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.     

An open library of relativistic core electron density function for the QTAIM analysis with pseudopotentials

Based on two‐component relativistic atomic calculations, a free electron density function (EDF) library has been developed for nearly all the known ECPs of the elements Li (Z = 3) up to Ubn (Z = 120), which can be interfaced into modern quantum chemistry programs to save the .wfx wavefunction file. The applicability of this EDF library is demonstrated by the analyses of the quantum theory of atoms in molecules (QTAIM) and other real space functions on HeCuF, , OgF₄, and TlCl₃(DMSO)₂. When a large‐core ECP is used, it shows that the corrections by EDF may significantly improve the properties of some density‐derived real space functions, but they are invalid for the wavefunction‐depending real space functions. To classify different chemical bonds and especially some nonclassical interactions, a list of universal criteria has also been proposed. © 2018 Wiley Periodicals, Inc.     

QTAIM charge-charge flux-dipole flux interpretation of electronegativity and potential models of the fluorochloromethane mean dipole moment derivatives

Infrared fundamental vibrational intensities and quantum theory atoms in molecules (QTAIM) charge-charge flux-dipole flux (CCFDF) contributions to the polar tensors of the fluorochloromethanes have been calculated at the QCISD/cc-pVTZ level. A root-mean-square error of 20.0 km mol(-1) has been found compared to an experimental error estimate of 14.4 and 21.1 km mol(-1) for MP2/6-311++G(3d,3p) results. The errors in the QCISD polar tensor elements and mean dipole moment derivatives are 0.059 e when compared with the experimental values. Both theoretical levels provide results showing that the dynamical charge and dipole fluxes provide significant contributions to the mean dipole moment derivatives and tend to be of opposite signs canceling one another. Although the experimental mean dipole moment derivative values suggest that all the fluorochloromethane molecules have electronic structures consistent with a simple electronegativity model with transferable atomic charges for their terminal atoms, the QTAIM/CCFDF models confirm this only for the fluoromethanes. Whereas the fluorine atom does not suffer a saturation effect in its capacity to drain electronic charge from carbon atoms that are attached to other fluorine and chlorine atoms, the zero flux electronic charge of the chlorine atom depends on the number and kind of the other substituent atoms. Both the QTAIM carbon charges (r = 0.990) and mean dipole moment derivatives (r = 0.996) are found to obey Siegbahn's potential model for carbon 1s electron ionization energies at the QCISD/cc-pVTZ level. The latter is a consequence of the carbon mean derivatives obeying the electronegativity model and not necessarily to their similarities with atomic charges. Atomic dipole contributions to the neighboring atom electrostatic potentials of the fluorochloromethanes are found to be of comparable size to the atomic charge contributions and increase the accuracy of Siegbahn's model for the QTAIM charge model results. Substitution effects of the hydrogen, fluorine, and chlorine atoms on the charge and dipole flux QTAIM contributions are found to be additive for the mean dipole derivatives of the fluorochloromethanes.     

Spin resolved electron number distribution functions: how spins couple in real space

The probabilities of finding arbitrary partitions of the N(alpha)m(s)=12 and N(beta)m(s)=-12 electrons of a molecule into m arbitrary regions that exhaust the physical space are developed and computed, both for atomic and electron localization function basins, in a number of test systems. These spin resolved electron number distribution functions provide access to the coarse-grained distribution of spins in space even for singlet states, a nontrivial result. It is found that atoms within molecules partially retain their in vacuo preferences for certain spin configurations. This may lead to long range spin coupling among basins. An aufbaulike rule favoring spin coupling, particularly for Hartree-Fock wave functions, has also been found.     

An atomic charge study of highly ionic diatomic molecular systems

Four atomic charge formalisms are compared using highly ionic diatomic molecules, such as LiF, NaF, KF, LiCl, NaCl, KCl, BF, AlF, GaF, BeO, and MgO. All calculations were done at the QCISD/6‐311G(2df) level. The only formalism consistent with the characteristics of all these systems is Quantum theory of atoms in molecules (QTAIM). Absolute Mulliken charge values are small. ChelpG charges are not reliable for systems in which the atoms are largely anisotropic. Generalized atomic polar tensor values are contaminated with charge fluxes and atomic dipole fluxes and fail when these contributions are important and do not cancel each other. Finally, the charge–charge flux–dipole flux model was applied to dipole moment derivatives with QTAIM. This analysis shows that charge flux and atomic dipole flux contributions during bond stretching are almost null, except for oxides. There are also evidences that the lone electron pair at Group 13 elements in fluorides becomes less localized as the bond is stretched. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

Chemical fragments in real space: definitions, properties, and energetic decompositions

The physical and chemical meaning of real space molecular fragments resulting from arbitrary partitions of the density is reviewed under a common unifying formalism. Both fuzzy (interpenetrating) and non-fuzzy (exhaustive) decompositions are treated on an equal basis. Density decompositions are consistently generalized to compatible density matrix partitions by using Li and Parr's ideas (Li and Parr J Chem Phys 1986, 84, 1704), and these are carried onto an energy partition. It is argued that the merits of a given decomposition should be judged against both the charge and the energetic image it provides. Atomic partitions are used to show how the interacting quantum atoms approach (IQA) allows us to cope with the most important energy cancellations of quantum chemistry. Binding results from a trade-off between atomic (or fragment) energy deformations with respect to a reference and interatomic (interfragment) interactions. Deformation energies are divided into charge transfer and redistribution terms and their relative roles are analyzed. A number of systems are compared against the fuzziness of different density decompositions. The results consistently show that fuzzy partitions tend to give low atomic net charges and enhanced covalency, while exhaustive partitions generate larger net charges and smaller covalencies, across a wide range of bonding regimes.     

How big are atoms in crystals?

Atoms and bonds are central concepts in structural chemistry, but neither are concepts that arise naturally from the physics of condensed phases. It is ironic that the internuclear distances in crystals that are readily measured depend on the sizes of atoms, but since atoms in crystals can be defined in many different ways, all of them arbitrary and often incompatible, there is no natural way to express atomic size. I propose a simple coherent picture of Atoms-in-Crystals which combines properties selected from three different physically sound definitions of atoms and bonds. The charge density of the free atom that is used to construct the procrystal is represented by a sphere of constant charge density having the quantum theory of atoms in molecules (QTAIM) bonded radius. The sum of these radii is equal to the bond length that correlates with the bond flux (bond valence) in the flux theory of the bond. The use of this model is illustrated by answering the question: How big are atoms in crystals? The QTAIM bonded radii are shown to be simple functions of two properties, the number of quantum shells in the atomic core and the flux of the bond that links neighbouring atoms. Various radii can be defined. The univalent bonded radius measures the intrinsic size of the atom and is the same for all cations in a given row of the periodic table, but the observed bonded radius depends also on the bond flux that reflects the chemical environment.     

Atoms in molecules interpretation of the anomeric effect in the O--C--O unit

The conformational preferences of two model compounds for the O--CH2--O anomeric unit: methanediol and dimethoxymethane analyzed within the framework of the QTAIM theory provide a new interpretation of the anomeric effect. The characteristic stabilization of the gauche conformers of these compounds is accompanied by a progressive reduction of the electron population of the hydrogens of the central methylene as the number of their gauche interactions to lone pairs rises. The electron population removed from these atoms during the conformational change is gained in the gauche conformers by atoms of larger atomic number, which results in a more negative molecular energy. Also, the variations displayed by atomic populations and the QTAIM delocalization indexes are not keeping in line with the hyperconjugative model of the anomeric effect.     

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

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

Comparison of direct and flow integration based charge density population analyses

Different exhaustive and fuzzy partitions of the molecular electron density (rho) into atomic densities (rho(A)) are used to compute the atomic charges (Q(A)) of a representative set of molecules. The Q(A)'s derived from a direct integration of rho(A) are compared to those obtained from integrating the deformation density rho(def) = rho - rho(0) within each atomic domain. Our analysis shows that the latter methods tend to give Q(A)'s similar to those of the (arbitrary) reference atomic densities rho(A)(0) used in the definition of the promolecular density, rho(0) = SigmaArho(A)(0). Moreover, we show that the basis set independence of these charges is a sign not of their intrinsic quality, as commonly stated, but of the practical insensitivity on the basis set of the atomic domains that are employed in this type of methods.     

Quantum theory of atoms in molecules charge-charge flux-dipole flux models for the infrared intensities of X(2)CY (X = H, F, Cl; Y = O, S) molecules

The molecular dipole moments, their derivatives, and the fundamental IR intensities of the X2CY (X = H, F, Cl; Y = O, S) molecules are determined from QTAIM atomic charges and dipoles and their fluxes at the MP2/6-311++G(3d,3p) level. Root-mean-square errors of +/-0.03 D and +/-1.4 km mol(-1) are found for the molecular dipole moments and fundamental IR intensities calculated using quantum theory of atoms in molecules (QTAIM) parameters when compared with those obtained directly from the MP2/6-311++G(3d,3p) calculations and +/-0.05 D and 51.2 km mol(-1) when compared with the experimental values. Charge (C), charge flux (CF), and dipole flux (DF) contributions are reported for all the normal vibrations of these molecules. A large negative correlation coefficient of -0.83 is calculated between the charge flux and dipole flux contributions and indicates that electronic charge transfer from one side of the molecule to the other during vibrations is accompanied by a relaxation effect with electron density polarization in the opposite direction. The characteristic substituent effect that has been observed for experimental infrared intensity parameters and core electron ionization energies has been applied to the CCFDF/QTAIM parameters of F2CO, Cl2CO, F2CS, and Cl2CS. The individual atomic charge, atomic charge flux, and atomic dipole flux contributions are seen to obey the characteristic substituent effect equation just as accurately as the total dipole moment derivative. The CH, CF, and CCl stretching normal modes of these molecules are shown to have characteristic sets of charge, charge flux, and dipole flux contributions.     

Novel properties from experimental charge densities: an application to the zwitterionic neurotransmitter taurine

The charge distribution of taurine (2-aminoethane-sulfonic acid) is revisited by using an orbital-based method that describes the density in a fixed molecular orbital basis with variable orbital occupation numbers. A new neutron data set is also employed to explore whether this improves the deconvolution of thermal motion and charge density. A range of molecular properties that are novel for experimentally determined charge densities are computed, including Weinhold population analysis, Mayer bond orders, and local kinetic energy densities, in addition to charge topological analysis and quantum theory of atoms-in-molecules (QTAIM) integrated properties. The ease with which a distributed multipole analysis can be performed on the fitted density matrix makes it straightforward to compute molecular moments, the lattice energy, and the electrostatic interaction energies of molecules removed from the crystal. Results are compared with high-level (QCISD) gas-phase calculations and band structure calculations employing density functional theory. Finally, the avenues available for extending the range of molecular properties that can be calculated from experimental charge densities still further using this approach are discussed.     

Bonding study in all-metal clusters containing Al4 units

The nature of the bonding of a series of gas-phase all-metal clusters containing the Al4 unit attached to an alkaline, alkaline earth, or transition metal is investigated at the DFT level using Mulliken, quantum theory of atoms in molecules (QTAIM), and Hirshfeld iterative (Hirshfeld-I) atomic partitionings. The characterization of ionic, covalent, and metallic bonds is done by means of charge polarization and multicenter electron delocalization. This Article uses for the first time Hirshfeld-I multicenter indices as well as Hirshfeld-I based atomic energy calculations. The QTAIM charges are in line with the electronegativity scale, whereas Hirshfeld-I calculations display deviations for transition metal clusters. The Mulliken charges fail to represent the charge polarization in alkaline metal clusters. The large ionic character of Li-Al and Na-Al bonds results in weak covalent bonds. On the contrary, scarcely ionic bonds (Be-Al, Cu-Al and Zn-Al) display stronger covalent bonds. These findings are in line with the topology of the electron density. The metallic character of these clusters is reflected in large 3-, 4- and 5-center electron delocalization, which is found for all the molecular fragments using the three atomic definitions. The previously reported magnetic inactivity (based on means of magnetic ring currents) of the pi system in the Al42- cluster contrasts with its large pi electron delocalization. However, it is shown that the different results not necessary contradict each other.     

Quantum chemical investigation on the structural and electronic properties of α-, β-, and γ-cyclodextrin complexes: DFT and QTAIM analysis

To characterize the structural, thermochemical and electronic aspects in complexes of leucine, vanillin and mechlorethamine with α-, β-, and γ-cyclodextrins (CDs), a density functional theory (DFT) study has been conducted in combination with quantum theory of atoms in molecules (QTAIM) analysis. The QTAIM method has been utilized to explore the nature of various possible interactions between leucine, vanillin and mechlorethamine with CDs in terms of bond critical points (BCPs). HOMO and LUMO and atomic charges studies show charge transfer occurs between drugs and cyclodextrins. This behavior has been also investigated via QTAIM charge analysis. On the other hand, based on QTAIM electronic energy indicators we have discussed electrostatic character of interactions between vanillin, leucine and mechlorethamine with inner surface CDs in the coordination sphere.     

Revisiting the calculation of condensed Fukui functions using the quantum theory of atoms in molecules

The analysis of previously reported shortcomings of the condensed Fukui functions obtained making use of the quantum theory of atoms in molecules indicates these drawbacks are due to the inadequacy of the definition employed to compute them and not to the partitioning. A new procedure, which respects the mathematical definition and solves these problems, is presented for the calculation of condensed Fukui functions for atomic basins defined according to the quantum theory of atoms in molecules. It is tested in a set of 18 molecules, which includes the most controversial reported cases.     

Toward the multi-component quantum theory of atoms in molecules: a variational derivation

The general formalism of an extended quantum theory of atoms in molecules (QTAIM) dealing with the multi-component quantum systems, composed of various types of quantum particles, is disclosed in this contribution. This novel methodology, termed as the multi-component QTAIM (MC-QTAIM), is able to deal with non-adiabatic ab initio wavefunctions extracting atoms in molecules quantifying their properties. It can also be applied to elucidate the AIM structure of exotic species and bound quantum systems consisting of fundamental elementary particles like positrons and muons. The formalism is based on the previously disclosed density combination idea that is extended to derive the multi-component subsystem hypervirial theorem as well as the extended subsystem energy functional. Through the extended subsystem variational procedure, inspired from Schrödinger’s original variational principle, the surface terms containing the flux of the current property densities are derived. Accordingly, the extended Gamma field is introduced during this variational procedure that is used as the basic scalar field in the topological analysis yielding atoms in molecules and their real space boundaries. The Gamma field is central to the MC-QTAIM, replacing the usual one-electron density employed in the orthodox QTAIM and corresponding topological analysis. Through the multi-component hypervirial theorem, various regional theorems are derived which are then used to quantify the mechanical properties of atoms in molecules; these include the force, virial, torque, power, continuity and current theorems. In order to demonstrate the capability of the formalism, isotopically asymmetric hydrogen molecules, HD, HT and DT as well as YX systems (Y = ⁶Li, ⁷Li; X = H, D, T) composed of electrons and two different nuclei, all treated equally as quantum waves instead of clamped particles, are analyzed within context of the MC-QTAIM. The resulting computational analysis demonstrates that the MC-QTAIM is able to yield reasonable topological structures similar to those observed previously for diatomic species within context of the orthodox QTAIM. The asymmetrical nature of these species, inherent in their non-Born–Oppenhiemer wavefunctions, manifests itself clearly in the MC-QTAIM analysis yielding two distinguishable atomic basins with different properties. These differences are rationalized generally by the observed electron transfer from one basin to the other. Finally, some possible future theoretical extensions are considered briefly.     

Joint QTAIM and Hirshfeld study of the sigma and pi charge distribution and electron delocalization in carbonyl compounds: a comparative study with the resonance model

Atomic charges and delocalization indexes (DIs) for a series of carbonyl compounds comprising dimethyl ketone, acetaldehyde, acetic acid, methyl acetate, acetamide, methyl vinyl ketone, divinyl ketone, and benzoic acid were studied using two different atomic partitionings: the QTAIM and the Hirshfeld (stockholder) scheme. The resonance model, traditionally employed to explain the reactivity of these compounds, is not in line with the total atomic charges and DIs calculated by both methodologies. However, the resonance model is supported to some extent by the pi charges and pi DIs calculated by both schemes, but the calculated values indicate that the pi population delocalizes only to a small degree. Although the absolute values of QTAIM and stockholder atomic charges are significantly different, the pi charges and the values of the DIs show similar trends for all the atoms and molecules of this study; this is especially the case for the pi DIs. A study of the electron density on the level of a single MO performed for CO, H2CO, F2CO, and H2CS reveals that the differences in the atomic sigma charges computed with both partitionings can be traced back to their different treatment of interatomic regions.     

Application of the quantum theory of atoms in molecules to selected physico-chemical and biophysical problems: focus on correlation with experiment

This article reviews how the quantum theory of atoms in molecules (QTAIM) can be used to predict experimental physico-chemical properties of molecules of biologic interest: the amino acids, the polycyclic aromatic hydrocarbons (PAH), and the opiates, for example, morphine and PEO. The predicted experimental properties are as diverse as the partial molar volumes, the free energies of hydration, the second code-letter in the genetic code, the resonance energies, and the proton spin-spin coupling constants. Recent examples of the utilization of QTAIM to construct excellent statistical models (with squared correlation coefficients (r(2)) > 0.9) correlating properties of the electron density and of the pair density to experiment are reviewed. Some new results on the solvent effects on electron delocalization are also presented.