Subshell fitting of relativistic atomic core electron densities for use in QTAIM analyses of ECP-based wave functions

Scalar-relativistic, all-electron density functional theory (DFT) calculations were done for free, neutral atoms of all elements of the periodic table using the universal Gaussian basis set. Each core, closed-subshell contribution to a total atomic electron density distribution was separately fitted to a spherical electron density function: a linear combination of s-type Gaussian functions. The resulting core subshell electron densities are useful for systematically and compactly approximating total core electron densities of atoms in molecules, for any atomic core defined in terms of closed subshells. When used to augment the electron density from a wave function based on a calculation using effective core potentials (ECPs) in the Hamiltonian, the atomic core electron densities are sufficient to restore the otherwise-absent electron density maxima at the nuclear positions and eliminate spurious critical points in the neighborhood of the atom, thus enabling quantum theory of atoms in molecules (QTAIM) analyses to be done in the neighborhoods of atoms for which ECPs were used. Comparison of results from QTAIM analyses with all-electron, relativistic and nonrelativistic molecular wave functions validates the use of the atomic core electron densities for augmenting electron densities from ECP-based wave functions. For an atom in a molecule for which a small-core or medium-core ECPs is used, simply representing the core using a simplistic, tightly localized electron density function is actually sufficient to obtain a correct electron density topology and perform QTAIM analyses to obtain at least semiquantitatively meaningful results, but this is often not true when a large-core ECP is used. Comparison of QTAIM results from augmenting ECP-based molecular wave functions with the realistic atomic core electron densities presented here versus augmenting with the limiting case of tight core densities may be useful for diagnosing the reliability of large-core ECP models in particular cases. For molecules containing atoms of any elements of the periodic table, the production of extended wave function files that include the appropriate atomic core densities for ECP-based calculations, and the use of these wave functions for QTAIM analyses, has been automated.     

Recent advances and perspectives in four-component Dirac-Kohn-Sham calculations

We review recent theoretical and computational advances in the full relativistic four-component Dirac-Kohn-Sham (DKS) approach and its application to the calculation of the electronic structure of chemical systems containing many heavy atoms. We describe our implementation of an all-electron DKS approach based on the use of G-spinor basis sets, Hermite Gaussian functions, state-of-the-art density-fitting techniques and memory distributed parallelism. This approach has enormously extended the applicability of the DKS method, including for example large clusters of heavy atoms, and opens the way for future key developments. We examine the current limitations and future possible applications of the DKS approach, including the implementation of four-current density functionals and real-time propagation schemes. This would make possible to describe molecules in strong fields, accurately accounting for relativistic kinematic effects and spin-orbit coupling.     

Long-range relativistic heavy atom effect on 1H NMR chemical shifts of selenium- and tellurium-containing compounds

Previously unknown manifestation of heavy atom effect on the NMR chemical shifts of β- and γ-protons initiated by the relativistic effects of the tellurium and selenium atoms has been investigated in the representative series of selenium- and tellurium-containing compounds. To approve the four-component density functional approach to be the appropriate tool for the investigation of the heavy atom on light atom effect (HALA), the benchmark calculations of the proton chemical shifts have been performed at the CCSD level using comprehensively chosen locally dense basis set with taking into account solvent, vibrational, and relativistic corrections. A good agreement with the experimental data was achieved. The magnitudes of the relativistic HALA corrections to β- and γ-proton chemical shifts were found to vary in a wide range, namely from −3.08 ppm for the γ-proton of methyltelluraldehyde to 14.51 ppm for β-proton in benzotelluraldehyde.     

对含重元素体系的接合二分量-标量相对论密度泛函计算方法

在相对论密度泛函ZORA方法的基础上,提出一种用于含重元素体系的接合二分量-标量相对论密度泛函计算方法.对于只含少数几个重元素的较大体系,仅对其中旋轨耦合作用强的重元素作二分量相对论计算,而对体系的其余部分则作标量相对论计算,通过对动能矩阵元的近似处理实现两种计算的接合.对一系列含6p区重元素分子进行计算的结果表明,当非重元素是第三周期以前的元素时,此方法与二分量ZO-RA方法的计算结果吻合得很好.当非重元素为第四周期元素时,计算结果有一定偏差,表明在后一种情况下旋轨耦合作用已比较显著,但误差仍在目前近似密度泛函计算的精度范围内.此方法可以有效地节省计算量,而且避免了Dyall方法的缺点.     

Chemical bonding in view of electron charge density and kinetic energy density descriptors

Stalke's dilemma, stating that different chemical interpretations are obtained when one and the same density is interpreted either by means of natural bond orbital (NBO) and subsequent natural resonance theory (NRT) application or by the quantum theory of atoms in molecules (QTAIM), is reinvestigated. It is shown that within the framework of QTAIM, the question as to whether for a given molecule two atoms are bonded or not is only meaningful in the context of a well‐defined reference geometry. The localized‐orbital‐locator (LOL) is applied to map out patterns in covalent bonding interaction, and produces results that are consistent for a variety of reference geometries. Furthermore, LOL interpretations are in accord with NBO/NRT, and assist in an interpretation in terms of covalent bonding. © 2008 Wiley Periodicals, Inc.J Comput Chem, 2009.     

Relativistic heavy-atom effects on heavy-atom nuclear shieldings

The principal relativistic heavy-atom effects on the nuclear magnetic resonance (NMR) shielding tensor of the heavy atom itself (HAHA effects) are calculated using ab initio methods at the level of the Breit-Pauli Hamiltonian. This is the first systematic study of the main HAHA effects on nuclear shielding and chemical shift by perturbational relativistic approach. The dependence of the HAHA effects on the chemical environment of the heavy atom is investigated for the closed-shell X(2+), X(4+), XH(2), and XH(3) (-) (X=Si-Pb) as well as X(3+), XH(3), and XF(3) (X=P-Bi) systems. Fully relativistic Dirac-Hartree-Fock calculations are carried out for comparison. It is necessary in the Breit-Pauli approach to include the second-order magnetic-field-dependent spin-orbit (SO) shielding contribution as it is the larger SO term in XH(3) (-), XH(3), and XF(3), and is equally large in XH(2) as the conventional, third-order field-independent spin-orbit contribution. Considering the chemical shift, the third-order SO mechanism contributes two-thirds of the difference of approximately 1500 ppm between BiH(3) and BiF(3). The second-order SO mechanism and the numerically largest relativistic effect, which arises from the cross-term contribution of the Fermi contact hyperfine interaction and the relativistically modified spin-Zeeman interaction (FC/SZ-KE), are isotropic and practically independent of electron correlation effects as well as the chemical environment of the heavy atom. The third-order SO terms depend on these factors and contribute both to heavy-atom shielding anisotropy and NMR chemical shifts. While a qualitative picture of heavy-atom chemical shifts is already obtained at the nonrelativistic level of theory, reliable shifts may be expected after including the third-order SO contributions only, especially when calculations are carried out at correlated level. The FC/SZ-KE contribution to shielding is almost completely produced in the s orbitals of the heavy atom, with values diminishing with the principal quantum number. The relative contributions converge to universal fractions for the core and subvalence ns shells. The valence shell contribution is negligible, which explains the HAHA characteristics of the FC/SZ-KE term. Although the nonrelativistic theory gives correct chemical shift trends in present systems, the third-order SO-I terms are necessary for more reliable predictions. All of the presently considered relativistic corrections provide significant HAHA contributions to absolute shielding in heavy atoms.     

“Through-Space” Relativistic Effects on NMR Chemical Shifts of Pyridinium Halide Ionic Liquids

We have investigated, using two-component relativistic density functional theory (DFT) at ZORA-SO-BP86 and ZORA-SO-PBE0 level, the occurrence of relativistic effects on the ¹H, ¹³C, and ¹⁵N NMR chemical shifts of 1-methylpyridinium halides [MP][X] and 1-butyl-3-methylpyridinium trihalides [BMP][X₃] ionic liquids (ILs) (X=Cl, Br, I) as a result of a non-covalent interaction with the heavy anions. Our results indicate a sizeable deshielding effect in ion pairs when the anion is I⁻ and I₃⁻. A smaller, though nonzero, effect is observed also with bromine while chlorine based anions do not produce an appreciable relativistic shift. The chemical shift of the carbon atoms of the aromatic ring shows an inverse halogen dependence that has been rationalized based on the little C-2s orbital contribution to the σ-type interaction between the cation and anion. This is the first detailed account and systematic theoretical investigation of a relativistic heavy atom effect on the NMR chemical shifts of light atoms in the absence of covalent bonds. Our work paves the way and suggests the direction for an experimental investigation of such elusive signatures of ion pairing in ILs.     

An efficient method for computing the QTAIM topology of a scalar field: The electron density case

An efficient method for computing the quantum theory of atoms in molecules (QTAIM) topology of the electron density (or other scalar field) is presented. A modified Newton–Raphson algorithm was implemented for finding the critical points (CP) of the electron density. Bond paths were constructed with the second‐order Runge–Kutta method. Vectorization of the present algorithm makes it to scale linearly with the system size. The parallel efficiency decreases with the number of processors (from 70% to 50%) with an average of 54%. The accuracy and performance of the method are demonstrated by computing the QTAIM topology of the electron density of a series of representative molecules. Our results show that our algorithm might allow to apply QTAIM analysis to large systems (carbon nanotubes, polymers, fullerenes) considered unreachable until now. © 2012 Wiley Periodicals, Inc.     

Halogen effect on structure and 13C NMR chemical shift of 3,6‐disubstituted‐N‐alkyl carbazoles

Structures of selected 3,6‐dihalogeno‐N‐alkyl carbazole derivatives were calculated at the B3LYP/6‐311++G(3df,2pd) level of theory, and their ¹³C nuclear magnetic resonance (NMR) isotropic shieldings were predicted using density functional theory (DFT). The model compounds contained 9H, N‐methyl and N‐ethyl derivatives. The relativistic effect of Br and I atoms on nuclear shieldings was modeled using the spin–orbit zeroth‐order regular approximation (ZORA) method. Significant heavy atom shielding effects for the carbon atom directly bonded with Br and I were observed (~?10 and ~?30 ppm while the other carbon shifts were practically unaffected). The decreasing electronegativity of the halogen substituent (F, Cl, Br, and I) was reflected in both nonrelativistic and relativistic NMR results as decreased values of chemical shifts of carbon atoms attached to halogen (C3 and C6) leading to a strong sensitivity to halogen atom type at 3 and 6 positions of the carbazole ring. The predicted NMR data correctly reproduce the available experimental data for unsubstituted N‐alkylcarbazoles. Copyright © 2013 John Wiley & Sons, Ltd.     

Normal halogen dependence of 13C NMR chemical shifts of halogenomethanes revisited at the four‐component relativistic level

The ‘Normal Halogen Dependence’ of ¹³C NMR chemical shifts in the series of halogenomethanes is revisited at the four‐component relativistic level. Calculations of ¹³C NMR chemical shifts of 70 halogenomethanes have been carried out at the density functional theory (DFT) and MP2 levels with taking into account relativistic effects using the four‐component relativistic theory of Dirac‐Coulomb within the different computational methods (4RPA, 4OPW91) and hybrid computational schemes (MP2 + 4RPA, MP2 + 4OPW91). The most efficient computational protocols are derived for practical purposes. Relativistic shielding effect reaches as much as several hundreds of ppm for heavy halogenomethanes, and to account for this effect in comparison with experiment at the qualitative level, relativistic Dyall's basis sets of triple‐zeta quality or higher are to be used within the framework of the four‐component relativistic theory taking into account solvent effects. Relativistic geometrical optimization (as compared with the non‐relativistic level) is essential for the molecules containing at least two iodines at one carbon atom. Copyright © 2016 John Wiley & Sons, Ltd.     

Atomic Contributions from Spin‐Orbit Coupling to 29Si NMR Chemical Shifts in Metallasilatrane Complexes

New members of a novel class of metallasilatrane complexes [X‐Si‐(μ‐mt)₄‐M‐Y], with M=Ni, Pd, Pt, X=F, Cl, Y=Cl, Br, I, and mt=2‐mercapto‐1‐methylimidazolide, have been synthesized and characterized structurally by X‐ray diffraction and by ²⁹Si solid‐state NMR. Spin‐orbit (SO) effects on the ²⁹Si chemical shifts induced by the metal, by the sulfur atoms in the ligand, and by heavy halide ligands Y=Cl, Br, I were investigated with the help of relativistic density functional calculations. Operators used in the calculations were constructed such that SO coupling can selectively be switched off for certain atoms. The unexpectedly large SO effects on the ²⁹Si shielding in the Ni complex with X=Y=Cl reported recently originate directly from the Ni atom, not from other moderately heavy atoms in the complex. With respect to Pd, SO effects are amplified for Ni owing to its smaller ligand‐field splitting, despite the smaller nuclear charge. In the X=Cl, Y=Cl, Br, I series of complexes the Y ligand strongly modulates the ²⁹Si shift by amplifying or suppressing the metal SO effects. The pronounced delocalization of the partially covalent M←Y bond plays an important role in modulating the ²⁹Si shielding. We also demonstrate an influence from the X ligand on the ²⁹Si SO shielding contributions originating at Y. The NMR spectra for [X‐Si‐(μ‐mt)₄‐M‐Y] must be interpreted mainly based on electronic and relativistic effects, rather than structural differences between the complexes. The results highlight the sometimes unintuitive role of SO coupling in NMR spectra of complexes containing heavy atoms.     

Biphenyl: A stress tensor and vector‐based perspective explored within the quantum theory of atoms in molecules

We use quantum theory of atoms in molecules (QTAIM) and the stress tensor topological approaches to explain the effects of the torsion φ of the C‐C bond linking the two phenyl rings of the biphenyl molecule on a bond‐by‐bond basis using both a scalar and vector‐based analysis. Using the total local energy density H( r _b), we show the favorable conditions for the formation of the controversial H–H bonding interactions for a planar biphenyl geometry. This bond‐by‐bond QTAIM analysis is found to be agreement with an earlier alternative QTAIM atom‐by‐atom approach that indicated that the H–H bonding interaction provided a locally stabilizing effect that is overwhelmed by the destabilizing role of the C‐C bond. This leads to a global destabilization of the planar biphenyl conformation compared with the twisted global minimum. In addition, the H( r _b) analysis showed that only the central torsional C‐C bond indicated a minimum for a torsion φ value coinciding with that of the conventional global energy minimum. The H–H bonding interactions are found to be topologically unstable for any torsion of the central C‐C bond away from the planar biphenyl geometry. Conversely, we demonstrate that for 0.0° < φ < 39.95° there is a resultant increase in the topological stability of the C nuclei comprising the central torsional C‐C bond. Evidence is found of the effect of the H–H bonding interactions on the torsion φ of the central C‐C bond of the biphenyl molecule in the form of the QTAIM response β of the total electronic charge density ρ( r _b). Using a vector‐based treatment of QTAIM we confirm the presence of the sharing of chemical character between adjacent bonds. In addition, we present a QTAIM interpretation of hyperconjugation and conjugation effects, the former was quantified as larger in agreement with molecular orbital (MO) theory. The stress tensor and the QTAIM H atomic basin path set areas are independently found to be new tools relevant for the incommensurate gas to solid phase transition occurring in biphenyl for a value of the torsion reaction coordinate φ ≈ 5°. © 2015 Wiley Periodicals, Inc.     

Relativistic density functional calculations using two-spinor minimax finite-element method and linear combination of atomic orbitals for ZnO, CdO, HgO, UubO and Cu2, Ag2, Au2, Rg2

In previous work the authors have presented a highly accurate two-spinor fully relativistic solution of the two-center Coulomb problem utilizing the finite-element method (FEM) and furthermore developed a relativistic minimax two-spinor linear combination of atomic orbitals (LCAO). In the present paper the authors present Dirac-Fock-Slater (DFS-) density functional calculations for two-atomic molecules up to super heavy systems using the fully nonlinear minimax FEM and the minimax LCAO in its linearized approximation (linear approximation to relativistic minimax). The FEM gives highly accurate benchmark results for the DFS functional. Especially considering molecules with up to super heavy atoms such as UubO and Rg2, the authors found that LCAO fails to give the correct systematic trends. The accurate FEM results shed a new light on the quality of the DFS-density functional.     

Latin American contributions to quantum chemical topology

We survey the contributions from Latin American theoretical chemists to the field of quantum chemical topology (QCT) over nearly the last 30 years with emphasis on the developments and applications of the quantum theory of atoms in molecules (QTAIM). Applications of QCT in the fields of excited states, electron delocalization, chemical bond, aromaticity, conformational analysis, spectroscopic properties, and chemical reactivity are presented. We also consider the coupling of QTAIM with time-dependent density functional theory, the virial theorem in the Kohn-Sham method and the inclusion of electron dynamical correlation in the interacting quantum atoms method using coupled cluster and multi-configurational densities. Additionally, we describe the development of efficient algorithms for the calculation of topological properties derived from the electron density. This review is aimed not only at providing an account of the contributions to QCT in Latin America but also at stimulating guides for further progress in the field.     

Toward a Consistent Interpretation of the QTAIM: Tortuous Link between Chemical Bonds,Interactions, and Bond/Line Paths

Currently, bonding analysis of molecules based on the Quantum Theory of Atoms in Molecules (QTAIM) is popular; however, “misinterpretations” of the QTAIM analysis are also very frequent. In this contribution the chemical relevance of the bond path as one of the key topological entities emerging from the QTAIM’s topological analysis of the one‐electron density is reconsidered. The role of nuclear vibrations on the topological analysis is investigated demonstrating that the bond paths are not indicators of chemical bonds. Also, it is argued that the detection of the bond paths is not necessary for the “interaction” to be present between two atoms in a molecule. The conceptual disentanglement of chemical bonds/interactions from the bonds paths, which are alternatively termed “line paths” in this contribution, dismisses many superficial inconsistencies. Such inconsistencies emerge from the presence/absence of the line paths in places of a molecule in which chemical intuition or alternative bonding analysis does not support the presence/absence of a chemical bond. Moreover, computational QTAIM studies have been performed on some “problematic” molecules, which were considered previously by other authors, and the role of nuclear vibrations on presence/absence of the line paths is studied demonstrating that a bonding pattern consistent with other theoretical schemes appears after a careful QTAIM analysis and a new “interpretation” of data is performed.