Relating polarizability to volume, ionization energy, electronegativity, hardness, moments of momentum, and other molecular properties

Why are information-theoretic descriptors powerful predictors of atomic and molecular polarizabilities

CONTEXT

We rationalize the excellent performance of information-theoretic descriptors for predicting atomic and molecular polarizabilities. It seems that descriptors which capture information about the change in valence-shell structure, especially the relative Fisher information measures, are particularly useful. Using this, we can rationalize why the G3 form of the relative Fisher information, which measures the deviation of effective nuclear charge between an atom-in-a-molecule and the reference pro-atom, is especially effective as a predictor of molecular polarizability.

METHODS

There are no methods used in this paper, which relies on mathematical derivation and analysis.

Four-Dimensional Scaling of Dipole Polarizability: From Single-Particle Models to Atoms and Molecules

Scaling laws enable the determination of physicochemical properties of molecules and materials as a function of their size, density, number of electrons or other easily accessible descriptors. Such relations can be counterintuitive and nonlinear, and ultimately yield much needed insight into quantum mechanics of many-particle systems. In this work, we show on the basis of single-particle models, multielectron atoms and molecules that the dipole polarizability of quantum systems is generally proportional to the fourth power of a characteristic length, computed from the ground-state wave function. This four-dimensional (4D) scaling is independent of the ratio of bound-to-bound and bound-to-continuum electronic transitions and applies to many-electron atoms when a correlated length metric is used. Finally, this scaling law is applied to predict the polarizability of molecules by electrostatically coupled atoms-in-molecules approach, obtaining approximately 8% absolute and relative accuracy with respect to hybrid density functional theory (DFT) on the QM7-X data set of organic molecules, providing an efficient and scalable model for the anisotropic polarizability tensors of extended (bio)molecules.

Size-dependent linear and nonlinear optical responses of silicon clusters

Owing to strong quantum confinement effects and no periodic constraints, the geometric and electronic structures of silicon clusters differ from those of crystalline silicon. Although previous studies have elucidated the optical properties of silicon clusters, some issues remain unresolved. To address these, this study examined the size-dependent linear and nonlinear optical responses of silicon clusters through first-principles calculations. Silicon clusters exhibited lone-pair-electron-dominated optical response behaviors. With the investigated size range, the orientationally average polarizability (αave) and second-order hyperpolarizability (γave) increased with cluster size. However, αave and γave per atom exhibited no evident size-dependent trends owing to co-modulation of the lone-pair-number-to-atomic-number ratio and geometry. αave and γave were notably sensitive to the nuclear binding strength of lone-pair electrons. Thus, the nonlinear optical effects of silicon clusters are superior to those of phosphorus and sulfur clusters. This investigation offers valuable insights into the optical responses of atomic-precision clusters.

"Freedom of design" in chemical compound space: towards rational in silico design of molecules with targeted quantum-mechanical properties

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure-property/property-property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space-the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS-our analysis reveals that one has a substantial degree of flexibility or "freedom of design" when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO-LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties.

Data-driven tailoring of molecular dipole polarizability and frontier orbital energies in chemical compound space

Understanding correlations - or lack thereof - between molecular properties is crucial for enabling fast and accurate molecular design strategies. In this contribution, we explore the relation between two key quantities describing the electronic structure and chemical properties of molecular systems: the energy gap between the frontier orbitals and the dipole polarizability. Based on the recently introduced QM7-X dataset, augmented with accurate molecular polarizability calculations as well as analysis of functional group compositions, we show that polarizability and HOMO-LUMO gap are uncorrelated when considering sufficiently extended subsets of the chemical compound space. The relation between these two properties is further analyzed on specific examples of molecules with similar composition as well as homooligomers. Remarkably, the freedom brought by the lack of correlation between molecular polarizability and HOMO-LUMO gap enables the design of novel materials, as we demonstrate on the example of organic photodetector candidates.

Lone Pair Electrons with Weak Nuclear Binding Inducing Sensitive Nonlinear Optical Responses in Phosphorus Clusters

Phosphorus clusters have broadband optical responses, adjustable geometries, and electronic structures, potentially balancing transparency and nonlinearity. In this study, the optical properties of phosphorus clusters are analyzed by using first-principles calculations. Phosphorus clusters exhibit strong light absorption in the ultraviolet region while remaining transparent in the visible to far-infrared bands. Importantly, the third-order nonlinear optical performance of phosphorus clusters surpasses that of p-nitroaniline with a D-π-A structure. The analysis reveals that lone pair electrons with weak nuclear binding induce sensitive nonlinear optical responses of phosphorus clusters. Furthermore, a practical approach for enhancing nonlinear optical effects in a medium via atom replacement and its application to hydride systems are discussed. Lone pair electron materials provide an alternative to conventional organic π-conjugated molecules for nonlinear optical devices, while potentially achieving a better trade-off of nonlinearity versus transparency. This study provides a novel concept for the development of high-performance nonlinear optical materials.

Hidden singularities in spontaneously polarized molecular solids

Films of dipolar molecules formed by physical vapor deposition are, in general, spontaneously polarized, with implications ranging from electron transfer in molecular optoelectronic devices to the properties of astrochemical ices in the interstellar medium. Polarization arises from dipole orientation, which should intuitively decrease with increasing deposition temperature, T. However, it is experimentally found that minimum or maximum values in polarization vs T may be observed for cis-methyl formate, 1-propanol, and ammonia. A continuous analytic form of polarization vs T is developed, which has the property that it is not differentiable at all T. The minima and maxima in polarization vs T are marked by singularities in the differential of this analytic form. This exotic behavior is presently unique to films of dipolar species and has not been reported, for example, in the related magnetic phases of spin glasses.

Excited-State Polarizabilities: A Combined Density Functional Theory and Information-Theoretic Approach Study

Accurate and efficient determination of excited-state polarizabilities (α) is an open problem both experimentally and computationally. Following our previous work, (Phys. Chem. Chem. Phys. 2023, 25, 2131−2141), in which we employed simple ground-state (S0) density-related functions from the information-theoretic approach (ITA) to accurately and efficiently evaluate the macromolecular polarizabilities, in this work we aimed to predict the lowest excited-state (S1) polarizabilities. The philosophy is to use density-based functions to depict excited-state polarizabilities. As a proof-of-principle application, employing 2-(2′-hydroxyphenyl)benzimidazole (HBI), its substituents, and some other commonly used ESIPT (excited-state intramolecular proton transfer) fluorophores as model systems, we verified that either with S0 or S1 densities as an input, ITA quantities can be strongly correlated with the excited-state polarizabilities. When transition densities are considered, both S0 and S1 polarizabilities are in good relationships with some ITA quantities. The transferability of the linear regression model is further verified for a series of molecules with little or no similarity to those molecules in the training set. Furthermore, the excitation energies can be predicted based on multivariant linear regression equations of ITA quantities. This study also found that the nature of both the ground-state and excited-state polarizabilities of these species are due to the spatial delocalization of the electron density.

Efficient and accurate density-based prediction of macromolecular polarizabilities

Accurately and efficiently predicting macromolecules' polarizabilities is an open problem. In this work, we employ a few simple density-based quantities from the information-theoretic approach (ITA) to predict polarizability of proteins. We first build quantitative structure/property relationships between molecular polarizabilities and ITA quantities. We then verify the broad applicability of ITA quantities for polarizability prediction for inorganic, organic, and biological systems with both localized and delocalized electronic structure. As a proof-of-concept application, we predict the molecular polarizabilities of complex proteins. Based on the linear regression equations for 20 natural amino acid residues, 400 dipeptides, and 8000 tripeptides, one then predicts the molecular polarizability of a larger peptide or even a protein once the molecular wavefunction is obtained. Because it is extremely costly to determine the wavefunction for a macromolecule like a protein, we propose to combine the ITA with the linear-scaling generalized energy-based fragmentation (GEBF) method to predict the macromolecular polarizability. In GEBF, the total molecular polarizability is obtained as a linear combination of the corresponding quantities from a series of small subsystems. We can predict them based on the subsystem wavefunction and linear regression equations rather than compute them from the nearly-intractable coupled-perturbed Hartree-Fock or Kohn-Sham equations for the whole macromolecule. Computational results showcase that the GEBF-ITA protocol should be an inexpensive yet accurate theoretical tool for predicting macromolecular polarizabilities.

A Density Functional Theory and Information-Theoretic Approach Study of Interaction Energy and Polarizability for Base Pairs and Peptides

Using density functional theory (DFT) and the information-theoretic approach (ITA) quantities to appreciate the energetics and properties of biopolymers is still an unaccomplished and ongoing task. To this end, we studied the building blocks of nucleic acid base pairs and small peptides. For base pairs, we have dissected the relative importance of energetic components by using two energy partition schemes in DFT. Our results convincingly show that the exchange-correlation effect predominantly governs the molecular stability of base pairs while the electrostatic potential plays a minor but indispensable role, and the steric effect is trivial. Furthermore, we have revealed that simple density-based ITA functions are in good relationships with molecular polarizabilities for a series of 30 hydrogen-bonded base pairs and all 20 natural α-amino acids, 400 dipeptides, and 8000 tripeptides. Based on these lines, one can easily predict the molecular polarizabilities of larger peptides, even proteins as long as the total molecular wavefunction is available, rather than solving the computationally demanding coupled-perturbed Hartree–Fock (CPHF) equation or its DFT counterpart coupled-perturbed Kohn–Sham (CPKS) equation.

Four-Dimensional Scaling of Dipole Polarizability in Quantum Systems

Polarizability is a key response property of physical and chemical systems, which has an impact on intermolecular interactions, spectroscopic observables, and vacuum polarization. The calculation of polarizability for quantum systems involves an infinite sum over all excited (bound and continuum) states, concealing the physical interpretation of polarization mechanisms and complicating the derivation of efficient response models. Approximate expressions for the dipole polarizability, α, rely on different scaling laws α∝R^{3}, R^{4}, or R^{7}, for various definitions of the system radius R. Here, we consider a range of single-particle quantum systems of varying spatial dimensionality and having qualitatively different spectra, demonstrating that their polarizability follows a universal four-dimensional scaling law α=C(4μq^{2}/ℏ^{2})L^{4}, where μ and q are the (effective) particle mass and charge, C is a dimensionless excitation-energy ratio, and the characteristic length L is defined via the L^{2} norm of the position operator. This unified formula is also applicable to many-particle systems, as shown by accurately predicting the dipole polarizability of 36 atoms, 1641 small organic molecules, and Bloch electrons in periodic systems.

Low temperature aging in a molecular glass: the case of cis-methyl formate

Glassy films of cis-methyl formate show spontaneous dipole orientation on deposition from the vacuum, the so-called 'spontelectric effect', creating surface potentials and electric fields within the films. We follow the decay of these fields, and their accompanying dipole orientation, on the hours timescale at deposition temperatures between 40 K and 55 K. Our data trace the low temperature 'secondary decay' mechanism, at tens of degrees below the glass transition temperature of 90 K. We show that secondary decay is due to molecular rotation, with associated activation energies lying between 0.1 and 0.2 eV. Diffusion is absent, as established from published neutron reflectivity data. Using an analytical model for the spontelectric effect, data are placed on a quantitative footing, showing that angular motion in excess of 50° reproduces the observed values of activation energies. Exploitation of the spontelectric effect is new in the study of glass aging and is shown here to give insight into the elusive processes which take place far from the molecular glass transition temperature.

A descriptor-based analysis to highlight the mechanistic rationale of mutagenicity

Cancer is a main concern for human health and there is a need of alternative methodologies to rapidly screen large quantitative of compounds that may represent a toxicological risk. Here a statistical analyses is performed on a benchmark database of experimental Ames data to identify chemical descriptors discriminating mutagens and non-mutagens. A total of 53 activating and deactivating modulators are identified, that flagged respectively a percentage of mutagen and non-mutagen up to 87%. Modulators are further combined to form synergistic cross-terms, accounting for the effect that combined properties may have on the final toxicity. Exclusion rules are defined as exception to the modulators. Synergistic cross-terms and exclusion rules improve the enrichment of mutagens/non-mutagens with respect of the original abundance in the dataset to values higher than 95%. The external predictivity of modulators and cross-terms reach balanced accuracy up to 0.775 that is analogous to other mutagenicity models from the literature, confirming the suitability of the rules to real-life screening of chemicals. Modulators are discussed for their mechanistic link to mutagenicity. This analysis confirms the key role of some properties (polarizability, shape, mass, presence of reactive functional groups or unsaturated planar systems) as driving elements for the initiation of the mutagenicity.

Multi-target approach for Alzheimer's disease treatment: computational biomolecular modeling of cholinesterase enzymes with a novel 4-N-phenylaminoquinoline derivative reveal promising potentials

The identification of dual inhibitors targeting the active sites of the cholinesterase enzymes, acetylcholinesterase (AChE) and butyrylcholinesterase (BuChE), have lately surfaced as a multi-approach towards Alzheimer treatment. More recently, a novel series of 4-N-phenylaminoquinolines was synthesized and evaluated against AChE and BuChE in which one of the compounds displayed appreciable inhibition compared to the standard compound, galantamine. To provide a clearer picture of the inhibition mechanism of this potent compound at the molecular level, computational biomolecular modeling was carried out. The investigation was initiated with the exploration of the chemical properties of the identified compound 11 b and reference drug, galantamine. Density functional theory (DFT) calculations reveal some conceptual parameters that provide information on the stability and reactivity of the compounds as potential inhibitors. To unveil the binding mechanism, energetics and enzyme-ligand interactions, molecular dynamics (MD) simulations of six different systems were executed over a period. Calculated binding free energy values are in the same order with experimental IC₅₀ data. Identification of the main residues driving optimum binding of the active compound 11 b to the binding region of both AChE and BuChE showed Trp81 and Trp110 as the most important, respectively. It was proposed that the studied compound could serve as a dual inhibitor for AChE and BuChE, therefore, would potentially be a promising moiety in a multi-target approach for the treatment of Alzheimer's disorder.Communicated by Ramaswamy H. Sarma.

Crystallites and Electric Fields in Solid Ammonia

Absorption spectra of vacuum-deposited films of ammonia have been obtained in the range 115 nm to 310 nm for a set of 15 deposition temperatures, Td, between 20 K and 80 K. Results focus upon the region 115 nm to 130 nm in overlapping D, E, F and G←X Rydberg transitions involving Wannier-Mott excitons. We identify two phases of ammonia, showing the solid to be polymorphic. Peak absorption wavelengths in the region of interest are found to shift to the red by 299 cm-1, for Td between 20 K to 50 K, and 1380 cm-1 for Td between 55 K to 80 K. Shifts provide evidence for the presence of spontaneously generated electric fields in these films, of values in excess of 108 V m-1 for Td of 20 K to 50 K to a few times 107 V m-1 for 55 K to 80 K. Results enable us to place a lower limit of 1.58 nm on the size of crystallites in the low temperature regime. This dimension represents 16 unit cells or 64 species, giving a more quantitative description than the nebulous term amorphous, as applied to solid ammonia. We also determine that crystallites formed in the high temperature regime contain, within ±20 %, 1688, 756 and 236 molecules of ammonia, respectively at Td of 65 K, 60 K and 55 K.

Dipole oscillator strength distributions, sum rules, mean excitation energies, and isotropic van der Waals coefficients for benzene, pyridazine, pyrimidine, pyrazine, s-triazine, toluene, hexafluorobenzene, and nitrobenzene

Experimental, theoretical, and additive-model photoabsorption cross sections combined with constraints provided by the Kuhn-Reiche-Thomas sum rule and the high-energy behavior of the dipole oscillator strength density are used to construct dipole oscillator strength distributions for benzene, pyridazine (1,2-diazine), pyrimidine (1,3-diazine), pyrazine (1,4-diazine), s-triazine (1,3,5-triazine), toluene (methylbenzene), hexafluorobenzene, and nitrobenzene. The distributions are used to predict dipole sum rules S(k) for -6 ≤ k ≤ 2, mean excitation energies I(k) for -2 ≤ k ≤ 2, and isotropic van der Waals C₆ coefficients. A popular combination rule for estimating C₆ coefficients for unlike interactions from the C₆ coefficients of the like interactions is found to be accurate to better than 1% for 606 of 628 cases (96.4%) in the test set.

Robust and Accurate Computational Estimation of the Polarizability Tensors of Macromolecules

Alignment of molecules through electric fields minimizes the averaging over orientations, e.g., in single-particle-imaging experiments. The response of molecules to external ac electric fields is governed by their polarizability tensor, which is usually calculated using quantum chemistry methods. These methods are not feasible for large molecules. Here, we calculate the polarizability tensor of proteins using a regression model that correlates the polarizabilities of the 20 amino acids with perfect conductors of the same shape. The dielectric constant of the molecules could be estimated from the slope of the regression line based on the Clausius-Mossotti equation. We benchmark our predictions against the quantum chemistry results for the Trp cagemini protein and the measured dielectric constants of larger proteins. Our method has applications in computing laser alignment of macromolecules, for instance, benefiting single-particle imaging, as well as for estimation of the optical and electrostatic characteristics of proteins and other macromolecules.

Quantum mechanical determination of atomic polarizabilities of ionic liquids

We present an accurate and simple quantum mechanical methodology to calculate atomic polarizabilities of charged species.

A coarse-grained polarizable force field for the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate

We present a coarse-grained polarizable molecular dynamics force field for the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIm][PF₆]). For the treatment of electronic polarizability, we employ the Drude model. Our results show that the new explicitly polarizable force field reproduces important static and dynamic properties such as mass density, enthalpy of vaporization, diffusion coefficients, or electrical conductivity in the relevant temperature range. In situations where an explicit treatment of electronic polarizability might be crucial, we expect the force field to be an improvement over non-polarizable models, while still profiting from the reduction of computational cost due to the coarse-grained representation.

Wannier-Mott Excitons in Nanoscale Molecular Ices

The absorption of light to create Wannier-Mott excitons is a fundamental feature dictating the optical and photovoltaic properties of low band gap, high permittivity semiconductors. Such excitons, with an electron-hole separation an order of magnitude greater than lattice dimensions, are largely limited to these semiconductors but here we find evidence of Wannier-Mott exciton formation in solid carbon monoxide (CO) with a band gap of >8  eV and a low electrical permittivity. This is established through the observation that a change of a few degrees K in deposition temperature can shift the electronic absorption spectra of solid CO by several hundred wave numbers, coupled with the recent discovery that deposition of CO leads to the spontaneous formation of electric fields within the film. These so-called spontelectric fields, here approaching 4×10^{7}  V m^{-1}, are strongly temperature dependent. We find that a simple electrostatic model reproduces the observed temperature dependent spectral shifts based on the Stark effect on a hole and electron residing several nm apart, identifying the presence of Wannier-Mott excitons. The spontelectric effect in CO simultaneously explains the long-standing enigma of the sensitivity of vacuum ultraviolet spectra to the deposition temperature.

Spontaneous polarization of solid CO on water ices and some astrophysical implications

Reflection absorption infrared spectroscopy (RAIRS) is used to show that when 20 monolayer (ML) films of solid CO are laid down on solid water substrates at 20 to 24 K, the films polarize spontaneously.

Spontaneous electric fields in solid carbon monoxide

Reflection–absorption infrared spectroscopy (RAIRS) is shown to provide a means of observing the spontelectric phase of matter, the defining characteristic of which is the occurrence of a spontaneous and powerful static electric field within a film of material.