A building-block database of distributed polarizabilities and dipole moments to estimate optical properties of biomacromolecules in isolation or in an explicitly solvated medium.

Since atomic or functional-group properties in the bulk are generally not available from experimental methods, computational approaches based on partitioning schemes have emerged as a rapid yet accurate pathway to estimate the materials behavior from chemically meaningful building blocks. Among several applications, a comprehensive and systematically built database of atomic or group polarizabilities and related opto-electronic quantities would be very useful not only to envisage linear or non-linear optical properties of biomacromolecules but also to improve the accuracy of classical force fields devoted to simulate biochemical processes. In this work, we propose the first entries of such database that contains distributed polarizabilities and dipole moments extracted from fragments of peptides. Twenty three prototypical conformers of the dipeptides alanine-alanine and glycine-glycine were used to extract functional groups such as CH2 , CHCH3 , NH2 , COOH, CONH, thus allowing construction of a diversity of chemically relevant environments. To evaluate the accuracy of our database, reconstructed properties of larger peptides containing up to six residues of alanine and glycine were tested against density functional theory calculations at the M06-HF/aug-cc-pVDZ level of theory. The procedure is particularly accurate for the diagonal components of the polarizability tensor with errors up to 15%. In order to include solvent effects explicitly, the peptides were also surrounded by a box of water molecules whose distribution was optimized using the CHARMM force field. Solvent effects introduced by a classical dipole-dipole interaction model were compared to those obtained from polarizable-continuum model calculations.

Benchmark of a functional-group database for distributed polarizability and dipole moment in biomolecules.

The extraction of functional-group properties in condensed phases is very useful for predicting material behaviors, including those of biomaterials. For this reason, computational approaches based on partitioning schemes have been developed aiming at rapidly and accurately estimating properties from chemically meaningful building blocks. A comprehensive database of group polarizabilities and dipole moments is useful not only to predict the optical properties of biomacromolecules but also to improve molecular force fields focused on simulating biochemical processes. In this work we benchmark a database of distributed polarizabilities and dipole moments for functional groups extracted from a series of polypeptides. This allows reconstruction of a variety of relevant chemical environments. The accuracy of our database was tested to predict the electro-optical properties of larger peptides and also simpler amino acids for which density functional theory calculations at the M06-HF/aug-cc-pVDZ level of theory was chosen as the reference. This approach is reasonably accurate for the diagonal components of the polarizability tensor, with errors not larger than 15-20%. The anisotropy of the polarizability is predicted with smaller efficacy though. Solvent effects were included explicitly by surrounding the database entries by a box of water molecules whose distribution was optimized using the CHARMM force field.

Accurate Atom-Dipole Interaction Model for Prediction of Electro-optical Properties: From van der Waals Aggregates to Covalently Bonded Clusters.

This work aims at the accurate estimation of the electro-optical properties of atoms and functional groups in organic crystals. A better understanding of the nature of building blocks and the way they interact with each other enables more efficient prediction of self-assembly, and thus physical properties in condensed matter. We propose a modified version of an atom-dipole interaction model that is based on atomic dipole moments calculated from the quantum theory of atoms in molecules. The method is very reliable for the prediction of various optical and electric properties in diverse chemical environments, ranging from hydrocarbon molecules bonded by dispersive interactions to polar rings connected by hydrogen bonds, or even polymeric structures whose monomers are covalently linked. Distributed polarizabilities and electrostatic potentials are compared to those obtained using a complete quantum-mechanical approach on finite-size aggregates. Our electrostatic approximation recovers isotropic polarizabilities with an accuracy of ca. 5 au and electrostatic potentials of ca. 0.05 au, even in the worst-case scenario in which polarization and charge-transfer effects are large. Functional groups are highly exportable, estimating the properties of small peptides and polyaromatics with a maximum deviation as low as ca. 15%.

Accurate Modelling of Group Electrostatic Potential and Distributed Polarizability in Dipeptides.

Within the scope of accurate structure-property correlations in biomolecules, this work investigates how conformations and electronic configurations of biologically relevant macromolecules affect their intermolecular potentials. With the purpose of testing the suitability of a simple and universal model, the dipeptides are made from the assembly of their building blocks, namely the amino acid residuals or, more finely tuned, the individual functional groups. The model makes use of functional-group electrostatic potentials (GEP) and distributed polarizabilities (GDP), which enable an in depth analysis of the correlation between structural features and property build-up. GEPs and GDPs are calculated for various conformers and protonation states of L-alanyl-L-alanine, glycyl-L-alanine, L-alanylglycine, and glycylglycine, which are prototypic molecules to model the pertinent functional groups. The model provides GEPs that reproduce the exact potential to an average accuracy of ca. 0.05 au. The good agreement between the properties estimated with the simple model and those calculated with state-of-the-art quantum chemical methods encourages further testing of the predictive power of this model, simulating for example interaction energies and optoelectronic properties.

Accurate Modelling of Group Electrostatic Potential and Distributed Polarizability in Dipeptides.

The front cover artwork is provided by the groups of Dr. Anna Krawczuk (Jagiellonian University, Poland), Prof. Leonardo H. R. Dos Santos (Universidade Federal de Minas Gerais, Brazil) and Prof. Piero Macchi (Polytechnics of Milan, Italy). The image shows electrostatic potentials and distributed polarizabilities of dipeptides reconstructed from functional-group methods based on quantum theory of atoms in molecules. Read the full text of the Article at 10.1002/cphc.202000441.

Crystal Field Effects on Atomic and Functional-Group Distributed Polarizabilities of Molecular Materials.

To rationally design new molecular materials with desirable linear optical properties, such as refractive index or birefringence, we investigated how atomic and functional-group polarizability tensors of prototypical molecules respond to crystal field effects. By building finite aggregates of urea, succinic acid, p-nitroaniline, 4-mercaptopyridine, or methylbenzoate, and by partitioning the cluster electronic density using quantum theory of atoms in molecules, we could extract atoms and functional groups from the aggregates and estimate their polarizability enhancements with respect to values calculated for molecules in isolation. The isotropic polarizability and its anisotropy for the molecular building blocks are used to understand the functional-group sources of optical properties in these model systems, which could help the synthetic chemist to fabricate efficient materials. This analysis is complemented by benchmarking density functionals for atomic distributed polarizabilities in gas phase, by comparing the results with refractive-index calculations under periodic boundary conditions, and by estimating functional-group optical properties from a classical electrostatic atom-dipole interaction model.

Quasi-2D Heisenberg Antiferromagnets [CuX(pyz)2](BF4) with X = Cl and Br.

Two Cu2+ coordination polymers [CuCl(pyz)2](BF4) 1 and [CuBr(pyz)2](BF4) 2 (pyz = pyrazine) were synthesized in the family of quasi two-dimensional (2D) [Cu(pyz)2]2+ magnetic networks. The layer connectivity by monatomic halide ligands results in significantly shorter interlayer distances. Structures were determined by single-crystal X-ray diffraction. Temperature-dependent X-ray diffraction of 1 revealed rigid [Cu(pyz)2]2+ layers that do not expand between 5 K and room temperature, whereas the expansion along the c-axis amounts to 2%. The magnetic susceptibility of 1 and 2 shows a broad maximum at ∼8 K, indicating antiferromagnetic interactions within the [Cu(pyz)2]2+ layers. 2D Heisenberg model fits result in J∥ = 9.4(1) K for 1 and 8.9(1) K for 2. The interlayer coupling is much weaker with | J⊥| = 0.31(6) K for 1 and 0.52(9) K for 2. The electron density, experimentally determined and calculated by density functional theory, confirms the location of the singly occupied orbital (the magnetic orbital) in the tetragonal plane. The analysis of the spin density reveals a mainly σ-type exchange through pyrazine. Kinks in the magnetic susceptibility indicate the onset of long-range three-dimensional magnetic order below 4 K. The magnetic structures were determined by neutron diffraction. Magnetic Bragg peaks occur below TN = 3.9(1) K for 1 and 3.8(1) K for 2. The magnetic unit cell is doubled along the c-axis ( k = 0, 0, 0.5). The ordered magnetic moments are located in the tetragonal plane and amount to 0.76(8) µB/Cu2+ for 1 and 0.6(1) µB/Cu2+ for 2 at 1.5 K. The moments are coupled antiferromagnetically both in the ab plane and along the c-axis. The Cu2+ g-tensor was determined from electron spin resonance spectra as g x = 2.060(1), g z = 2.275(1) for 1 and g x = 2.057(1), g z = 2.272(1) for 2 at room temperature.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets.

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Distributed Atomic Polarizabilities of Amino Acids and their Hydrogen-Bonded Aggregates.

With the purpose of rational design of optical materials, distributed atomic polarizabilities of amino acid molecules and their hydrogen-bonded aggregates are calculated in order to identify the most efficient functional groups, able to buildup larger electric susceptibilities in crystals. Moreover, we carefully analyze how the atomic polarizabilities depend on the one-electron basis set or the many-electron Hamiltonian, including both wave function and density functional theory methods. This is useful for selecting the level of theory that best combines high accuracy and low computational costs, very important in particular when using the cluster method to estimate susceptibilities of molecular-based materials.

Experimental charge density and topological analysis of tetraaquabis(hydrogenmaleato)nickel(II): a comparison with Hirshfeld atom refinement.

Experimental charge density analysis is conducted on the coordination compound tetraaquabis(hydrogenmaleato)nickel(II), which exhibits a short intramolecular hydrogen bond. Through topological analysis, the nature of Ni-O bonds is concluded to be intermediate between ionic and covalent, but mainly presenting an ionic character, while the short hydrogen bond is classified as covalent in nature. The compound was also analysed after Hirshfeld atom refinement performed using NoSpherA2. A topological analysis was conducted on the molecular wavefunction and the results are compared with those obtained from experiment. In general, there is good agreement between the refinements, and the chemical bonds involving H atoms are in better agreement with what is expected from neutron data after HAR than they are after multipole refinement.

Distributed functional-group polarizabilities in polypeptides and peptide clusters toward accurate prediction of electro-optical properties of biomacromolecules.

CONTEXT: Aiming at accurately predicting electro-optical properties of biomolecules, this work presents distributed atomic and functional-group polarizability tensors for a series of polypeptides and peptide clusters constructed from glycine and its residuals. By partitioning the electron density using the quantum theory of atoms in molecules, we demonstrated a very good transferability of the group polarizabilities. We were able to identify and extract the most efficient functional groups capable of generating the largest electrical susceptibility in condensed phases. Both the isotropic polarizability and its anisotropy were used to understand the way functional groups act as sources of linear optical responses, how they interact with each other reinforcing the macroscopic optical behavior within the material, and how covalent bonds and non-covalent interactions, such as hydrogen bonds, determine refractive indices and birefringence. Particular attention is devoted to the peptide bonds as they provide links to build biomacromolecules or polymers. An adequate quantum-mechanical treatment of at least the first interaction sphere of a given functional group is required to properly describe the effects of mutual polarization, but we identified optimum cluster size and shape to better estimate polarizabilities and dipole moments of larger molecules or molecular aggregates from the knowledge of the electron density of a central molecule or amino acid residual that is representative of the bulk. The strategy outlined here is a fast yet effective tool for estimating the optical properties of proteins but could eventually find application in the rational design of optical organic materials as well. METHODS: Electronic-structure calculations were performed on the Gaussin16 program at the DFT level using the CAMB3LYP functional and the double-ζ quality Dunning basis set aug-cc-pVDZ. Electron density partitioning followed the concepts of the Quantum Theory of Atoms and Molecules (QTAIM) and was performed using the AIMAll program. The locally developed Polaber routine was applied to calculate dipole moment vectors and polarizability tensors. It was amended to include the effects of the local field on a given central molecule by means of a modified Atom-Dipole Interaction Model (ADIM).

Crystal structure, vibrational frequencies and polarizability distribution in hydrogen-bonded salts of pyromellitic acid.

Structural features of moderate-to-strong O-H...O hydrogen bonds are related to the frequencies of O-H stretching vibrations and to the electric polarizability distribution in the donor and acceptor functional groups for crystals synthesized from the 1,2,4,5-benzenetetracarboxylic (pyromellitic) acid, namely: bis(3-aminopyridinium) dihydrogen pyromellitate tetrahydrate, (1); bis(3-carboxypyridinium) dihydrogen pyromellitate, (2); bis(3-carboxyphenylammonium) dihydrogen pyromellitate dihydrate, (3); and bis(4-carboxyphenylammonium) dihydrogen pyromellitate, (4). A combination of single-crystal X-ray diffraction, powder Raman spectroscopy and first-principle calculations in both crystalline and gaseous phases has shown that changes in the O-H...O hydrogen-bond geometry can be followed by changes in the corresponding spectral modes. Vibrational properties of moderate hydrogen bonds can be estimated from correlations based on statistical analysis of several compounds [Novak (1974). Struct. Bond. 18, 177-216]. However, frequencies related to very short O-H...O bonds can only be predicted by relationships built from a subset of structurally similar systems. Moreover, the way in which hydrogen bonds affect the polarizability of donor and acceptor groups depends on their strength. Moderate interactions enhance the polarizability and make it more anisotropic. Shorter hydrogen bonds may decrease the polarizability of a group as a consequence of the volume restraint implied by the neighbour molecule within a hydrogen-bonded aggregate. This is significant for evaluation of the electric susceptibility in crystals and, therefore, for estimation of refractive indices and birefringence.

Understanding metal-ligand interactions in coordination polymers using Hirshfeld surface analysis.

Properties related to the size and shape of Hirshfeld surfaces provide insight into the nature and strength of interactions among the building blocks of molecular crystals. In this work, we demonstrate that functions derived from the curvatures of the surface at a point, namely, shape index (S) and curvedness (C), as well as the distances from the surface to the nearest external (de) and internal (di) nuclei, can be used to help understand metal-ligand interactions in coordination polymers. The crystal structure of catena-poly[[[(1,10-phenanthroline-κ2N,N')copper(II)]-µ-4-nitrophthalato-κ2O1:O2] trihydrate], {[Cu(C8H3NO6)(C12H8N2)]·3H2O}n, described here for the first time, was used as a prototypical system for our analysis. Decomposition of the coordination polymer into its metal centre and ligand molecules followed by joint analysis of the Hirshfeld surfaces generated for each part unveil qualitative and semi-quantitative information that cannot be easily obtained either from conventional crystal packing analysis or from Hirshfeld surface analysis of the entire polymeric units. The shape index function S is particularly sensitive to the coordination details and its mapping on the surface of the metallic centre is highly dependent on the nature of the ligand and the coordination bond distance. Correlations are established between the shape of the Hirshfeld surface of the metal and the geometry of the metal-ligand contacts in the crystals. This could be applied not only to estimate limiting coordination distances in metal-organic compounds, but also to help establish structure-property relationships potentially useful for the crystal engineering of such materials.

Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation?

The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.