Exploring the Gradient Paths and Zero Flux Surfaces of Molecular Electrostatic Potential

Probing microhydration-induced effects on carbonyl compounds

Characterizing the microhydration of organic molecules is a crucial step in understanding many phenomena relevant to atmospheric, biological, and industrial applications. However, its precise experimental and theoretical description remains a challenge. For four organic solutes containing a CO bond, and included in the recent HyDRA challenge [T. L. Fischer, M. Bödecker, A. Zehnacker-Rentien, R. A. Mata and M. A. Suhm, Phys. Chem. Chem. Phys., 2022, 24, 11442-11454.], we performed a detailed study of different monohydrate isomers and their properties; these were cyclooctanone (CON), 1,3-dimethyl-2-imidazolidinon (DMI), methyl lactate (MLA), and 2,2,2-trifluoroacetophenone (TPH) molecules. As reported in the literature, the O-H elongation shift of the water molecule appears to be a good candidate for characterizing complexation-induced effects. We also show that CO elongation shift and UV-vis spectroscopy can be successfully used for these purposes. Besides, we present a comparative analysis of the strengths of non-covalent interactions within these monohydrated complexes based on interpretative tools of quantum chemistry, including topological analysis of electron density (ρ), topological analysis of electron pairing function, and analysis of the core-valence bifurcation index (CVBI), which exhibits a close linear dependency on ρ. Accordingly, a classification of intermolecular water-solute interactions is proposed.

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

Electrostatic Potential Topology for Probing Molecular Structure, Bonding and Reactivity

Following the pioneering investigations of Bader on the topology of molecular electron density, the topology analysis of its sister field viz. molecular electrostatic potential (MESP) was taken up by the authors’ groups. Through these studies, MESP topology emerged as a powerful tool for exploring molecular bonding and reactivity patterns. The MESP topology features are mapped in terms of its critical points (CPs), such as bond critical points (BCPs), while the minima identify electron-rich locations, such as lone pairs and π-bonds. The gradient paths of MESP vividly bring out the atoms-in-molecule picture of neutral molecules and anions. The MESP-based characterization of a molecule in terms of electron-rich and -deficient regions provides a robust prediction about its interaction with other molecules. This leads to a clear picture of molecular aggregation, hydrogen bonding, lone pair–π interactions, π-conjugation, aromaticity and reaction mechanisms. This review summarizes the contributions of the authors’ groups over the last three decades and those of the other active groups towards understanding chemical bonding, molecular recognition, and reactivity through topology analysis of MESP.

Orbital-free quantum crystallography: view on forces in crystals

Quantum theory of atoms in molecules and the orbital-free density functional theory (DFT) are combined in this work to study the spatial distribution of electrostatic and quantum electronic forces acting in stable crystals. The electron distribution is determined by electrostatic electron mutual repulsion corrected for exchange and correlation, their attraction to nuclei and by electron kinetic energy. The latter defines the spread of permissible variations in the electron momentum resulting from the de Broglie relationship and uncertainty principle, as far as the limitations of Pauli principle and the presence of atomic nuclei and other electrons allow. All forces are expressed via kinetic and DFT potentials and then defined in terms of the experimental electron density and its derivatives; hence, this approach may be considered as orbital-free quantum crystallography. The net force acting on an electron in a crystal at equilibrium is zero everywhere, presenting a balance of the kinetic F kin( r ) and potential forces F ( r ). The critical points of both potentials are analyzed and they are recognized as the points at which forces F kin( r ) and F ( r ) individually are zero (the Lagrange points). The positions of these points in a crystal are described according to Wyckoff notations, while their types depend on the considered scalar field. It was found that F ( r ) force pushes electrons to the atomic nuclei, while the kinetic force F kin( r ) draws electrons from nuclei. This favors formation of electron concentration bridges between some of the nearest atoms. However, in a crystal at equilibrium, only kinetic potential v kin( r ) and corresponding force exhibit the electronic shells and atomic-like zero-flux basins around the nuclear attractors. The force-field approach and quantum topological theory of atoms in molecules are compared and their distinctions are clarified.

Efficient Evaluation of Molecular Electrostatic Potential in Large Systems

An algorithm for the efficient computation of molecular electrostatic potential is reported. It is based on the partition/expansion of density into (pseudo) atomic fragments with the method of Deformed Atoms in Molecules, which allows to compute the potential as a sum of atomic contributions. These contributions are expressed as a series of irregular spherical harmonics times effective multipole moments and inverse multipole moments, including short-range terms. The problem is split into two steps. The first one consists of the partition/expansion of density accompanied by the computation of multipole moments, and its cost depends on the size of the basis set used in the computation of electron density within the Linear Combination of Atomic Orbitals framework. The second one is the actual computation of the electrostatic potential from the quantities calculated in the first step, and its cost depends on the number of computation points. For a precision in the electrostatic potential of six decimal figures, the algorithm leads to a dramatic reduction of the computation time with respect to the calculation from electron density matrix and integrals involving basis set functions.

Theoretical Study on Pyramidal C7N6–H3R3 Molecules

The pyramidal molecule C7N6H6 and its nine symmetric tri-substituted derivatives C7N6–H3R3 (R=OH, F, CN, N3, NH2, NO2, N=NH, N2H3, and C≡CH) were investigated computationally using the GAUSSIAN 09 program package. Natural bond orbital and atoms in molecules analyses, as well as valence bond theory were applied to investigate the bonding properties. In comparison to their well known analogues C6N7–R3, i.e. generic heptazines, it is found that these 10 molecules are all reactive. Further studies on the topological structures and ionization energy values indicate that the reactive site of the molecules is located at the carbon atom of the core frame. Even though C7N6–H3R3 are neutral molecules, the structures and properties of some are consistent with those of a carbanion, and indeed, they act like carbanions, or so-called carbanionoids. These carbanionoids may have an extensive impact in organic chemistry and organometallic chemistry.

Electronic Rearrangement in Molecular Plasmons: An Electron Density and Electrostatic Potential-Based Study

Plasmonic modes in single-molecule systems have been previously identified by scaling two-electron interactions in calculating excitation energies. Analysis of transition dipole moments for states of polyacenes based on configuration interaction is another method for characterising molecular plasmons. The principal features in the electronic absorption spectra of polyacenes are a low-intensity, lower-in-energy peak and a high-intensity, higher-in-energy peak. From calculations using time-dependent density functional theory with the B3LYP/cc-pVTZ basis set, both these peaks are found to result from the same set of electronic transitions, that is, HOMO-n to LUMO and HOMO to LUMO+n, where n varies as the number of fused rings increases. In this work, the excited states of polyacenes, naphthalene through pentacene, are analysed using electron densities and molecular electrostatic potential (MESP) topography. Compared to other excited states the bright and dark plasmonic states involve the least electron rearrangement. Quantitatively, the MESP topography indicates that the variance in MESP values and the displacement in MESP minima positions, calculated with respect to the ground state, are lowest for plasmonic states. The excited-state electronic density profiles and electrostatic potential topographies suggest the least electron rearrangement for the plasmonic states. Conversely, high electron rearrangement characterises a single-particle excitation. The molecular plasmon can be called an excited state most similar to the ground state in terms of one-electron properties. This is found to be true for silver (Ag₆ ) and sodium (Na₈ ) linear chains as well.

Reversibility of imido-based ionic liquids: a theoretical and experimental study

Theoretical and experimental methods were used to study the reversibility of a series of imido-based ionic liquids.

Molecular Electrostatic Potential-Based Atoms in Molecules: Shielding Effects and Reactivity Patterns

The Atoms in Molecules (AIM) concept based on the zero-flux surface (ZFS) of the gradient of molecular electrostatic potential (MESP) has been recently proposed by the present authors. The nature of MESP-based atomic basins brings out the asymmetric electronic distribution in a molecule. An electron-rich atom among the two bonded atoms is seen to possess a completely closed MESP-based atomic basin. The present article illustrates the nature of atomic basins for a variety of molecules such as BF, BH3, AlCl3, B2H6, and Al2Cl6, and a Lewis acid–base pair, viz. NH3BH3 wherein the electronic distribution is not merely guided by difference in the electronegativity of the atoms. The study also explores some transition metal complexes, viz. Ni(CO)4, Fe(CO)5, Cr(CO)6, Mn2(CO)10, Co2(CO)8, Fe(η5-C5H5)2, Co(η3-C3H5), and Co(η3-C3H5)(CO)3, which show a similar phenomenon of intricate charge transfer among the ligands and the metal centre. The present article employs MESP-based AIM for a qualitative explanation of the shielding or deshielding effects revealed by NMR data as well as susceptibility of an atomic region towards an electrophilic or nucleophilic attack. Because the topographical features of MESP and thus the nature of atomic basins are not very sensitive to the level of theory and basis set, the present article demonstrates the capability of MESP as a consistent and simple tool for the portrayal of asymmetry in molecular charge distribution.