The heat of formation of the uranyl dication: theoretical evaluation based on relativistic density functional calculations

By using a set of model reactions, we estimated the heat of formation of gaseous UO2(2+) from quantum-chemical reaction enthalpies and experimental heats of formation of reference species. For this purpose, we performed relativistic density functional calculations for the molecules UO2(2+), UO2, UF6, and UF5. We used two gradient-corrected exchange-correlation functionals (revised Perdew-Burke-Ernzerhof (PBEN) and Becke-Perdew (BP)) and we accounted for spin-orbit interaction in a self-consistent fashion. Indeed, spin-orbit interaction notably affects the energies of the model reactions, especially if compounds of U(IV) are involved. Our resulting theoretical estimates for delta fH(o)0 (UO2(2+)), 365+/-10 kcal mol(-1) (PBEN) and 370+/-12 kcal mol(-1) (BP), are in quantitative agreement with a recent experimental result, 364+/-15 kcal mol(-1). Agreement between the results of the two different exchange-correlation functionals PBEN and BP supports the reliability of our approach. The procedure applied offers a general means to derive unknown enthalpies of formation of actinide species based on the available well-established data for other compounds of the element in question.     

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.     

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.     

Stability and migration of large oxygen clusters in UO(2+x): density functional theory calculations

Using ab initio molecular dynamics simulations and nudged elastic band calculations we examine the finite temperature stability, transition pathways, and migration mechanisms of large oxygen clusters in UO(2+x). Here we specifically consider the recently proposed split quad-interstitial and cuboctahedral oxygen clusters. It is shown that isolated cuboctahedral clusters may transform into more stable configurations that are closely linked to the split quad-interstitial. The split quad-interstitial is stable with respect to single interstitials occupying the empty octahedral holes of the UO(2) lattice. In order to better understand discrepancies between theory and experiments, the simulated atomic pair distribution functions for the split quad-interstitial structures are analyzed with respect to the distribution function for U(4)O(9) previously obtained from neutron diffraction data. Our nudged elastic band calculations suggest that the split quad-interstitial may migrate by translating one of its constituent di-interstitial clusters via a barrier that is lower than the corresponding barrier for individual interstitials, but higher than the barrier for the most stable di-interstitial cluster.     

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.     

Atomic multiplet energies from density functional calculations

Atomic multiplet term energies for dⁿ configurations have been estimated within density functional theory (DFT) exploiting symmetry to the largest possible extent. The electrostatic two-electron integrals, as well as term energies, are expressed in function of only three non-redundant single determinants (NRSDs), each of them being obtained from density functional calculations. The influence of correlation effects described with a gradient-corrected functional (GGA) is examined and discussed. Comparison with experimental data shows the reliability of this symmetry-based density functional approach.     

Stable isomers for trifluoroacetic acid (TFA) pentahydrates obtained from density functional calculations

Stable isomers of trifluoroacetic acid (TFA) pentahydrate clusters, TFA-(H₂O)₅, have been explored by using density functional theory calculations. As done for TFA-(H₂O)₄ (Ito, 2013), structure optimization and vibrational calculations were performed for 70 isomeric structures (68 for neutral and 2 for ion-pair species, respectively) at the B971/6–311++G(3df,3pd) level. We found that the edge-sharing bicyclic isomer is at the global minimum and that three other isomers lie energetically within 100 cm⁻¹. Two types of ion-pair species were found to be unstable by 1100 cm⁻¹ in comparison with the global minimum. The results were compared with infrared spectra observed in nitrogen matrix.     

Lithium adsorption on graphite from density functional theory calculations

The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes.     

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.     

The mechanism of N2O formation via the (NO)2 dimer: a density functional theory study

Catalytic formation of N(2)O via a (NO)(2) intermediate was studied employing density functional theory with generalized gradient approximations. Dimer formation was not favored on Pt(111), in agreement with previous reports. On Pt(211) a variety of dimer structures were studied, including trans-(NO)(2) and cis-(NO)(2) configurations. A possible pathway involving (NO)(2) formation at the terrace near to a Pt step is identified as the possible mechanism for low-temperature N(2)O formation. The dimer is stabilized by bond formation between one O atom of the dimer and two Pt step atoms. The overall mechanism has a low barrier of approximately 0.32 eV. The mechanism is also put into the context of the overall NO + H(2) reaction. A consideration of the step-wise hydrogenation of O(ads) from the step is also presented. Removal of O(ads) from the step is significantly different from O(ads) hydrogenation on Pt(111). The energetically favored structure at the transition state for OH(ads) formation has an activation energy of 0.63 eV. Further hydrogenation of OH(ads) has an activation energy of 0.80 eV.     

CO2 adsorption on TiO2(110) rutile: insight from dispersion-corrected density functional theory calculations and scanning tunneling microscopy experiments

Adsorption of CO(2) on the rutile(110) surface was investigated using dispersion-corrected density functional theory and scanning tunneling microscopy (STM). On the oxidized surface the CO(2) molecules are found to bind most strongly at the five-fold coordinated Ti sites adopting tilted or flat configurations. The presence of bridging oxygen defects introduces two new adsorption structures, the most stable of which involves CO(2) molecules bound in tilted configurations at the defect sites. Inclusion of dispersion corrections in the density functional theory calculations leads to large increases in the calculated adsorption energies bringing these quantities into good agreement with experimental data. The STM measurements confirm two of the calculated adsorption configurations.     

H2S splitting on Cu(110): Insight from combined periodic density functional theory calculations and microkinetic simulation

Practical copper (Cu)‐based catalysts for the water–gas shift (WGS) reaction was long believed to expose a large proportion of Cu(110) planes. In this work, as an important first step toward addressing sulfur poisoning of these catalysts, the detailed mechanism for the splitting of hydrogen sulfide (H₂S) on the open Cu(110) facet has been investigated in the framework of periodic, self‐consistent density functional theory (DFT‐GGA). The microkinetic model based on the first‐principles calculations has also been developed to quantitatively evaluate the two considered decomposition routes for yielding surface atomic sulfur (S*): (1) H₂S → H₂S* → SH* → S* and (2) 2H₂S → 2H₂S* → 2SH* → S* + H₂S* → S* + H₂S. The first pathway proceeding through unimolecular SH* dissociation was identified to be feasible, whereas the second pathway involving bimolecular SH* disproportionation made no contribution to S* formation. The molecular adsorption of H₂S is the slowest elementary step of its full decomposition, being related with the large entropy term of the gas‐phase reactant under realistic reaction conditions. A comparison of thermodynamic and kinetic reactivity between the substrate and the close‐packed Cu(111) surface further shows that a loosely packed facet can promote the S* formation from H₂S on Cu, thus revealing that the reaction process is structure sensitive. The present DFT and microkinetic modeling results provide a reasonably complete picture for the chemistry of H₂S on the Cu(110) surface, which is a necessary basis for the design of new sulfur‐tolerant WGS catalysts. © 2013 Wiley Periodicals, Inc.     

Acrylate formation via metal-assisted C-C coupling between CO2 and C2H4: reaction mechanism as revealed from density functional calculations

The reaction path for the formation of a binuclear hydrido-acrylate complex in a CO(2)-C(2)H(4) coupling process is explored in detail by locating the key intermediates and transition states on model potential energy surfaces derived from density functional calculations on realistic models. The formation of the new C-C bond is shown to take place via oxidative coupling of coordinated CO(2) and C(2)H(4) ligands resulting in a metalla-lactone intermediate, which can rearrange to an agostic species allowing for a beta-hydrogen shift process. The overall reaction is predicted to be clearly exothermic with all intermediates lying below the reactants in energy, and the highest barrier steps correspond to C-C coupling and beta-hydrogen transfer. The phosphine ligands are found to play an important role in various phases of the reaction as their dissociation controls the coordination of CO(2), the formation of the agostic intermediate, and the dimerization process; furthermore, their presence facilitates the oxidative coupling by supplying electrons to the metal center. Our results provide a theoretical support for the reaction mechanism proposed from experimental observations. The effect of the solvent medium on the relative energy of reaction intermediates and transition states is examined and found important in order to predict reliable energetics.     

Infrared spectra and density functional calculations for the Sc(OH)2,3 and HOScO molecules and the Sc(OH)2+ cation in solid argon

Reactions of laser-ablated Sc atoms with H2O2 molecules or H2 and O2 mixtures in excess solid argon gives four major new products, which are identified from concentration dependence, isotopic substitution, the effect of electron trap doping, and comparison to frequencies calculated by the B3LYP density functional. These are the Sc(OH)3 trihydroxide, the Sc(OH)2 dihydroxide, the Sc(OH)2+ cation, and the trihydroxide anhydride HOScO molecule. The Sc(OH)2+ cation forms a complex in solid argon that is effectively modeled by calculations for the [(Ar)4Sc(OH)2]+ cation including frequency shifts between the neutral and cation dihydroxides. Finally, the Sc(OH)4- anion is detected in H2O2 experiments.     

Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, H2O, and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.     

Investigation of spin-flip reactions of Zr + CH3CN by relativistic density functional theory

To explore the details of the reaction mechanisms of Zr atoms with acetonitrile molecules, the triplet and singlet spin-state potential energy surfaces have been investigated. Density functional theory (DFT) with the relativistic zero-order regular approximation at the PW91/TZ2P level has been applied. The complicated minimum energy reaction path involves four transition states (TS), stationary states 1-5 and one spin inversion (indicated by ?): (3)Zr + NCCH(3) → (3)Zr-η(1)-NCCH(3) ((3)1) → (3)TS(1/2) → (3)Zr-η(2)-(NC)CH(3) ((3)2) → (3)TS(2/3) → (3)ZrH-η(3)-(NCCH(2)) ((3)3) → (3)TS(3/4) → CNZrCH(3) ((3)4) ? (1)TS(4/5) → CN(ZrH)CH(2) ((1)5). The minimum energy crossing point was determined with the help of the DFT fractional-occupation-number approach. The spin inversion leading from the triplet to the singlet state facilitates the activation of a C-H bond, lowering the rearrangement-barrier by 78 kJ/mol. The overall reaction is calculated to be exothermic by about 296 kJ/mol. All intermediate and product species were frequency and NBO analyzed. The species can be rationalized with the help of Lewis type formulas.     

Infrared spectra and density functional calculations for M(OH)(2,3) and HOMO molecules and M(OH)2+ cations (M = Y, La)

Reactions of laser-ablated Y and La atoms with H2O2 gives the M(OH)2 and M(OH)3 molecules and the HOMO dehydration product, and the cation M(OH)2+ in solid argon. Density functional calculations show that the dihydroxide molecules and cations are bent at the metal center, and the symmetric and antisymmetric O-H stretching modes are both observed in the infrared spectra. The trihydroxide molecules have calculated C(3h) structures characterized by strong antisymmetric O-H and M-O stretching modes. Mulliken charges increase for all product molecules going down the Group 3 family and increase as one, two, and three OH ligands are bonded to the metal center. Evidence is also presented for the Y(OH)4- anion.