Relativistic Basis Sets Research Articles

Relativistic Coupled Cluster with Completely Renormalized and Perturbative Triples Corrections.

We have implemented noniterative triples corrections to the energy from coupled-cluster with single and double excitations (CCSD) within the 1-electron exact two-component (1eX2C) relativistic framework. The effectiveness of both the CCSD(T) and the completely renormalized (CR) CC(2,3) approaches are demonstrated by performing all-electron computations of the potential energy curves and spectroscopic constants of copper, silver, and gold dimers in their ground electronic states. Spin-orbit coupling effects captured via the 1eX2C framework are shown to be crucial for recovering the correct shape of the potential energy curves, and the correlation effects due to triples in these systems change the dissociation energies by about 0.1-0.2 eV or about 4-7%. We also demonstrate that relativistic effects and basis set size and contraction scheme are significantly more important in Au2 than in Ag2 or Cu2.

Quantum mechanical study of transition metal hydrides: Comparison of determined molecular properties with experimental data.

This study compares results of four relativistic pseudopotential basis sets, which differ mainly by their size: double-zeta introduced by Hay and Wadt from Los Alamos National Laboratory (LANL2DZ), triple-zeta based on Stuttgart energy-consistent scalar-relativistic pseudopotential (SDD3), its extension with 2fg polarization functions, and combination of Stuttgart pseudopotentials with quintuple-zeta cc-pV5Z base (SDD5). Hydrides of transition metals from Cr to Zn group are chosen as reference molecules. The coupled cluster method (CCSD(T)) is used for evaluation of selected molecular characteristics. Interatomic distances, dissociation energies, vibration modes, and anharmonicity constants are determined and compared with available experimental data. As expected, the accuracy of basis depends mainly on its size. However, only moderate modification of SDD3 basis set significantly improves its accuracy, which becomes comparable to the largest basis set. Nevertheless, the time consumption is significantly lower.

The surface chemistry of norbornadiene and norbornene on Pd(111) and Pd(100): a comparative DFT study.

The interaction of norbornadiene (NBD) and norbornene (NBE) with the palladium (111) and (100) surfaces have been investigated using density functional theory (DFT). Five configurations of adsorbed NBD may be formed on Pd(111): endo-tetra-σ, endo-di-σ,π, endo-di-π, exo-di-σ, and exo-π. The NBE molecule adsorbed on Pd(111) may exist in 4 configurations: endo-di-σ, endo-π, exo-di-σ, and exo-π. On Pd(100), a smaller number adsorption configurations of NBD and NBE are formed, since the double bonds of these molecules in the endo-orientation are bound only in a di-σ mode. The adsorption energy of NBD and NBE molecules on Pd(100) is noticeably higher compared to Pd(111), which is due to the surface geometry of Pd(100). The most stable configurations on both Pd facets are endo-tetra-σ for NBD and exo-di-σ for NBE. However, due to smaller adsorption area of the exo-di-σ configuration on Pd(111), a larger number of NBD molecules may adsorbed on the same surface area. Energetically favorable endo-tetra-σ (NBD) and exo-di-σ (NBE) configurations are very mobile on Pd(111). On Pd(100), only NBE molecules can migrate, while NBD migration is hindered due to the high activation barrier. All DFT calculations were performed using the Perdew-Burke-Ernzerhof density functional (PBE) with the relativistic SBK effective core potential and TZ2P basis set in the PRIRODA program.

Water Solvated Zn(II)-Guanine Complex: Structural Aspects and Luminescence Properties.

Understanding the role of metal ions in living organisms and their interactions with biological compounds is fundamental for our health and for developing technological devices for bioinorganic applications. In this work, structural aspects and photophysical mechanisms involved in the luminescence of the Zn(II)-guanine complex in water were studied by using computational quantum chemical methods, providing molecular-level explanations for reported experimental findings. Structural aspects were investigated with def2-SVP basis sets, Density Functional Theory, Resolution of Identity Algebraic Diagrammatic Construction in Second-Order (RI-ADC(2)), Polarizable Continuum Model (PCM), and Conductor-like Screening Model (COSMO) methods. Spectroscopic properties and photophysical deactivation mechanisms were explored with the atomic natural orbital basis sets including relativistic and semicore correlation (ANO-RCC-VDZP) basis sets, Multistate Complete-Active-Space Second-Order Perturbation Theory (MS-CASPT2), and Polarizable Continuum Model (PCM) methods. Our results indicate that Zn(II) ions bind preferentially to the N7 position, and three water molecules in its coordination sphere are sufficient for describing the photophysical properties. The complexation with Zn(II) ions and solvation effects favor fluorescence because the minimum energy region of the S1 (La) (1ππ*) ((La)min) potential energy hypersurface is stabilized, the (La/GS) crossing region is destabilized, and a high energetic barrier along the pathway from the (La)min and (La/GS) regions hampers fast nonradiative return of the electronic population to the ground state, as observed for isolated 9H-guanine.

Diffuse Basis Functions for Relativistic s and d Block Gaussian Basis Sets

Diffuse s, p, and d functions have been optimized for use with previously reported relativistic basis sets for the s and d blocks of the periodic table. The functions were optimized on the 4:1 weighted average of the s2 and p2 configurations of the anion, with the d shell in the dn+1 configuration for the d blocks. Exponents were extrapolated for groups 2 and 12, which have unstable or weakly bound anions. The diffuse basis sets have been tested by application to calculations of electron affinities of the group 11 elements (Cu, Ag, and Au), double electron affinities of the group 11 monocations, and potential energy curves of Mg2 and Ca2 van der Waals dimers, as well as some response properties of the group 1 anions (Rb-, Cs-, and Fr-), the group 2 elements (Sr, Ba, and Ra), and RbLi, CsLi, and FrLi molecules.

ADVANCED STUDY OF SPECTRAL AND HYPERFINE STRUCTURE PARAMETERS FOR Li-LIKE MULTICHARGED IONS WITHIN Relativistic Theory

The relativistic many-body perturbation theory with the optimized Dirac zeroth approximation is applied to calculation of some fundamental characteristics of the hyperfine structure of middle and heavy Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with performance of the gauge invariance principle. There are listed the calculated values of derivatives of the one-electron characteristics, including the hyperfine structure parameters, on nuclear radius for the Li-like multicharged ions with the corresponding analysis.

Relativistic Segmented Correlation Consistent Basis Sets for the 5p and 6p Elements.

The relativistic all-electron triple-ζ (TZ) and quadruple-ζ (QZ) correlation-consistent basis sets for the 5p and 6p elements were reoptimized to have a segmented contraction scheme. Properties computed with the segmented basis sets using the coupled-cluster level of theory with single, double, and perturbative triple excitations closely match the results obtained using the generally contracted analogues. Deviations in the ionization potentials and electron affinities computed using the segmented basis sets compared with those computed with the generally contracted basis sets are within 1 kcal mol-1. The relative deviation in the computed bond lengths for a selection of diatomic molecules is within 0.02 Å, and the computed harmonic vibrational frequencies differ by less than 3%. The mean absolute deviations (MADs) in the computed bond dissociation energies are 1.01 and 1.31 kcal mol-1 for the TZ and QZ basis sets, respectively, when only the valence electrons are correlated and 0.14 and 0.10 kcal mol-1 for the TZ and QZ basis sets, respectively, when the valence and outer-core electrons are correlated. The segmented basis sets also retain the systematically convergent behavior intrinsic to the correlation-consistent family of basis sets while affording speedups for the average time required to form the Fock matrix from 32.8 to 82.9× compared to the time required with the generally contracted versions when used with integral algorithms employed by many computational chemistry software packages.

Chemical kinetic properties of HNgF → HF + Ng (Ng = Ar, Kr, Xe, and Rn) reactions: An example of fortuitous cancelling of relevant relativistic effects

The relativistic effects on energetic quantities of the HNgF → HF + Ng (Ng = Ar, Kr, Xe, and Rn) reactions were evaluated by means of advanced four-component calculations with high-level electron correlation treatment and adequate relativistic basis sets. The results indicate that the scalar relativistic corrections can provide classical barrier height increments of as much as 4.8% (1.9 kcal mol−1) for the reaction with the heaviest noble gas, radon, while the spin-orbit coupling is almost as important in this case, lowering the value by 3.8% (−1.5 kcal mol−1). Therefore, these two relevant relativistic corrections cancel almost completely. A similar picture is seen for the energy variation from the reactant (HRnF) to the products (HF + Rn), but the contribution signs are reversed now (−4.0 and 3.4 kcal mol−1). A partial cancelling is also noticed for the HXeF → HF + Xe reaction. Such pattern is surprising since scalar relativistic effects usually predominate by magnitude orders over the spin-orbit coupling. These conclusions are reflected in the changes observed in rate constant values. Finally, an alternative decomposition route catalyzed by HF is suggested for these HNgF compounds, which can shed some light on the controversies regarding their thermal stability.

NMR Indirect Spin–Spin Coupling Constants in a Modern Quasi-Relativistic Density Functional Framework

A quasi-relativistic implementation of NMR indirect spin-spin coupling constants is presented. The exact two-component (X2C) Hamiltonian and its diagonal local approximation to the unitary decoupling transformation (DLU) are utilized together with the (modified) screened nuclear spin-orbit approach. In a restricted kinetic balance, the finite nucleus model is available for both the scalar and vector potentials. The implementation supports density functionals up to the fourth rung of Jacob's ladder, i.e., (range-separated) hybrid and local hybrid functionals based on a seminumerical ansatz. We assess the quality of our quasi-relativistic X2C approach by comparison with "fully" relativistic four-component results for small main-group molecules and alkynyl compounds. The mean absolute error introduced by the DLU scheme is less than 0.05 × 1019 T J-2 of the reduced coupling constant for the small main-group molecules and 0.5 Hz for the alkynyl compounds. Thus, the error is significantly smaller than finite nucleus size effects for heavy elements. The basis set convergence and the impact of different density functional approximations are further studied. We propose a simple scheme to develop segmented-contracted relativistic all-electron basis sets for NMR spin-spin couplings. Our implementation allows us to perform calculations of extended molecules with reasonable computational effort, which is illustrated for the 1J(119Sn, 31P) coupling constant of a low-valent tin phosphinidenide complex. The corresponding results are in good agreement with the experimental findings.

Spin-Orbit Coupling Effect on the Electrophilicity Index, Chemical Potential, Hardness and Softness of Neutral Gold Clusters: A Relativistic Ab-initio Study

Electrophilicity index (𝜔) is related to the energy lowering associated with a maximum amount of electron flow between a donor and an acceptor and possesses adequate information regarding structure, stability, reactivity and interactions. Chemical potential (μ) measures charge transfer from a system to another having a lower value of μ, while chemical hardness (η) is a measure of characterizing relative stability of clusters. The main purpose of the present research work is to examine the Spin-Orbit Coupling (SOC) effect on the behavior of the electrophilicity index, chemical potential, hardness and softness of neutral gold clusters Aun (n=2-6). Using the second-order Douglas-Kroll-Hess Hamiltonian, geometries are optimized at the DKH2-B3P86/DZP-DKH level of theory. Spin-orbit coupling energies are computed using the fourth-order Douglas-Kroll-Hess Hamiltonian, generalized Hartree-Fock method and all-electron relativistic double-ζ level basis set. Then, spin-orbit coupling (SOC) corrections to the electrophilicity index, chemical potential, hardness and softness are calculated. It is revealed that spin-orbit correction to the vertical chemical hardness has important effect on Au3 and Au6, i.e. SOC decreases (increases) the hardness of gold trimer (hexamer). Due to the relationship between hardness and softness, σ = , inclusion of spin-orbit coupling increases (decreases) the softness of Au3 (Au6) and thus destabilizes (stabilizes) it. Spin-orbit coupling (SOC) also has more important effect on the chemical potential of Au3 by decreasing its value. It is found that spin-orbit coupling has considerable effect on the electrophilicity index of gold trimer and greatly increases its value. Furthermore, SOC increases the maximal charge acceptance of Au3 more and thus destabilizes it more. As a result, spin-orbit coupling effect appears to be important in calculating the electrophilicity index of the gold trimer. Doi: 10.28991/HIJ-2021-02-01-05 Full Text: PDF

QUANTUM CHEMICAL INVESTIGATION OF TIN–SUBSTITUENT BONDS IN TIN(II) ORGANIC COMPOUNDS

The tin–substituent bonds in Sn(II) organic compounds are studied by quantum chemical methods using the PC GAMESS-Firefly program package. The geometry optimization for the studied molecules is carried out by the DFT method (B3PW91functional, using the aug-cc-pVTZ-pp basis set with an effective core potential for tin and the 6-311++(2d,p) basis set for other atoms. The wave functions and the NBOs of tin–substituent bonds were calculated by the HF method using the x2c-TZVPall-electron relativistic basis set for the tin atom and the 6-311G(2d,p) basis set for other atoms. The values of topological characteristics of tin–substituent bonds are obtained by the AIM method. These bonds can be classified as “intermediate bonds” characterized by small contributions of Sn AOs in the MOs of the bonds, large differences between the charges on tin atoms, and low occupancies of the MOs of the bonds. The energies of Sn–R bonds are estimated.

1H and 195Pt NMR prediction for inclusion compounds formed by cisplatin and oxidized carbon nanostructures.

Prediction of NMR chemical shifts can assist experimentalists in the characterization of drug delivery systems based on carbon nanocomposites. Chemical shifts are strongly correlated to the nucleus position and its chemical neighborhood. Therefore, to predict structures and NMR properties of complex chemical models, choosing a more consistent theoretical level capable of providing more realistic results and moderate computational demand is a major challenge. In this work, we predicted the NMR spectra of inclusion compounds formed by cisplatin (cDDP) and an oxidized carbon nanotube (CNTox) and nanocone (CNCox) considered by specialists as potential drug delivery systems. The 195Pt NMR chemical shifts calculated at the DFT level with the new relativistic NMR-DKH basis set were −2314 ppm and −2192 ppm for cDDP@CNTox and cDDP@CNCox complexes, respectively, which are both high-field shifted relative to the free cDDP (−2110 ppm). 1H NMR chemical shifts are also sensitive to the inclusion process. The H (NH3) signals are found on average at +4.3 (cDDP), −5.1 (cDDP@CNTox) and +6.6 ppm (cDDP@CNCox). Interestingly, despite the similar inclusion modes in CNTox and CNCox cavities, the 1H NMR shifts were in opposite directions. A possible reason might be the higher stability of cDDP@CNTox (ΔEF = −19.9 kcal mol−1) than that of cDDP@CNCox (ΔEF = −5.7 kcal mol−1), which suggests a short guest–host contact in the former and consequently, a more efficient shielding of hydrogen atoms due to the electron-rich carbon structure. These results may be helpful as comparison data in the NMR spectra assignment in solution and the inclusion compounds' structural elucidation.

All-electron scalar relativistic basis sets for the elements Rb-Xe.

Segmented all-electron relativistically contracted (SARC) basis sets are presented for the elements 37 Rb-54 Xe, for use with the second-order Douglas-Kroll-Hess approach and the zeroth-order regular approximation. The basis sets have a common set of exponents produced with established heuristic procedures, but have contractions optimized individually for each scalar relativistic Hamiltonian. Their compact size and loose segmented contraction, which is in line with the construction of SARC basis sets for heavier elements, makes them suitable for routine calculations on large systems and when core spectroscopic properties are of interest. The basis sets are of triple-zeta quality and come in singly or doubly polarized versions, which are appropriate for both density functional theory and correlated wave function theory calculations. The quality of the basis sets is assessed against large decontracted reference basis sets for a number of atomic and ionic properties, while their general applicability is demonstrated with selected molecular examples.

HYPERFINE STRUCTURE PARAMETERS FOR Li-LIKE MULTICHARGED IONS WITHIN RELATIVISTIC MANY-BODY PERTURBATION THEORY

The relativistic many-body perturbation theory with the optimized Dirac-Kohn-Sham zeroth approximation is applied to calculation of the hyperfine structure parameters for some Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with fulfilment of the gauge invariance principle. The obtained data on the hyperfine structure parameters of the Li-like multicharged ions are analyzed and compared with alternative theoretical and experimental results.

Quasi-Atomic Bond Analyses in the Sixth Period: I. Relativistic Accurate Atomic Minimal Basis Sets for the Elements Cesium to Radon

Full-valence relativistic accurate atomic minimal basis set (AAMBS) orbitals are developed for the sixth-row elements from cesium to radon, including the lanthanides. Saturated primitive atomic basis sets are developed and subsequently used to form the AAMBS orbitals. By virtue of the use of a saturated basis, properties computed based on the AAMBS orbitals are basis set independent. In molecules, the AAMBS orbitals can be used to construct valence virtual orbitals (VVOs) that provide chemically meaningful ab initio lowest unoccupied molecular orbitals (LUMOs) with basis set independent orbital energies. The optimized occupied molecular orbitals complemented with the VVOs form a set of full-valence molecular orbitals. They can be transformed into a set of oriented quasi-atomic orbitals (QUAOs) that provide information on intramolecular bonding via an intrinsic density analysis. In the present work, the development of the AAMBS for the sixth row is presented.

Error-consistent segmented contracted all-electron relativistic basis sets of double- and triple-zeta quality for NMR shielding constants.

We present property-tailored all-electron relativistic Karlsruhe basis sets for the elements hydrogen to radon. The modifications described herein use at most four additional primitive basis functions and re-optimized contraction coefficients of the inner-most segment. Thus, the shielding constants are improved while maintaining the compactness of the basis set. A large set of 255 closed-shell molecules was used to assess the quality of the developed bases throughout the periodic table of elements.

Хвильові і осциляторні сильні сторони Li-подібних багатозарядних іонів в рамках теорії відносного збудження багатьох тіл

The relativistic many-body perturbation theory with the optimized Dirac-Kohn-Sham zeroth approximation is applied to calculation of the radiative transitions wavelengths and oscillator strengths for some Li-like multicharged ions. The relativistic, exchange-correlation and other corrections are accurately taken into account. The optimized relativistic orbital basis set is generated in the optimal many-body perturbation theory approximation with fulfilment of the gauge invariance principle. An accurate treatment of the QED perturbation theory fourth order (a second order of the atomic perturbation theory) Feynman diagrams (whose contribution into the energy shift imaginary part (radiation width) for the multi-electron atoms accounts for multi-body correlation effects) is performed. The obtained data on the radiative transition wavelengths and oscillator strengths for some transition in spectra of the Li-like multicharged ions are analyzed and compared with alternative theoretical and experimental results.

New compact density matrix averaged ANO basis sets for relativistic calculations.

When including relativistic effects in quantum chemical calculations, basis sets optimized for relativistic Hamiltonians such as the atomic natural orbital-relativistic core-correlated (ANO-RCC) basis set have to be used to avoid large errors that appear upon contraction of the basis set. While the large size of the ANO-RCC basis set in terms of primitive basis functions allows for highly accurate calculations, it also hinders its applicability to large sized systems due to the computational costs. To tackle this problem, a new compact relativistic ANO basis set, the ANO-eXtra Small (XS) basis set, is introduced for elements H-Ca. The number of primitive basis functions in ANO-XS is about half that of the ANO-RCC basis set. This greatly reduces the computational costs in the integral calculations especially when used in combination with Cholesky decomposition. At the same time, the ANO-XS basis set is able to predict molecular properties such as bond lengths and excitation energies with reasonable errors compared to the larger ANO-RCC basis set. The main intention for the ANO-XS basis set is to be used in conjunction with the ANO-RCC basis set for large systems that can be divided with regions demanding different qualities of basis sets. This is exemplified in CASPT2 calculations for an Ir(C3H4N)3 complex, where substituting the larger ANO-RCC for the compact ANO-XS basis set at the ligand atoms yields only minor differences for a large number of excited states compared to calculations employing the ANO-RCC basis set on all atoms. Thus, accurate calculations including relativistic effects for large systems become more affordable with the new ANO-XS basis set.

Structure, stability, catalytic activity, and polarizabilities of small iridium clusters**Project supported by the CNPq, CAPES, and FAPES (Brazilian Agencies).

At the second order Douglas–Kroll–Hess (DKH2) level, the B3PW91 functional in conjunction with the relativistic all-electron basis set of valence triple zeta quality plus polarization functions are employed to compute bond lengths, dissociation energies, vertical ionization potentials, and the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the small iridium clusters (Irn, n ⩽ 8). These results are compared with the experimental and theoretical data available in the literature. Our results confirm the theoretical predictions made by Feng et al. about the catalytic activities of the Ir4 and Ir6 clusters. From the optimized geometries, DKH2 calculations of static electric mean dipole polarizabilities and polarizability anisotropies are also carried out. It is the first time that the polarizabilities of small iridium clusters have been studied. For n ⩽ 4, the mean dipole polarizabilities per atom present an odd–even oscillatory behavior, whereas from Ir5 to Ir8, they decrease with the cluster size increasing. The dependence of the polarizability anisotropy on the structure symmetry of the iridium cluster is verified.

Chemical Shift of the Kα1 and Kα2 Lines of the X-ray Emission Spectrum of Yb(II)/Yb(III) Fluorides: a Quantum-Chemical Investigation

Chemical shifts of the Kα1 and Kα2 lines (the 2p3/2 → 1s1/2 and 2p1/2 → 1s1/2 transitions, respectively) of the X-ray emission spectrum of the Yb atom in fluorides have been calculated by ab initio modeling the electronic structure. The valence transition Yb(II) → Yb(III) has been analyzed by examples of YbF2, YbF3, and Yb2F4 molecules and YbF2+ cation. The relativistic pseudopotential and basis sets corresponding to it have been constructed for the ytterbium atom. They were used in calculations by the two-component noncollinear version of the density functional theory (DFT) with the PBE0 exchange-correlation functional. Results for the three-coordinated Yb(II) in the FYbF2YbF dimer demonstrated a very weak dependence of the chemical shift on the coordination number of the Yb atom and on the molecular association of ytterbium difluoride. Chemical shifts of the X-ray emission spectrum for the ytterbium compound are related mainly to the change in the occupation of the 4 f shell.