Relativistic Zeroth-order Regular Approximation Research Articles

Equilibrium mercury and lead isotope fractionation caused by nuclear volume effects in crystals

To investigate equilibrium mercury (Hg) and lead (Pb) isotope fractionation caused by the nuclear volume effect (NVE) in crystals, the electron densities at nuclei (i.e., |Ψ(0)|2) for Hg- or Pb-bearing crystalline compounds were investigated by using the relativistic spin orbit zeroth-order regular approximation (ZORA) method with a three-dimensional periodic boundary condition based on the density functional theory (DFT). Many isotope fractionation factors of crystalline compounds are provided for the first time. Our results show, even at 1000 °C, NVE-driven Hg and Pb isotope fractionation are meaningfully large, i.e., range from 0.12‰ to 0.49‰ (202Hg/198Hg), from − 0.20‰ to 0.17‰ (208Pb/206Pb) and from − 0.08‰ to 0.06‰ (207Pb/206Pb) relative to Hg0 vapor and Pb0 vapor, respectively. Specifically, the fractionations range from − 0.06‰ to − 0.20‰ (208Pb/206Pb) and from − 0.02‰ to − 0.08‰ (207Pb/206Pb) for Pb2+-bearing species, from 0.10‰ to 0.17‰ (208Pb/206Pb) and from 0.04‰ to 0.06‰ (207Pb/206Pb) for Pb4+-bearing species in crystals. All calculated Hg-bearing species in crystals will enrich heavier isotope (202Hg) relative to Hg0 vapor. Meanwhile, Pb4+-bearing species enrich heavier Pb isotopes (208Pb and 207Pb) than Pb2+-bearing species in crystals, which the enrichment can be up to 0.37‰ (208Pb/206Pb) and 0.14‰ (207Pb/206Pb) at 1000 °C, due to their NVEs are in opposite directions. The NVE-driven MIFs of Hg isotopes, which are compared to the Hg202- Hg198 baseline, are up to − 0.158‰ ( $$\Delta {}_{{{\text{NV}}}}^{199} {\text{Hg}}$$ ), − 0.024‰ ( $$\Delta {}_{{{\text{NV}}}}^{200} {\text{Hg}}$$ ) and − 0.094‰ ( $$\Delta {}_{{{\text{NV}}}}^{201} {\text{Hg}}$$ ) relative to Hg0 vapor at 500 °C. For all studied Hg-bearing species in crystals, the MIFs of two odd-mass isotopes (i.e., $$\Delta {}_{{{\text{NV}}}}^{199} {\text{Hg}}$$ and $$\Delta {}_{{{\text{NV}}}}^{201} {\text{Hg}}$$ ) will be changed proportionally and their ratio (i.e., $$\Delta {}_{{{\text{NV}}}}^{199} {\text{Hg}}$$ / $$\Delta {}_{{{\text{NV}}}}^{201} {\text{Hg}}$$ ) will be a constant 1.67. The NVE can also cause mass-independent fractionations for 207Pb and 204Pb compared to the baseline of 208Pb and 206Pb. The largest NVE-driven MIFs are 0.043‰ ( $$\Delta {}_{{{\text{NV}}}}^{207} {\text{Pb}}$$ ) and − 0.040‰ ( $$\Delta {}_{{{\text{NV}}}}^{204} {\text{Pb}}$$ ) among all the studied species relative to Pb0 vapor at 500 °C. The magnitudes of odd-mass isotope MIF ( $$\Delta {}_{{{\text{NV}}}}^{207} {\text{Pb}}$$ ) and even-mass isotope MIF ( $$\Delta {}_{{{\text{NV}}}}^{204} {\text{Pb}}$$ ) are almost the same but with opposite signs, leading to the MIF ratio of them (i.e., $$\Delta {}_{{{\text{NV}}}}^{207} {\text{Pb}}$$ / $$\Delta {}_{{{\text{NV}}}}^{204} {\text{Pb}}$$ ) is − 1.08.

S2p core level spectroscopy of short chain oligothiophenes.

The Near-Edge X-ray-Absorption Fine-Structure (NEXAFS) and X-ray Photoemission Spectroscopy (XPS) of short-chain oligothiophenes (thiophene, 2,2'-bithiophene, and 2,2':5',2″-terthiophene) in the gas phase have been measured in the sulfur L2,3-edge region. The assignment of the spectral features is based on the relativistic two-component zeroth-order regular approximation time dependent density functional theory approach. The calculations allow us to estimate both the contribution of the spin-orbit splitting and of the molecular-field splitting to the sulfur binding energies and give results in good agreement with the experimental measurements. The deconvolution of the calculated S2p NEXAFS spectra into the two manifolds of excited states converging to the LIII and LII edges facilitates the attribution of the spectral structures. The main S2p NEXAFS features are preserved along the series both as concerns the energy positions and the nature of the transitions. This behaviour suggests that the electronic and geometrical environment of the sulfur atom in the three oligomers is relatively unaffected by the increasing chain length. This trend is also observed in the XPS spectra. The relatively simple structure of S2p NEXAFS spectra along the series reflects the localized nature of the virtual states involved in the core excitation process.

Relativistic (SR-ZORA) quantum theory of atoms in molecules properties.

The Quantum Theory of Atoms in Molecules (QTAIM) is used to elucidate the effects of relativity on chemical systems. To do this, molecules are studied using density-functional theory at both the nonrelativistic level and using the scalar relativistic zeroth-order regular approximation. Relativistic effects on the QTAIM properties and topology of the electron density can be significant for chemical systems with heavy atoms. It is important, therefore, to use the appropriate relativistic treatment of QTAIM (Anderson and Ayers, J. Phys. Chem. 2009, 115, 13001) when treating systems with heavy atoms. © 2016 Wiley Periodicals, Inc.

DFT as a Powerful Predictive Tool in Photoredox Catalysis: Redox Potentials and Mechanistic Analysis

Visible-light photoredox catalysis has come forth as a powerful activation mode in chemical synthesis, affording the development of a multitude of new strategies for molecular construction. However, detailed mechanistic knowledge of the various subprocesses involved is lacking, and new tools for addressing this are needed to drive innovation forward in the area. Herein, we describe predictions of ground- and excited-state redox potentials of ruthenium and iridium photocatalysts using nonrelativistic and scalar relativistic zero-order regular approximation density functional theory (DFT) methods. The computed redox potentials were correlated with experimental values and found to reproduce them well. Relativistic corrections were found to be important to reproduce experimental data. Moreover, the computational protocol allows us to estimate redox potentials that are not currently available in the literature or are difficult to determine experimentally. The mechanistic details of the photocatalyzed C–H funct...

Investigation of the Electronic Excited States of Small Gold Clusters in Rare Gas Matrices: Spin-Orbit Time-Dependent Density Functional Theory Calculation.

The effects of the weak interactions of rare gas atoms on the UV-visible absorption spectra of gold dimer and tetramer clusters are investigated. The time-dependent density functional theory based on the two-component relativistic zeroth-order regular approximation that considered spin-orbit coupling is performed to estimate the absorption spectra of Au2,4-Rgn (Rg = Ne-Xe, and n = 1-6) complexes. Using spin-orbit, including the appropriate functional, shows a close correlation between experiment and our calculations. It is also demonstrated that the weak interactions between rare gas atoms and gold clusters affect the UV-vis spectra of Au2,4 clusters by shifting the electronic transition toward the blue. Moreover, we find that the order of change in peak position, Δν̃, is proportional to the strength of interactions: Δν̃Au2,4-Xe > Δν̃Au2,4-Kr > Δν̃Au2,4-Ar > Δν̃Au2,4-Ne. In addition, comparing the UV-visible spectra of Au2,4-Rgn complexes with those of isolated Au2 and Au4 clusters shows that for Au2,4-Rg2,4,6 complexes in which Rg atoms interacted symmetrically with gold clusters no additional peaks are observed compared to isolated clusters; however, for Au2,4-Rg1,3,5 complexes, extra peaks appear because of the decrease in symmetry.

Ligand‐Field Strength and Symmetry‐Restricted Covalency in Cu II Complexes – a Near‐Edge X‐ray Absorption Fine Structure Spectroscopy and Time‐Dependent DFT Study

The low-lying empty orbitals of bis(acetylacetonato)copper have been probed by near-edge X-ray absorption fine structure (NEXAFS) spectroscopy at the Cu L2,3 edges and time-dependent density functional theory (TDDFT) calculations within the Tamm–Dancoff approximation (TDA) coupled to the relativistic zeroth-order regular approximation including spin–orbit effects (SO-ZORA TDDFT-TDA). Both the relative positions of NEXAFS features and their linear dichroism are satisfactorily reproduced. Moreover, a comparison with literature data pertaining to two other square-planar CuII complexes ([CuCl4]2– and copper phthalocyanine) provided information about how metal-to-ligand charge-transfer transitions associated with excitations from CuII 2p orbitals to low-lying, ligand-based π* molecular orbitals in a simplified one-electron picture may contribute to the CuII L2,3 edge intensity and, thus, weaken its believed relationship with the CuII–ligand symmetry-restricted covalency.

Does the 4f-shell contribute to bonding in tetravalent lanthanide halides?

Lanthanide tetrahalide molecules LnX4 (Ln = Ce, Pr, Tb; X = F, Cl, Br, I) have been investigated by density functional theory at the levels of the relativistic Zero Order Regular Approximation and the relativistic energy-consistent pseudopotentials, using frozen small- and medium-cores. The calculated bond lengths and vibrational frequencies are close to the experimental data. Our calculations indicate 4f shell contributions to bonding in LnX4, in particular for the early lanthanides, which show significant overlap between the Ln 4f-shell and the halogen np-shells. The 4f shells contribute to Ln-X bonding in LnX4 about one third more than in LnX3.

Redox properties of biscyclopentadienyl uranium(V) imido-halide complexes: a relativistic DFT study

Calculations of ionization energies (IE) and electron affinities (EA) of a series of biscyclopentadienyl imido-halide uranium(V) complexes Cp*2U(=N-2,6-(i)Pr2-C6H3)(X) with X = F, Cl, Br, and I, related to the U(IV)/U(V) and U(V)/U(VI) redox systems, were carried out, for the first time, using density functional theory (DFT) in the framework of the relativistic zeroth order regular approximation (ZORA) coupled with the conductor-like screening model (COSMO) solvation approach. A very good linear correlation (R(2) = 0.993) was obtained, between calculated ionization energies at the ZORA/BP86/TZP level, and the experimental half-wave oxidation potentials E1/2. A similar linear correlation between the computed electron affinities and the electrochemical reduction U(IV)/U(III) potentials (R(2) = 0.996) is obtained. The importance of solvent effects and of spin-orbit coupling is definitively confirmed. The molecular orbital analysis underlines the crucial role played by the 5f orbitals of the central metal whereas the Nalewajski-Mrozek (N-M) bond indices explain well the bond distances variations following the redox processes. The IE variation of the complexes, i.e., IE(F) < IE(Cl) < IE(Br) < IE(I) is also well rationalized considering the frontier MO diagrams of these species. Finally, this work confirms the relevance of the Hirshfeld charges analysis which bring to light an excellent linear correlation (R(2) = 0.999) between the variations of the uranium charges and E1/2 in the reduction process of the U(V) species.

Time-Dependent Density Functional Theory Modeling of Spin–Orbit Coupling in Ruthenium and Osmium Solar Cell Sensitizers

We report on the relevance of spin–orbit coupling on the optical properties of Ru(II)- and Os(II)-polypyridyl dyes effectively employed in dye-sensitized solar cells (DSCs). We include relativistic effects on time-dependent density functional theory calculations of selected complexes by using different levels of calculations, i.e., the scalar zero-order regular approximation (ZORA) and the fully relativistic ZORA including spin–orbit coupling, in such a way so as to disentangle and evaluate the spin–orbit effect. The widely investigated [M(bpy)3]2+ (M = Ru(II) and Os(II)) have been selected as benchmark complexes in our calculations; this is followed by investigation of “realistic” dyes used in DSCs, such as the prototypical N3 dye, its Os-based analogue, and a panchromatic Os(II) dye. We find that in Ru(II) complexes, spin–orbit coupling leads to a slight correction of the spectral shape, whereas only when we include the spin–orbit coupling we are able to reproduce the low-energy absorption bands charact...

Multinuclear Solid‐State Magnetic Resonance as a Sensitive Probe of Structural Changes upon the Occurrence of Halogen Bonding in Co‐crystals

Although the understanding of intermolecular interactions, such as hydrogen bonding, is relatively well-developed, many additional weak interactions work both in tandem and competitively to stabilize a given crystal structure. Due to a wide array of potential applications, a substantial effort has been invested in understanding the halogen bond. Here, we explore the utility of multinuclear ((13)C, (14/15)N, (19)F, and (127)I) solid-state magnetic resonance experiments in characterizing the electronic and structural changes which take place upon the formation of five halogen-bonded co-crystalline product materials. Single-crystal X-ray diffraction (XRD) structures of three novel co-crystals which exhibit a 1:1 stoichiometry between decamethonium diiodide (i.e., [(CH3)3N(+)(CH2)10N(+)(CH3)3][2 I(-)]) and different para-dihalogen-substituted benzene moieties (i.e., p-C6X2Y4, X=Br, I; Y=H, F) are presented. (13)C and (15)N NMR experiments carried out on these and related systems validate sample purity, but also serve as indirect probes of the formation of a halogen bond in the co-crystal complexes in the solid state. Long-range changes in the electronic environment, which manifest through changes in the electric field gradient (EFG) tensor, are quantitatively measured using (14)N NMR spectroscopy, with a systematic decrease in the (14)N quadrupolar coupling constant (CQ) observed upon halogen bond formation. Attempts at (127)I solid-state NMR spectroscopy experiments are presented and variable-temperature (19)F NMR experiments are used to distinguish between dynamic and static disorder in selected product materials, which could not be conclusively established using solely XRD. Quantum chemical calculations using the gauge-including projector augmented-wave (GIPAW) or relativistic zeroth-order regular approximation (ZORA) density functional theory (DFT) approaches complement the experimental NMR measurements and provide theoretical corroboration for the changes in NMR parameters observed upon the formation of a halogen bond.

Relativistic diffusion Monte Carlo method: Zeroth-order regular approximation-diffusion Monte Carlo method in a spin-free formalism

A diffusion Monte Carlo (DMC) method for the relativistic zeroth-order regular approximation (ZORA) is proposed. In this scheme, a novel approximate Green's function is derived for the spin-free ZORA Hamiltonian. Several numerical tests on atoms and small molecules showed that by combining with the relativistic cusp-correction scheme, the present approach can include both relativistic and electron-correlation effects simultaneously. The correlation energies recovered by the ZORA-DMC method are comparable with the nonrelativistic DMC results and superior to the coupled cluster singles and doubles with perturbative triples correction results when the correlation-consistent polarized valence triple-zeta Douglas-Kroll basis set is used. For the heavier CuH molecule, the ZORA-DMC estimation of its dissociation energy agrees with the experimental value within the error bar.

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.

Scalar Relativistic Computations and Localized Orbital Analyses of Nuclear Hyperfine Coupling and Paramagnetic NMR Chemical Shifts.

A method is reported by which calculated hyperfine coupling constants (HFCCs) and paramagnetic NMR (pNMR) chemical shifts can be analyzed in a chemically intuitive way by decomposition into contributions from localized molecular orbitals (LMOs). A new module for density functional calculations with nonhybrid functionals, global hybrids, and range-separated hybrids, utilizing the two-component relativistic zeroth-order regular approximation (ZORA), has been implemented in the parallel open-source NWChem quantum chemistry package. Benchmark results are reported for a test set of few-atom molecules with light and heavy elements. Finite nucleus effects on (199)Hg HFCCs are shown to be on the order of -11 to -15%. A proof of concept for the LMO analysis is provided for the metal and fluorine HFCCs of TiF3 and NpF6. Calculated pNMR chemical shifts are reported for the 2-methylphenyl-t-butylnitroxide radical and for five cyclopentadienyl (Cp) sandwich complexes with 3d metals. Nickelocene and vanadocene carbon pNMR shifts are analyzed in detail, demonstrating that the large carbon pNMR shifts calculated as +1540 for Ni (exptl.: +1514) and -443 for V (exptl.: -510) are caused by different spin-polarization mechanisms. For Ni, Cp to Ni π back-donation dominates the result, whereas for vanadocene, V to Cp σ donation with relaxation of the carbon 1s shells can be identified as the dominant mechanism.

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

In order to explore the details of the reaction mechanisms of Nb atoms with acetonitrile molecules, the sextet, quartet, and doublet 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) to (5) and two intersystem crossings from spin sextets to quartets to doublets (indicated by ⇒): (6)Nb + NCCH3→(6)Nb η(1)-NCCH3 ((6)1) →(6)TS1/2⇒(4)Nb η(2)-(NC)CH3 ((4)2) →(4)TS2/3→(4)NbH η(3)-(NCCH2) ((4)3) →(4)TS3/4→ CNNbCH3 ((4)4) ⇒(2)TS4/5→ CN(NbH)CH2 ((2)5). The minimum energy crossing points were determined with the help of the DFT fractional-occupation-number approach. The first spin inversion leads from the sextet to an energetically low intermediate quartet ((4)2) with final insertion of Nb into the C-C bond. The second one from the quartet to the doublet state facilitates the activation of a C-H bond, lowering the rearrangement-barrier by 44 kJ mol(-1). The overall reaction is calculated to be exothermic by about 170-180 kJ mol(-1). All intermediate and product species were frequency and NBO analyzed. The species can be rationalized with the help of Lewis type formulas.

Scalar Relativistic Computations of Nuclear Magnetic Shielding and g-Shifts with the Zeroth-Order Regular Approximation and Range-Separated Hybrid Density Functionals.

Density functional theory (DFT) calculations of NMR chemical shifts and molecular g tensors with Gaussian-type orbitals are implemented via second-order energy derivatives within the scalar relativistic zeroth order regular approximation (ZORA) framework. Nonhybrid functionals, standard (global) hybrids, and range-separated (Coulomb-attenuated, long-range corrected) hybrid functionals are tested. Origin invariance of the results is ensured by use of gauge-including atomic orbital (GIAO) basis functions. The new implementation in the NWChem quantum chemistry package is verified by calculations of nuclear shielding constants for the heavy atoms in HX (X = F, Cl, Br, I, At) and H2X (X = O, S, Se, Te, Po) and (125)Te chemical shifts in a number of tellurium compounds. The basis set and functional dependence of g-shifts is investigated for 14 radicals with light and heavy atoms. The problem of accurately predicting (19)F NMR shielding in UF6-nCln, n = 1-6, is revisited. The results are sensitive to approximations in the density functionals, indicating a delicate balance of DFT self-interaction vs correlation. For the uranium halides, the range-separated functionals are not clearly superior to global hybrids.

Calculation of Hyperfine Tensors and Paramagnetic NMR Shifts Using the Relativistic Zeroth-Order Regular Approximation and Density Functional Theory.

Density functional theory (DFT) calculations of molecular hyperfine tensors were implemented as a second derivative property within the two-component relativistic zeroth-order regular approximation (ZORA). Hyperfine coupling constants were computed for systems ranging from light atomic radicals to molecules with heavy d and f block elements. For comparison, computations were also performed with a ZORA first-order derivative approach. In each set of computations, Slater-type basis sets have been used. The implementation allows for nonhybrid and hybrid DFT calculations and incorporates a Gaussian finite nucleus model. A comparison of results calculated with the PBE nonhybrid and the PBE0 hybrid functional is provided. Comparisons with differing basis sets and incorporation of finite-nucleus corrections are discussed. The second derivative method is applied to calculations of paramagnetic NMR ligand chemical shifts of three Ru(III) complexes. The results are consistent with those calculated using a first-order derivative method, and the results are consistent for different functionals used. A comparison of two different methods of calculating pseudo-contact shifts, one using the full hyperfine tensor and one assuming a point-charge paramagnetic center, is made for the Ru(III) complexes.

NMR J‐Coupling Constants in Cisplatin Derivatives Studied by Molecular Dynamics and Relativistic DFT

Solvent effects on J((195)Pt-(15)N) one-bond nuclear spin-spin coupling constants (J(PtN)) of cisplatin [cis-diamminedichloroplatinum(II)] and three cisplatin derivatives are investigated using a combination of density functional theory (DFT) based ab initio molecular dynamics (aiMD) and all-electron relativistic DFT NMR calculations employing the two-component relativistic zeroth-order regular approximation (ZORA). Good agreement with experiment is obtained when explicit solvent molecules are considered and when the computations are performed with a hybrid functional. Spin-orbit coupling causes only small effects on J(PtN) . Key factors contributing to the magnitude of coupling constants are elucidated, with the most significant being the presence of solvent as well as the quality of the density functional and basis set combination. The solvent effects are of the same magnitude as J(PtN) calculated for gas-phase geometries. However, the trends of J(PtN) among the complexes are already present in the gas phase. Results obtained with a continuum solvent model agree quite well with the aiMD results, provided that the Pt solvent-accessible radius is carefully chosen. The aiMD results support the existence of a partial hydrogen-bond-like inverse-hydration-type interaction affording a weak (1)J(Pt⋅⋅⋅H(w)) coupling between the complexes and the coordinating water molecule.

Calculation of molecular g-tensors using the zeroth-order regular approximation and density functional theory: expectation value versus linear response approaches

Density functional theory (DFT) calculations of molecular g-tensors were implemented as a second derivative property within the two-component relativistic zeroth-order regular approximation (ZORA). g-tensors were computed for systems ranging from light atomic radicals to molecules with heavy d and f block elements. For comparison, computations were also performed with a ZORA first-order derivative approach and with a second derivative method based on the Pauli Hamiltonian. In each set of computations, Slater-type basis sets have been used. The new ZORA implementation allows for non-hybrid and hybrid DFT calculations. A comparison of the PBE non-hybrid and the PBE0 hybrid functional yielded mixed results for our test set. For the lanthanide complex $$[\hbox{Ce}(\hbox{DPA})_3]^{3-}$$ (DPA = pyridine-2,6-dicarboxylate), calculations of the g-tensor were used to estimate paramagnetic NMR pseudocontact shifts for protons and carbon atoms in the ligands. The results are in reasonable agreement with experimental data.

Near-Infrared-Emitting Phthalocyanines. A Combined Experimental and Density Functional Theory Study of the Structural, Optical, and Photophysical Properties of Pd(II) and Pt(II) α-Butoxyphthalocyanines

The structural, optical, and photophysical properties of 1,4,8,11,15,18,22,25-octabutoxyphthalocyaninato-palladium(II), PdPc(OBu)(8), and the newly synthesized platinum analogue PtPc(OBu)(8) are investigated combining X-ray crystallography, static and transient absorption spectroscopy, and relativistic zeroth-order regular approximation (ZORA) Density Functional Theory (DFT)/Time Dependent DFT (TDDFT) calculations where spin-orbit coupling (SOC) effects are explicitly considered. The results are compared to those previously reported for NiPc(OBu)(8) (J. Phys. Chem. A 2005, 109, 2078) in an effort to highlight the effect of the central metal on the structural and photophysical properties of the group 10 transition metal octabutoxyphthalocyanines. Different from the nickel analogue, PdPc(OBu)(8) and PtPc(OBu)(8) show a modest and irregular saddling distortion of the macrocycle, but share with the first member of the group similar UV-vis spectra, with the deep red and intense Q-band absorption experiencing a blue shift down the group, as observed in virtually all tetrapyrrolic complexes of this triad. The blue shift of the Q-band along the MPc(OBu)(8) (M = Ni, Pd, Pt) series is interpreted on the basis of the metal-induced electronic structure changes. Besides the intense deep red absorption, the title complexes exhibit a distinct near-infrared (NIR) absorption due to a transition to the double-group 1E (π,π*) state, which is dominated by the lowest single-group (3)E (π,π*) state. Unlike NiPc(OBu)(8), which is nonluminescent, PdPc(OBu)(8) and PtPc(OBu)(8) show both deep red fluorescence emission and NIR phosphorescence emission. Transient absorption experiments and relativistic spin-orbit TDDFT calculations consistently indicate that fluorescence and phosphorescence emissions occur from the S(1)(π,π*) and T(1)(π,π*) states, respectively, the latter being directly populated from the former, and the triplet state decays directly to the S(0) surface (the triplet lifetime in deaerated benzene solution was 3.04 μs for Pd and 0.55 μs for Pt). Owing to their triplet properties, PdPc(OBu)(8) and PtPc(OBu)(8) have potential for use in photodynamic therapy (PDT) and are potential candidates for NIR light emitting diodes or NIR emitting probes.

Electric Field Gradients Calculated from Two-Component Hybrid Density Functional Theory Including Spin-Orbit Coupling.

An implementation of a four-component density corrected approach for calculations of nuclear electric field gradients (EFGs) in molecules based on the two-component relativistic zeroth-order regular approximation (ZORA) is reported. The program module, which is part of the NWChem package, allows for scalar and spin-orbit relativistic computations of EFGs. Benchmark density functional calculations are reported for a large set of main group diatomic molecules, a set of Cu and Au diatomics, several Ru and Nb complexes, the free uranyl ion, and two uranyl carbonate complexes. Data obtained from nonhybrid as well as fixed and range-separated hybrid functionals are compared. To allow for a chemically intuitive interpretation of the results, a breakdown of the EFGs of selected systems in terms of localized molecular orbitals is given. For CuF, CuCl, AuCl, UO2(2+), and a uranyl carbonate complex, the localized orbital decomposition demonstrates in particular the role of the valence metal d and f shells, respectively, and leads to rather compact analyses. For f orbitals, a Townes-Dailey-like model is set up to assist the analysis.