Classical Electrostatic Interactions Research Articles

Derivation of Morse potential

The Morse potential is widely used in chemistry, physics, and material science to describe interatomic interactions. We show that the Morse potential can be derived from a simple screened charge model accounting for the shielding of the nuclear charge by electron density. In this model, the parameter governing the width of the potential is related to the average shielding strength and the exponents of the atomic orbitals used in electronic structure calculations. The parameter representing the bond dissociation energy of a diatomic molecule is derived by combining the quantum mechanical covalent and classical electrostatic interactions. Moreover, the revealed connection between the parameters of the Morse potential and Pauling’s bond order and electronegativity provides insight into the relation between the classical and quantum mechanical descriptions of chemical bonds. This derivation of the Morse potential from the atomic quantities is expected to contribute to the development of the new basis sets incorporating Slater-type orbitals for electronic structure calculations and the transferable reactive force fields for molecular dynamics simulations. Furthermore, this interpretation of the Morse potential helps to understand the relationships between widely used chemical concepts, including effective atomic charge, bond dissociation energy, electronegativity, and bond order.

Establishing Fluorine-Containing Amino Acids as an Orthogonal Tool in Coiled Coil Assembly.

The α-helical coiled coil (CC) is one of the best-characterized folding motifs in the protein world. In this context, fluorinated amino acids have been shown to be capable of tuning the properties of CC assemblies, and especially fluorinated derivatives of aliphatic amino acids can significantly increase the stability of this folding motif when placed in the hydrophobic a and d positions. However, it has not been shown yet whether fluorinated amino acids, by means of rational design, can be used as an orthogonal tool to control CC assembly processes. In the current work, we approached this question by creating a combinatorial peptide library based on a VPE/VPK heteromeric CC system previously established and characterized in our group. This CC model allowed us to screen fluorinated amino acids for interaction with different potential binding partners in position a of the VPE/VPK model with a particular emphasis on studying the impact of stereochemistry within the side chain of α-branched aliphatic fluorinated amino acids on CC properties such as oligomerization state, thermodynamic stability, and orientation. 28 combinations of library members were characterized regarding structure, oligomerization, and thermal stability utilizing circular dichroism, size exclusion chromatography, and Förster resonance energy transfer measurements. This detailed approach showed that the stability and oligomerization state of the motif were not only dependent on the steric demand and the fluorination of corresponding amino acids but also on the stereochemistry within the side chain. The results were applied for a rational design of the fluorine-driven orthogonal assembly, and we could show that CC dimer formation occurred based on specific interactions between fluorinated amino acids. These results demonstrate the potential of fluorinated amino acids as an orthogonal tool besides classical electrostatic and hydrophobic interactions for the fine-tuning and direction of peptide-peptide interactions. Furthermore, within the space of fluorinated amino acids, we could demonstrate the specificity of interactions between differently fluorinated side chains.

Quantum corrections to the classical electrostatic interaction between induced dipoles

We study, in the presence of an external electrostatic field, the interatomic interaction between two ground-state atoms coupled with vacuum electromagnetic fluctuations within the dipole coupling approximation based on the perturbation theory. We show that, up to the fourth order, the electrostatic-field-induced interatomic interaction is just the classical dipole-dipole interaction, which disagrees with the recent result from Fiscelli et al. [G. Fiscelli et al., Phys. Rev. Lett. 124, 013604 (2020)]. However, to higher orders, there exist external-field-related quantum corrections to the induced classical electrostatic dipole-dipole interaction. In the sixth order, the external field effectively modifies the atomic polarizability to give rise to a two-photon-exchange quantum correction, while in the eighth order, the external field enables an additional process of three-photon exchange which is not allowed in the absence of the external field, and this process generates an $r^{-11}$ term in the interaction potential in the far regime, where $r$ is the interatomic separation. Numerical estimations show that these external-field-related quantum corrections are much smaller than the two-photon-exchange Casimir-Polder interaction.

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.

VeloxChem: A Python‐driven density‐functional theory program for spectroscopy simulations in high‐performance computing environments

AbstractAn open‐source program named VeloxChem has been developed for the calculation of electronic real and complex linear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theories. With an object‐oriented program structure written in a Python/C++ layered fashion, VeloxChem enables time‐efficient prototyping of novel scientific approaches without sacrificing computational efficiency, so that molecular systems involving up to and beyond 500 second‐row atoms (or some 10,000 contracted and in part diffuse Gaussian basis functions) can be routinely addressed. In addition, VeloxChem is equipped with a polarizable embedding scheme for the treatment of the classical electrostatic interactions with an environment that in turn is modeled by atomic site charges and polarizabilities. The underlying hybrid message passing interface (MPI)/open multiprocessing (OpenMP) parallelization scheme makes VeloxChem suitable for execution in high‐performance computing cluster environments, showing even slightly beyond linear scaling for the Fock matrix construction with use of up to 16,384 central processing unit (CPU) cores. An efficient—with respect to convergence rate and overall computational cost—multifrequency/gradient complex linear response equation solver enables calculations not only of conventional spectra, such as visible/ultraviolet/X‐ray electronic absorption and circular dichroism spectra, but also time‐resolved linear response signals as due to ultra‐short weak laser pulses. VeloxChem distributed under the GNU Lesser General Public License version 2.1 (LGPLv2.1) license and made available for download from the homepage https://veloxchem.org.This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory Theoretical and Physical Chemistry > Spectroscopy

Classical Electrostatic Interaction Is the Origin for Blue-Shifting Halogen Bonds.

Studies have shown that, on the one hand, charge transfer (CT) plays a key role in halogen bonds (D···X-A) (D = donor; X = halogen atom; A = acceptor), suggesting considerable covalent character of halogen bonding. But, on the other hand, it has been proposed that halogen bonding is dominated by the electrostatic attraction between the electropositive σ-hole at the halogen atom X and the electronegative donor D. It has also been well-recognized that the CT from the donor D to the antibonding σ*(X-A) would weaken and lengthen the X-A bond. Yet, intriguingly, there is a blue-shifting phenomenon in halogen bonding, where the X-A bond contracts with an enhanced stretching vibrational frequency. Here we explored the nature of blue-shifting halogen bonds with the iconic case of H3N···ClNO2, which exhibits the blue-shifting phenomenon along with a strong CT interaction and its analogous H3N···XNY2 (X = Cl, Br, and I; Y = O, S). By decomposing the binding energy to a number of energy components and exploring their energy profiles along with the halogen-bonding distances with the block-localized wave function (BLW) method, we showed that the classical electrostatic interaction is the governing factor for the blue-shifting of the X-N bonds. This is further supported by the similar magnitudes of blue-shifting obtained when NH3 is replaced with atomic point charges in the complexes. Alternatively, by applying external electric field (E-field) along the X-N bond direction, the blue-to-red shifting transition can be identified. This is because both polarization and CT interactions tend to stretch the X-N bond, and both are enhanced simultaneously under the external E-field. Finally, roles of individual energy components are reconfirmed using the force analysis based on the BLW energy decomposition approach.

Analysis of Stability and (Anti)aromaticity of BN‐Dibenzo[a,e]pentalenes

Relatively scarce literature data on BN/CC isosterism in 4nπ‐electronic systems have prompted us to investigate theoretically the influence of BN pair position within the central butadiene fragment of dibenzo[a,e]pentalene on two fundamental molecular properties: stability and (anti)aromaticity. It was found that stability and aromaticity follow the same trend only for BN‐orientational isomers. The source of different stability of other isomers was examined first by an analysis of bond types and their dissociation energies and then by isomerization energy decomposition analysis and was explained in terms of classical electrostatic interactions, quantum‐mechanical orbital interactions, structural changes and electronic changes (transition from charge‐separated π‐system to the neutral one). (Anti)aromaticity was investigated by using three kinds of indices, HOMA, FLUπ, and NICS(1)zz, which indicated that delocalization at the central pentalene motif is almost unaffected by various BN arrangements, molecular perimeter is slightly affected, while the most affected subunits are five‐membered rings and benzene‐fused five‐membered rings containing only one heteroatom.

Revealing Factors Governing Self-Assembly Morphology of Fatty Acid on Graphene Synthesized by Surfactant-Assisted LPE: A Joint MD, SAPT(DFT), and Experimental Study

The production of graphene nanosheets from graphite with the assistance of biological molecules in water medium as well as understanding the morphology of the resulting self-assembly are important in fields of drug delivery, cell imaging, and photothermal therapy. Hence, in this contribution, we have applied docosahexaenoic acid (DHA) fatty acid to disperse graphite. The morphology of self-assembly on the graphene surface and the factors tailoring the morphology were surveyed in light of classical molecular dynamic (MD) and symmetry-adapted perturbation theory (SAPT). The factors such as surface density, environment pH, substrate size, and number of layers were taken into account. The results show that the decrease in pH transmutes the nature of the classical electrostatic interaction between the surfactants from repulsion to attraction, leading to a decline in the stability of the colloidal systems. When the lateral size of the graphene sheet is three times larger than the length of DHA, hemicylinder str...

The ‘non-Coulombic’ character of classical electrostatic interaction between charges near interfaces

The textbook problem of classical electrostatics concerning the charge–charge interaction energy W in a two-layer system is revisited. In particular, the actual dependence of W on the horizontal distance L between the charges located at the same distance x from the interface is shown to substantially differ from the original Coulomb law due to image charges. The deviations are governed by the ratio L/x and the ratio between the dielectric constants of adjacent media. Thus, the dependence W(L) is never conventionally Coulombic (∼L−1) and may even be close to a dipole–dipole one (∼L−3). Although these results are implicitly contained in the well-known formulas, they are often overlooked while teaching electrostatics. The results are of interest not only from a purely academic viewpoint but are important for modern surface science, where the electrostatic contribution to the ion–ion interaction is often treated as Coulombic without any reservations.

Spectroscopic probe of the van der Waals interaction between polar molecules and a curved surface

We study the shift of rotational levels of a diatomic polar molecule due to its van der Waals (vdW) interaction with a gently curved dielectric surface at temperature $T$, and submicron separations. The molecule is assumed to be in its electronic and vibrational ground state, and the rotational degrees are described by a rigid rotor model. We show that under these conditions retardation effects and surface dispersion can be neglected. The level shifts are found to be independent of $T$, and given by the quantum state averaged classical electrostatic interaction of the dipole with its image on the surface. We use a derivative expansion for the static Green's function to express the shifts in terms of surface curvature. We argue that the curvature induced line splitting is experimentally observable, and not obscured by natural line widths and thermal broadening.

Polarizable embedding with a multiconfiguration short-range density functional theory linear response method.

We present here the coupling of a polarizable embedding (PE) model to the recently developed multiconfiguration short-range density functional theory method (MC-srDFT), which can treat multiconfigurational systems with a simultaneous account for dynamical and static correlation effects. PE-MC-srDFT is designed to combine efficient treatment of complicated electronic structures with inclusion of effects from the surrounding environment. The environmental effects encompass classical electrostatic interactions as well as polarization of both the quantum region and the environment. Using response theory, molecular properties such as excitation energies and oscillator strengths can be obtained. The PE-MC-srDFT method and the additional terms required for linear response have been implemented in a development version of Dalton. To benchmark the PE-MC-srDFT approach against the literature data, we have investigated the low-lying electronic excitations of acetone and uracil, both immersed in water solution. The PE-MC-srDFT results are consistent and accurate, both in terms of the calculated solvent shift and, unlike regular PE-MCSCF, also with respect to the individual absolute excitation energies. To demonstrate the capabilities of PE-MC-srDFT, we also investigated the retinylidene Schiff base chromophore embedded in the channelrhodopsin protein. While using a much more compact reference wave function in terms of active space, our PE-MC-srDFT approach yields excitation energies comparable in quality to CASSCF/CASPT2 benchmarks.

Second‐order Nonlinear Optical Susceptibilities and Refractive Indices of Organic Crystals from a Multiscale Numerical Simulation Approach

The performance of a simple multiscale approach to rapidly screen the second‐order nonlinear optical (NLO) susceptibilities [χ(2)] as well as the refractive indices of organic crystals solely from the knowledge of their crystal structure is demonstrated. The method combines first principles calculations of the molecular properties with a classical electrostatic interactions scheme to account for the crystal environment effects. The calculated values reproduce closely the measured χ(2) response for 10 organic crystals, including ionic crystalline salts, covering a χ(2) range from 10 to 600 pm V–1. The agreement between calculations and measurements is also excellent in the case of the refractive indices. Moreover, the method allows to analyze the relationship between the macroscopic responses [χ(2)] and the molecular first hyperpolarizabilities, highlighting the effects of crystal packing and chromophore density as well as the role played by the crystal dressing field.

Stark effect on vibration frequencies of sulfate on Pt(1 1 1) electrode

Stark effect on vibration frequencies of sulfate on Pt(111) electrode is studied by density functional theory calculations on a neutral surface model under a homogeneous external electric field. The calculations indicate that the Stark effect is dominated by the classical electrostatic interaction of the dipole moment of sulfate with the external electric field. The large potential-dependence of the S–O (uncoordinated) vibration mode, which was observed at 1250cm−1 by infrared reflection absorption spectroscopy (IRAS), is attributed to its large dynamic dipole moment normal to the surface. The large dynamic dipole moment significantly changes the equilibrium S–O (uncoordinated) bond distance in the external electric field, which results in the significant change in the vibration frequency.

Photoionization-Induced Water Migration in the Hydrated trans-Formanilide Cluster Cation Revealed by Gas-Phase Spectroscopy and Ab Initio Molecular Dynamics Simulation

Photoionization-induced water migration in the trans-formanilide-water 1:1 cluster, FA-(H(2)O)(1), has been investigated by using IR-dip spectroscopy, quantum chemical calculations, and ab initio molecular dynamics simulations. In the S(0) state, FA-(H(2)O)(1) has two structural isomers, FA(NH)-(H(2)O)(1) and FA(CO)-(H(2)O)(1), where a water molecule is hydrogen-bonded (H-bonded) to the NH group and the CO group, respectively. In addition, the S(1)-S(0) origin transition of FA(CO)-(H(2)O)(2), where a water dimer is H-bonded to the CO group, was observed only in the [FA-(H(2)O)(1)](+) mass channel, indicating that one of the water molecules evaporates completely in the D(0) state. These results are consistent with a previous report [Robertson, E. G. Chem. Phys. Lett., 2000, 325, 299]. In the D(0) state, however, [FA-(H(2)O)(1)](+) produced by photoionization via the S(1)-S(0) origin transitions of FA(NH)-(H(2)O)(1) and FA(CO)-(H(2)O)(1) shows essentially the same IR spectra. Compared with the theoretical calculations, [FA-(H(2)O)(1)](+) can be assigned to [FA(NH)-(H(2)O)(1)](+). This means that the water molecule in [FA-(H(2)O)(1)](+) migrates from the CO group to the NH group when [FA-(H(2)O)(1)](+) is produced by photoionization of FA(CO)-(H(2)O)(1). [FA-(H(2)O)(1)](+) produced by photoionization of FA(CO)-(H(2)O)(2) also shows the IR spectrum corresponding to [FA(NH)-(H(2)O)(1)](+). In this case, the water migration from the CO group to the NH group occurs with the evaporation of a water molecule. Ab initio molecular dynamics simulations revealed the water migration pathway in [FA-(H(2)O)(1)](+). The calculations of classical electrostatic interactions show that charge-dipole interaction between FA(+) and H(2)O induces an initial structural change in [FA-(H(2)O)(1)](+). An exchange repulsion between the lone pairs of the CO group and H(2)O in [FA-(H(2)O)(1)](+) also affects the initial direction of the water migration. These two factors play important roles in determining the initial water migration pathway.

Stereoelectronic Interactions and the One-Bond C–F Coupling Constant in Sevoflurane

The conformational preference of the widely utilized anesthetic fluoromethyl-1,1,1,3,3,3-hexafluoro-2-propyl ether (sevoflurane) has been investigated computationally and by NMR spectroscopy. Three conformational minima were located at the B3LYP/aug-cc-pVDZ level, but one is significantly more stable (by ca. 4 kcal/mol) than the other two. This is the case both for gas phase calculations and for solution NMR data. Although the main conformer is stabilized by electron delocalization (n(O) → σ*(C-F)), this type of hyperconjugation was not found to be the main driver for the conformer stabilization in the gas phase and, consequently, for the apparent anomeric effect in sevoflurane. Instead, more classical steric and electrostatic interactions appear to be responsible for the conformational energies. Also the (1)J(CF) coupling constants do not appear to be dominated by hyperconjugation; again, dipolar interactions are invoked instead.

Modeling the electrophoresis of oligolysines

CE is used to measure the electrophoretic mobility of low molecular mass oligo-L-lysines (n=1-8) in aqueous LiH₂PO₄ buffer, BGE, at pH 2.5 over a range of temperatures (25-50 °C) and ionic strengths (10-100 mM). Mobilities are corrected for Joule heating and under the conditions of the experiment, interaction of the peptides with the capillary walls can be ignored. A "coarse grained" bead modeling methodology (BMM) (H. Pei et al., J. Chromatogr. A 2009, 1216, 1908-1916) is used to model the mobilities. This model partially accounts for peptide conformation as well as the assumed form of its secondary structure. For highly charged oligolysines, it is necessary to properly account for the relaxation effect. In the present study, the BMM approach tends to overestimate oligolysine mobility and that effect tends to increase with increasing ionic strength and peptide length. It is proposed that association between the oligolysines and buffer components (H₂PO₄⁻ in this case) that go beyond classical electrostatic interactions are responsible for this discrepancy. A simple binding model is introduced that illustrates how this association can reconcile model and experiment.

Synthesis, characterization and DNA binding and cleavage properties of ruthenium(II) complexes with various polypyridyls

Polypyridyl chlororuthenium(II) complexes have been synthesized and characterized. The binding mode of the complexes to DNA has been evaluated from the combined results of electronic absorption spectroscopy and viscosity measurement study. The results suggest that complexes 1, 2 and 3 bind to DNA via classical intercalation, electrostatic interaction and partial intercalation mode, respectively. Complex 2 shows less affinity for DNA. Cleavage of pUC19 DNA by complexes has been checked using gel electrophoresis. The data disclose that complex 1 has the highest cleaving ability.

Origin of anomeric effect: A density functional steric analysis

The anomeric effect (the tendency of heteroatomic substituents adjacent to a heteroatom within the cyclohexane ring to prefer the axial orientation instead of the sterically less hindered equatorial position) is traditionally explained through either the dipole moment repulsion or the hyperconjugation effect. In this work, by employing our recent work in density functional steric analysis, we provide a novel two-component explanation, which is consistent with the common belief in chemistry that the effect has a stereoelectronic origin. With α-D-glucopyranose as the prototype, we systematically explore its conformational space and generate 32 isomers, leading to a total of 80 axial-equatorial conformation pairs. The energy difference analysis of these pairs shows that while statistically speaking the tendency is valid, the anomeric effect is not always true and can be violated. Three energy components, exchange-correlation, classical electrostatic, and density functional steric, are found to be directly proportional to the total energy difference between axial and equatorial isomers. We also found that the total dipole moment change, not the hyperconjugation effect, is a reasonable indicator of the total energy difference. However, all these correlations alone are not strong enough to provide a compellingly convincing explanation for the general validity of the effect. With the help of strong correlations between energy components, an explanation with two energy components, steric and electrostatic, was proposed in this work. We show that the axial-equatorial energy difference in general, with the anomeric effect as a special case, is dictated by two factors of the stereoelectronic origin, steric hindrance and classical electrostatic interactions, synchronously working together. Another explanation in terms of exchange-correlation and electrostatic interactions has also been obtained in this work.

Electrostatic correlations at the Stern layer: Physics or chemistry?

We introduce a minimal free energy describing the interaction of charged groups and counterions including both classical electrostatic and specific interactions. The predictions of the model are compared against the standard model for describing ions next to charged interfaces, consisting of Poisson-Boltzmann theory with additional constants describing ion binding, which are specific to the counterion and the interfacial charge ("chemical binding"). It is shown that the "chemical" model can be appropriately described by an underlying "physical" model over several decades in concentration, but the extracted binding constants are not uniquely defined, as they differ depending on the particular observable quantity being studied. It is also shown that electrostatic correlations for divalent (or higher valence) ions enhance the surface charge by increasing deprotonation, an effect not properly accounted within chemical models. The charged phospholipid phosphatidylserine is analyzed as a concrete example with good agreement with experimental results. We conclude with a detailed discussion on the limitations of chemical or physical models for describing the rich phenomenology of charged interfaces in aqueous media and its relevance to different systems with a particular emphasis on phospholipids.

Self-consistent polarization neglect of diatomic differential overlap: Application to water clusters

Semiempirical self-consistent field (SCF) methods based on the neglect of diatomic differential overlap (NDDO) formalism have the ability to treat the formation and breaking of chemical bonds but have been found to poorly describe hydrogen bonding and weak electrostatic complexes. In contrast, most empirical potentials are not able to describe bond breaking and formation but have the ability to add missing elements of hydrogen bonding by using classical electrostatic interactions. We present a new method which combines aspects of both NDDO-based SCF techniques and classical descriptions of polarization to describe the diffuse nature of the electronic wavefunction in a self-consistent manner. We develop the "self-consistent polarization neglect of diatomic differential overlap" (SCP-NDDO) theory with the additional description of molecular dispersion developed as a second-order perturbation theory expression. The current study seeks to model water-water interactions as a test case. To this end, we have parametrized the method to accurate ab initio complete basis set limit estimates of small water cluster binding energies of Xantheas and co-workers [J. Chem. Phys. 116, 1493 (2002); 120, 823 (2004)]. Overall agreement with the ab initio binding energies (n=2-6, and 8) is achieved with a rms error of 0.19 kcal/mol. We achieve noticeable improvements in the structure, vibrational frequencies, and energetic predictions of water clusters (n< or =21) relative to standard NDDO-based methods.