggest that Al(III) can follow the iron pathway to get access into cells, although once there, it may show a different binding mode, leading to a different mechanism for its release.

Homolytic molecular dissociation in natural orbital functional theory.

The dissociation of diatomic molecules of the 14-electron isoelectronic series N(2), O(2)(2+), CO, CN(-) and NO(+) is examined using the Piris natural orbital functional. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms, in contrast to the fractional charges obtained when using the variational two-particle reduced density matrix method under the D, Q and G positivity necessary N-representability conditions. The chemistry of the considered systems is discussed in terms of their dipole moments, natural orbital occupations and bond orders as well as atomic Mulliken populations at the dissociation limit. The values obtained agree well with accurate multiconfigurational wave function based CASSCF results and the available experimental data.

Pro-oxidant activity of aluminum: stabilization of the aluminum superoxide radical ion.

The pro-oxidant activity of aluminum, a nonredox metal, through superoxide formation is studied by theoretical methods, determining the ESR g-tensor values of O2(•­) with a variety of metals and the reaction energies for Al3+ superoxide affinity in solution. First, the intrinsic ability of aluminum to induce a splitting of the πg levels is compared to that of other significant biological metals, such as Na+, K+, Mg2+, and Ca2+. Additional properties such as bond lengths, ionization potentials, and electron affinities are also determined, and the coherency with the trends observed from ESR g-tensor values is analyzed. As it corresponds to the high charge and its small size, there is a strong interaction between Al3+ and the superoxide. We predict that this strong inherent interaction remains when aluminum is microsolvated. Finally, we analyze the possibility of Al3+ superoxide formation in solution, leading to the conclusion that substitution of the first coordination shell water molecules is plausible, but not of hydroxides. This points to the possibility of Al3+ superoxide formation in solution, which would be pH-dependent. Taking into account the earlier established linear relationship between metal­superoxide interactions and promoting effects in electron-transfer reactions, our work reinforces the idea that the presence of aluminum in biological systems could lead to an important pro-oxidant activity through a superoxide formation mechanism.

A natural orbital functional for multiconfigurational states.

An explicit formulation of the Piris cumulant λΔ,Π matrix is described herein, and used to reconstruct the two-particle reduced density matrix (2-RDM). Then, we have derived a natural orbital functional, the Piris Natural Orbital Functional 5, PNOF5, constrained to fulfill the D, Q, and G positivity necessary conditions of the N-representable 2-RDM. This functional yields a remarkable accurate description of systems bearing substantial (near)degeneracy of one-particle states. The theory is applied to the homolitic dissociation of selected diatomic molecules and to the rotation barrier of ethylene, both paradigmatic cases of near-degeneracy effects. It is found that the method describes correctly the dissociation limit yielding an integer number of electrons on the dissociated atoms. PNOF5 predicts a barrier of 65.6 kcal/mol for the ethylene torsion in an outstanding agreement with Complete Active Space Second-order Perturbation Theory (CASPT2). The obtained occupation numbers and pseudo one-particle energies at the ethylene transition state account for fully degenerate π orbitals. The calculated equilibrium distances, dipole moments, and binding energies of the considered molecules are presented. The values obtained are accurate comparing those obtained by the complete active space self-consistent field method and the experimental data.

Communication: The role of the positivity N-representability conditions in natural orbital functional theory.

The positivity conditions for the N-representability of the reduced density matrices are considered to propose a new natural orbital functional. The Piris reconstruction functional, which is based on an explicit form of the two-particle cumulant λ(Δ,Π) is used to reconstruct the two-particle reduced density matrix. A new approach for Π matrix, satisfying rigorously D, Q, and G necessary conditions, leads to Piris Natural Orbital Functional 4 (PNOF4). The theory is applied to the dissociation of selected diatomic molecules. The equilibrium distances, dipole moments, harmonic frequencies, anharmonicity constants, and binding energies of the considered molecules are presented. The values we have obtained are very accurate results comparing with the experimental data.

Ab initio study of microsolvated Al3+-aromatic amino acid complexes.

The systematic microhydration of Al(3+)-aromatic amino acid complexes is studied by both B3LYP/G03 and PBE/CPMD methods, considering the different binding sites available. The binding affinity of water molecules together with the structural and thermochemical changes triggered by the solvation of the metal are discussed, which are found to be dominated by the charge and size of the metal cation, yielding a very subtle equilibrium between the steric hindrance and the charge transfer to the metal. Some structures previously seen to be unfavored in the gas phase are stabilized upon microhydration, without the need of including bulk solvent effects.

Performance of PNOF3 for reactivity studies: X[BO] and X[CN] isomerization reactions (X = H, Li) as a case study.

Natural Orbital Functional Theory in its PNOF3 implementation is used to investigate the potential energy surfaces of four isomerization reactions: (i) BOH to HBO; (ii) BOLi to LiBO; (iii) CNH to HCN; and (iv) CNLi to LiCN. These reactions are taken as a case study to illustrate the potentiality of PNOF3 to yield the correct topology for reactions sensible to electron correlation. The perfomance of PNOF3 to yield accurate reaction barriers and isomerization energies is also discussed. We have found that PNOF3 shows promising behaviour in the description of these delicate PESs, and yield the correct trends in isomerization energies and reaction barriers, although the latter trends tend to be somewhat lower than the ones calculated at highly correlated levels of theory. The present results show that PNOF3 can give a balanced description of electron correlation in both equilibrium and non-equilibrium structures.

Communications: Accurate description of atoms and molecules by natural orbital functional theory.

The spin-conserving density matrix functional theory is used to propose an improved natural orbital functional. The Piris reconstruction functional, PNOF, which is based on an explicit form of the two-particle cumulant lambda(Delta,Lambda) satisfying necessary positivity conditions for the two-particle reduced density matrix, is used to reconstruct the latter. A new approach Lambda((3)), as well as an extension of the known Delta(alphabeta) to spin-uncompensated systems lead to PNOF3. The theory is applied to the calculation of the total energies of the first- and second-row atoms (H-Ne) and a number of selected small molecules. The energy differences between the ground state and the lowest-lying excited state with different spin for these atoms, and the atomization energies of the considered molecules are also presented. The obtained values agree remarkably well with their corresponding both CCSD(T, full) and experimental values.

Spin conserving natural orbital functional theory.

The natural orbital functional theory is considered for spin uncompensated systems, i.e., systems that have one or more unpaired electrons. The well-known cumulant expansion is used to reconstruct the two-particle reduced density matrix. A new condition to ensure the conservation of the total spin is obtained for the two-particle cumulant matrix. An extension of the Piris natural orbital functional 1 (PNOF1), based on an explicit form for the cumulant, to spin uncompensated systems is also considered. The theory is applied to the calculation of energy differences between the ground state and the lowest lying excited state with different spins for first-row atoms (Li, Be, B, C, N, O, and F) and diatomic oxygen molecule (O(2)). The values we obtained are very accurate results as compared to the CCSD(T) method and the experimental data.

Iterative diagonalization for orbital optimization in natural orbital functional theory.

A challenging task in natural orbital functional theory is to find an efficient procedure for doing orbital optimization. Procedures based on diagonalization techniques have confirmed its practical value since the resulting orbitals are automatically orthogonal. In this work, a new procedure is introduced, which yields the natural orbitals by iterative diagonalization of a Hermitian matrix F. The off-diagonal elements of the latter are determined explicitly from the hermiticity of the matrix of the Lagrange multipliers. An expression for diagonal elements is absent so a generalized Fockian is undefined in the conventional sense, nevertheless, they may be determined from an aufbau principle. Thus, the diagonal elements are obtained iteratively considering as starting values those coming from a single diagonalization of the matrix of the Lagrange multipliers calculated with the Hartree-Fock orbitals after the occupation numbers have been optimized. The method has been tested on the G2/97 set of molecules for the Piris natural orbital functional. To help the convergence, we have implemented a variable scaling factor which avoids large values of the off-diagonal elements of F. The elapsed times of the computations required by the proposed procedure are compared with a full sequential quadratic programming optimization, so that the efficiency of the method presented here is demonstrated.