GenLocDip: A Generalized Program to Calculate and Visualize Local Electric Dipole Moments

Local dipole moments (i.e., dipole moments of atomic or molecular subsystems) are essential for understanding various phenomena in nanoscience, such as solvent effects on the conductance of single molecules in break junctions or the interaction between the tip and the adsorbate in atomic force microscopy. We introduce Gen Loc Dip , a program for calculating and visualizing local dipole moments of molecular subsystems. Gen Loc Dip currently uses the Atoms‐In‐Molecules (AIM) partitioning scheme and is interfaced to various AIM programs. This enables postprocessing of a variety of electronic structure output formats including cube and wavefunction files, and, in general, output from any other code capable of writing the electron density on a three‐dimensional grid. It uses a modified version of Bader's and Laidig's approach for achieving origin‐independence of local dipoles by referring to internal reference points which can (but do not need to be) bond critical points (BCPs). Furthermore, the code allows the export of critical points and local dipole moments into a POVray readable input format. It is particularly designed for fragments of large systems, for which no BCPs have been calculated for computational efficiency reasons, because large interfragment distances prevent their identification, or because a local partitioning scheme different from AIM was used. The program requires only minimal user input and is written in the Fortran 90 programming language. To demonstrate the capabilities of the program, examples are given for covalently and non‐covalently bound systems, in particular molecular adsorbates. © 2016 Wiley Periodicals, Inc.     

Advancing beyond charge analysis using the electronic localization function: Chemically intuitive distribution of electrostatic moments

We propose here an evaluation of chemically intuitive distributed electrostatic moments using the topological analysis of the electron localization function (ELF). As this partition of the total charge density provides an accurate representation of the molecular dipole, the distributed electrostatic moments based on the ELF partition (DEMEP) allows computing of local moments located at non atomic centers such as lone pairs, sigma bonds and pi systems. As the local dipole contribution can be decomposed in polarization and charge transfer components, our results indicate that local dipolar polarization of the lone pairs and chemical reactivity are closely related whereas the charge transfer contribution is the key factor driving the local bond dipole. Results on relevant molecules show that local dipole contributions can be used to rationalize inductive polarization effects in alcohols derivatives and typical hydrogen bond interactions. Moreover, bond quadrupole polarization moments being related to a pi character enable to discuss bond multiplicities, and to sort families of molecules according to their bond order. That way, the nature of the C-O bond has been revisited for several typical systems by means of the DEMEP analysis which appears also helpful to discuss aromaticity. Special attention has been given to the carbon monoxide molecule, to the CuCO complex and to a weak intramolecular N|-CO interaction involved in several biological systems. In this latter case, it is confirmed that the bond formation is mainly linked to the CO bond polarization. Transferability tests show that the approach is suitable for the design of advanced force fields.     

How the oxazole fragment influences the conformation of the tetraoxazocane ring in a cyclohexanespiro‐3′‐(1,2,4,5,7‐tetraoxazocane): single‐crystal X‐ray and theoretical study

Single crystals of (2S,5R)‐2‐isopropyl‐5‐methyl‐7‐(5‐methylisoxazol‐3‐yl)cyclohexanespiro‐3′‐(1,2,4,5,7‐tetraoxazocane), C₁₆H₂₆N₂O₅, have been studied via X‐ray diffraction. The tetraoxazocane ring adopts a boat–chair conformation in the crystalline state, which is due to intramolecular interactions. Conformational analysis of the tetraoxazocane fragment performed at the B3LYP/6‐31G(d,2p) level of theory showed that there are three minima on the potential energy surface, one of which corresponds to the conformation realized in the solid state, but not to a global minimum. Analysis of the geometry and the topological parameters of the electron density at the (3,?1) bond critical points (BCPs), and the charge transfer in the tetraoxazocane ring indicated that there are stereoelectronic effects in the O—C—O and N—C—O fragments. There is a two‐cross hyperconjugation in the N—C—O fragment between the lone electron pair of the N atom (lpN) and the antibonding orbital of a C—O bond (σ*_C—O) and vice versa between lpO and σ*_C—N. The oxazole substituent has a considerable effect on the geometry and the topological parameters of the electron density at the (3,?1) BCPs of the tetraoxazocane ring. The crystal structure is stabilized via intermolecular C—H…N and C—H…O hydrogen bonds, which is unambiguously confirmed with PIXEL calculations, a quantum theory of atoms in molecules (QTAIM) topological analysis of the electron density at the (3,?1) BCPs and a Hirshfeld analysis of the electrostatic potential. The molecules form zigzag chains in the crystal due to intermolecular C—H…N interactions being electrostatic in origin. The molecules are further stacked due to C—H…O hydrogen bonds. The dispersion component in the total stabilization energy of the crystal lattice is 68.09%.     

Single‐electron halogen bond: Ab initio study

Ab initio calculations have been performed on single‐electron halogen bonds between methyl radical and bromine‐containing molecules to gain a deeper insight into the nature of such noncovalent interactions. Bader's atoms in molecules (AIM) theory have also been applied to the analysis of the linking of the single‐electron halogen bond. Various characteristics of the R? Br…CH₃ interaction, i.e., binding energies, geometrical parameters and topological properties of the electron density have been determined. The presence of the bond critical points (BCPs) between the bromine atom and methyl radical and the values of electron density and Laplacian of electron density at these BCPs indicate the closed‐shell interactions in the complexes. The single‐electron halogen bonds, which are significantly weaker than the normal halogen bonds, exhibit equally bond strength as compared to the single‐electron hydrogen bond. It has been also found that plotting of the binding energies versus topological properties of the electron density at the BCPs gives two straight lines. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Ab initio quality properties for macromolecules using the ADMA approach

We describe new developments of an earlier linear scaling algorithm for ab initio quality macromolecular property calculations based on the adjustable density matrix assembler (ADMA) approach. In this approach, a large molecule is divided into fuzzy fragments, for which quantum chemical calculations can easily be done using moderate-size "parent molecules" that contain all the local interactions within a selected distance. If greater accuracy is required, a larger distance is chosen. With the present extension of this approximation, properties of the large molecules, like the electron density, the electrostatic potential, dipole moments, partial charges, and the Hartree-Fock energy are calculated. The accuracy of the method is demonstrated with test cases of medium size by comparing the ADMA results with direct quantum chemical calculations.     

基于电负性均衡理论快速计算多肽分子中原子电荷的新方法

Atomic charges play a crucial role in the understanding and modeling of the chemical behavior of proteins. Fast assessment of atomic charge distributions in larger molecules can be performed by implementing the electronegativity equalization method (EEM). To further improve the accuracy of the EEM approach, a novel and efficient method based on Bader's concept of high degree fragment transferability of atomic charges has been proposed for the parameterization of atoms-in-molecules (AIM) charges of polypeptides or proteins. The EEM parameterization method considers both the factors of connectivity and hybridized states, and the effect of the local chemical environment in fragments or groups. The types of atoms were defined on the basis of the local chemical environments of the fragments or functional groups of these atoms. The fragment transferability feature of QTAIM indicates that the atomic properties for the contributing atoms can be reproduced if the chemical environment is comparable. The constituent fragments or functional groups of macromolecules such as polypeptides and proteins can be utilized as building blocks for the additive generation of their electronic densities. The main peptide group (NH―HαCα―C＝O) of the polypeptide in the backbone was used as a building block to model the EEM parameters for reproducing the atomic charges in the polypeptides. A training set of 20 terminally blocked amino acids (Ac-X-NHMe, X = any neutral residue), which recreated the immediate local environment of the main chain fragments or functional groups of the polypeptides, were chosen for the calibration of AIM charges using the differential evolution (DE) algorithm. The effects of the optimized methods on the results were discussed and it was found that the DE algorithm showed a better performance for the objective function. The quality of the AIM charges obtained from the EEM method presented in this study was evaluated by comparison with those obtained from B3LYP/6-31G+(d, p) calculations for the two test tetrapeptides not contained in the training set. It was found that a remarkable improvement was achieved using the EEM model developed in this study as compared to the previous studies. The introduction of Bader's high fragment charge transfer model into the EEM provided a new scheme for its calibration and parameterization for larger systems such as polypeptides or polynucleotides, which possess highly repetitive segments. Among all types of atomic charges, only the AIM charges showed a significant meaning in experiments and could be obtained by X-ray diffraction experiments. Rapidly reproducing the accurate AIM charge for large systems seems to be more meaningful, especially for the prediction of protein-protein, protein-DNA, and drug-receptor recognition and interactions.     

Generalized energy-based fragmentation approach for computing the ground-state energies and properties of large molecules

We present a generalized energy-based fragmentation (GEBF) approach for approximately predicting the ground-state energies and molecular properties of large molecules, especially those charged and polar molecules. In this approach, the total energy (or properties) of a large molecule can be approximately obtained from energy (or properties) calculations on various small subsystems, each of which is constructed to contain a certain fragment and its local surroundings within a given distance. In the quantum chemistry calculation of a given subsystem, those distant atoms (outside this subsystem) are modeled as background point charges at the corresponding nuclear centers. This treatment allows long-range electrostatic interaction and polarization effects between distant fragments to be taken into account approximately, which are very important for polar and charged molecules. We also propose a new fragmentation scheme for constructing subsystems. Our test calculations at the Hartree-Fock and second-order M?ller-Plesser perturbation theory levels demonstrate that the approach could yield satisfactory ground-state energies, the dipole moments, and static polarizabilities for polar and charged molecules such as water clusters and proteins.     

Information distance analysis of molecular electron densities

The information‐theoretic basis of the Hirshfeld partitioning of the molecular electronic density into the densities of the “stockholder” atoms‐in‐molecules (AIM) is summarized. It is argued that these AIM densities minimize both the directed divergence (Kullback–Leibler) and divergence (Kullback) measures of the entropy deficiency between the AIM and their free atom analogs of the promolecule. The local equalization of the information distance densities of the Hirshfeld components, at the local value of the corresponding global entropy deficiency density, is outlined and several approximate relations are established between the alternative local measures of the missing information and the familiar function of a difference between the molecular and promolecule densities. Various global (of the system as a whole) and atomic measures of the entropy deficiency or the displacements relative to the isoelectronic promolecule, defined for densities or probabilities (shape functions) in both the local resolution and the Hirshfeld AIM discretization, are introduced and tested. This analysis is performed also for the valence electron (frozen‐core) approximation. Illustrative results for representative linear molecules, including diatomics, triatomics, and tetraatomics, are reported. They are interpreted as complementary characteristics of changes in the net AIM charge distribution and of the displacements in the information content of the electron distributions of bonded atoms. These numerical results confirm the overall similarity of the stockholder AIM to their free atom analogs and reflect the information displacements due to the AIM polarization and charge transfer in molecules. They also demonstrate the semiquantitative nature of the approximate relations established between the entropy deficiency densities and the related functions involving the density difference function. This development extends the range of interpretations based on the density difference diagrams into probing the associated information displacements in a molecule accompanying the formation of the chemical bonds. © 2002 John Wiley & Sons, Inc. Int J Quantum Chem, 2002     

Prediction of conformationally dependent atomic multipole moments in carbohydrates

The conformational flexibility of carbohydrates is challenging within the field of computational chemistry. This flexibility causes the electron density to change, which leads to fluctuating atomic multipole moments. Quantum Chemical Topology (QCT) allows for the partitioning of an “atom in a molecule,” thus localizing electron density to finite atomic domains, which permits the unambiguous evaluation of atomic multipole moments. By selecting an ensemble of physically realistic conformers of a chemical system, one evaluates the various multipole moments at defined points in configuration space. The subsequent implementation of the machine learning method kriging delivers the evaluation of an analytical function, which smoothly interpolates between these points. This allows for the prediction of atomic multipole moments at new points in conformational space, not trained for but within prediction range. In this work, we demonstrate that the carbohydrates erythrose and threose are amenable to the above methodology. We investigate how kriging models respond when the training ensemble incorporating multiple energy minima and their environment in conformational space. Additionally, we evaluate the gains in predictive capacity of our models as the size of the training ensemble increases. We believe this approach to be entirely novel within the field of carbohydrates. For a modest training set size of 600, more than 90% of the external test configurations have an error in the total (predicted) electrostatic energy (relative to ab initio) of maximum 1 kJ mol^?1 for open chains and just over 90% an error of maximum 4 kJ mol^?1 for rings. © 2015 Wiley Periodicals, Inc.     

Toward deformation densities for intramolecular interactions without radical reference states using the fragment,atom, localized,delocalized, and interatomic (FALDI) charge density decomposition scheme

A novel approach for calculating deformation densities is presented, which enables to calculate the deformation density resulting from a change between two chemical states, typically conformers, without the need for radical fragments. The Fragment, Atom, Localized, Delocalized, and Interatomic (FALDI) charge density decomposition scheme is introduced, which is applicable to static electron densities (FALDI‐ED), conformational deformation densities (FALDI‐DD) as well as orthodox fragment‐based deformation densities. The formation of an intramolecular NH⋅⋅⋅N interaction in protonated ethylene diamine is used as a case study where the FALDI‐based conformational deformation densities (with atomic or fragment resolution) are compared with an orthodox EDA‐based approach. Atomic and fragment deformation densities revealed in real‐space details that (i) pointed at the origin of density changes associated with the intramolecular H‐bond formation and (ii) fully support the IUPAC H‐bond representation. The FALDI scheme is equally applicable to intra‐ and intermolecular interactions. © 2017 Wiley Periodicals, Inc.     

Chiral aromaticities. AIM and ELF critical point and NICS magnetic analyses of Mobius-type aromaticity and homoaromaticity in lemniscular annulenes and hexaphyrins

An atoms-in-molecules (AIM) and electron localization function (ELF) critical point analysis is reported for two types of lemniscular system, each of which exhibits double-half-twist Mobius topology. This reveals that this type of conformation for [14]annulene 1 has, in addition to the obvious bond critical points (BCPs), two weaker transannular points in the central cross-over region. These can be interpreted in terms of local rings showing single-half-twist Mobius homoaromaticity in addition to the double-half-twist aromaticity revealed by the annulene as a whole. Another example of a single-half-twist Mobius homoaromatic 9 is suggested here to show aromatic properties as strong as its nonhomoaromatic analogue 8. The AIM critical points in 1 are relatively insensitive to the ring size (varied from 12 to 16), and only small changes are seen in the critical point properties when the pi-electron count is incremented from 4n+2 to 4n by dianion formation. These results are discussed in terms of the reported transformation of the 14-pi-electron octalene 10 by reduction/alkylation into 12, an isomer of 1. Another class of molecule that exhibits lemniscular topology is the phyrins. A transannular BCP in the central cross-over region for the double-half-twist aromatic [26]hexaphyrin 3 is revealed, which is not present for the double-half-twist antiaromatic [28]hexaphyrin 2. The NICS(rcp) for the former indicates strong Mobius homoaromaticity.     

Theoretical insight into pyrrole inversion and planarity in 5,10,15,20-tetraphenylsapphyrin and 5,10,15,20-tetraphenyl-26,28-diheterosapphyrins with two O, S, or Se atoms

Density functional calculations at the B3LYP/6-31+G(d) (LACVP(D) for Se) theory level have been carried out on 5,10,15,20-tetraphenylsapphyrin ( TPS), 5,10,15,20-tetraphenyl-26,28-dioxasapphyrin ( TP2OS), 5,10,15,20-tetraphenyl-26,28-dithiasapphyrin ( TP2SS), and 5,10,15,20-tetraphenyl-26,28-diselenasapphyrin ( TP2SeS). In agreement with experimental findings, our theoretical results show that TPS and TP2OS present an inverted conformation, whereas TP2SS and TP2SeS are more stable in the normal one. It was found that the relative stability of the normal and inverted conformers of the just mentioned sapphyrins correlates positevily with their degree of planarity and aromaticity, which depends on the size of the heteroatom, the steric repulsions produced by phenyl rings at the meso C atoms, and the network and nature of the bond critical points (BCPs) inside the macrocycle. These BCPs have been characterized by means of the AIM analysis and, some selected ones, by the changes in the total energy of significant fragments when distorted to avoid them.     

Ab initio quality one-electron properties of large molecules: development and testing of molecular tailoring approach

The development of a linear-scaling method, viz. "molecular tailoring approach" with an emphasis on accurate computation of one-electron properties of large molecules is reported. This method is based on fragmenting the reference macromolecule into a number of small, overlapping molecules of similar size. The density matrix (DM) of the parent molecule is synthesized from the individual fragment DMs, computed separately at the Hartree-Fock (HF) level, and is used for property evaluation. In effect, this method reduces the O(N(3)) scaling order within HF theory to an n.O(N'(3)) one, where n is the number of fragments and N', the average number of basis functions in the fragment molecules. An algorithm and a program in FORTRAN 90 have been developed for an automated fragmentation of large molecular systems. One-electron properties such as the molecular electrostatic potential, molecular electron density along with their topography, as well as the dipole moment are computed using this approach for medium and large test chemical systems of varying nature (tocopherol, a model polypeptide and a silicious zeolite). The results are compared qualitatively and quantitatively with the corresponding actual ones for some cases. This method is also extended to obtain MP2 level DMs and electronic properties of large systems and found to be equally successful.     

How does hybrid bridging core modification enhance the nonlinear optical properties in donor‐π‐acceptor configuration? A case study of dinitrophenol derivatives

This study spotlights the fundamental insights about the structure and static first hyperpolarizability (β) of a series of 2,4‐dinitrophenol derivatives (1–5), which are designed by novel bridging core modifications. The central bridging core modifications show noteworthy effects to modulate the optical and nonlinear optical properties in these derivatives. The derivative systems show significantly large amplitudes of first hyperpolarizability as compared to parent system 1 , which are 4, 46, 66, and 90% larger for systems 2, 3, 4 , and 5 , respectively, at Moller–Plesset (MP2)/6‐31G* level of theory. The static first hyperpolarizability and frequency dependent coupled‐perturbed Kohn–Sham first hyperpolarizability are calculated by means of MP2 and density functional theory methods and compared with respective experimental values wherever possible. Using two‐level model with full‐set of parameters dependence of transition energy (ΔΕ), transition dipole moment (μ⁰) as well as change in dipole moment from ground to excited state (Δμ), the origin of increase in β amplitudes is traced from the change in dipole moment from ground to excited state. The causes of change in dipole moments are further discovered through sum of Mulliken atomic charges and intermolecular charge transfer spotted in frontier molecular orbitals analysis. Additionally, analysis of conformational isomers and UV‐Visible spectra has been also performed for all designed derivatives. Thus, our present investigation provides novel and explanatory insights on the chemical nature and origin of intrinsic nonlinear optical (NLO) properties of 2,4‐dinitrophenol derivatives. © 2014 Wiley Periodicals, Inc.     

On the Additivity of Molecular Fragment Dipole Moments of 5‐Substituted Indole Derivatives

The estimate of the magnitude and the orientation of molecular electric dipole moments from the vector sum of bond or fragment dipole moments is a widely used approach in chemistry. However, the limitations of this intuitive model have rarely been tested experimentally, particularly for electronically excited states. Herein, we find rules for a number of indole derivatives by using rotationally resolved electronic Stark spectroscopy and ab initio calculations. Based on a natural‐bond‐orbital analysis, we discuss whether the vector additivity rule can be applied in a given electronic state. From a comparison of the experimental data with ab initio calculations, we deduced that the additivity model does not apply when the flow of electron density from the substituent is opposed to that inside the chromophore.     

Atomic dipole moments calculated using analytical molecular second-moment gradients

We have implemented analytical second-moment gradients for Hartree-Fock and multiconfigurational self-consistent-field wave functions. The code is used to calculate atomic dipole moments based on the generalized atomic polar tensor (GAPT) formalism [Phys. Rev. Lett. 62, 1469 (1989)], and the proposal of Dinur and Hagler (DH) for the calculation of atomic multipoles [J. Chem. Phys. 91, 2949 (1989)]. Both approaches display smooth basis-set convergence toward a well-defined basis-set limit and give reasonable electron correlation effects on the calculated atomic properties. However, the atomic charges and atomic dipole moments obtained from the GAPT partitioning scheme are unable to provide even qualitatively meaningful molecular quadrupole moments for some molecules, and thus the atomic multipole moments calculated in this scheme cannot be considered well suited for analyzing the electron density in molecules and for calculating intermolecular interaction energies. In contrast, the DH approach gives atomic charges and dipole moments that by definition exactly reproduce the molecular quadrupole moments. The approach of DH is, however, restricted to planar molecules and thus suffers from not being applicable to molecules of arbitrary shape. Both the GAPT and DH approaches give rather poor results for octupole and hexadecapole moments, indicating that at least atomic quadrupole moments are required for an accurate representation of the molecular charge distribution in terms of atomic electric moments.     

The Role of Computational Chemistry in the Experimental Determination of the Dipole Moment of Molecules in Solution

The methods for the experimental determination of electric dipole moment of molecules in solution from measurements of dielectric permittivity and refractive index are traditionally based on the classical Onsager model. In this model the molecular solute is approximated as a simple polarizable point dipole inside a spherical or ellipsoidal cavity of a dielectric medium representing the solvent. However, the inadequacies of the model resulting from the assumption of a simple shape of the cavity, for the evaluation of the cavity field effect, and from the uncertainty of the polarizability of the molecular solute influences the results and hampers the comparison with the electric dipole moments computed from quantum chemical solvation models. In this article we propose a new method for the experimental determination of the electric dipole moment in solution in which information from the Polarizable Continuum Model calculations are used in place of the Onsager model. The new method overcomes the limitations of this latter model regarding both the cavity field effect and the polarizability of the molecular solutes, and thus allows a coherent comparison between experimental and computed dipole moments of solvated molecules. © 2019 Wiley Periodicals, Inc.     

Description of high‐spin restricted open‐shell molecules with the Piris natural orbital functional

The Piris natural orbital functional (PNOF) based on a new approach for the two‐electron cumulant is considered for the case of high‐spin restricted open‐shell systems. The theory is applied to the calculation of molecular energies, dipole moments, vertical ionization potentials (IP), and electron affinities (EA) of 10 open‐shell molecules. Vertical values of IP and EA were used to evaluate the hardness. It was observed that the results obtained using the PNOF method are comparable to the corresponding results obtained using CCSD(T) in the case of energies and dipole moments. Best agreement between theory and experiment is achieved by PNOF for EA and hardness values. The calculated PNOF values for the mentioned properties are in good agreement with the available experimental data, considering the basis sets used (6–31 ++G**). © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007