The hydration of the uranyl dication: Incorporation of solvent effects in parallel density functional calculations with the program PARAGAUSS

The parallel density functional program PARA GAUSS has been extended by a tool for computing solvent effects based on the conductor‐like screening model (COSMO). The molecular cavity in the solvent is constructed as a set of overlapping spheres according to the GEPOL algorithm. The cavity tessellation scheme and the resulting set of point charges on the cavity surface comply with the point group symmetry of the solute. Symmetry is exploited to reduce the computational effort of the solvent model. To allow an automatic geometry optimization including solvent effects, care has been taken to avoid discontinuities due to the discretization (weights of tesserae, number of spheres created by GEPOL). In this context, an alternative definition for the grid points representing the tesserae is introduced. In addition to the COSMO model, short‐range solvent effects are taken into account via a force field. We apply the solvent module to all‐electron scalar‐relativistic density functional calculations on uranyl, UO₂²⁺, and its aquo complexes in aqueous solution. Solvent effects on the geometry are very small. Based on the model [UO₂(H₂O)₅]²⁺, the solvation energy of uranyl is estimated to be about ?400 kcal/mol, in agreement with the range of experimental data. The major part of the solvation energy, about ?250 kcal/mol, is due to a donor–acceptor interaction associated with a coordination shell of five water ligands. One can interpret this large solvation energy also as a compounded effect of an effective reduction of the uranyl moiety plus a solvent polarization. The energetic effect of the structure relaxation in the solution is only about 8 kcal/mol. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

The heat of formation of gaseous PuO(2)2+ from relativistic density functional calculations

Using a set of model reactions, we estimated the heat of formation of gaseous PuO2(2+) from quantum-chemical reaction enthalpies and experimental heats of formation of reference species. To this end, we carried out relativistic density functional calculations on the molecules PuO(2)2+, PuO2, PuF6, and PuF4. We used a revised variant (PBEN) of the Perdew-Burke-Ernzerhof gradient-corrected exchange-correlation functional, and we accounted for spin-orbit interaction in a self-consistent fashion. As open-shell Pu species with two or more unpaired 5f electrons are involved, spin-orbit interaction significantly affects the energies of the model reactions. Our theoretical estimate for the heat of formation DeltafH degree 0(PuO2(2+),g), 418+/-15 kcal mol-1, evaluated using plutonium fluorides as references, is in good agreement with a recent experimental result, 413+/-16 kcal mol-1. The theoretical value connected to the experimental heat of formation of PuO2(g) has a notably higher uncertainty and therefore was not included in the final result.     

Analytical energy gradient evaluation in relativistic and nonrelativistic density functional calculations

The expressions of analytical energy gradients in density functional theory and their implementation in programs are reported. The evaluation of analytical energy gradients can be carried out in the fully 4-component relativistic, approximate relativistic, and nonrelativistic density functional calculations under local density approximation or general gradient approximation with or without frozen core approximation using different basis sets in our programs. The translational invariance condition and the fact that the one-center terms do not contribute to the energy gradients are utilized to improve the calculation accuracy and to reduce the computational effort. The calculated results of energy gradients and optimized geometry as well as atomization energies of some molecules by the analytical gradient method are in very good agreement with results obtained by the numerical derivative method.     

Complexation of the carbonate, nitrate, and acetate anions with the uranyl dication: density functional studies with relativistic effective core potentials

The structures and vibrational frequencies of uranyl carbonates, [UO2(CO3)n](2-2n) and [(UO2)3(CO3)6]6-, uranyl nitrates, [UO2(NO3)n](2-n), and uranyl acetates, [UO2(CH3COO)n](2-n) (n = 1,2,3) have been calculated by using local density functional theory (LDFT). Only bidentate ligand coordination modes to the uranyl dication have been modeled. The calculated structures and frequencies are compared to available experimental data, including IR, Raman, X-ray diffraction, and EXAFS solution and crystal structure data. The energetics of ligand binding have been calculated using the B3LYP hybrid functional. In general, the structural and vibrational results at the LDFT level are in good agreement with experimental results and provide realistic pictures of solution phase and solid-state behavior. For the [UO2(CO3)3]6- anion, calculations suggest that complexity in the CO3(2-) stretching signature upon complexation is due to the formation of C=O and C-O domains, the latter of which can split by as much as 300 cm(-1). Assessment of the binding energies indicate that the [UO2(CO3)2]2- anion is more stable than the [UO2(CO3)3]4- anion due to the accumulation of excess charge, whereas the tri-ligand species are the most stable in the nitrate and acetate anions.     

Scalar relativistic all-electron density functional calculations on periodic systems

Scalar relativistic effects are included in periodic boundary conditions calculations with Gaussian orbitals. This approach is based on the third-order Douglas-Kroll-Hess approximation, allowing the treatment of all electrons on an equal footing. With this methodology, we are able to perform relativistic all-electron density functional calculations using the traditional local spin-density and generalized gradient approximations (GGA), as well as meta-GGA and hybrid density functionals. We present benchmark results for the bulk metals Pd, Ag, Pt, and Au, and the large band gap semiconductors AgF and AgCl.     

Role of solvation in the reduction of the uranyl dication by water: a density functional study

We have studied the solvation of uranyl, UO(2)(2+), and the reduced species UO(OH)(2+) and U(OH)(2)(2+) systematically using three levels of approximation: direct application of a continuum model (M1); explicit quantum-chemical treatment of the first hydration sphere (M2); a combined quantum-chemical/continuum model approach (M3). We have optimized complexes with varying numbers of aquo ligands (n = 4-6) and compared their free energies of solvation. Models M1 and M2 have been found to recover the solvation energy only partially, underestimating it by approximately 100 kcal/mol or more. With our best model M3, the calculated hydration free energy Delta(h)G degrees of UO(2)(2+) is about -420 kcal/mol, which shifts to about -370 kcal/mol when corrected for the expected error of the model. This value agrees well with the experimentally determined interval, -437 kcal/mol < Delta(h)G degrees < -318 kcal/mol. Complexes with 5 and 6 aquo ligands have been found to be about equally favored with models M2 and M3. The same solvation models have been applied to a two-step reduction of UO(2)(2+) by water, previously theoretically studied in the gas phase. Our results show that the solvation contribution to the reaction free energy, about 60 kcal/mol, dominates the endoergicity of the reduction.     

Spin densities in two-component relativistic density functional calculations: noncollinear versus collinear approach

With present day exchange-correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar-relativistic calculations, the spin density can be defined conventionally, but if spin-orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the "spin density" is. In many applications, a fixed quantization axis is used to define the spin density ("collinear approach"), but one can also use the length of the local spin magnetization vector without any reference to an external axis ("noncollinear approach"). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange-correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn-Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I+2 and PbF indicate that the error introduced by the collinear approximation is approximately 0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort.     

Vibrational spectroscopy investigation and density functional theory calculations on N-benzoylhydrazine ligand and the corresponding uranyl complex

Infrared spectra of N-benzoylhydrazine (BHZ) phCONHNH2 and its uranyl complex have been studied in the 4000-50 cm(-1) frequency range. Complete equilibrium geometry of the ligand molecule have been determined by DFT and BLYP/6-31G* force field calculations. Theoretical calculations reveal the existence of a keto tautomer. No enol form is present in the molecule in the solid. A complete vibrational assignment of the solid state IR and Raman spectra of BHZ was performed on the basis of normal coordinate analysis of a single molecule. The coordination of oxygen and nitrogen centers of BHZ to UO2(II) has been confirmed by study of the IR spectra of UO2 (phCONHNH2)2 complexes.     

Method for evaluation of density functional integrals in molecular calculations

Numerical methods for computing variationally optimized molecular orbitals within the Hartree–Fock approximation are augmented to include correlation functionals of the density in the energy and the numerical methods for carrying this out are described. The approach is applied explicitly to the Colle–Salvetti correlation energy functional. It is found that the gradient terms in the Colle–Salvetti functional present numerical problems associated with the low-density behavior, but also that they make a relatively small contribution to the correlation energy. In the three cases considered, HF, H₂O and N₂, it is found that the Colle–Salvetti correction considerably underestimates the correlation energies obtained in coupled-cluster theory.     

Periodic trends in indirect nuclear spin-spin coupling tensors: relativistic density functional calculations for interhalogen diatomics

There have been significant advances in the calculation and interpretation of indirect nuclear spin-spin coupling (J) tensors during the past few years; however, much work remains to be done, especially for molecules containing heavy atoms where relativistic effects may play an important role. Many J tensors cannot be explained based solely on a nonrelativistic Fermi-contact mechanism. In the present work, the relativistic zeroth-order regular approximation density-functional (ZORA-DFT) implementation for the calculation of J has been applied to the complete series of homonuclear and heteronuclear diatomic halogen molecules: F(2), Cl(2), Br(2), I(2), At(2), ClF, BrF, IF, ClBr, ClI, and BrI. For all of these compounds, the reduced isotropic coupling constant (K(iso)) is positive and the reduced anisotropic coupling constant (DeltaK) is negative. With the exception of molecular fluorine, the magnitudes of K(iso) and DeltaK are shown to increase linearly with the product of the atomic numbers of the coupled nuclei. ZORA-DFT calculations of J for F(2) and ClF are in excellent agreement with the results obtained from multiconfigurational self-consistent-field calculations. The relative importance of the various coupling mechanisms is approximately constant for all of the compounds, with the paramagnetic spin-orbit term being the dominant contributor to K(iso), at approximately 70-80%. Available experimental stimulated resonant Raman spectroscopy data are exploited to extract the complete J((127)I,(127)I) tensor for iodine in two rotational states. The dependence of K(iso) and DeltaK on bond length and rovibrational state is investigated by using calculated results in combination with available experimental data. In addition to providing new insights into periodic trends for J coupling tensors, this work further demonstrates the utility of the ZORA-DFT method and emphasizes the necessity of spin-orbit relativistic corrections for J calculations involving heavy nuclei.     

A density functional study of uranyl monocarboxylates

We studied uranium(VI) monocarboxylate complexes by a relativistic density functional method using simple carboxylic acids as ligands, i.e. [UO2(OOCR)]+ (R = H, CH3, CH2CH3). These complexes exist in aqueous solution and, for R = CH3 and CH2CH3, may also be considered as models of uranyl complexated by humic substances. We investigated mono- and bidentate coordination modes. Short-range solvent effects were accounted for explicitly via aqua ligands of the first hydration shell and long-range electrostatic interactions were described via a polarizable continuum model. The calculated results for the uranyl U=O bond, the bond to aqua ligands, and the averaged uranium distances to equatorial oxygen atoms, U-Oeq, agreed quite well with EXAFS-derived interatomic distances. However, the uranyl-carboxylate bond was calculated to be notably shorter than the experimentally determined value. Experimental differences between mono- and bidentate coordination, obtained mainly from crystal structures, were qualitatively reproduced for the U-C distance but not for the average bond length, U-Oeq. We discuss these discrepancies between calculated and experimental results in some detail and suggest changes in the coordination number rather than variations of the coordination geometry as the main source of the experimentally observed variation of the U-Oeq distance.     

Interactions of phosphorylated cyclohexapeptides with uranyl: insights from experiments and theoretical calculations

Two phosphorylated cyclohexapeptides (CPs) bearing one (CP1) or two phosphates (CP2) were synthesized to explore the interactions between uranyl ions and very small cyclic peptides. According to the results of the ESI–MS and fluorescence titrations, the 1:1 uranyl-CPs complexes are the main products with the affinity constants of 7.3?×?10⁴ and 2.0?×?10⁵ for CP1 and CP2, respectively. Density functional theory calculations indicate phosphoryl and carboxyl groups coordinate uranyl in mono-dentate and bi-dentate fashions due to steric effects, which is consistent with the results of extended X-ray absorption fine structure spectroscopy.

     

Structures and spectroscopic properties of bis(phthalocyaninato) yttrium and lanthanum complexes: theoretical study based on density functional theory calculations

Density functional theory (DFT) calculations were carried out to describe the molecular structures, molecular orbitals, atomic charges, UV-vis absorption spectra, IR, and Raman spectra of bis(phthalocyaninato) rare earth(III) complexes M(Pc)(2) (M = Y, La) as well as their reduced products [M(Pc)(2)](-) (M = Y, La). Good consistency was found between the calculated results and experimental data. Reduction of the neutral M(Pc)(2) to [M(Pc)(2)]- induces the reorganization of their orbitals and charge distribution and decreases the inter-ring interaction. With the increase of ionic size from Y to La, the inter-ring distance of both the neutral and reduced double-decker complexes M(Pc)(2) and [M(Pc)(2)](-) (M = Y, La) increases, the inter-ring interaction and splitting of the Q bands decrease, and corresponding bands in the IR and Raman spectra show a red shift. The orbital energy level and orbital nature of the frontier orbitals are also described and explained in terms of atomic character. The present work, representing the first systemic DFT study on the bis(phthalocyaninato) yttrium and lanthanum complexes sheds further light on clearly understanding structure and spectroscopic properties of bis(phthalocyaninato) rare earth complexes.     

Accelerating the convergence of the total energy evaluation in density functional theory calculations

A special feature of the Strutinsky shell correction method (SCM) [D. Ullmo et al., Phys. Rev. B 63, 125339 (2001)] and the recently proposed orbital-corrected orbital-free density functional theory (OO-DFT) [B. Zhou and Y. A. Wang, J. Chem. Phys. 124, 081107 (2006)] is that the second-order corrections are incorporated in the total energy evaluation. In the SCM, the series expansion of the total electronic energy is essentially the Harris functional with its second-order correction. Unfortunately, a serious technical problem for the SCM is the lack of the exact Kohn-Sham (KS) density rho KS(r) required for the evaluation of the second-order correction. To overcome this obstacle, we design a scheme that utilizes the optimal density from a high-quality density mixing scheme to approximate rho KS(r). Recently, we proposed two total energy density functionals, i.e., the Zhou-Wang-lambda (ZW lambda) and the Wang-Zhou-alpha (WZ alpha) functionals, for use in the OO-DFT method. If the two interpolation parameters, lambda and alpha, are chosen to allow the second-order errors of the ZW lambda and the WZ alpha functionals to vanish, these two functionals reduce to the Hohenberg-Kohn-Sham functional with its second-order correction. Again, the optimal density from a high-quality density mixing scheme is used to approximate rho KS(r) in the evaluation of lambda and alpha. This approach is tested in iterative KS-DFT calculations on systems with different chemical environments and can also be generalized for use in other iterative first-principles quantum chemistry methods.     

Analysis of vibrational spectra of L-alanylglycine based on density functional theory calculations

FT Raman and IR spectra of the crystallized biologically active molecule, L-alanylglycine (L-Ala-Gly) have been recorded and analyzed. The equilibrium geometry, bonding features and harmonic vibrational frequencies of L-Ala-Gly have been investigated with the help of B3LYP density functional theory (DFT) method. The calculated molecular geometry has been compared with the experimental data. The assignments of the vibrational spectra have been carried out with the help of normal coordinate analysis (NCA) following the scaled quantum mechanical force field methodology (SQMFF). The optimized geometry shows the non-planarity of the peptide group of the molecule. Potential energy surface (PES) scan studies has also been carried out by ab initio calculations with B3LYP/6-311+G** basis set. The red shifting of NH3+ stretching wavenumber indicates the formation of N-H...O hydrogen bonding. The change in electron density (ED) in the sigma* antibonding orbitals and E2 energies have been calculated by natural bond orbital analysis (NBO) using DFT method. The NBO analysis confirms the occurrence of strong intermolecular hydrogen bonding in the molecule.     

Effect of metal complex formation on the antibacterial activity of nitazoxanide: Spectroscopic and density functional theory calculations

In the present work, experimental and theoretical structural studies of two new nitazoxanide (NTZ) complexes, [Co(NTZ)(NO₃)₂(OH₂)] ( 1 ) and [Ni(NTZ)(CH₃COO)(OH₂)]·CH₃COO ( 2 ) were reported. The susceptibility of Staphylococcus aureus and Escherichia coli towards NTZ and its complexes was assessed. NTZ behaves as a monodentate ligand via the thiazole N atom forming distorted octahedral and tetrahedral complexes with Co(II) and Ni(II) ions, respectively. The d‐d transitions were assigned by the aid of time‐dependent density functional theory calculations. The magnetic susceptibility value of 1 remains unchanged in the temperature range of 298–77K, while that of 2 decreases linearly with the temperature to attain 2.79 μ_B at 77K. Coordination of NTZ (0.084 μmol ml^?1) to Co(II) ( 1 ) (0.028 μmol ml^?1) and Ni(II) ions ( 2 ) (0.079 μmol ml^?1) leads to an improvement in the toxicity against S. aureus.     

Reaction mechanism of platinum dimer cation with ammonia based on the relativistic density functional study

The gas‐phase reactions between Pt and NH₃ have been investigated using the relativistic density functional approach (ZORA‐PW91/TZ2P). The quartet and doublet potential energy surfaces of Pt + NH₃ have been explored. The minimum energy reaction path proceeds through the following steps: Pt(⁴Σ_u) + NH₃ → q‐1 → d‐2 → d‐3 → d‐4 → d‐Pt₂NH⁺ + H₂. In the whole reaction pathway, the step of d‐2 → d‐3 is the rate‐determining step with a energy barrier of 36.1 kcal/mol, and exoergicity of the whole reaction is 12.0 kcal/mol. When Pt₂NH⁺ reacts with NH₃ again, there are two rival reaction paths in the doublet state. One is degradation of NH and another is loss of H₂. In the case of degradation of NH, the activation energy is only 3.4 kcal/mol, and the overall reaction is exothermic by 8.9 kcal/mol. Thus, this reaction is favored both thermodynamically and kinetically. However, in the case of loss of H₂, the rate‐determining step's energy barrier is 64.3 kcal/mol and the overall reaction is endothermic by 8.5 kcal/mol, so it is difficult to take place. Predicted relative energies and barriers along the suggested reaction paths are in reasonable agreement with experimental observations. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Grid-free density functional calculations on periodic systems

Density fitting scheme is applied to the exchange part of the Kohn-Sham potential matrix in a grid-free local density approximation for infinite systems with translational periodicity. It is shown that within this approach the computational demands for the exchange part scale in the same way as for the Coulomb part. The efficiency of the scheme is demonstrated on a model infinite polymer chain. For simplicity, the implementation with Dirac-Slater Xalpha exchange functional is presented only. Several choices of auxiliary basis set expansion coefficients were tested with both Coulomb and overlap metric. Their effectiveness is discussed also in terms of robustness and norm preservation.     

Accurate density functional calculations on large systems

The theoretical underpinnings of the linear combination of Gaussian-type orbitals (LCGTO ) calculations of the density functional (DF ) energy of molecules and clusters are described. The generating function for three-center integrals of arbitrary angular momenta is given in the solid-spherical-harmonic basis. Variational fitting is described and its accuracy tested. The LCGTO-DF method is used to address questions related to the problem of how it is that the methods of cluster science, i.e., high-energy beams or currents, can be used to make C₆₀ in bulk quantities. In particular, it is shown that C₆₀ is neither especially stable nor is it the only large, stable, perfectly round, approximately sp² carbon molecule. © 1996 John Wiley & Sons, Inc.     

Exploring odd-even effects of simple oligomer-like DRCNnT series: a study based on density functional theory/time-dependent density functional theory calculations

Odd-even effects of short-circuit current density and power conversion efficiency (PCE) are an interesting phenomenon in some organic solar cells. Although some explanations have been given, why they behave in such a way is still an open question. In the present work, we investigate a set of acceptor-donor-acceptor simple oligomer-like small molecules, named the DRCNnT (n = 5-9) series, to give an insight into this phenomenon because the solar cells based on them have high PCE (up to 10.08%) and show strong odd-even effects in experiments. By modeling the DRCNnT series and using density functional theory, we have studied the ground-state electronic structures of the DRCNnT (n = 5-9) series in condensed phase. The calculated results reproduce the experimental trends well. Furthermore, we find that the exciton-binding energies of the DRCNnT series may be one of the key parameters to explain this phenomenon because they also show odd-even effects. In addition, by studying the effects of alkyl branch and terminal group on odd-even effects of dipole moment, we find that eliminating one or two alkyl branches does not break the odd-even effects of dipole moments, but eliminating one or two terminal groups does. Finally, we conclude that removing one alkyl branch close to the terminal group of DRCN5T can decrease highest occupied molecular orbital (HOMO) energy (thus increasing open circuit voltage) and increase dipole moment (thus enhancing charge separation and short-circuit current). This could be a new and simple method to increase the PCE of DRCN5T-based solar cells.