Third-row Elements Research Articles

A new parameterization of the DFT/CIS method with applications to core-level spectroscopy.

Time-dependent density functional theory (TD-DFT) within a restricted excitation space is an efficient means to compute core-level excitation energies using only a small subset of the occupied orbitals. However, core-to-valence excitation energies are significantly underestimated when standard exchange-correlation functionals are used, which is partly traceable to systemic issues with TD-DFT's description of Rydberg and charge-transfer excited states. To mitigate this, we have implemented an empirically modified combination of configuration interaction with single substitutions (CIS) based on Kohn-Sham orbitals, which is known as "DFT/CIS." This semi-empirical approach is well-suited for simulating x-ray near-edge spectra, as it contains sufficient exact exchange to model charge-transfer excitations yet retains DFT's low-cost description of dynamical electron correlation. Empirical corrections to the matrix elements enable semi-quantitative simulation of near-edge x-ray spectra without the need for significant a posteriori shifts; this should be useful in complex molecules and materials with multiple overlapping x-ray edges. Parameter optimization for use with a specific range-separated hybrid functional makes this a black-box method intended for both core and valence spectroscopy. Results herein demonstrate that realistic K-edge absorption and emission spectra can be obtained for second- and third-row elements and 3d transition metals, with promising results for L-edge spectra as well. DFT/CIS calculations require absolute shifts that are considerably smaller than what is typical in TD-DFT.

Real-Space Pseudopotential Method for the Calculation of Third-Row Elements X-ray Photoelectron Spectroscopic Signatures.

X-ray photoelectron spectroscopy (XPS) is a powerful characterization technique that unveils subtle chemical environment differences via core-electron binding energy (CEBE) analysis. We extend the development of real-space pseudopotential methods to calculating 1s, 2s, and 2p3/2 CEBEs of third-row elements (S, P, and Si) within the framework of Kohn-Sham density-functional theory (KS-DFT). The new approach systematically prevents variational collapse and simplifies core-excited orbital selection within dense energy level distributions. However, careful error cancellation analysis is required to achieve accuracy comparable to all-electron methods and experiments. Combined with real-space KS-DFT implementation, this development enables large-scale simulations with both Dirichlet boundary conditions and periodic boundary conditions.

Intelligent interpretation of the astronomical UIE bands: the spectra similarity

The limitations of visual inspection and interpretation of Infrared (IR) spectra from either laboratories or astronomical observations to cover a wide range of molecular types motivated us to apply a mathematical approach via a matching method called spectra similarity to identify the carriers of UIE bands in a sample of astronomical objects. The reliability of such a purely mathematical approach in targeting the correct molecular structures was tested by applying two sets of experimental IR spectra against the large pool of theoretical IR databases composed of 300,000 organic, organometallic, and, inorganic molecules. Spectra similarity calculations show that the second-row elements C, H, N, and O dominate the elemental composition of HD 44179, M 82, NGC 7023, NGC 7027, and Orion bar. In addition, the signatures of third-row elements S and Si were also identified. Our preliminary results confirm the signatures of complex organic molecules in interstellar environments. These are composed of benzene rings, five-membered rings, and side chain aliphatic groups in the cited astronomical sources. In some cases, the similarity approach suggested the fully aliphatic structures as the origin of UIE carriers.

Accurate Spin-Orbit Coupling by Relativistic Mixed-Reference Spin-Flip-TDDFT.

Relativistic mixed-reference spin-flip (MRSF)-TDDFT is developed considering the spin-orbit coupling (SOC) within the mean-field approximation. The resulting SOC-MRSF faithfully reproduces the experiments with very high accuracy, which is also consistent with the values by four-component (4c) relativistic CASSCF and 4c-CASPT2 in the spin-orbit-energy splitting calculations of the C, Si, and Ge atoms. Even for the fifth-row element Sn, the SOC-MRSF yielded accurate splittings (∼ 3 % error). In the SOC calculations of the molecular 4-thiothymine with a third-row element, SOC-MRSF values are in excellent agreement with those of the SO-GMC-QDPT2 level, regardless of geometries and exchange-correlation functionals. The same SOC-MRSF predicted the anticipated chance of S1 (nπ*) → T1 (ππ*) intersystem crossing, even in thymine with only second-row elements. With its accuracy and practicality, thus, SOC-MRSF is a promising electronic structure protocol in challenging situations such as nonadiabatic molecular dynamics (NAMD) incorporating both internal conversions and intersystem crossings in large systems.

The Reaction Mechanism of the Cu(I) Catalyzed Alkylation of Heterosubstituted Alkynes

Alkynes may be regioselectively alkylated to alkenes by organocopper reagents in a reaction known as “carbocupration”, where an alkylCu(I) binds to the alkyne and transfers its organic moiety to one of the alkyne carbon atoms. Alkynes hetero-substituted with third-row elements yield alkenes with a regiochemistry opposite to that obtained when using alkynes hetero-substituted with second-row elements. Early computational investigations of his reaction mechanism have identified the importance of the organocopper counter-cation (Li+) to the achievement of good reaction rates, but in the subsequent two decades no further progress has been reported regarding the exploration of the mechanism or the explanation of the experimental regiochemistry. In this work, density-functional theory is used to investigate the mechanism used and to describe a model that correctly explains both the reaction rates at sub-zero temperatures and the regiochemistry profiles obtained with each of the heteroalkynes. The rate-determining step is shown to vary depending on the heterosubstituent, and the alkyl transfer is consistently shown to occur, somewhat counter-intuitively, to the alkyne carbon that is complexed by Cu rather than to the “free” alkyne carbon atom, which instead interacts with the counter-cation that stabilizes the developing electronic charge distribution.

Electron Correlation or Basis Set Quality: How to Obtain Converged and Accurate NMR Shieldings for the Third-Row Elements?

The quality of theoretical NMR shieldings calculated at the quantum-chemical level depends on various theoretical aspects, of which the basis set type and size are among the most important factors. Nevertheless, not much information is available on the basis set effect on theoretical shieldings of the NMR-active nuclei of the third row. Here, we report on the importance of proper basis set selection to obtain accurate and reliable NMR shielding parameters for nuclei from the third row of the periodic table. All calculations were performed on a set of eleven compounds containing the elements Na, Mg, Al, Si, P, S, or Cl. NMR shielding tensors were calculated using the SCF-HF, DFT-B3LYP, and CCSD(T) methods, combined with the Dunning valence aug-cc-pVXZ, core-valence aug-cc-pCVXZ, Jensen polarized-convergent aug-pcSseg-n and Karlsruhe x2c-Def2 basis set families. We also estimated the complete basis set limit (CBS) values of the NMR parameters. Widely scattered nuclear shieldings were observed for the Dunning polarized-valence basis set, which provides irregular convergence. We show that the use of Dunning core-valence or Jensen basis sets effectively reduces the scatter of theoretical NMR results and leads to their exponential-like convergence to CBS. We also assessed the effect of vibrational, temperature, and relativistic corrections on the predicted shieldings. For systems with single bonds, all corrections are relatively small, amounting to less than 4% of the CCSD(T)/CBS value. Vibrational and temperature corrections were less reliable for H3PO and HSiCH due to the high anharmonicity of the molecules. An abnormally high relativistic correction was observed for phosphorus in PN, reaching ~20% of the CCSD(T)/CBS value, while the correction was less than 7% for other tested molecules.

Theoretical and X-Ray Evidence of Electrostatic Phosphonium anti and gauche Effects.

Sulphur, not phosphorus, is the only known third-row element capable of experiencing an electrostatic gauche effect with fluorine. Some six-membered rings containing an endocyclic phosphorus atom and a β-fluorine substituent that can interconvert to axial (gauche relative to phosphorus) and equatorial positions were then analysed. While phosphines do not establish an electrostatic attraction between fluorine and phosphorus, some oxidised forms exhibit surprising stability for the sterically disfavoured axial orientation. Because the nature of this behaviour was not obvious, since an intramolecular hydrogen bond can appear, a phosphonium derivative was further studied and its axial conformation was found to be highly stable. A preference for the gauche arrangement appears even for the acyclic and sterically hindered (2-fluoroethyl)triphenylphosphonium cation. On the other hand, (ethane-1,2-diyl)bis(phosphonium) cations are exclusively in anti conformation due to an (+/+)-electrostatic repulsion between the positively charged phosphonium groups.

Benchmark relativistic delta-coupled-cluster calculations of K-edge core-ionization energies of third-row elements.

A benchmark computational study of K-edge core-ionization energies of third-row elements using relativistic delta-coupled-cluster (ΔCC) methods and a revised core-valence separation (CVS) scheme is reported. High-level relativistic (HLR) corrections beyond the spin-free exact two-component theory in its one-electron variant (SFX2C-1e), including the contributions from two-electron picture-change effects, spin-orbit coupling, the Breit term, and quantum electrodynamics effects, have been taken into account and demonstrated to play an important role. Relativistic ΔCC calculations are shown to provide accurate results for core-ionization energies of third-row elements. The SFX2C-1e-CVS-ΔCC results augmented with HLR corrections show a maximum deviation of less than 0.5 eV with respect to experimental values.

Grids III: Hydrogen Bridges in Introductory Chemistry

Based on IUPAC recommendations for the definition of the hydrogen bond, we present a series of grids to provide instructors of general chemistry with visual examples of H-bridged systems. The grids show the interactions among various groups and sort the interactions into types, based on their significance in general chemistry. Examples are organized by second-row elements, third-row elements, anions and cations.

Synthesis, characterisation and biological investigation of some third-row elements with halo- substituted coumarin schiff base with N and O as donors

The present work involves in the synthesis, spectral characterisation and the biological analysis of the metal complexes which were derived from 3-Chloro-8-formyl-7-hydroxy-4-methylcoumarin and benzylamine. The molar conductivity values indicated that the complexes are non-electrolytes. Elemental analysis was carried out to assign the [ML2(H2O)2] stoichiometry to the metal complexes, where M=Co (II), Ni (II) and Cu(II) and L=deprotonated ligand. The IR data confirmed coordination of metal ions to the ligand. The presence of a coordinated water molecule was investigated by thermal studies and the electronic spectral results were helpful in assigning the geometry to synthesised complexes. The both Schiff base and the derived metal complexes were subjected various biological activities to check their potency.

Computation of Dipole Moments: A Recommendation on the Choice of the Basis Set and the Level of Theory.

Together with experimental data, theoretically predicted dipole moments represent a valuable tool for different branches in the chemical and physical sciences. With the diversity of levels of theory and basis sets available, a reliable combination must be carefully chosen in order to achieve accurate predictions. In a recent publication (J. Chem. Theory Comput. 2018, 14 (4), 1969-1981), Hait and Head-Gordon took a first step in this regard by providing recommendations on the best density functionals suitable for these purposes. However, no extensive study has been performed to provide recommendations on the basis set choice. Here, we shed some light into this matter by evaluating the performance of 38 general-purpose basis sets of single- up to triple-ζ-quality, when coupled with nine different levels of theory, in the computation of dipole moments. The calculations were performed on a data set with 114 small molecules containing second- and third-row elements. We based our analysis in regularized root-mean-square errors (regularized RMSE), in which the difference between the calculated μcalc and benchmark μbmk dipole moment values is derived as (μcalc[D] - μbmk[D])/(max(μbmk[D],1[D])). This procedure ensures relative errors for ionic species and absolute errors for species with small dipole moment values. Our results indicate that the best compromise between accuracy and computational efficiency is achieved by performing the computations with an augmented double-ζ-quality basis set (i.e., aug-pc-1, aug-pcseg-1, aug-cc-pVDZ) together with a hybrid functional (e.g., ωB97X-V, SOGGA11-X). Augmented triple-ζ basis sets could enhance the accuracy of the computations, but the computational cost of introducing such a basis set is substantial compared with the small improvement provided. These findings also highlight the crucial role that augmentation of the basis set with diffuse functions on both hydrogen and non-hydrogen atoms plays in the computation of dipole moments.

Theoretical kinetic studies of Venus chemistry. Formation and destruction of SCl, SCl2, and HSCl

Accurate and thorough characterization of the chemistry of compounds containing the third-row elements sulfur and chlorine is critical for modeling the composition of the atmosphere of Venus. We have used a combination of ab initio quantum chemistry and kinetic theory to characterize a group of nine exothermic reactions that involve the exotic sulfur‑chlorine species SCl, SCl2, and HSCl, which are thought to be present in trace quantities in the atmosphere of Venus and are included to various degrees in the published atmospheric models. Reaction pathways were characterized with coupled cluster theory at the RCCSD(T) level with triple ζ quality correlation consistent basis sets. For reactions with barriers that lie above the reactant asymptote, the barrier height was extrapolated to the RCCSD(T) complete basis set level via single-point calculations with quadruple and quintuple ζ quality sets. Rate coefficients were predicted with capture theory and transition state theory as appropriate. We have found that in some cases addition-elimination reactions can compete with abstraction reactions due to the tendency of sulfur to form hypervalent compounds and intermediates via recoupled pair bonding.

Probing Sulfur Chemical and Electronic Structure with Experimental Observation and Quantitative Theoretical Prediction of Kα and Valence-to-Core Kβ X-ray Emission Spectroscopy.

An extensive experimental and theoretical study of the Kα and Kβ high-resolution X-ray emission spectroscopy (XES) of sulfur-bearing systems is presented. This study encompasses a wide range of organic and inorganic compounds, including numerous experimental spectra from both prior published work and new measurements. Employing a linear-response time-dependent density functional theory (LR-TDDFT) approach, strong quantitative agreement is found in the calculation of energy shifts of the core-to-core Kα as well as the full range of spectral features in the valence-to-core Kβ spectrum. The ability to accurately calculate the sulfur Kα energy shift supports the use of sulfur Kα XES as a bulk-sensitive tool for assessing sulfur speciation. The fine structure of the sulfur Kβ spectrum, in conjunction with the theoretical results, is shown to be sensitive to the local electronic structure including effects of symmetry, ligand type and number, and, in the case of organosulfur compounds, to the nature of the bonded organic moiety. This agreement between theory and experiment, augmented by the potential for high-access XES measurements with the latest generation of laboratory-based spectrometers, demonstrates the possibility of broad analytical use of XES for sulfur and nearby third-row elements. The effective solution of the forward problem, i.e., successful prediction of detailed spectra from known molecular structure, also suggests future use of supervised machine learning approaches to experimental inference, as has seen recent interest for interpretation of X-ray absorption near-edge structure (XANES).

The challenging equilibrium structure of HSSH: Another success of the rotational spectroscopy / quantum chemistry synergism

The simplest molecule with a disulfide bond, hydrogen disulfide (HSSH), represents an ideal test model for the determination of accurate gas-phase equilibrium structures for molecules containing third-row elements. First, pure theoretical composite schemes based on the coupled-cluster (CC) theory, which take into account the extrapolation to the complete basis set limit, core-valence correlation contributions, higher excitations in the CC expansion, and relativistic effects, allow for calculating accurate reference geometrical parameters. Second, using experimental vibrational ground-state rotational constants for a set of isotopologues, in conjunction with vibrational corrections based on second-order vibrational perturbation theory formulation and the recently developed Molecular Structure Refinement (MSR) software, we have determined the semi-experimental (SE) equilibrium structure of HSSH. The comparison of SE parameters with the computational best estimates shows an agreement within 0.001 Å for distances and 0.1° for angles, thus further validating the SE approach as cost-effective, provided that the required experimental data are available. Together with the intrinsic interest of HSSH, also in connection with astrochemistry, highly accurate structural properties of a prototypical disulfide bond can serve as references for future studies of larger molecules of biological interest containing this challenging moiety.

On the Lewis Basicity of Phosphoramides: A Critical Examination of Their Donor Number through Comparison of Enthalpies of Adduct Formation with SbCl5 and BF3.

The Lewis basicity of a series of phosphoryl compounds was examined using DFT and ab initio methods, including solvation effects. The enthalpies of adduct formation with two archetypal Lewis acids, antimony pentachloride and boron trifluoride, used to define the donor number DN and the BF3 affinity (BF3 A) respectively, were examined. The BF3 adducts allow the use of the high-accuracy G4 approach, whereas for SbCl5 adducts, three different DFT formalisms, including empirical dispersion corrections, were used because the G4 formalism is not available for third-row elements. For a comparison with experimental data, solvation effects were taken into account by using the polarizable continuum model. The experimental BF3 affinities were well reproduced by G4 calculations when including PCM solvation. Conversely, comparisons of our calculated values and experimental results reported in the literature show that SbCl5 enthalpies for phosphoramides are in error. In particular the DN for HMPA should be revised.

The complex non-collinear magnetic orderings in Ba2YOsO6: a new approach to tuning spin-lattice interactions and controlling magnetic orderings in frustrated complex oxides

Frustrated magnets are one class of fascinating materials that host many intriguing phases such as spin ice, spin liquid and complex long-range magnetic orderings at low temperatures. In this work we use first-principles calculations to find that in a wide range of magnetically frustrated oxides, at zero temperature a number of non-collinear magnetic orderings are more stable than the type-I collinear ordering that is observed at finite temperatures. The emergence of non-collinear orderings in those complex oxides is due to higher-order exchange interactions that originate from second-row and third-row transition metal elements. This implies a collinear-to-noncollinear spin transition at sufficiently low temperatures in those frustrated complex oxides. Furthermore, we find that in a particular oxide Ba2YOsO6, experimentally feasible uniaxial strain can tune the material between two different non-collinear magnetic orderings. Our work predicts new non-collinear magnetic orderings in frustrated complex oxides at very low temperatures and provides a mechanical route to tuning complex non-collinear magnetic orderings in those materials.

Spin-Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods.

The spin-orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ nd] q ( q = 1-4 and 6-9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin-orbit couplings (SOC) using one-electron Breit-Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations-relativistic elimination of small components (RESC), third-order Douglas-Kroll-Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction-were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ nd]5, the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d] q configuration ( q = 2-4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d] q configuration ( q = 6-8), the energy lowering of all 4F7/2, 5D1, and 5D3 states due to the SOC effects is smaller than those of the other SM states. This difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

Accurate Prediction of Hyperfine Coupling Tensors for Main Group Elements Using a Unitary Group Based Rigorously Spin-Adapted Coupled-Cluster Theory.

We present the development of a perturbative triples correction scheme for the previously reported unitary group based spin-adapted combinatoric open-shell coupled-cluster (CC) singles and doubles (COS-CCSD) approach and report on the applications of the newly developed method, termed "COS-CCSD(T)", to the calculation of hyperfine coupling (HFC) tensors for radicals consisting of hydrogen, second- and third-row elements. The COS-CCSD(T) method involves a single noniterative step with [Formula: see text] scaling of the computational cost for the calculation of triples corrections to the energy. The key feature of this development is the use of spatial semicanonical orbitals generated from standard restricted open-shell Hartree-Fock (ROHF) orbitals, which allows the unperturbed Hamiltonian operator to be defined in terms of a diagonal spin-free Fock operator. The HFC tensors are computed as a first-order property via implementation of an analytic derivative scheme. The required one-particle spin density matrix is computed by using one- and two-particle spin-free density matrices that are obtained from the analytic derivative implementation, in this way avoiding the use of any spin-dependent operator and maintaining spin adaptation of the CC wavefunction. Benchmark calculations of HFC tensors for a set of 21 radicals indicate reasonably good agreement of the COS-CCSD(T) results with experiment and a consistent improvement over the COS-CCSD method. We demonstrate that the accuracies of the isotropic hyperfine coupling constants obtained in unrestricted HF (UHF) reference based spin-orbital CCSD(T) calculations deteriorate when spin contamination in the UHF wavefunction is large, and the results may even become qualitatively incorrect when spin polarization is the driving mechanism. Within a similar noniterative perturbative treatment of triple excitations, the spin-adapted COS-CCSD(T) approach produces accurate results, thus ensuring cost-effectiveness together with reliability.

Simulating X-ray Emission Spectroscopy with Algebraic Diagrammatic Construction Schemes for the Polarization Propagator.

The calculation of X-ray emission spectra has been addressed with the algebraic diagrammatic construction (ADC) scheme, using a core-ionized wave function as the reference state. With this, the valence-to-core transitions are found as the first eigenstates with negative eigenvalues. The performance of the ADC hierarchical methods ADC(2), ADC(2)-x, and ADC(3/2) has been investigated on 17 transition of second-row elements (C, N, O, F, and Ne), and 5 transitions of third-row elements (S and Cl). We report ADC(2) results within 0.20 ± 0.36 eV of experimental values with an appropriate choice of basis set and when accounting for relativistic effects, with a slight tendency toward underestimating emission energies. By comparison, ADC(2)-x yields a similar spread in relative energies, but a consistent overestimation of approximately 1.5 eV. Going to ADC(3/2), we now observe an underestimation of emission energies and a larger error spread. By comparison, calculations of X-ray absorption spectra have been reported to favor the ADC(2)-x method, with ADC(2) showing the largest error when comparing to experimental values. The difference in ADC performance trends between these core spectroscopies are attributed to the different electron rearrangement effects in X-ray absorption and emission processes.

Confirmation of the link between central star binarity and extreme abundance discrepancy factors in planetary nebulae

It has recently been noted that there seems to be a strong correlation between planetary nebulae with close binary central stars, and highly enhanced recombination line abundances. We present new deep spectra of seven objects known to have close binary central stars, and find that the heavy element abundances derived from recombination lines exceed those from collisionally excited lines by factors of 5-95, placing several of these nebulae among the most extreme known abundance discrepancies. This study nearly doubles the number of nebulae known to have a binary central star and an extreme abundance discrepancy. A statistical analysis of all nebulae with measured recombination line abundances reveals no link between central star surface chemistry and nebular abundance discrepancy, but a clear link between binarity and the abundance discrepancy, as well as an anticorrelation between abundance discrepancies and nebular electron densities: all nebulae with a binary central star with a period of less than 1.15 days have an abundance discrepancy factor exceeding 10, and an electron density less than $\sim$1000 cm$^{-3}$; those with longer period binaries have abundance discrepancy factors less than 10 and much higher electron densities. We find that [O~{\sc ii}] density diagnostic lines can be strongly enhanced by recombination excitation, while [S~{\sc ii}] lines are not. These findings give weight to the idea that extreme abundance discrepancies are caused by a nova-like eruption from the central star system, occurring soon after the common-envelope phase, which ejects material depleted in hydrogen, and enhanced in CNONe but not in third-row elements.