PolaBer: a program to calculate and visualize distributed atomic polarizabilities based on electron density partitioning

Unveiling GruPol: Predicting Electric and Electrostatic Properties of Macromolecules via the Building Block Approach

Understanding electrostatics and electric properties of macromolecules is crucial in uncovering the intricacies of their behavior and functionality. The precise knowledge of these properties enhances our ability to manipulate and engineer macromolecules for diverse applications, spanning from drug design to materials science. Having that in mind, we present here the GruPol database approach to characterize and accurately predict dipole moments, static polarizabilities, and electrostatic potential of proteins and their subunits. The method involves partitioning of the electron density, calculated at the M06-HF/aug-cc-pVDZ level of theory, of small peptides into predefined building blocks that are averaged over the database. By manipulating and positioning these building blocks, GruPol enables the description of proteins assembled from over nearly 100 residual entries, allowing for efficient and precise computation of the above-mentioned properties across a broad range of proteins. The database enables the user to include solvent effects as well as define protonation states on the protein's backbone to account for pH variations. The precision of the proposed scheme is benchmarked against experimental data for myoglobin species.

Single-Crystal-to-Single-Crystal Photosynthesis of Supramolecular Organoboron Polymers with Dynamic Effects

The solid-state synthesis of single-crystalline organic polymers, having functional properties, remains an attractive and developing research area in polymer chemistry and materials science. However, light-triggered topochemical synthesis of crystalline polymers comprising an organoboron backbone has not yet been reported. Here, we describe an intriguing example of single-crystal-to-single-crystal (SCSC) rapid photosynthesis (occurs on a seconds-scale) of two structurally different linear organoboron polymers, driven by environmentally sustainable visible/sun light, obtained from the same monomer molecule. A newly designed Lewis acid-base type molecular B ← N organoboron adduct (consisting of an organoboron core and naphthylvinylpyridine ligands) crystallizes in two solid-state forms featuring the same chemical structure but different 3D structural topologies, namely, monomers 1 and 2. The solvate molecule-free crystals of 1 undergo topochemical photopolymerization via an unusual olefin-naphthyl ring [2 + 2] cyclization to yield the single crystalline [3]-ladderane polymer 1P growing along the B ← N linkages, accompanied by instantaneous and violent macroscopic mechanical motions or photosalient effects (such as bending-reshaping and jumping motions). In contrast, visible light-harvesting single crystals of 2 quantitatively polymerize to a B ← N bond-stabilized polymer 2P in a SCSC fashion owing to the rapid [2 + 2] cycloaddition reaction among olefin double bonds. Such olefin bonds in the crystals of 2 are suitably preorganized for photoreaction due to the presence of solvate molecules in the crystal packing. Single crystals of 2 also show photodynamic jumping motions - in response to visible light but in a relatively slower fashion than the crystals of 1. In addition to SCSC topochemical polymerization and dynamic motions, both monomer crystals and their single-crystalline polymers feature green emissive and short-lived room-temperature phosphorescence properties upon excitation with visible-light wavelength.

Polaronic Mechanism of Vibronic Localization in Mixed-Valence Cation Radicals with a Non-Conjugated Chromophore on the Bridge

In quest of a controllable intramolecular electron transfer (ET) across a bridge, we study the cation-radical form of the parent 1,4-diallyl-butane (I) and its derivatives (II)-(VI). In these mixed-valence (MV) compounds, the bridge of variable length connecting allyl redox sites can be either saturated (-CH₂ CH₂-) (I, III, and V) or unsaturated, modified by the π-spacer (-HC═CH-) (II, IV, and VI). Ab initio calculations for the charge delocalized transition structure and for fully optimized localized form of 1,ω-diallyl cation radicals I-VI allowed us to estimate the potential barriers for ET between the terminal allyl groups, vibronic coupling, and ET parameters. The ET barrier in all compounds with the π-fragment on the bridge is shown to be higher with respect to that in the systems with a saturated bridge. We propose a model based on the concept of a specific polaronic effect of the spacer. Charge localization at an allyl group creates an electric field polarizing the π-fragment and the bridge as a whole. The induced dipole moment interacts with the localized charge giving rise to the additional vibronic stabilization in a self-consistent manner without an appreciable change of localized charge. Utilization of this spacer-driven polaronic effect is expected to provide a route to a controllable ET in bridged MV compounds.

Inverse molecular design and parameter optimization with Hückel theory using automatic differentiation

Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel's π-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations using standard gradient-based optimization algorithms.

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.

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).

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.

The Dielectric Behavior of Protected HKUST-1

We investigated the adsorption properties and the dielectric behavior of a very well-known metal-organic framework (MOF), namely Cu3(BTC)2 (known as HKUST-1; BTC = 1,3,5-benzenetricarboxylate), before and after protection with some amines. This treatment has the purpose of reducing the inherent hygroscopic nature of HKUST-1, which is a serious drawback in its application of as low-dielectric-constant (low-κ) material. Moreover, we investigated the structure of HKUST-1 under a strong electric field, confirming the robustness of the framework. Even under dielectric perturbation, the water molecules adsorbed by the MOF remained almost invisible to X-ray diffraction, apart from those directly bound to the metal ions. However, the replacement of H2O with a more visible guest molecule such as CH2Br2 made the cavity that traps the guest more visible. Finally, in this work we demonstrate that impedance spectroscopy is a valuable tool for identifying water sorption in porous materials, providing information that is complementary to that of adsorption isotherms.

Ultrafast Vibrational Response of Activated C-D Bonds in a Chloroform-Platinum(II) Complex

The vibrational response of the activated C-D bond in the chloroform complex [Pt(C₆H₅)₂(btz-N,N')·CDCl₃, where btz = 2,2'-bi-5,6-dihydro-4H-1,3-thiazine] is studied by linear and nonlinear two-dimensional infrared (2D-IR) spectroscopy. The change of the C-D stretching vibration of metal-coordinated CDCl₃ relative to the free solvent molecule serves as a measure of the non-classical Pt···D-C interaction strength. The stretching absorption band of the activated C-D bond displays a red shift of 119 cm^-1 relative to uncoordinated CDCl₃, a strong broadening, and an 8-fold enhancement of spectrally integrated absorption. The infrared (IR) absorption and 2D-IR line shapes are governed by spectral diffusion on 200 fs and 2 ps time scales, induced by the fluctuating solvent CDCl₃. The enhanced vibrational absorption and coupling to solvent forces are assigned to the enhanced electric polarizability of the activated C-D bond. Density functional theory calculations show a significant increase of C-D bond polarizability of CDCl₃ upon coordination to the 16 valence electron Pt(II) complex.

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%.

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.

Polarization of Electron Density Databases of Transferable Multipolar Atoms

Polarizability is a key molecular property involved in either macroscopic (i.e., dielectric constant) and microscopic properties (i.e., interaction energies). In rigid molecules, this property only depends on the ability of the electron density (ED) to acquire electrostatic moments in response to applied electric fields. Databases of transferable electron density fragments are a cheap and efficient way to access molecular EDs. This approach is rooted in the relative conservation of the atomic ED between different molecules, termed transferability principle. The present work discusses the application of this transferability principle to the polarizability, an electron density-derived property, partitioned in atomic contributions using the Quantum Theory of Atoms In Molecules topology. The energetic consequences of accounting for in situ deformation (polarization) of database multipolar atoms are investigated in detail by using a high-quality quantum chemical benchmark.

Electron Density and Dielectric Properties of Highly Porous MOFs: Binding and Mobility of Guest Molecules in Cu3(BTC)2 and Zn3(BTC)2

Two isostructural highly porous metal-organic frameworks, the well-known {Cu₃(BTC)₂} _n (BTC = 1,3,5-benzenetricarboxylate), often appointed with the name HKUST-1, and {Zn₃(BTC)₂} _n, have been investigated as models for the buildup of dielectric properties, differentiating the role of chemi- and physisorbed guest molecules and that of specific intraframework and framework-guest linkages. For this purpose, electron charge density analysis, impedance spectroscopy, density functional theory simulations, and atomic partitioning of the polarizabilities have been exploited. These analyses at different degrees of pores filling enabled one to observe structural and electronic changes induced by guest molecules, especially when chemisorbed. The electrostatic potential inside the pores allows one to describe the absorption mechanism and to estimate the polarization of guests induced by the framework. The dielectric constant shows very diverse frequency dependence and magnitude of real and imaginary components as a consequence of (I) capture of guest molecules in the pores during synthesis, (II) MOF activation, and (III) water absorption from the atmosphere after activation. Comparison with calculated static-dielectric constant and atomic polarizabilities of the material has allowed for evaluating building blocks' contribution to the overall property, paving the way for reverse crystal engineering of these species.

Toward Prediction of Electrostatic Parameters for Force Fields That Explicitly Treat Electronic Polarization

The derivation of atomic polarizabilities for polarizable force field development has been a long-standing problem. Atomic polarizabilities were often refined manually starting from tabulated values, rendering an automated assignment of parameters difficult and hampering reproducibility and transferability of the obtained values. To overcome this, we trained both a linear increment scheme and a multilayer perceptron neural network on a large number of high-quality quantum mechanical atomic polarizabilities and partial atomic charges, where only the type of each atom and its connectivity were used as input. The predicted atomic polarizabilities and charges had average errors of 0.023 ų and 0.019 e using the neural net and 0.063 ų and 0.069 e using the simple increment scheme. As the algorithm relies only on the connectivities of the atoms within a molecule, thus omitting dependencies on the three-dimensional conformation, the approach naturally assigns like charges and polarizabilities to symmetrical groups. Accordingly, a convenient utility is presented for generating the partial atomic charges and atomic polarizabilities for organic molecules as needed in polarizable force field development.

Origin of chromic effects and crystal-to-crystal phase transition in the polymorphs of tyraminium violurate

Chromic materials are nowadays widely used in various technological applications, however understanding the effect and the possibility of tuning the obtained colour of a material are still challenging. Here a combined experimental and theoretical study is presented on the solvatochromic and crystallochromic effects in the (pseudo)polymorphs of tyraminium violurate. This organic material exhibits a large solvatochromic shift (ca 192 nm) associated with broad colour change (from yellow to dark violet). Tyraminum violurate crystallizes as red crystals of form (I) from water as a solvate, and as an unsolvated form [violet crystals of (II)] from methanol solution. Form (I), when heated, undergoes two crystal-to-crystal phase transformations associated with colour change of the crystals. Crystals of (II) show extreme birefringence (ca 0.46) and high refractive index (n γ above 1.90), which can be correlated with preferential orientation of the resultant dipole moments of the ions. Examination of optical effects (UV-Vis spectra) along with theoretical calculations (QTAIM, atomic and bond polarizabilities) enabled the description of the origin of colour in the studied materials.

New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 1. Theory and accuracy

A new method was developed to compute atom-in-material polarizabilities and dispersion coefficients for diverse material types.

Characterization of fluorine-centred `F...O' σ-hole interactions in the solid state

In the current study, the crystal structure of 1-(3-nitrophenyl)-2,2,2-trifluoroethanone (A1) and (E)-4-((4-fluorophenyl) diazenyl)phenol (A2) has been analyzed for the characterization of the presence of a `unique' and `rare' intermolecular C(sp3/sp2)—F...O contact, which has been observed to play a significant role in the crystal packing. Theoretical charge-density calculations have been performed to study the nature and strength associated with the existence of this intermolecular F...O contact, wherein the F atom is attached to ansp3-hybridized C atom in the case of A1 and to ansp2hybridized carbon in the case of A2. The crystal packing of the former contains two `electronically different' Csp3—F...O contacts which are present across and in between the layers of molecules. In the latter case, it is characterized by the presence of a very `short' (2.708 Å) and `highly directional' (168° at ∠C4—F1...O1 and 174° at ∠C10—O1...F1) Csp2—F...O contact. According to the Cambridge Structural Database (CSD) study, it is a rare example in molecular crystals. Topological features of F...O contacts in the solid state were compared with the gas-phase models. The two-dimensional and three-dimensional static deformation density obtained from theoretical multipole modeling confirm the presence of a charge depleted region on the F atoms. Minimization of the electrostatic repulsion between like charges are observed through subtle arrangements in the electronic environment in two of the short intermolecular F...O contacts. These contacts were investigated using inputs from pair energy decomposition analysis, Bader's quantum theory of atoms in molecules (QTAIM), Hirshfeld surface analysis, delocalization index, reduced density gradient (RDG) plot, electrostatic potential surface and distributed atomic polarizability. The intermolecular energy decomposition (PIXEL) and RDG–NCI (non-covalent interaction) analysis of the F...O contacts establish the interaction to be dispersive in nature. The mutual polarization of an O atom by fluorine andviceversaprovides real physical insights into the role of atomic polarizability in interacting atoms in molecules in crystals.

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 GenLocDip, a program for calculating and visualizing local dipole moments of molecular subsystems. GenLocDip 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 Fortran90 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.

Local electric dipole moments: A generalized approach

We present an approach for calculating local electric dipole moments for fragments of molecular or supramolecular systems. This is important for understanding chemical gating and solvent effects in nanoelectronics, atomic force microscopy, and intensities in infrared spectroscopy. Owing to the nonzero partial charge of most fragments, "naively" defined local dipole moments are origin-dependent. Inspired by previous work based on Bader's atoms-in-molecules (AIM) partitioning, we derive a definition of fragment dipole moments which achieves origin-independence by relying on internal reference points. Instead of bond critical points (BCPs) as in existing approaches, we use as few reference points as possible, which are located between the fragment and the remainder(s) of the system and may be chosen based on chemical intuition. This allows our approach to be used with AIM implementations that circumvent the calculation of critical points for reasons of computational efficiency, for cases where no BCPs are found due to large interfragment distances, and with local partitioning schemes other than AIM which do not provide BCPs. It is applicable to both covalently and noncovalently bound systems. © 2016 Wiley Periodicals, Inc.

“Conformational lock” via unusual intramolecular C–F⋯OC and C–H⋯Cl–C parallel dipoles observed in in situ cryocrystallized liquids

This study highlights the unusual features associated with the arrangement of parallel bond dipoles play a role in conformational locking in in situ cryocrystallized liquids.

Charge density analysis for crystal engineering

This review reports on the application of charge density analysis in the field of crystal engineering, which is one of the most growing and productive areas of the entire field of crystallography. While methods to calculate or measure electron density are not discussed in detail, the derived quantities and tools, useful for crystal engineering analyses, are presented and their applications in the recent literature are illustrated. Potential developments and future perspectives are also highlighted and critically discussed. Graphical abstractᅟ