Experimental electron density and electrostatic properties ofpeptides by high resolution X-ray diffraction

On the calculation of the electrostatic potential, electric field and electric field gradient from the aspherical pseudoatom model. II. Evaluation of the properties in an infinite crystal

The previously reported exact potential and multipole moment (EP/MM) method for fast and precise evaluation of the intermolecular electrostatic interaction energies in molecular crystals using the pseudoatom representation of the electron density [Nguyen, Macchi & Volkov (2020), Acta Cryst. A76, 630-651] has been extended to the calculation of the electrostatic potential (ESP), electric field (EF) and electric field gradient (EFG) in an infinite crystal. The presented approach combines an efficient Ewald-type summation (ES) of atomic multipoles up to the hexadecapolar level in direct and reciprocal spaces with corrections for (i) the net polarization of the sample (the `surface term') due to a net dipole moment of the crystallographic unit cell (if present) and (ii) the short-range electron-density penetration effects. The rederived and reported closed-form expressions for all terms in the ES algorithm have been augmented by the expressions for the surface term available in the literature [Stenhammar, Trulsson & Linse (2011), J. Chem. Phys. 134, 224104] and the exact potential expressions reported in a previous study [Volkov, King, Coppens & Farrugia (2006), Acta Cryst. A62, 400-408]. The resulting algorithm, coded using Fortran in the XDPROP module of the software package XD, was tested on several small molecular crystal systems (formamide, benzene, L-dopa, paracetamol, amino acids etc.) and compared with a series of EP/MM-based direct-space summations (DS) performed within a certain number of unit cells generated along both the positive and negative crystallographic directions. The EP/MM-based ES technique allows for a noticeably more precise determination of the EF and EFG and significantly better precision of the evaluated ESP when compared with the DS calculations, even when the latter include contributions from an array of symmetry-equivalent atoms generated within four additional unit cells along each crystallographic direction. In terms of computational performance, the ES/EP/MM method is significantly faster than the DS calculations performed within the extended unit-cell limits but trails the DS calculations within the reduced summation ranges. Nonetheless, the described EP/MM-based ES algorithm is superior to the direct-space summations as it does not require the user to monitor continuously the convergence of the evaluated properties as a function of the summation limits and offers a better precision-performance balance.

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

The gradient vector field of molecular electrostatic potential, ∇V(r), has remained relatively unexplored in molecular quantum mechanics. The present article explores the conceptual as well as practical aspects of this vector field. A three-dimensional atomic partition of molecular space has been achieved on the basis of zero flux surfaces (ZFSs) of ∇V(r). Such ZFSs may completely enclose some of the atoms in the molecule, unlike what is observed in density-based atomic partitioning. The demonstration of this phenomenon is elucidated through typical examples, e.g., N2, CO, H2O, H2CO, OF(•), :CH2, and NH3BF3, where the electronegative atoms or group of atoms (group electronegativity) exhibits a closed ZFS of ∇V(r) around them. The present article determines an explicit reason for this phenomenon and also provides a necessary and sufficient condition for such a closed ZFS of ∇V(r) to exist. It also describes how the potential-based picture of atoms in molecules differs from its electron density-based analogue. This work further illustrates the manifestation of anisotropy in the gradient paths of MESP of some molecular systems, with respect to CO, (•)OH, H2O, and H2CO, and points to its potential in understanding the reactivity patterns of the interacting molecules.

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.

Reactivity differences between α,β-unsaturated carbonyls and hydrazones investigated by experimental and theoretical electron density and electron localizability analyses

It is still a challenge to predict a compound's reactivity from its ground-state electronic nature although Bader-type topological analyses of the electron density (ED) and electron localizability indicator (ELI) give detailed and useful information on electron concentration and electron-pair localization, respectively. Both ED and ELI can be obtained from theoretical calculations as well as high-resolution X-ray diffraction experiments. Besides ED and ELI descriptors, the delocalization index is used here; it is likewise derived from theoretical calculations as well as from experimental X-ray results, but in the latter case, demonstrated here for the first time. We investigate α,β-unsaturated carbonyl and hydrazone compounds because resonance exhibited by these compounds in the electronic ground-state determines their reactive behavior. The degree of resonance as well as the reactivity contrast are quantified with the electronic descriptors. Moreover, competitive mesomeric substituent effects are studied using the two biologically important compounds acrolein and acrylamide. The reactivity differences predicted from the analyses are in line with the known reactivity of these compounds in organic synthesis. Hence, the capability of the ED and ELI for rationalizing and predicting different and competing substituent effects with respect to reactivity is demonstrated.

Multipole correction of atomic monopole models of molecular charge distribution. I. Peptides

The defects in atomic monopole models of molecular charge distribution have been analyzed for several model-blocked peptides and compared with accurate quantum chemical values. The results indicate that the angular characteristics of the molecular electrostatic potential around functional groups capable of forming hydrogen bonds can be considerably distorted within various models relying upon isotropic atomic charges only. It is shown that these defects can be corrected by augmenting the atomic point charge models by cumulative atomic multipole moments (CAMMs). Alternatively, sets of off-center atomic point charges could be automatically derived from respective multipoles, providing approximately equivalent corrections. For the first time, correlated atomic multipoles have been calculated for N-acetyl, N'-methylamide-blocked derivatives of glycine, alanine, cysteine, threonine, leucine, lysine, and serine using the MP2 method. The role of the correlation effects in the peptide molecular charge distribution are discussed.