Structure and electronic configurations of the intermediates of water oxidation in blue ruthenium dimer catalysis

Catalytic O(2) evolution with cis,cis-[(bpy)(2)(H(2)O)Ru(III)ORu(III)(OH(2))(bpy)(2)](4+) (bpy is 2,2-bipyridine), the so-called blue dimer, the first designed water oxidation catalyst, was monitored by UV-vis, EPR, and X-ray absorption spectroscopy (XAS) with ms time resolution. Two processes were identified, one of which occurs on a time scale of 100 ms to a few seconds and results in oxidation of the catalyst with the formation of an intermediate, here termed [3,4]'. A slower process occurring on the time scale of minutes results in the decay of this intermediate and O(2) evolution. Spectroscopic data suggest that within the fast process there is a short-lived transient intermediate, which is a precursor of [3,4]'. When excess oxidant was used, a highly oxidized form of the blue dimer [4,5] was spectroscopically resolved within the time frame of the fast process. Its structure and electronic state were confirmed by EPR and XAS. As reported earlier, the [3,4]' intermediate likely results from reaction of [4,5] with water. While it is generated under strongly oxidizing conditions, it does not display oxidation of the Ru centers past [3,4] according to EPR and XAS. EXAFS analysis demonstrates a considerably modified ligand environment in [3,4]'. Raman measurements confirmed the presence of the O-O fragment by detecting a new vibration band in [3,4]' that undergoes a 46 cm(-1) shift to lower energy upon (16)O/(18)O exchange. Under the conditions of the experiment at pH 1, the [3,4]' intermediate is the catalytic steady state form of the blue dimer catalyst, suggesting that its oxidation is the rate-limiting step.     

Theoretical study of O--O single bond formation in the oxidation of water by the ruthenium blue dimer

The first key step in the oxidation of water to O(2) by the oxidized species [(bpy)(2)(O)Ru(V)ORu(V)(O)(bpy)(2)](4+) of the Ru blue dimer is studied using density functional theory (DFT) and an explicit solvent treatment. In the model reaction system [L(2)(O)Ru(V)ORu(V)(O)L(2)](4+)·(H(2)O)(4)·W(76), the surrounding water solvent molecules W are described classically while the inner core reaction system is described quantum mechanically using smaller model ligands (L). The reaction path found for the O--O single bond formation involves a proton relay chain: direct participation of two water molecules in two proton transfers to yield the product [L(2)(HOO)Ru(IV)ORu(IV)(OH)L(2)](4+)·(H(2)O)(3)·W(76). The calculated ～3 kcal/mol reaction free energy and ～15 kcal/mol activation free energy barrier at 298 K are consistent with experiment. Structural changes and charge flow along the intrinsic reaction coordinate, the solvent's role in the reaction barrier, and their significance for water oxidation catalysis are examined in detail.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Explicit correlation and basis set superposition error: the structure and energy of carbon dioxide dimer

We have investigated the slipped parallel and t-shaped structures of carbon dioxide dimer [(CO(2))(2)] using both conventional and explicitly correlated coupled cluster methods, inclusive and exclusive of counterpoise (CP) correction. We have determined the geometry of both structures with conventional coupled cluster singles doubles and perturbative triples theory [CCSD(T)] and explicitly correlated cluster singles doubles and perturbative triples theory [CCSD(T)-F12b] at the complete basis set (CBS) limits using custom optimization routines. Consistent with previous investigations, we find that the slipped parallel structure corresponds to the global minimum and is 1.09 kJ mol(-1) lower in energy. For a given cardinal number, the optimized geometries and interaction energies of (CO(2))(2) obtained with the explicitly correlated CCSD(T)-F12b method are closer to the CBS limit than the corresponding conventional CCSD(T) results. Furthermore, the magnitude of basis set superposition error (BSSE) in the CCSD(T)-F12b optimized geometries and interaction energies is appreciably smaller than the magnitude of BSSE in the conventional CCSD(T) results. We decompose the CCSD(T) and CCSD(T)-F12b interaction energies into the constituent HF or HF CABS, CCSD or CCSD-F12b, and (T) contributions. We find that the complementary auxiliary basis set (CABS) singles correction and the F12b approximation significantly reduce the magnitude of BSSE at the HF and CCSD levels of theory, respectively. For a given cardinal number, we find that non-CP corrected, unscaled triples CCSD(T)-F12b/VXZ-F12 interaction energies are in overall best agreement with the CBS limit.     

Theoretical basis of the empirical reaction field approximations through continuum model

We derive from exact integral equations of classical electrostatics some approximate expressions of the interaction energy of a point charge distribution with a dielectric medium. We show how they can be used for computing the wave functions of solvated species imbedded in cavities formed by interlocking spheres in a polarizable continuum. We discuss the relation between these formulae and the ones proposed earlier on empirical basis and we especially emphasize the improvement that they bring out.     

Contribution of water dimer absorption to the millimeter and far infrared atmospheric water continuum

We present a rigorous calculation of the contribution of water dimers to the absorption coefficient alpha(nu,T) in the millimeter and far infrared domains, over a wide range (276-310 K) of temperatures. This calculation relies on the explicit consideration of all possible transitions within the entire rovibrational bound state manifold of the dimer. The water dimer is described by the flexible 12-dimensional potential energy surface previously fitted to far IR transitions [C. Leforestier et al., J. Chem. Phys. 117, 8710 (2002)], and which was recently further validated by the good agreement obtained for the calculated equilibrium constant Kp(T) with experimental data [Y. Scribano et al., J. Phys. Chem. A. 110, 5411 (2006)]. Transition dipole matrix elements were computed between all rovibrational states up to an excitation energy of 750 cm(-1), and J=K=5 rotational quantum numbers. It was shown by explicit calculations that these matrix elements could be extrapolated to much higher J values (J=30). Transitions to vibrational states located higher in energy were obtained from interpolation of computed matrix elements between a set of initial states spanning the 0-750 cm(-1) range and all vibrational states up to the dissociation limit (approximately 1200 cm(-1)). We compare our calculations with available experimental measurements of the water continuum absorption in the considered range. It appears that water dimers account for an important fraction of the observed continuum absorption in the millimeter region (0-10 cm(-1)). As frequency increases, their relative contribution decreases, becoming small (approximately 3%) at the highest frequency considered nu=944 cm(-1).     

Complete basis set model chemistry applied to molecules of increasing molecular complexity: Thermochemical properties of organic sulfur derivatives

To estimate the thermochemical properties, bond dissociation energies and atomization energies of sulfur organic derivatives, the complete basis set (CBS) method was employed at the lower computational level (CBS‐4) owing to the large molecular size of a number of the molecules chosen. By comparison with experimental values, calculated values of thermochemical properties are subject to error, which increases in line with the increase in molecular complexity. The main source of error affecting the calculated enthalpy of formation stems from the difference between the energy of the molecule and that of the single atoms: the greater the size of the molecule, the greater the accumulation of error. By acting on the empirical correction to the CBS energy and minimizing the error due to the contribution of the single atoms to the dissociation energy a parameter d_i for each atom i is obtained. Application of these corrections does not greatly affect the heats of formation of the small molecules included in test sets employed for previous comparisons of calculated and experimental values, while there is a great improvement in the case of large molecules, for example, diphenyl disulfide. The mean absolute deviation turns out to be 2.52, which is greater than that obtained in recent reexaminations of model chemistry methods including the G3 and G3(MP3) approaches. The improvement in the results calculated for large molecules, whose heats of formation are calculated with large errors at the CBS‐4 level, in comparison also with the CBS‐4M version, justify our approach. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1405–1418, 2000     

Estimating the basis set superposition error in the CCSD(T)(F12) explicitly correlated method using the example of a water dimer

Changes in the basis set superposition errors upon transitioning from conventional CCSD(T) to the CCSD(T)(F12) explicitly correlated method is studied using the example of a water dimer. A comparison of the compensation errors for CCSD(T) and CCSD(T)(F12) reveals a substantial reduction in the superposition error upon use of the latter. Numerical experiments with water dimers show it is possible theoretically predict an equilibrium distance between oxygen atoms that is similar to the experimental data (2.946 Å), as is the predicted energy of dissociation of a dimer (5.4 ± 0.7 kcal/mol). It is found that the structural and energy parameters of hydrogen bonds in water dimers can be calculated precisely even with two-exponential correlation-consistent basis sets if we use the explicitly correlated approach and subsequently correct the basis set superposition error.     

Formulation of the LCAS MS SCF method within the Gaussian basis set

Within the presented LCAS MS (linear combination of atomic spinors–molecular spinors) SCF formalism both large and small components of the spinor radial parts have been expanded within the Gaussian basis set. The respective expressions for matrix elements as well as for one- and two-electron integrals are given.     

Generation of a basis set for the calculation of molecular magnetic properties

Completeness conditions have been applied in the theory of molecular magnetic properties to determine the best gauge for a given basis set. They can similarly be used to optimise the basis for a fixed gauge origin. Test results indicate that the gauge dependence of the calculated properties can be significantly reduced in this way.     

Fast assembly of Fock matrices utilising symmetry properties of the basis set

A method of assembling the elements of the Fock matrix is described which is a modification of that due to Dacre. Lists of symmetry equivalent one-elec     

On "the complete basis set limit" and plane-wave methods in first-principles simulations of water

Water structure, measured by the height of the first peak in oxygen-oxygen radial distributions, is converged with respect to plane-wave basis energy cutoffs for ab initio molecular dynamics simulations, confirming the reliability of plane-wave methods.     

The basis set superposition error in multilevel methods: a test on the H2O and HF dimer

The basis set superposition error (BSSE) is often very important in the accurate calculation of dimerization energies. Accurate prediction of thermochemical properties requires appropriate consideration of the basis set incompleteness error. Multilevel methods introduce adjustable parameters to reproduce experimental data, that is, the higher level correction (HLC) in G3 and adjustable coefficients in the MCCM. However, the HLC term is cancelled out and the adjustable coefficients in the MCCM do not remove the BSSE completely. We have calculated the BSSE involved in the multilevel methods. The H₂O and HF dimer systems were used as a test case. This study shows that empirical coefficients do reduce the BSSE in some cases and an MCCM with good parameters can be used to reproduce dimerization energies within chemical accuracy without the BSSE correction.     

An application of the method of conjugate gradients to the calculation of minimal basis set localized orbitals

Using an STO -3G basis set, energy localized molecular orbitals (LMO ) were determined for the ten electron series HF, H₂O, NH₃, and CH₄ as well as for CH₃OH and C₂H₂F₂. The method of conjugate gradients is shown to be a viable alternative to other non-eigenvalue methods. The characterization of the LMO in terms of first and second moment measures indicates that the STO -3G basis set LMO may be accurately correlated to larger sp basis set LMO . Also, it is shown that the first and second moment measures display a good linear correlation with the classical concept of electronegativity.     

On finite basis set implementation of the exchange-only optimized effective potential method

In this paper, we analyze a structure of the basis set optimized effective potential (OEP) equations from the Fredholm alternative point of view and present one of possible numerical schemes to solve the OEP equation in a stable manner. The solution is constructed as a sum of a unique solution on the subspace of eigenfunctions of the response matrix with non-zero eigenvalues and a non-unique solution on a counterpart subspace with singular eigenvalues. Non-uniqueness of a solution is exploited to obtain a local effective potential that satisfies the condition for the highest occupied molecular orbital (HOMO) without restricting the variational freedom of the optimization procedure. Unlike the existing methods we implement the HOMO condition using the functions of the null-subspace. Numerical results for the total and orbital energies based on the proposed scheme are close to the corresponding literature data.