Improved relativistic energy-consistent pseudopotentials for 3d-transition metals

The electronic structure of diatomic nickel oxide

The nature of the Ni-O bond is relevant to catalytic and environmental applications. The vibrational frequency and electronic structure of NiO were calculated using CASSCF, icMRCI+Q, CCSD(T), and DFT. CASSCF predicted a quintet state (5Σ-) ground state for the equilibrium bond distance with a state crossing at 1.65 Å, where the triplet (3Σ-) state becomes of lower energy. These states arise from the 3d8(3F)4s2 (3F) and 3d9(2D)4s1 (3D) configurations of Ni. The icMRCI+Q method predicts a triplet (3Σ-) ground state and does not predict a state crossing with the quintet. This state has significant ionic character with the 2pz of O bonding with the 4s/3dz2 of the Ni to form a σ bond. The NiO frequency at the icMRCI+Q level of 835.0 cm-1 is in excellent agreement with experiment; the value of re is 1.5992 Å at this computational level. CCSD(T) predicts ωe = 888.80 cm-1 when extrapolated to the complete basis set limit. Frequencies predicted using CCSD(T) deviate from experiment consistent with the calculations showing large multireference character. A wide array of density functionals were benchmarked. Of the 43 functionals tested, the ones that gave the best prediction of the frequency are ωB97XD, CAM-B3LYP, and τ-HCTH with respective values of 831.8, 838.3, and 837.4 cm-1 respectively. The bond dissociation energy (BDE) of NiO is predicted to be 352.4 kJ mol-1 at the Feller-Peterson-Dixon (FPD) level in good agreement with one of the experimental values. The calculated BDEs at the DFT level are sensitive to the choice of functional and atomic asymptote. Sixteen functionals predicted the BDE within 20 kJ mol-1 of the FPD value.

Prediction of the pKa's of Hydrated Metal Carbonates and Bicarbonates for Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn Dications

The gas- and aqueous-phase acidities of hydrated metal dication carbonates, bicarbonates, and hydroxide complexes M(CO3)(H2O)n for n = 1 to 3, M(HCO3)2, M(HCO3)2(H2O)2, M(HCO3)(OH), and M(HCO3)(H2O)2(OH) for M = Mg, Ca, Mn, Fe, Co, Ni, Cu, and Zn were calculated at the CCSD(T)/aug-cc-pwCVDZ/cc-pwCVDZ level in the gas phase and at the B3LYP/aug-cc-pVTZ/cc-pVTZ(-PP) level with the COSMO self-consistent reaction field (SCRF) method in the aqueous phase. The composite correlated molecular orbital theory G3(MP2) and G3(MP2)B3 methods were used to predict the pKa's of the Mg structures and cis-cis carbonic acid to provide additional benchmarks. Using values scaled to experiment for H2CO3, the pKa's of bicarbonate ligands in group 2 and transition-metal complexes were compared to carbonic acid to gauge the effect of the metal complex on the bicarbonate. The group 2 metal complexes M(HCO3)2 and M(HCO3)(OH) decreased the acidity of the bicarbonate ligands, whereas their dihydrates were even less acidic. The transition-metal di-bicarbonate and bicarbonate hydroxide complexes generally made the bicarbonate more acidic especially when reduction of the metal occurs consistent with electron donation from the ligands; this is accompanied by spin transfer which typically increases in the order Mn < Fe < Co < Ni < Cu. The transition-metal dihydrates were less acidic than carbonic acid. Using values scaled to experiment for hydrated metal dications, the pKa's of water coordinated to group 2 and transition-metal complexes were generally more acidic than the hydrated metal dications, with the exception of Ca bicarbonate dihydrate, Co carbonate, Ni di-bicarbonate dihydrate, and Cu bicarbonate hydroxide di-bicarbonate.

Ni, Cu, Zn, Pd, Ag and Cd Tetraphenylporphyrin Ab Initio Thermochemistry: Enthalpy of Formation of ZnTPP Revisited

Groups 10-12 metalloporphyrins have been recognized for their numerous properties essential for the development of new sensing materials. In this work, accurate gas-phase enthalpies of formation, ΔfHm0(g,298.15), are predicted for the series of Ni, Cu, Zn, Pd, Ag, and Cd tetraphenylporphyrins (MTPPs) on the basis of the reaction-based Feller-Peterson-Dixon approach and high-level ab initio DLPNO-CCSD(T) calculations. Our recently developed automatic generator of the balanced chemical reactions was employed to reduce the bias of the theoretical ΔfHm0(g,298.15) toward a particular reaction. Theoretical ΔfHm0(g,298.15) for ZnTPP (227.0 ± 3.4 kcal mol-1) does not support the previously reported experimental value of 132 ± 2 kcal mol-1. The origin of the discrepancy probably lies in the experimental solid-state ΔfHm0(ZnTPP, cr,298.15) as it stems from our theoretical evaluations of the ΔfHm0(cr,298.15) values for the entire set of transition metal TPP complexes. The large discrepancy between experiment and theory also holds when different DFT functionals (ωB97M-V, PBE0-D4, and B3LYP-D4) paired with quadruple-ζ quality basis sets are used for the theoretical calculations. Experimental revisiting of the solid-state enthalpy of formation of ZnTPP and analogue measurements for other transition metal TPPs are needed to resolve the observed discrepancy. Based on the predicted enthalpies of formation of MTPPs, the relative energies of the metal-ligand bonding are evaluated and the trends are compared to those for the complexes of the unsubstituted porphyrin with the same set of metals derived in [Can. J. Chem., 2009, 87, 1063]. According to both studies, Pd complexes exhibit the strongest bonding, while the Cd species are the least stable metallocomplexes within the considered series.

Thermodynamics of the Metal Carbonates and Bicarbonates of Mn, Co, Ni, Cu, and Zn Relevant to Mineral Energetics

The gas phase heats of formation of ground-state MCO₃, M(HCO₃)₂, and M(HCO₃)(OH), where M = Mn, Co, Ni, Cu, and Zn, have been predicted using the correlated molecular orbital theory at the CCSD(T) level extrapolated to the complete basis set limit using the Feller-Peterson-Dixon (FPD) approach. Cohesive energies of the carbonates were predicted based on the calculated gas phase and experimental solid heats of formation. Coulombic dissociation energies (CDEs) between metal cations and anions show a near-linear correlation with Shannon metal cation atomic radii, yet no correlation is found with the hardness of these cations. The total reaction dissociation energies (TRDEs) of transition metals are higher than their CDEs for the di-bicarbonates, in contrast to those for Mg and Ca based on our prior work. In addition to differences in the energies needed to prepare the transition metal dications, electron donation from the ligands to the 3d orbitals of open-shell transition metal dications from lone pairs of adjacent O atoms also plays a role. No electron donation from the ligands to the fully occupied 3d orbitals of Zn and Cd was found. Decomposition energies for generating MO, CO₂, and/or H₂O were calculated. Gas phase metal exchange energies only partially correlate with the electrochemical series for M(s) → M²⁺(aq). The FPD heats of formation were used to benchmark a range of density functional theory exchange-correlation functionals, including those commonly used in solid-state mineral calculations. None of the functionals provided chemical accuracy agreement (±1 kcal/mol) with the FPD results. The best agreement with the FPD results is predicted for the τ-HCTH functional with an average unsigned error of 8.3 kcal/mol.

Metal Coordination Effects on the Photophysics of Dipyrrinato Photosensitizers

Within this work, we review the metal coordination effect on the photophysics of metal dipyrrinato complexes. Dipyrrinato complexes are promising candidates in the search for alternative transition metal photosensitizers for application in photodynamic therapy (PDT). These complexes can be activated by irradiation with light of a specific wavelength, after which, cytotoxic reactive oxygen species (ROS) are generated. The metal coordination allows for the use of the heavy atom effect, which can enhance the triplet generation necessary for generation of ROS. Additionally, the flexibility of these complexes for metal ions, substitutions and ligands allows the possibility to tune their photophysical properties. A general overview of the mechanism of photodynamic therapy and the properties of the triplet photosensitizers is given, followed by further details of dipyrrinato complexes described in the literature that show relevance as photosensitizers for PDT. In particular, the photophysical properties of Re(I), Ru(II), Rh(III), Ir(III), Zn(II), Pd(II), Pt(II), Ni(II), Cu(II), Ga(III), In(III) and Al(III) dipyrrinato complexes are discussed. The potential for future development in the field of (dipyrrinato)metal complexes is addressed, and several new research topics are suggested throughout this work. We propose that significant advances could be made for heteroleptic bis(dipyrrinato)zinc(II) and homoleptic bis(dipyrrinato)palladium(II) complexes and their application as photosensitizers for PDT.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T₁), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M³⁺ and X^- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔH_f°(0 K)/ΔH_f°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc₂F₆, Sc₂Br₆, and Sc₂I₆ species. For ScBr₃, ScI₃, Sc₂Cl₆, and Y₂Cl₆, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX₃ (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s²p⁶ electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

Bonding and metastability for Group 12 dications

Electronic structure and bonding properties of the Group 12 dications M₂ ²⁺ (M = Zn, Cd, Hg) are investigated and electron density-derived quantities are used to characterize the metastability of these species. Of particular interest are the complementary descriptions afforded by the Laplacian of the electron density ∇² ρ(r) and the one-electron Bohm quantum potential (Q =  ∇ 2 ρ r / 2 ρ r ) along the bond path. Further, properties derived from the pair density including the localization-delocalization matrices (LDMs) and the interacting quantum atoms (IQA) energies are analyzed within the framework of the quantum theory of atoms in molecules (QTAIM). From the crossing points of the singlet (ground) and triplet (excited) potential energy curves, the barriers for dissociation (BFD) are estimated to be 25.2 kcal/mol (1.09 eV) for Zn₂ ²⁺ , 22.8 kcal/mol (0.99 eV) for Cd₂ ²⁺ , and 26.4 kcal/mol (1.14 eV) for Hg₂ ²⁺ . For comparison and benchmarking purposes, the case of N₂ ²⁺ is considered as a texbook example of metastability. At the equilibrium geometries, LDMs, which are used here as an electronic fingerprinting tool, discriminate and group together Group 12 M₂ ²⁺ from its isoelectronic Group 11 M₂ . While "classical" bonding indices are inconclusive in establishing regions of metastability in the bonding, it is shown that the one-electron Bohm quantum potential is promising in this regard.

Chemical bonding in groups 10, 11, and 12 transition metal homodimers — An electron density study

The properties of metal–metal bonding for transition metal homonuclear diatomics from groups 10, 11 and 12 are studied within the framework of the quantum theory of atoms in molecules (QTAIM) at the coupled cluster CCSD and CCSD(T) levels of theory. A novel approximate method developed by Keith and Frisch is used to augment electron densities calculated with pseudopotentials with the missing relativistic core densities to obtain approximations to the total densities of the dimers. The calculated delocalization indices for group 10 dimers are: Ni2 (1.6), Pd2 (0.44, an outlier in the group), and Pt2 (1.8); for group 11 dimers: Cu2 and Ag2 (1.01), and Au2 (1.13), all covalent bonds; for group 12: Zn2 (0.06), Cd2 (0.08), and Hg2 (0.09), all consistent with weak van der Waals complexes. The picture of bonding obtained by examining the values of the electron density at the bond critical points is consistent with the one obtained on the basis of these delocalization indices. A curious linear (instead of exponential) dependence of the delocalization index on the electron density at the bond critical point is presented here as an observation and will be investigated in more depth in later work. Several correlations between bond properties and bond dissociation energies are also explored. It is found that, with the exception of the Ni2 dimer that exhibits considerable multi-reference character, there are correlations between the calculated bond dissociation energies of the studied diatomics and several bond critical point properties. These correlations are novel as they span a set of bonds between different pairs of elements, while traditionally these correlations were reported for bonds between the same pair or elements but with different substituents.

Accurate relativistic small-core pseudopotentials for actinides. energy adjustment for uranium and first applications to uranium hydride

The options to adjust accurate relativistic energy-consistent pseudopotentials for actinides are explored using uranium as an example. The choice of the reference data and the core-valence separation is discussed in view of a targeted accuracy of 0.04 eV or better in atomic energy differences such as excitation energies and ionization potentials. A new small-core pseudopotential attributing 60 electrons to the core has been generated by an energy adjustment to state-averaged multiconfiguration Dirac-Hartree-Fock/Dirac-Coulomb-Breit Fermi nucleus reference data of 100 nonrelativistic configurations of U to U(7+) corresponding to 30190 reference J levels. At the finite-difference multiconfiguration Hartree-Fock level the mean absolute errors are 0.002 and 0.024 eV for the configurations and J levels, respectively. A first molecular application to uranium monohydride UH yields very satisfactory agreement with results from all-electron calculations based on the Douglas-Kroll-Hess Hamiltonian.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Energy-consistent relativistic pseudopotentials and correlation consistent basis sets for the 4d elements Y–Pd

Scalar-relativistic pseudopotentials and corresponding spin-orbit potentials of the energy-consistent variety have been adjusted for the simulation of the [Ar]3d(10) cores of the 4d transition metal elements Y-Pd. These potentials have been determined in a one-step procedure using numerical two-component calculations so as to reproduce atomic valence spectra from four-component all-electron calculations. The latter have been performed at the multi-configuration Dirac-Hartree-Fock level, using the Dirac-Coulomb Hamiltonian and perturbatively including the Breit interaction. The derived pseudopotentials reproduce the all-electron reference data with an average accuracy of 0.03 eV for configurational averages over nonrelativistic orbital configurations and 0.1 eV for individual relativistic states. Basis sets following a correlation consistent prescription have also been developed to accompany the new pseudopotentials. These range in size from cc-pVDZ-PP to cc-pV5Z-PP and also include sets for 4s4p correlation (cc-pwCVDZ-PP through cc-pwCV5Z-PP), as well as those with extra diffuse functions (aug-cc-pVDZ-PP, etc.). In order to accurately assess the impact of the pseudopotential approximation, all-electron basis sets of triple-zeta quality have also been developed using the Douglas-Kroll-Hess Hamiltonian (cc-pVTZ-DK, cc-pwCVTZ-DK, and aug-cc-pVTZ-DK). Benchmark calculations of atomic ionization potentials and 4d(m-2)5s(2)-->4d(m-1)5s(1) electronic excitation energies are reported at the coupled cluster level of theory with extrapolations to the complete basis set limit.

On the spectroscopic and thermochemical properties of ClO, BrO, IO, and their anions

A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X1(2)II(3/2) states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-. After determining the frozen core, complete basis set (CBS) limit CCSD(T) values, corrections were added for core-valence correlation, relativistic effects (scalar and spin-orbit), the pseudopotential approximation (BrO and IO), iterative connected triple excitations (CCSDT), and iterative quadruples (CCSDTQ). The final ab initio equilibrium bond lengths and harmonic frequencies for ClO and BrO differ from their accurate experimental values by an average of just 0.0005 A and 0.8 cm-1, respectively. The bond length of IO is overestimated by 0.0047 A, presumably due to an underestimation of molecular spin-orbit coupling effects. Spectroscopic constants for the spin-orbit excited X2(2)III(1/2) states are also reported for each species. The predicted bond lengths and harmonic frequencies for the closed-shell anions are expected to be accurate to within about 0.001 A and 2 cm-1, respectively. The dissociation energies of the radicals have been determined by both direct calculation and through use of negative ion thermochemical cycles, which made use of a small amount of accurate experimental data. The resulting values of D0, 63.5, 55.8, and 54.2 kcal/mol for ClO, BrO, and IO, respectively, are the most accurate ab initio values to date, and those for ClO and BrO differ from their experimental values by just 0.1 kcal/mol. These dissociation energies lead to heats of formation, DeltaH(f) (298 K), of 24.2 +/- 0.3, 29.6 +/- 0.4, and 29.9 +/- 0.6 kcal/mol for ClO, BrO, and IO, respectively. Also, the final calculated electron affinities are all within 0.2 kcal/mol of their experimental values. Improved pseudopotential parameters for the iodine atom are also reported, together with revised correlation consistent basis sets for this atom.