Dynamics of electronic polarization in molecular crystals

Dynamics of electronic polarization in the vicinity of charge carriers in molecular crystals is for the first time investigated here in connection with the carrier transport and intramolecular vibronic polarization. According to standard picture it has been assumed that the electronic polarization relaxation time is extremely short, as estimated from the relation τ_c = τ_d1 ≈ h/E_exc, where E_exc is the energy of the first single exciton state. In the case of anthracene (Ac) crystals, the value of τ_e is about 2 × 10⁻¹⁶ s, i.e. by several orders of magnitude shorter than a typical hopping (residence) time of charge carriers τ_h = 10⁻¹⁴ -10⁻¹³ s. It is argued that typical time of full reconstruction of the electronic polarization after individual carrier hops equals, in the slow carrier regime, approximately to t_d2 ≈ h/ΔE_exc is the width of the lowest singlet-exciton band. In Ac, this means t_d2 ≈ 0.73 × 10⁻¹⁴ s. Physical implications of this relatively high value of t_d2 in connection with carrier transport and molecular (vibronic) polarization are discussed.     

Accounting for electronic polarization in non-polarizable force fields

The issues of electronic polarizability in molecular dynamics simulations are discussed. We argue that the charges of ionized groups in proteins, and charges of ions in conventional non-polarizable force fields such as CHARMM, AMBER, GROMOS, etc should be scaled by a factor about 0.7. Our model explains why a neglect of electronic solvation energy, which typically amounts to about a half of total solvation energy, in non-polarizable simulations with un-scaled charges can produce a correct result; however, the correct solvation energy of ions does not guarantee the correctness of ion-ion pair interactions in many non-polarizable simulations. The inclusion of electronic screening for charged moieties is shown to result in significant changes in protein dynamics and can give rise to new qualitative results compared with the traditional non-polarizable force field simulations. The model also explains the striking difference between the value of water dipole μ～ 3D reported in recent ab initio and experimental studies with the value μ(eff)～ 2.3D typically used in the empirical potentials, such as TIP3P or SPC/E. It is shown that the effective dipole of water can be understood as a scaled value μ(eff) = μ/√ε(el), where ε(el) = 1.78 is the electronic (high-frequency) dielectric constant of water. This simple theoretical framework provides important insights into the nature of the effective parameters, which is crucial when the computational models of liquid water are used for simulations in different environments, such as proteins, or for interaction with solutes.     

Reevaluation of electronic polarization energies in organic molecular crystals

Effective electronic polarization energies for positive P⁺_eff and negative P⁻_eff charge carriers in polyacene crystals have been reevaluated. By comparing the P⁺_eff and P⁻_eff values obtained from the analyses of reported energy parameters with calculated data, it is shown that the widely accepted assumption that P⁺_eff = P⁻_eff in polyacene crystals is not valid. By applying recently reported data on optical E^opt_G and adiabatic E^ad_G energy gap values, the contribution of molecular (vibronic) polarization in the total effective polarization energies W⁺_eff and W⁻_eff has been estimated, and modified energy diagrams for polyacene crystals have been presented. Further, due to practically constant values of observed and calculated P⁺_eff and P⁻_eff in polyacenes, the gap energies between positive and negative charge carrier conduction levels have been estimated for several related aromatic hydrocarbons.     

Solid effect dynamic nuclear polarization and polarization pathways

Using dynamic nuclear polarization (DNP)/nuclear magnetic resonance instrumentation that utilizes a microwave cavity and a balanced rf circuit, we observe a solid effect DNP enhancement of 94 at 5 T and 80 K using trityl radical as the polarizing agent. Because the buildup rate of the solid effect increases with microwave field strength, we obtain a sensitivity gain of 128. The data suggest that higher microwave field strengths would lead to further improvements in sensitivity. In addition, the observation of microwave field dependent enhancements permits us to draw conclusions about the path that polarization takes during the DNP process. By measuring the time constant for the polarization buildup and enhancement as a function of the microwave field strength, we are able to compare models of polarization transfer, and show that the major contribution to the bulk polarization arises via direct transfer from electrons, rather than transferring first to nearby nuclei and then transferring to bulk nuclei in a slow diffusion step. In addition, the model predicts that nuclei near the electron receive polarization that can relax, decrease the electron polarization, and attenuate the DNP enhancement. The magnitude of this effect depends on the number of near nuclei participating in the polarization transfer, hence the size of the diffusion barrier, their T(1), and the transfer rate. Approaches to optimizing the DNP enhancement are discussed.     

The F130L mutation in streptavidin reduces its binding affinity to biotin through electronic polarization effect

Recently, Baugh et al. discovered that a distal point mutation (F130L) in streptavidin causes no distinct variation to the structure of the binding pocket but a 1000‐fold reduction in biotin binding affinity. In this work, we carry out molecular dynamics simulations and apply an end‐state free energy method to calculate the binding free energies of biotin to wild type streptavidin and its F130L mutant. The absolute binding affinities based on AMBER charge are repulsive, and the mutation induced binding loss is underestimated. When using the polarized protein‐specific charge, the absolute binding affinities are significantly enhanced. In particular, both the absolute and relative binding affinities are in line with the experimental measurements. Further investigation indicates that polarization effect is indispensable in both the generation of structural ensembles and the calculation of interaction energies. This work verifies Baugh's conjecture that electrostatic polarization effect plays an essential role in modulating the binding affinity of biotin to the streptavidin through F130L mutation. © 2013 Wiley Periodicals, Inc.     

Protein's electronic polarization contributes significantly to its catalytic function

Ab initio quantum mechanical/molecular mechanical method is combined with the polarized protein-specific charge to study the chemical reactions catalyzed by protein enzymes. Significant improvement in the accuracy and efficiency of free-energy simulation is demonstrated by calculating the free-energy profile of the primary proton transfer reaction in triosephosphate isomerase. Quantitative agreement with experimental results is achieved. Our simulation results indicate that electronic polarization makes important contribution to enzyme catalysis by lowering the energy barrier by as much as 3 kcal/mol.     

Relativistic two-component calculations of electronic g-tensors that include spin polarization

The first two-component relativistic density-functional approach for the calculation of electronic g-tensors is reported that includes spin polarization using noncollinear spin-density functionals. The method is based on the relativistic Douglas-Kroll-Hess Hamiltonian and has been implemented into the ReSpect program package. Using three self-consistent-field calculations with orthogonal orientations of total magnetization J, the full g-matrix may be obtained. In contrast to previous spin-restricted two-component treatments, results with the new approach agree excellently with spin-polarized one-component calculations for light-atom radicals. Additionally, unlike one-component approaches, the method also reproduces successfully the negative deltag(parallel)-values of heavy-atom 2sigma radicals and the negative deltag(perpendicular) components in cysteinyl. The new method removes effectively the dilemma existing up to now regarding the simultaneous inclusion of spin polarization and higher-order spin-orbit effects in g-tensor calculations. It is straightforwardly applicable to higher than doublet spin multiplicities and has been implemented with hybrid functionals.     

Manipulating multidimensional electronic spectra of excitons by polarization pulse shaping

A simulation study demonstrates how coherent control, combined with adaptive polarization pulse shaping and a genetic algorithm, may be used to simplify femtosecond coherent nonlinear optical signals of excitons. Cross peaks are amplified and resolved, and diagonal peaks are suppressed in the heterodyne-detected two-pulse echo signal from the Soret band of a porphyrin dimer coupled to a Brownian oscillator bath. Various optimization strategies involving the spectral, temporal, and polarization profiles of the second pulse are compared.     

Influence of polarization fluctuations on the electronic structure of molecular solids

Fluctuations in the intermolecular polarization energies of charge states in molecular solids can lead to broad (ΔE ≈ 0.5 eV) distributions of localized states, especially in polymers. Such fluctuations are caused by defects (e.g. surfaces) and thermal vibrations in molecular crystals and also by variations in the local structure in polymers. The resulting energy distributions yield natural interpretations of such diverse observations on the broadening of the photoemission spectra of molecular solids and the contact charge exchange spectra of polymers.     

Electric polarization effects on the electronic spectral shift of centrosymmetric compounds

The classic dielectric dipolar Onsager model was extended to include quadrupolar interactions between solute molecules and solvents with different polarities. A multiparametric solvatochromic expression, based on the point quadrupole moment inside a spherical cavity embedded in a dielectric continuum, is applied to centrosymmetric sulfonamide porphyrins, zinc tetraphenyl porphyrin, squaraine and 9,10-dicyanoanthracene, in order to account for the quadrupolar polarization effect of solute molecules. The reaction field polarity functions created respectively by dipole and quadrupole moments are compared and found to be linearly correlated.     

Effect of electronic polarization on charge-transport parameters in molecular organic semiconductors

Theoretical investigations of charge transport in organic materials are generally based on the "energy splitting in dimer" method and routinely assume that the transport parameters (site energies and transfer integrals) determined from monomer and dimer calculations can be reliably used to describe extended systems. Here, we demonstrate that this transferability can fail even in molecular crystals with weak van der Waals intermolecular interactions, due to the substantial (but often ignored) impact of polarization effects, particularly on the site energies. We show that the neglect of electronic polarization leads to qualitatively incorrect values and trends for the transfer integrals computed with the energy splitting method, even in simple prototypes such as ethylene or pentacene dimers. The polarization effect in these systems is largely electrostatic in nature and can change dramatically upon transition from a dimer to an extended system. For example, the difference in site energy for a prototypical "face-to-edge" one-dimensional stack of pentacene molecules is calculated to be 30% greater than that in the "face-to-edge" dimer, whereas the site energy difference in the pentacene crystal is vanishingly small. Importantly, when computed directly in the framework of localized monomer orbitals, the transfer integral values for dimer and extended systems are very similar.     

On the description of the environment polarization response to electronic transitions

This paper addresses the issue of accurately describing the structures and properties of electronically excited systems embedded in an environment, through multiscale approaches combining quantum-mechanical (QM) and polarizable classical representations of the system and environment, respectively. Such approaches represent an efficient strategy and allow to effectively study the excited states of molecular systems in the condensed phase, still maintaining the computational efficiency and the physical reliability of the ground-state calculations. The most important theoretical and computational aspects of the coupling between the QM system and the polarizable environment are presented and discussed. Even if these approaches already reached an evident degree of maturity, they can still be subject to further development, in order to achieve their full potential. This perspective presents an overview of the state of the art of these strategies, showing the fields of applicability and indicating the current limitations, which need to be overcome in future developments.     

Continuum electrostatics for electronic structure calculations in bulk amorphous polymers: application to polylactide

The bond rotational energy landscapes of polylactide (PLA) oligomers were estimated using electron density functional theory (DFT) at the B3LYP/6-31G** level, both in vacuo and with a self-consistent reaction field (SCRF) method to simulate the electronic environment within the condensed phase. The SCRF method was evaluated for application to polymeric systems, and we demonstrate the difficulties involved in applying the method to bulk amorphous polymers with specific attention to the selection of the solvent probe radius. In addition, rotational isomeric states (RIS) calculations were performed, showing the effect of accounting for the bulk phase reaction field on the bond rotational energetics and characteristic ratio. We conclude that present methods of accounting for bulk environments in electronic structure calculations are not well suited for use with polymeric systems, and the development of improved methods is needed in this area.     

AIM and NPA studies of the role of polarization in electronic structures

Atomic charges, as measured by Atoms in Molecule (AIM) or Natural Population Analyses (NPA), of the enolate anions of acetaldehyde and crotonaldehyde and of pentadienyl anion and cation show both charge transfer and polarization effects. In general, normal resonance structures and "curved arrow" symbolism give good representations of π-electron distributions, but back-polarizations in the σ-system complicate these electronic structures and can obscure the correspondence to resonance symbols. Twisting a vinyl group to orthogonality disrupts the π-system, but the vinyl group retains significant charge transfers and polarizations. The role of polarization is also demonstrated by the effect of external positive and negative charges on the electronic structure of ethylene. The π-electronic changes again are straightforward but are changed significantly by σ-polarizations. The polarizability of ethane is about half that of ethylene.     

Conformational identification of tryptamine embedded in superfluid helium droplets using electronic polarization spectroscopy

We report electronic polarization spectroscopy of tryptamine embedded in superfluid helium droplets. In a dc electric field, dependence of laser induced fluorescence from tryptamine on the polarization direction of the excitation laser is measured. Among the three observed major conformers A, D, and E, conformers D and E display preference for perpendicular excitation relative to the orientation field, while conformer A is insensitive to the polarization direction of the excitation laser. We attribute the behavior of conformer A to the fact that the angle between the permanent dipole and the transition dipole is close to the magic angle. Using a linear variation method, we can reproduce the polarization preference of the three conformers and determine the angle between the transition dipole and the permanent dipole. Since the side chain exerts small effect on the direction of the transition dipole in the frame of the indole chromophore, all three conformers have a common transition dipole more or less in the indole plane at an angle of approximately 60 degrees relative to the long axis of the chromophore. The orientation of the side chain, on the other hand, determines the size and direction of the permanent dipole, thereby affecting the angle between the permanent dipole and the transition dipole. For conformer D in the droplet, our results agree with the Anti(ph) structure, rather than the Anti(py) structure. Our work demonstrates that polarization spectroscopy is effective in conformational identification for molecules that contain a known chromophore. Although coupling of the electronic transition with the helium matrix is not negligible, it does not affect the direction of the transition dipole.     

Quantum control of molecular motion including electronic polarization effects with a two-stage toolkit

A method for incorporating strong electric field polarization effects into optimal control calculations is presented. A Born-Oppenheimer-type separation, referred to as the electric-nuclear Born-Oppenheimer (ENBO) approximation, is introduced in which variations of both the nuclear geometry and the external electric field are assumed to be slow compared with the speed at which the electronic degrees of freedom respond to these changes. This assumption permits the generation of a potential energy surface that depends not only on the relative geometry of the nuclei but also on the electric field strength and on the orientation of the molecule with respect to the electric field. The range of validity of the ENBO approximation is discussed in the paper. A two-stage toolkit implementation is presented to incorporate the polarization effects and reduce the cost of the optimal control dynamics calculations. As an illustration of the method, it is applied to optimal control of vibrational excitation in a hydrogen molecule aligned along the field direction. Ab initio configuration interaction calculations with a large orbital basis set are used to compute the H-H interaction potential in the presence of the electric field. The significant computational cost reduction afforded by the toolkit implementation is demonstrated.     

The effects of hydrogen-bonding environment on the polarization and electronic properties of water molecules

Adequate representation of the interactions that take place between water molecules has long been a goal of force field design. A full understanding of how the molecular charge distribution of water is altered by adjacent water molecules and by the hydrogen-bonding environment is a vital step toward achieving this task. For this purpose we generated ab initio electron densities of pure water clusters and hydrated serine and tyrosine. Quantum chemical topology enabled the study of a well-defined water molecule inside these clusters, by means of its volume, energy, and multipole moments. Intra- and intermolecular charge transfer was monitored and related to the polarization of water in hydrogen-bonded networks. Our analysis affords a way to define different types of water molecules in clusters.