Multi-Higgs models with CP symmetries of increasingly high order

When building CP-symmetric models beyond the Standard Model, one can impose CP-symmetry of higher order. This means that one needs to apply the CP-transformation more than two times to get the identity transformation, but still the model is perfectly CP-conserving. A multi-Higgs-doublet model based on CP-symmetry of order 4, dubbed CP4, was recently proposed and its phenomenology is being explored. Here, we show that the construction does not stop at CP4. We build examples of renormalizable multi-Higgs-doublet potentials which are symmetric under CP8 or CP16, without leading to any accidental symmetry. If the vacuum conserves CP-symmetry of order 2k, then the neutral scalars become CP-eigenstates, which are characterized not by CP-parities but by CP-charges defined modulo 2k. One or more lightest states can be the dark matter candidates, which are protected against decay not by the internal symmetry but by the exotic CP. We briefly discuss their mass spectra and interaction patterns for CP8 and CP16.Comment: 13 pages; v2: extra comments and references; v3: extra clarifications, matches published versio

From Static to Dynamic: Electron Density of HOMO at Biaryl Linkage Controls the Mechanism of Hole Delocalization

In order to extend the physical length of hole delocalization in a molecular wire, chromophores of increasing size are often desired. However, the effect of size on the efficacy and mechanism of hole delocalization remains elusive. Here, we employ a model set of biaryls to show that with increasing chromophore size, the mechanism of steady-state hole distribution switches from static delocalization in biaryls with smaller chromophores to dynamic hopping, as exemplified in the largest system, tBuHBC2 (i.e., “superbiphenyl”), which displays a vanishingly small electronic coupling. This important finding is analyzed with the aid of Hückel molecular orbital and Marcus–Hush theories. Our findings will enable the rational design of the novel molecular wires with length-invariant redox/optical properties suitable for long-range charge transfer

Game of Frontier Orbitals: A View on the Rational Design of Novel Charge-Transfer Materials

Since the first application of frontier molecular orbitals (FMOs) to rationalize stereospecificity of pericyclic reactions, FMOs have remained at the forefront of chemical theory. Yet, the practical application of FMOs in the rational design and synthesis of novel charge transfer materials remains under-appreciated. In this Perspective, we demonstrate that molecular orbital theory is a powerful and universal tool capable of rationalizing the observed redox/optoelectronic properties of various aromatic hydrocarbons in the context of their application as charge-transfer materials. Importantly, the inspection of FMOs can provide instantaneous insight into the interchromophoric electronic coupling and polaron delocalization in polychromophoric assemblies, and therefore is invaluable for the rational design and synthesis of novel materials with tailored properties

Novel Numerical Models of Electrostatic Interactions and Their Application to S-Nitrosothiol Simulations

Atom-centered point charge model of the molecular electrostatics remains a major workhorse in the atomistic biomolecular simulations. However, this approximation fails to reproduce anisotropic features of the molecular electrostatic potential (MEP), and the existing methods of the charge derivation are often associated with the numerical instabilities. This work provides an in-depth analysis of these limitations and offers a novel approach to describe electrostatic interactions that paves the way toward efficient next-generation force fields. By analyzing the charge fitting problem from first principles, as an example of the mathematical inverse problem, we show that the numerical instabilities of the charge-fitting problem arise due to the decreasing contribution from the higher multipole moments to the overall MEP. This insight suggests that if the point charges are arranged over the sphere using Lebedev quadrature, the resulting point charge model is able to exactly reproduce multipoles up to a given rank. At the same time, point charge values can be derived without fitting to the MEP, avoiding numerically unstable method of the charge derivation. This approach provides a systematic way to reproduce multipole moments up to any rank within the point charge approximation, which makes this model a computationally efficient analog of the multipolar expansion. Moreover, the proposed charged sphere model can be also used in the multi-site expansions with the expansion centers located at each atom in a molecule. This provides a natural approach to expand the traditional atom-centered point charge approximation to include higher-rank atomic multipoles and to account for the anisotropy of the MEP. We applied the proposed charged sphere model to S-nitrosothiols (RSNOs)—a class of biomolecules that serves to store and transmit nitric oxide, a biologically important signaling molecule. We showed that when the atom-centered charged spheres are optimized together with the Lennard-Jones parameters, the resulting force field can accurately reproduce the anisotropic features of the intermolecular interactions that play a crucial role in the biological regulation of RSNO chemistry. Overall, the developed charge model is a promising approach that can be used in the biomolecular simulations and beyond, e.g. in the multipolar force fields for atomistic and coarse-grained simulations

Wargames: Non-Linear Experiential Modes of Historical Knowledge

This project is on wargames, a type of board and digital game concerned with the practice of war, leadership, command, strategy, tactics, and decision-making. The goal of the project is to explore whether wargames, as non-linear experiential forms of historical knowledge have any value in understanding how the public views, understands, and relates to the historical past. Moreover, the goal of the project is to help historical academia understand what wargames are as they have not been studied in any substantial way and open the door for further research projects regarding wargames, or in fact use wargames as a research aid

Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Unraveling the Coulombic Forces in Electronically Decoupled Bichromophoric Systems during Two Successive Electron Transfers

Coulombic forces are vital in modulating the electron transfer dynamics in both synthetic and biological polychromophoric assemblies, yet quantitative studies of the impact of such forces are rare, as it is difficult to disentangle electrostatic forces from simple electronic coupling. To address this problem, the impact of Coulombic interactions in the successive removal of two electrons from a model set of spirobifluorenes, where the interchromophoric electronic coupling is nonexistent, is quantitatively assessed. By systematically varying the separation of the bifluorene moieties using model compounds, ion pairing, and solvation, these interactions, with energies up to about 0.4 V, are absent at distances greater than about 9 Å. These findings can be (quantitatively) applied for the design of polychromophoric assemblies, whereby the redox properties of donors and/or acceptors can be tuned by judicious positioning of the charged groups to control the electron‐transfer dynamics

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields