Isoelectronic changes in total Hartree-Fock energy of atoms

It is shown numerically that to a reasonably good accuracy, the isolectronic changes in total Hartree-Fock energy of atomic systems can be predicted, in terms of the energy ratio between the adjacent members in a given isoelectronic series, simply as a function of atomic numbers.Alexander von Humboldt Fellow, on leave from School of Chemistry, University of Hyderabad, India.     

Fast density matrix-based partitioning of the energy over the atoms in a molecule consistent with the Hirshfeld-I partitioning of the electron density

For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree-Fock level are efficiently determined in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix (1DM). Starting from the Hirshfeld-I AIM model for the electron density, the molecular 1DM is partitioned with a previously introduced double-atom scheme (Vanfleteren et al., J Chem Phys 2010, 132, 164111). Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. As the Hartree-Fock energy can be expressed solely in terms of the 1DM, the partitioning of the latter over the AIM naturally leads to a corresponding partitioning of the Hartree-Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared with other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

Study of gas-liquid partitioning of alkane solutes in several organic solvents by using principal component analysis and linear solvation energy relationships

Principal component analysis (PCA) was used to extract the number of factors which can describe the 737 gas-liquid partition coefficients of five linear, four branched, and two cyclic alkanes in 67 common solvents. Based on the reconstruction of partition coefficient data matrix, we concluded that the experimental dataset could readily be reduced to two relevant factors. Using only these two factors, there were no errors larger than 3%, 7 cases had errors larger than 2%, and in 34 cases, errors were between 1 and 2%. n-Hexane and ethylcyclohexane were chosen as the test factors, and all other partition coefficients were expressed in terms of these two test factors. Prediction of the logarithmic partition coefficient of these alkanes in seven chemically different solvents, which were originally excluded from the data matrix, was excellent: the root mean square error was 0.064, only in 11 cases the errors were larger than 1%, and only 3 had errors larger than 4%.Linear solvation energy relationships (LSERs) using both theoretical and empirical solvent parameters were used to explain the molecular interactions responsible for partition. Several combinations of parameters were tried but the standard deviations were not less than 0.31. This could be attributed to the model itself, imprecisions in the data matrix or in some of the LSER parameters. Solvent cohesive parameters and surface tension in combination with polarity-polarizability or dispersion parameters perform the best.Finally, the two principal component factors were rotated onto the most relevant physicochemical parameters that control the gas-liquid partitioning phenomena.     

Hydrogen–hydrogen interaction in planar biphenyl: A theoretical study based on the interacting quantum atoms and Hirshfeld atomic energy partitioning methods

The nature of H‐H interaction between ortho‐hydrogen atoms in planar biphenyl is investigated by two different atomic energy partitioning methods, namely fractional occupation iterative Hirshfeld (FOHI) and interacting quantum atoms (IQA), and compared with the traditional virial‐based approach of quantum theory of atoms in molecules (QTAIM). In agreement with Bader's hypothesis of H? H bonding, partitioning the atomic energy into intra‐atomic and interatomic terms reveals that there is a net attractive interaction between the ortho‐hydrogens in the planar biphenyl. This falsifies the classical view of steric repulsion between the hydrogens. In addition, in contrast to the traditional QTAIM energy analysis, both FOHI and IQA show that the total atomic energy of the ortho‐hydrogens remains almost constant when they participate in the H‐H interaction. Although, the interatomic part of atomic energy of the hydrogens plays a stabilizing role during the formation of the H? H bond, it is almost compensated by the destabilizing effects of the intra‐atomic parts and consequently, the total energy of the hydrogens remains constant. The trends in the changes of intra‐atomic and interatomic energy terms of ortho‐hydrogens during H? H bond formation are very similar to those observed for the H₂ molecule. © 2014 Wiley Periodicals, Inc.     

Coarse-graining kinetic networks in photosynthetic energy transport

Photosynthetic systems utilize hundreds of chlorophylls to collect sunlight and transport the energy to the reaction center with remarkably high quantum efficiency, however, the large size of the system together with the complex interactions among the components make it extremely challenging to understand the dynamics of light harvesting in large photosynthetic systems. To shed light on this problem, we present a structure-based theoretical framework that can be used to calculate transition rate matrix describing energy transport in photosynthetic systems and network clustering methods that provide simplified coarse-grained model revealing key structures guiding the light harvesting process. We constructed an effective model for energy transport in a Photosystem II supercomplex and applied several network clustering methods to generate coarse-grained kinetic cluster models for the system. Furthermore, we evaluated the performances of the network clustering methods, and show that a spectral clustering method and a minimum cut approach produce accurate coarse-grained models for the PSII-sc system. The results indicate that finding bottlenecks of energy transport is a crucial factor for reduced representations of photosynthetic light harvesting, and the overall work presented in this paper should provide a comprehensive theoretical framework to elucidate the dynamics of light harvesting in photosynthetic systems.     

Multireference perturbation theory with optimized partitioning. II. Applications to molecular systems

The second‐order multireference perturbation theory using an optimized partitioning, denoted as MROPT(2), is applied to calculations of various molecular properties—excitation energies, spectroscopic parameters, and potential energy curves—for five molecules: ethylene, butadiene, benzene, N₂, and O₂. The calculated results are compared with those obtained with second‐ and third‐order multireference perturbation theory using the traditional partitioning techniques. We also give results from computations using the multireference configuration interaction (MRCI) method. The presented results show very close resemblance between the new method and MRCI with renormalized Davidson correction. The accuracy of the new method is good and is comparable to that of second‐order multireference perturbation theory using Møller‐Plesset partitioning. © 2003 Wiley Periodicals, Inc. J Comput Chem 24: 1390–1400, 2003     

Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham-type approximation that uses the multipole moment expansion of molecular/atomic charge distributions. In the mid-1980s it was shown that the pseudoatom model commonly used in experimental X-ray charge density studies can be easily combined with the Buckingham-type approach for calculation of electrostatic interactions, plus atom-atom potentials for evaluation of the total interaction energies in molecular systems. While many such studies have been reported, little attention has been paid to the accuracy of evaluation of the purely electrostatic interactions as errors may be absorbed in the semiempirical atom-atom potentials that have to be used to account for exchange repulsion and dispersion forces. This study is aimed at the evaluation of the accuracy of the calculation of electrostatic interaction energies with the Buckingham approach. To eliminate experimental uncertainties, the atomic moments are based on theoretical single-molecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of alpha-glycine, N-acetylglycine and L-(+)-lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms-in-molecules moments are compared with those evaluated with the Morokuma-Ziegler energy decomposition scheme. For alpha-glycine a comparison with direct "pixel-by-pixel" integration method, recently developed Gavezzotti, is also made. It is found that the theoretical pseudoatom moments combined with the Buckingham model do predict the correct relative electrostatic interactions energies, although the absolute interaction energies are underestimated in some cases. The good agreement between electrostatic interaction energies computed with Morokuma-Ziegler partitioning, Gavezzotti's method, and the Buckingham approach with atoms-in-molecules moments demonstrates that reliable and accurate evaluation of electrostatic interactions in molecular systems of considerable complexity is now feasible.     

Theoretical study of atoms by the electronic kinetic energy density and stress tensor density

The electronic structure of atoms in the first, second, and third periods were analyzed using the electronic kinetic energy density and stress tensor density, which are local quantities motivated by quantum field theoretic consideration, specifically the rigged quantum electrodynamics. The zero surfaces of the electronic kinetic energy density, which are called as the electronic interfaces, of the atoms were computed. It was found that their sizes exhibited clear periodicity and were comparable to the conventional atomic and ionic radii. The electronic stress tensor density and its divergence, tension density, of the atoms, were also computed and how their electronic structures were characterized by them was discussed. © 2016 Wiley Periodicals, Inc.     

When hydroquinone meets methoxy radical: Hydrogen abstraction reaction from the viewpoint of interacting quantum atoms

Interacting Quantum Atoms methodology is used for a detailed analysis of hydrogen abstraction reaction from hydroquinone by methoxy radical. Two pathways are analyzed, which differ in the orientation of the reactants at the corresponding transition states. Although the discrepancy between the two barriers amounts to only 2 kJ/mol, which implies that the two pathways are of comparable probability, the extent of intra‐atomic and inter‐atomic energy changes differs considerably. We thus demonstrated that Interacting Quantum Atoms procedure can be applied to unravel distinct energy transfer routes in seemingly similar mechanisms. Identification of energy components with the greatest contribution to the variation of the overall energy (intra‐atomic and inter‐atomic terms that involve hydroquinone's oxygen and the carbon atom covalently bound to it, the transferring hydrogen and methoxy radical's oxygen), is performed using the Relative energy gradient method. Additionally, the Interacting Quantum Fragments approach shed light on the nature of dominant interactions among selected fragments: both Coulomb and exchange‐correlation contributions are of comparable importance when considering interactions of the transferring hydrogen atom with all other atoms, whereas the exchange‐correlation term dominates interaction between methoxy radical's methyl group and hydroquinone's aromatic ring. This study represents one of the first applications of Interacting Quantum Fragments approach on first order saddle points. © 2018 Wiley Periodicals, Inc.     

Transferability of quantum topological atoms in terms of electrostatic interaction energy

Understanding atomic transferability is important to guide the design of a force field. Atoms in molecules are defined and computed according to the theory of quantum chemical topology (QCT). The electron density associated with such topological atoms is conveniently described by high-rank multipole moments. Here, we assess the transferability of atoms by means of their electrostatic interaction energy, using a convergent multipole expansion. The test systems are (H2O)3 and serine...(H2O)5. The effect of a varying electron density cutoff (i.e., truncating the atoms) is discussed and the effect of polarization is quantified.     

Zero virial reaction processes. Reactions of Si and Mg atoms with H2 and HF molecules

By adopting the bond angle as a reaction coordinate and imposing on appropriate conditions, we determine a reaction path named the zero virial path starting from the reactant and arriving at the product via the transition state. At every point on this path, the polyatomic virial theorem is reduced to the simple atom-like form, and within the LCAO framework the total energy including the nuclear repulsion is partitioned exactly into the one center (atomic) and two center (bond) terms through the negative kinetic energy. Using these advantages of the zero virial path, the processes of bond formation and fission are examined in detail for the reactions of Si and Mg atoms with H₂ and HF molecules.     

Partitioning of atomization energy

The present work provides a technique for partitioning the atomization energy of a molecule into diatomic contributions. The method is largely based on the redistribution of the kinetic energy term in Mayer's energy partitioning and uses free‐atom energies as a reference. The comparison of Mayer's original method, the alternative Ichikawa–Yoshida approach, and the new atomization energy partitioning (AEP) shows that the new approach has advantages in describing trends in diatomic energies in molecules with triple bonds, as well as for hydrogen bonds. The proposed AEP is a viable alternative to Mayer's energy partitioning method. © 2007 Wiley Periodicals, Inc. Int. J. Quantum Chem, 2008     

Pulsed-laser production and detection of spin-polarized hydrogen atoms.

Spin-polarized hydrogen (SPH) atoms have traditionally been produced and detected using complex experimental methods with poor time resolution. Recently, SPH has been produced by pulsed-laser photodissociation of HCl using circularly polarized light. In combination with the proposed detection of SPH via polarized fluorescence, this approach should allow the production and spatially resolved detection of SPH with a higher sensitivity than that currently available, and with a time resolution in the nanosecond regime. This represents an improvement of several orders of magnitude over the existing methods.     

Estimation of Lattice Enthalpies of Ionic Liquids Supported by Hirshfeld Analysis

New measurements of vaporization enthalpies for 15 1:1 ionic liquids are performed by using a quartz‐crystal microbalance. Collection and analysis of 33 available crystal structures of organic salts, which comprise 13 different cations and 12 anions, is performed. Their dissociation lattice enthalpies are calculated by a combination of experimental and quantum chemical quantities and are divided into the relaxation and Coulomb components to give an insight into elusive short‐range interaction enthalpies. An empirical equation is developed, based on interaction‐specific Hirshfeld surfaces and solvation enthalpies, which enables the estimation of the lattice enthalpy by using only the crystal‐structure data.     

Molecular states of atoms. I. Orbital energy parameters

Atomic valence state energies are analyzed to obtain values of orbital energy parameters that may be used in semiempirical molecular orbital calculations. Difficulty in defining the interaction between orbitals with non-integer electron populations is systematically avoided by distinguishing between a valence state and a molecular state of an atom, only the latter state having non-integer spin paired orbital occupancy. Application of the virial theorem to the molecular state enables a value for the orbital kinetic energy to be obtained from the valence state orbital energy parameters once an arbitrary configuration is defined as reference. The orbitals then are eigenfunctions of the atomic Fock operator for that reference molecular state and, with their energy parameters, may be employed as a fixed basis set for molecular orbital calculations.     

Statistical Equivalence of Quantum Chemical Methods for Energy Distribution in Water Clusters

Methods of quantum chemistry are instrumental in understanding molecular structures and properties. However, the results demonstrate significant variability, which is difficult to predict and rationalize. The fundamental question is whether some molecular systems exhibit properties invariant with respect to the computational method. The idea explored here is that collective properties of statistical ensembles should be more robust than characteristics of individual molecules and their arbitrary sets. This effect is demonstrated for the complete set of hydrogen-bond topologies of the dodecahedral water cluster (H₂O)₂₀. Non-Gaussian energy distributions produced by various methods have the same functional form despite strong differences in mean values and standard deviations. The conclusion is tested on methods of different complexity and origin employing a number of criteria. A linear mapping between the energies produced by different methods is discussed. The significance of the results is in establishing a collective equivalence property of quantum chemical methods.     

Ordering of thermotropic nematogen in dielectric medium — a computational analysis

A computational analysis of ordering in homologous series of 4-cyano-4′-alkylbiphenyls (nCB) with alkyl group heptyl (7CB) has been carried out with respect to translatory and orientational motions. The complete neglect differential overlap (CNDO/2) method was employed to evaluate the net atomic charge and atomic dipole components at each atomic center of the molecule. The modified Rayleigh-Schrödinger perturbation theory along with multicentered-multipole expansion method was employed to evaluate the long-range intermolecular interactions, while 6-exp potential function was assumed for short-range interactions. The total interaction energy values obtained through these computations were used as input to calculate the probability of each configuration in non-interacting and non-mesogenic solvent (i.e., benzene) at room temperature (300 K) using the Maxwell-Boltzmann formula. On the basis of stacking, in-plane and terminal interaction energy calculations, all possible geometrical arrangements of molecular pairs were considered and the most favorable configuration of pairing was obtained. The present article offers theoretical support to the experimental findings.     

Revisiting the foundations of the quantum theory of atoms in molecules: Some open problems

In a series of papers in the last 10 years, various aspects of the mathematical foundations of the quantum theory of atoms in molecules have been considered by this author and his coworkers in some details. Although these considerations answered part of the questions raised by some critics on the mathematical foundations of the quantum theory of atoms in molecules, however, new mathematical problems also emerged during these studies that were reviewed elsewhere [Sh. Shahbazian Int. J. Quantum Chem. 2011 , 111, 4497.]. Beyond mathematical subtleties of the formalism that were the original motivation for initial exchanges and disputes, the questions raised by critics had a constructive effect and prompted the author to propose a novel extension of the theory, now called the multi‐component quantum theory of atoms in molecules [M. Goli, Sh. Shahbazian Theor. Chem. Acc. 2013 , 132, 1365.]. Taking this background into account, in this paper a new set of open problems is put forward that the author believes proper answers to these questions, may open new doors for future theoretical developments of the quantum theory of atoms in molecules. Accordingly, rather than emphasizing on the rigorous mathematical formulation, the practical motivations behind proposing these questions are discussed in detail and the relevant literature are reviewed while when possible, evidence and routes to answers are also provided. The author hopes that proposing these open questions as a compact package may motivate more mathematically oriented people to participate in future developments of the quantum theory of atoms in molecules and its multi‐component version.