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.     

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.     

Actinium coordination chemistry: A density functional theory study with monodentate and bidentate ligands

In the current study, the coordination chemistry of nine-coordinate Ac(III) complexes with 35 monodentate and bidentate ligands was investigated using density functional theory (DFT) in terms of their geometries, charges, reaction energies, and bonding interactions. The energy decomposition analysis with naturals orbitals for chemical valence (EDA-NOCV) and the quantum theory of atoms in molecules (QTAIM) were employed as analysis methods. Trivalent Ac exhibits the highest affinities toward hard acids (such as charged oxophilic donors, fluoride), so its classification as a hard acid is justified. Natural population analysis quantified the involvement of 5f orbitals on Ac to be about 30% of total valence electron natural configuration indicating that Ac is a member of the actinide series. Pearson correlation coefficients were used to study the pairwise correlations among the bond lengths, ΔG reaction energies, charges on Ac and donor atoms, and data from EDA-NOCV and QTAIM. Strong correlations and anticorrelations were found between Voronoi charges on donor atoms with ΔG, EDA-NOCV interaction energies and QTAIM bond critical point densities.     

Reinvestigation of intramolecular hydrogen bond in malonaldehyde derivatives: An ab initio,AIM and NBO study

The RAHB systems in malonaldehyde and its derivatives at MP2/ 6‐311++G(d,p) level of theory were studied and their intramolecular hydrogen bond energies by using the related rotamers method was obtained. The topological properties of electron density distribution in O? H···O intramolecular hydrogen bond have been analyzed in term of quantum theory of atoms in molecules (QTAIM). Correlations between the H‐bond strength and topological parameters are probed. The results of QTAIM clearly showed that the linear correlation between the electron density distribution at HB critical point and RAHB ring critical point with the corresponding hydrogen bond energies was obtained. Moreover, it was found a linear correlation between the electronic potential energy density, V(r_cp), and hydrogen bond energy which can be used as a simple equation for evaluation of HB energy in complex RAHB systems. Finally, the similar linear treatment between the geometrical parameters, such as O···O or O? H distance, and Lp(O)→σ*_OH charge transfer energy with the intramolecular hydrogen bond energy is observed. © 2010 Wiley Periodicals, Inc., Int J Quantum Chem, 2011     

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.     

Performance of the density matrix functional theory in the quantum theory of atoms in molecules

The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.     

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.     

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.     

Progress in the understanding of drug-receptor interactions, part 2: experimental and theoretical electrostatic moments and interaction energies of an angiotensin II receptor antagonist (C30H30N6(O)3S)

A combined experimental and theoretical charge density study of an angiotensin II receptor antagonist (1) is presented focusing on electrostatic properties such as atomic charges, molecular electric moments up to the fourth rank and energies of the intermolecular interactions, to gain an insight into the physical nature of the drug-receptor interaction. Electrostatic properties were derived from both the experimental electron density (multipole refinement of X-ray data collected at T=17 K) and the ab initio wavefunction (single molecule and fully periodic calculations at the DFT level). The relevance of SO and SN intramolecular interactions on the activity of 1 is highlighted by using both the crystal and gas-phase geometries and their electrostatic nature is documented by means of QTAIM atomic charges. The derived electrostatic properties are consistent with a nearly spherical electron density distribution, characterised by an intermingling of electropositive and -negative zones rather than by a unique electrophilic region opposed to a nucleophilic area. This makes the first molecular moment scarcely significant and ill-determined, whereas the second moment is large, significant and highly reliable. A comparison between experimental and theoretical components of the third electric moment shows a few discrepancies, whereas the agreement for the fourth electric moment is excellent. The most favourable intermolecular bond is show to be an NHN hydrogen bond with an energy of about 50 kJ mol(-1). Key pharmacophoric features responsible for attractive electrostatic interactions include CHX hydrogen bonds. It is shown that methyl and methylene groups, known to be essential for the biological activity of the drug, provide a significant energetic contribution to the total binding energy. Dispersive interactions are important at the thiophene and at both the phenyl fragments. The experimental estimates of the electrostatic contribution to the intermolecular interaction energies of six molecular pairs, obtained by a new model proposed by Spackman, predict the correct relative electrostatic energies with no exceptions.     

How dependent are molecular and atomic properties on the electronic structure method? Comparison of Hartree‐Fock,DFT, and MP2 on a biologically relevant set of molecules

This article compares molecular properties and atomic properties defined by the quantum theory of atoms in molecules (QTAIM) obtained from three underlying levels of theory: MP2(full), density functional theory (DFT) (B3LYP), and Hartree‐Fock (H‐F). The same basis set (6‐311++G(d,p)) has been used throughout the study. The calculations and comparisons were applied to a set of 30 small molecules representing common fragments of biological molecules. The molecular properties investigated are the energies and the electrostatic moments (up to and including the quadrupoles), and the atomic properties include electron populations (and atomic charge), atomic dipolar and quadrupolar polarizations, atomic volumes, and corrected and raw atomic energies. The Cartesian distance between dipole vectors and the Frobenius distance between the quadrupole tensors calculated at the three levels of theory provide a measure of their correlation (or lack thereof). With the exception of energies (atomic and molecular), it is found that both DFT and H‐F are in excellent agreement with MP2, especially with regards to the electrostatic mutipoles up to the quadrupoles, but DFT and MP2 agree better in almost all studied properties (with the exception of molecular geometries). QTAIM properties whether obtained from H‐F, DFT(B3LYP), or MP2 calculations when used in the construction of empirical correlations with experiment such as quantitative structure‐activity‐(or property)‐relationships (QSAR/QSPR) are equivalent (because the properties calculated at the three levels are very highly correlated among themselves with r² typically >0.95, and therefore preserving trends). These results suggest that the massive volume of results that were published in the older literature at the H‐F level is valid especially when used to study trends or in QSAR or QSPR studies, and, as long as our test set of molecules is representative, there is no pressing need to re‐evaluate them at other levels of theory except when inadequate basis sets were used by today's standards. Extensive tabulation of molecular and atomic properties at the three theoretical levels is available in the Supporting Information, including optimized geometries, molecular energies, virial ratios, molecular electrostatic moments up to and including hexadecapoles, atomic populations, atomic volumes, atomic electrostatic moments up to and including the quadrupoles, and atomic energies. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

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.     

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.     

Isatin‐Schiff base copper(II) complexes—A DFT study of the metal‐ligand bonding situation

Herein, we report results of calculations based on density functional theory (BP86/TZVP) of a set of isatin‐Schiff base copper(II) and related complexes, 1‐12, that have shown significant pro‐apoptotic activity toward diverse tumor cells. The interaction of the copper(II) cation with different ligands has been investigated at the same level of theory. The strength and character of the Cu(II)‐L bonding was characterized by metal‐ligand bond lengths, vibrational frequencies, binding energies, ligand deformation energies, and natural population analysis. The metal‐ligand bonding situation was also characterized by using two complementary topological approaches, the quantum theory of atoms‐in‐molecules (QTAIM) and the electron localization function (ELF). The calculated electronic g‐tensor and hyperfine coupling constants present significant agreement with the EPR experimental data. The calculated parameters pointed to complex 10 as the most stable among the isatin‐Schiff base copper(II) species, in good agreement with experimental data that indicate this complex as the most reactive in the series. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Atoms in molecules as non-overlapping, bounded, space-filling open quantum systems

The quantum theory of atoms in molecules (QTAIM) uses physics to define an atom and its contribution to observable properties in a given system. It does so using the electron density and its flow in a magnetic field, the current density. These are the two fields that Schrödinger said should be used to explain and understand the properties of matter. It is the purpose of this paper to show how QTAIM bridges the conceptual gulf that separates the observations of chemistry from the realm of physics and do so in a manner that is both rigorous and conceptually simple. Since QTAIM employs real measurable fields, it enables one to present the findings of complex quantum mechanical calculations in a pictorial manner that isolates the essential physics. The time has arrived for a sea change in our attempts to predict and classify the observations of chemistry, time to replace the use of simplified and arbitrary models with the full predictive power of physics, as applied to an atom in a molecule.     

Electron Density of Two Bioactive Oligocyclic Indole and Oxindole Derivatives Obtained from Low‐Order X‐Ray Data and Invariom Application

For two indole and oxindole bioactive molecules, low‐order room‐temperature X‐ray data were used to generate aspherical electron density (ED) distributions by application of the invariom formalism. An analysis of the ED using the quantum theory of atoms in molecules (QTAIM) was carried out, which allowed for quantitatively examining bond orders and charge separations in various parts of the molecules. The inspection of electrostatic potentials (ESPs) and Hirshfeld surfaces provided additional information on the intermolecular interactions. Thus, reactive regions of the molecules could be identified, covalent and electrostatic contributions to interactions could be visualized, and the forces causing the crystal packing scheme could be rationalized. As the used invariom formalism needs no extra experimental effort compared to routine X‐ray analysis, its wide application is recommended because it delivers information far beyond the normally obtained steric properties. In this way, complementary contributions to drug design can be given as is demonstrated for indoles in this study, which are involved in the metabolism of plants and animals as well as in cancer therapy.     

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.     

Properties of interatomic surfaces: relation to bond energies

A number of properties of interatomic surfaces, as defined by the quantum theory of atoms in molecules (QTAIM), are calculated for approximately 50 molecules. These integrated surface properties are then tested for their ability to correlate and predict bond energies from MP2 atomisation energies. Three surface properties, each with units of energy, are found to show strong correlations with bond energy: single parameter models work well for non-polar bonds, but fail for polar and ionic bonds, where multi-variate methods are required. The local curvature of the interatomic surface is found to be useful this respect, reflecting charge transfer effects.     

Study of noncovalent interactions of end-caped sulfur-doped carbon nanotubes using DFT,QTAIM, NBO and NCI calculations

In the current study, the interactions of carbon nanotube and sulfur-doped carbon nanotubes (SCNTs) with methanol, methanethiol, water and dihydrogen sulfide at on-body and dead-end positions of nanotubes have been studied. Interaction energies in the gas and solvent (via PCM model) were calculated using density functional theory calculations. Atomic charges, interaction energies, electron densities and their Laplacians at bond critical points have been calculated. Moreover, noncovalent interaction isosurfaces have been visualized using NCI index calculations. Interactions in gaseous phase were more favorable than those in solvent phase, and among considered solvents (benzene, chloroform and cyclohexane), cyclohexane showed the most preferred interactions. In addition, oxygen-bearing molecules (methanol and water) showed more favorable interactions compared with sulfur-bearing ones. NBO analyses revealed the stronger donor–acceptor interactions with methanol and methanethiol. QTAIM calculation results indicated the reasonable electron densities at BCPs, and the Laplacians of electron densities showed ionic-like (closed shell) interactions. Moreover, isosurfaces of these interactions were also studied to depict the interaction surfaces, and DOS plots for SCNTs were obtained to define their HOMO–LUMO levels and electric conduction properties. The increasing of the global softness and decreasing of total hardness was resulted by sulfur doping of nanotubes, which causes the heterodoped nanotubes to become less electrophilic species.