Inclusion Of Scalar Relativistic Effects Research Articles

Samarium Diiodide Acting on Acetone-Modeling Single Electron Transfer Energetics in Solution.

Samarium diiodide is a versatile single electron transfer (SET) agent with various applications in organic chemistry. Lewis structures regularly insinuate the existence of a ketyl radical when samarium diiodide binds a carbonyl group. The study presented here investigates this electron transfer by the means of computational chemistry. All electron CASPT2 calculations with the inclusion of scalar relativistic effects predict an endotherm electron transfer from samarium diiodide to acetone. Energies calculated with the PBE0-D3(BJ) functional and a small core pseudopotential are in good agreement with CASPT2. The calculations confirm the experimentally measured increase of the samarium diiodide reduction potential through the addition of hexamethylphosphoramide also known as HMPA.

Low-Lying Electronic States of the Nickel Dimer.

The generalized Van Vleck second order multireference perturbation theory (GVVPT2) method was used to investigate the low-lying electronic states of Ni2. Because the nickel atom has an excitation energy of only 0.025 eV to its first excited state (the least in the first row of transition elements), Ni2 has a particularly large number of low-lying states. Full potential energy curves (PECs) of more than a dozen low-lying electronic states of Ni2, resulting from the atomic combinations 3F4 + 3F4 and 3D3 + 3D3, were computed. In agreement with previous theoretical studies, we found the lowest lying states of Ni2 to correlate with the 3D3 + 3D3 dissociation limit, and the holes in the d-subshells were in the subspace of delta orbitals (i.e., the so-dubbed δδ-states). In particular, the ground state was determined as X 1Γg and had spectroscopic constants: bond length (R e) = 2.26 Å, harmonic frequency (ωe) = 276.0 cm−1, and binding energy (D e) = 1.75 eV; whereas the 1 1Σg + excited state (with spectroscopic constants: R e = 2.26 Å, ωe = 276.8 cm−1, and D e = 1.75) of the 3D3 + 3D3 dissociation channel lay at only 16.4 cm−1 (0.002 eV) above the ground state at the equilibrium geometry. Inclusion of scalar relativistic effects through the spin-free exact two component (sf-X2C) method reduced the bond lengths of both of these two states to 2.20 Å, and increased their binding energies to 1.95 eV and harmonic frequencies to 296.0 cm−1 for X 1Γg and 297.0 cm−1 for 1 1Σg +. These values are in good agreement with experimental values of R e = 2.1545 ± 0.0004 Å, ωe = 280 ± 20 cm−1, and D 0 = 2.042 ± 0.002 eV for the ground state. All states considered within the 3F4 + 3F4 dissociation channel proved to be energetically high-lying and van der Waals-like in nature. In contrast to most previous theoretical studies of Ni2, full PECs of all considered electronic states of the molecule were produced.

An ab initio study of the O1s and Mg1s, Mg2s, Mg2p core electron binding energies in bulk MgO

Embedded cluster models combined with wavefunction based quantum chemical ab initio methods were used to calculate the O1s and Mg1s, Mg2s, Mg2p core electron binding energies (CEBEs) of bulk MgO. The calculations were performed at three levels of theory: Koopmans' theorem (KT, initial state effects), ΔSCF (relaxation of the electronic wavefunction after core ionization, final state effects, with inclusion of scalar relativistic effects), and approximate coupled cluster (CC) approach to account for electron correlation. Several basis sets as well as MgO clusters of various design and size were employed to study their influence on the CEBEs. The contribution of electron correlation being in the order of 1 eV, but very much different for the different core levels, was analyzed in detail. Our final results are 529.5 eV for the O1s CEBE and 1303.5, 87.7 and 48.8 eV for Mg1s, Mg2s, Mg2p, respectively (all relative to the Fermi level). They agree with recent experimental XPS data within about 0.5 eV.

Copper-Chalcogen Bonds in Olfaction: Accurate ab Initio Characterization of CuSH and CuOH.

From highly correlated ab initio methods at the CCSD(T) level, with and without the inclusion of scalar relativistic effects, accurate 3D potential energy surfaces (PESs) of CuSH and CuOH were generated in their electronic ground state. The PESs are incorporated into perturbative and variational treatments of nuclear motions. Using these approaches, we derived a set of accurate spectroscopic parameters and the pattern of the vibrational states of CuXH (X = O,S) up to 4000 cm-1. The applied calculations at the CCSD(T)/aug-cc-pV5Z-DK level of theory are validated using several experimental high-resolution spectroscopy data (including rotational spectroscopy) available in the literature. The optimized equilibrium geometries of CuSH and CuOH with bending angles of 93.9° and 110.2°, Cu-X bond lengths of 2.088 and 1.764 Å, and X-H bond lengths of 1.344 and 0.961 Å, respectively, accurately reproduce the experimental structures and clearly show the importance of the scalar relativistic effects. The anharmonic frequencies, ν1, ν2, and ν3, are computed at 3655.5, 746.3, and 623.3 cm-1 for CuOH and at 2572.9, 588.9, and 396.6 cm-1 for CuSH, respectively. Finally, the PESs are derived as anharmonic force fields for CuXH (X = O, S) that can be incorporated into large scale molecular dynamics simulations of Cu-X containing compounds. The results are discussed within the scope of available literature on the effects of substitution of oxygen by sulfur for putative molecular recognition mechanisms.

Structural and Electronic Properties of Fluoride Complexes of NbV, TaV, and PaV: The Influence of Relativistic Effects on Group V Elements

Aqueous fluorido complexes of niobium and tantalum were studied by using synchrotron‐based extended X‐ray absorption spectroscopy (EXAFS) as model systems for comparison of the structural and coordination chemistry of the group V metals Nb, Ta, and their pseudo‐homologue PaV. The EXAFS measurements indicate differences in the coordination chemistry of Nb and Ta in these systems that were not intuitively based on their similar charge and ionic radii. The Ta speciation is dominated by six‐ and seven‐coordinate fluorido complexes, while the chemical speciation of Nb under the same conditions is dominated by its hydrolyzed oxyfluoride complexes. Quantum chemical computations were performed to more fully describe these observations, and these results are compared to our earlier study on the fluorido complexes of protactinium. Computations performed with and without the inclusion of scalar relativistic effects reveal that the differences in chemistry among the group V elements and their pseudo‐homologue protactinium are due to the increasing influence of relativistic effects as Z increases from niobium to protactinium.

Theoretical Modeling of (99)Tc NMR Chemical Shifts.

Technetium-99 (Tc) displays a rich chemistry due to its wide range of accessible oxidation states (from -I to +VII) and ability to form coordination compounds. Determination of Tc speciation in complex mixtures is a major challenge, and (99)Tc nuclear magnetic resonance (NMR) spectroscopy is widely used to probe chemical environments of Tc in odd oxidation states. However, interpretation of (99)Tc NMR data is hindered by the lack of reference compounds. Density functional theory (DFT) calculations can help to fill this gap, but to date few computational studies have focused on (99)Tc NMR of compounds and complexes. This work evaluates the effectiveness of both pure generalized gradient approximation and their corresponding hybrid functionals, both with and without the inclusion of scalar relativistic effects, to model the (99)Tc NMR spectra of Tc(I) carbonyl compounds. With the exception of BLYP, which performed exceptionally well overall, hybrid functionals with inclusion of scalar relativistic effects are found to be necessary to accurately calculate (99)Tc NMR spectra. The computational method developed was used to tentatively assign an experimentally observed (99)Tc NMR peak at -1204 ppm to fac-Tc(CO)3(OH)3(2-). This study examines the effectiveness of DFT computations for interpretation of the (99)Tc NMR spectra of Tc(I) coordination compounds in high salt alkaline solutions.

Predicting Near Edge X-ray Absorption Spectra with the Spin-Free Exact-Two-Component Hamiltonian and Orthogonality Constrained Density Functional Theory.

Orthogonality constrained density functional theory (OCDFT) provides near-edge X-ray absorption (NEXAS) spectra of first-row elements within one electronvolt from experimental values. However, with increasing atomic number, scalar relativistic effects become the dominant source of error in a nonrelativistic OCDFT treatment of core-valence excitations. In this work we report a novel implementation of the spin-free exact-two-component (X2C) one-electron treatment of scalar relativistic effects and its combination with a recently developed OCDFT approach to compute a manifold of core-valence excited states. The inclusion of scalar relativistic effects in OCDFT reduces the mean absolute error of second-row elements core-valence excitations from 10.3 to 2.3 eV. For all the excitations considered, the results from X2C calculations are also found to be in excellent agreement with those from low-order spin-free Douglas-Kroll-Hess relativistic Hamiltonians. The X2C-OCDFT NEXAS spectra of three organotitanium complexes (TiCl4, TiCpCl3, TiCp2Cl2) are in very good agreement with unshifted experimental results and show a maximum absolute error of 5-6 eV. In addition, a decomposition of the total transition dipole moment into partial atomic contributions is proposed and applied to analyze the nature of the Ti pre-edge transitions in the three organotitanium complexes.

Accuracy of DLPNO-CCSD(T) method for noncovalent bond dissociation enthalpies from coinage metal cation complexes.

The performance of the domain based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) method has been tested to reproduce the experimental gas phase ligand dissociation enthalpy in a series of Cu(+), Ag(+), and Au(+) complexes. For 33 Cu(+)-noncovalent ligand dissociation enthalpies, all-electron calculations with the same method result in MUE below 2.2 kcal/mol, although a MSE of 1.4 kcal/mol indicates systematic underestimation of the experimental values. Inclusion of scalar relativistic effects for Cu either via effective core potential (ECP) or Douglass-Kroll-Hess Hamiltonian, reduces the MUE below 1.7 kcal/mol and the MSE to -1.0 kcal/mol. For 24 Ag(+)-noncovalent ligand dissociation enthalpies, the DLPNO-CCSD(T) method results in a mean unsigned error (MUE) below 2.1 kcal/mol and vanishing mean signed error (MSE). For 15 Au(+)-noncovalent ligand dissociation enthalpies, the DLPNO-CCSD(T) methods provides larger MUE and MSE, equal to 3.2 and 1.7 kcal/mol, which might be related to poor precision of the experimental measurements. Overall, for the combined data set of 72 coinage metal ion complexes, DLPNO-CCSD(T) results in a MUE below 2.2 kcal/mol and an almost vanishing MSE. As for a comparison with computationally cheaper density functional theory (DFT) methods, the routinely used M06 functional results in MUE and MSE equal to 3.6 and -1.7 kcal/mol. Results converge already at CC-PVTZ quality basis set, making highly accurate DLPNO-CCSD(T) estimates affordable for routine calculations (single-point) on large transition metal complexes of >100 atoms.

No-Pair Bonding in Coinage Metal Dimers

High-level ab initio calculations at the coupled cluster with single and double substitutions and perturbative treatment of triple substitutions, CCSD(T), level of theory have been carried out for the dimers of coinage metal atoms Cu, Ag, and Au in the ground 1Sigma(g)+ state and in the excited 3Sigma(u)+ state. All of the calculations have been carried out with the inclusion of scalar-relativistic effects via the normalized elimination of the small component (NESC) method. For the dimers in the triplet state, nonzero bond dissociation energies are obtained which vary from 1.3 kcal/mol for 3Cu2 to 4.6 kcal/mol for 3Au2. Taking into account that, in bulky high-spin copper clusters, the bond dissociation energy per atom increases steeply to the value of ca. 19 kcal/mol, the results obtained in the present paper suggest that the bond dissociation energy per atom in high-spin gold clusters may reach extremely high values exceeding 20 kcal/mol thus becoming comparable to the usual bonding due to the spin-pairing mechanism.

Prediction of Iron K-Edge Absorption Spectra Using Time-Dependent Density Functional Theory

Iron K-edge X-ray absorption pre-edge features have been calculated using a time-dependent density functional approach. The influence of functional, solvation, and relativistic effects on the calculated energies and intensities has been examined by correlation of the calculated parameters to experimental data on a series of 10 iron model complexes, which span a range of high-spin and low-spin ferrous and ferric complexes in O(h) to T(d) geometries. Both quadrupole and dipole contributions to the spectra have been calculated. We find that good agreement between theory and experiment is obtained by using the BP86 functional with the CP(PPP) basis set on the Fe and TZVP one of the remaining atoms. Inclusion of solvation yields a small improvement in the calculated energies. However, the inclusion of scalar relativistic effects did not yield any improved correlation with experiment. The use of these methods to uniquely assign individual spectral transitions and to examine experimental contributions to backbonding is discussed.

Low-Lying Singlet and Triplet Electronic States of RhB

The low-lying XSigma+, a3Delta, A1Delta, b3Sigma+, B1Pi, c3Pi, C1Phi, D1Sigma+, E1Pi, d3Phi, and e3Pi electronic states of RhB have been investigated at the ab initio level, using the multistate multiconfigurational second-order perturbation (MS-CASPT2) theory, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the eleven electronic states included in this work, only three (the X1Sigma+, D1Sigma+, and E1Pi states) have been investigated experimentally. Potential energy curves, spectroscopic constants, dipole moments, binding energies, and chemical bonding aspects are presented for all electronic states.

Benchmarking approximate density functional theory for s/d excitation energies in 3d transition metal cations

Holthausen has recently provided a comprehensive study of density functional theory for calculating the s/d excitation energies of the 3d transition metal cations. This study did not include the effects of scalar relativistic effects, and we show here that the inclusion of scalar relativistic effects significantly alters the conclusions of the study. We find, contrary to the previous study, that local functionals are more accurate for the excitation energies of 3d transition method cations than hybrid functionals. The most accurate functionals, of the 38 tested, are SLYP, PBE, BP86, PBELYP, and PW91.

On the ground and some low-lying excited states of ScB: A multiconfigurational study

The electronic structure of a series of low-lying excited triplet and quintet states of scandium boride (ScB) was examined using multireference configuration interaction (including Davidson's correction for quadruple excitations) and single-reference coupled cluster (CC) methods with averaged natural orbital (ANO) basis sets. The CC approach was used only for the lowest quintet state. The authors have analyzed eight low-lying triplets 3Sigma-(2), 3Sigma+, 3Pi(3), and 3Delta(2) dissociating to Sc(2D)/B(2P) atoms and eight low-lying quintet states 5Sigma-, 5Sigma+, 5Pi(2), 5Phi, and 5Delta(3) dissociating to Sc(4F)/B(2P) atoms. They report the potential energy curves and spectroscopic parameters of ScB obtained with the multireference configuration interaction (MRCI) technique including all singly and doubly excited configurations obtained with the ANO-S basis set. For the two lowest states they obtained also improved ANO-L spectroscopic constants, dipole and quadrupole moments as well as scalar relativistic effects based on the Douglas-Kroll-Hess Hamiltonian. They provide the analysis of the bonding based on Mulliken populations and occupation numbers. Since the two lowest states, 3Sigma- and 5Sigma-, lie energetically very close, their principal goal was to resolve the nature of the ground state of ScB. Their nonrelativistic MRCI(Q) (including Davidson correction) results indicate that the quintet is more stable than the triplet by about 800 cm(-1). Inclusion of scalar relativistic effects reduces this difference to about 240 cm(-1). The dissociation energies for 5Sigma- ScB range from 3.20 to 3.30 eV while those for the 3Sigma- range from 1.70 to 1.80 eV.

Time-dependent density functional calculations of ligand K-edge X-ray absorption spectra

The Cl K-edge spectra of a series of metal tetrachloride complexes have been simulated using a simple TD-DFT based protocol. The influence of the chosen density functional, relativistics, basis set, and solvation has been systematically investigated. The results show that good agreement between the calculated spectra and the relative experimental energies and intensities can be achieved by using the BP86 functional with standard polarized triple-ζ basis sets (such as the TZVP basis of Ahlrichs’s and co-workers). Calculated energies and intensities are improved by using the more flexible CP(PPP) basis set on the metal atom. The inclusion of scalar-relativistic effects or solvation does not yield any significant improvement in the results. The subtleties arising from the incorporation of electric quadrupole and magnetic dipole intensity contributions into the calculations are discussed in some detail, and the contributions are shown to be negligible (∼1%) at the Cl K-edge.

The nature of the [20.0]Σ+1 electronic state of RhB: A multiconfigurational study

Multiconfigurational second order perturbation theory, with extended atomic basis sets and inclusion of scalar relativistic effects, was employed to investigate the low-lying (1)Sigma(+) electronic states of RhB. The [20.0] (1)Sigma(+) state is represented by a single configuration, mid R:[ellipsis (horizontal)]10sigma(2)11sigma(1)5pi(4)2delta(4)12sigma(1), derived from a single excitation (11sigma-->12sigma) from the ground state, which defines its electronic nature. A new excited state, coined as [9.0] (1)Delta (R(0)=1.786A, DeltaG(12)=792 cm(-1)), located 9221 cm(-1) above the X(1)Sigma(+) state, and described by the |...10sigma(2)11sigma(2)5pi(4)2delta(3)12sigma(1)> electronic configuration, was also identified.

Ground and Lowest-Lying Electronic States of CoN. A Multiconfigurational Study

The lowest-lying X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II electronic states of CoN have been investigated at the ab initio MRCI and MS-CASPT2 levels, with extended atomic basis sets and inclusion of scalar relativistic effects. Among the singlet states, the A1Phi and B1II states have been described for the first time. Potential energy curves, excitation energies, spectroscopic constants, and bonding character for all states are reported. Comparison with other early transition-metal nitrides (ScN, TiN, VN, and CrN), isoelectronic (NiC) and isovalent (RhN and IrN) species has been made, besides analyzing the B1II <=> X1+ electronic transition in terms of Franck-Condon factors, Einstein coefficients, and radiative lifetimes. At both levels of theory, the following energetic order has been obtained: X1Sigma+, a3Phi, b3II, c5Delta, A1Phi, and B1II, with good agreement with experimental results. In contrast, previous DFT and MRCI calculations predicted the ground state to be the 5Delta state.

Competition between Metal-Amido and Metal-Imido Chemistries in the Alkaline Earth Series: An Experimental and Theoretical Study of BaNH

The pure rotational spectrum of BaNH in its X(1)Sigma(+) ground electronic state has been recorded using millimeter/submillimeter direct absorption methods; data for the deuterium and barium 137 isotopomers have been measured as well. The molecules were produced by the reaction of ammonia or ND(3) and barium vapor in the presence of a dc discharge. Transitions arising from the ground vibrational state and the excited vibrational bending (01(1)0) and heavy atom stretching (100) modes were measured. The rotational spectrum indicates a linear structure, with B(0)(BaNH) = 7984.549 MHz and B(0)(BaND) = 7060.446 MHz. An r(m)((1)) structure has been determined, yielding r(BaN) = 2.077 +/- 0.002 Angstroms and r(NH) = 1.0116 +/- 0.0006 Angstroms. Density functional calculations using an extensive Slater-type basis set with inclusion of scalar relativistic effects gives geometrical parameters and vibrational frequencies for BaNH in excellent agreement with those determined by experiment. The molecular orbital and natural bond order analyses of the BaNH wave function show Ba-N pi bonds formed by electron donation from the formally filled N 2p orbitals of the imido group to the empty Ba 5d orbitals. The multiple bonding between Ba and N stabilizes the linear geometry and, along with the relative ease of oxidation of the Ba atom, favors formation of the metal-imido species over that of the metal-amido species that have been found from similar studies with Mg, Ca, and Sr atoms in this group.

Interfacing relativistic and nonrelativistic methods. IV. One- and two-electron scalar approximations

Two approximations for the inclusion of scalar relativistic effects into otherwise nonrelativistic molecular self-consistent field calculations are described, which continue the sequence of approximations from previous work. In the first, the two-electron contributions are confined to those where each small component density is one-center. In the second, the two-electron contributions are approximated by using the bare Coulomb operator, an approach which parallels the Douglas–Kroll–Hess method. The results show that both approximations yield results close to the full two-electron scalar relativistic method, within 0.001 Å in bond lengths and 0.1 kcal/mol in dissociation energies. The approximations also give results which are very similar to those of the Douglas–Kroll–Hess method. The second approximation is similar in cost to the Douglas–Kroll–Hess method and only contains simple operators whose integrals are easy to evaluate.

A fully ab initio potential curve of near-spectroscopic quality for OH − ion: importance of connected quadruple excitations and scalar relativistic effects

A benchmark study has been carried out on the ground-state potential curve of the hydroxyl anion, OH −, including detailed calibration of both the 1-particle and n-particle basis sets. The CCSD(T) basis set limit overestimates ω e by about 10 cm −1, which is only remedied by inclusion of connected quadruple excitations in the coupled cluster expansion — or, equivalently, the inclusion of the 2π orbitals in the active space of a multireference calculation. Upon inclusion of scalar relativistic effects (−3 cm −1 on ω e), a potential curve of spectroscopic quality (sub-cm −1 accuracy) is obtained. Our best computed EA(OH), 1.828 eV, agrees to three decimal places with the best available experimental value. Our best computed dissociation energies, D 0(OH −)=4.7796 eV and D 0(OH)=4.4124 eV, suggest that the experimental D 0(OH)=4.392 eV may possibly be about 0.02 eV too low.

Relativistic effects on the optical response of InSb by time-dependent density-functional theory

In this paper we show how relativistic effects can be included in the time-dependent density-functional theory (DFT) for the optical response properties of nonmetallic crystals. The dominant scalar relativistic effects have been included using the zeroth-order regular approximation (ZORA) in the ground-state DFT calculations, as well as in the time-dependent response calculations. We show that this theory can also be applied to indium antimonide in the zinc-blende structure, notwithstanding the fact that it turns into a semimetal when scalar relativistic effects are included. Results are given for the band structure, the static dielectric constant ε∞ and the dielectric function ε(ω), for the various levels on which relativity can be included, i.e., nonrelativistic, only in the ground-state, or also in the response calculation. Comparisons of our calculated results are made with experiment and other theoretical investigations. With the inclusion of scalar relativistic effects, the band structure of InSb becomes semimetallic within the local density approximation and we find a deviation of 5% from experiment for the static dielectric constant. Also the dielectric function is improved and the spectra are in good agreement with experiment, although the spectral features are shifted to somewhat lower energies compared to experiment.