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.     

Excited state dipole moments and polarizabilities of centrosymmetric and dimeric molecules. II. Polyenes, polyynes and cumulenes

Electro-optical absorption spectra are measured for a series of polyenes, polyynes and cumulenes with centrosymmetric π-chromophores in cyclohexane solution at 298 K. For all molecules the long-axis component of the polarizability tensor is considerably larger in the first dipole-allowed singlet state compared to the ground state. The transition moments are found to be parallel to the long molecular axis. All polyenes and one cumulene show a linear Stark component indicating a long-axis excited state dipole moment. Both the dipole moments and the polarizabilities are corrected within the extended Onsager model for solvent cavity and reaction field effects. It is suggested that symmetry lowering solvent perturbations are the reason for the apparent excited state dipole moments.     

The experimental studies on the determination of the ground and excited state dipole moments of some hemicyanine dyes

The ground state (mu(g)) and excited state (mu(e)) dipole moments of 15 hemicyanine dyes were studied at room temperature. They were estimated from solvatochromic shifts of the absorption and the fluorescence spectra as function of the solvent dielectric constant (varepsilon) and refractive index (n). In this paper we applied the Stokes shift phenomena not only for the determination of the difference in the dipole moment of excited state and ground state, but to determine the value of polarizability alpha as well. The obtained results show that excited state dipole moments of hemicyanine dyes are in the range from 5 to 15 Debye, and the difference between the excited and ground state dipole moments vary from 1 to 7 Debye. The excited and ground state dipole moments difference (mu(e)-mu(g)) obtained for selected dyes are positive. It means that the excited states of the dyes under the study are more polar than the ground state ones. Additionally, the value of both polarizability (alpha) and the Onsager radius (a) of each investigated hemicyanine dye molecule are determined, and the ratio of alpha/a(3) for each dye were calculated, which oscillate from 0.29 to 5.21. The increase in dipole moment has been explained in terms of the nature of excited state and its resonance structure.     

Electric dipole moments of particle aggregates in magnetite colloidal solutions in liquid dielectrics

The permanent electric moments and the electric polarizability anisotropy of particle aggregates are determined from the results of measuring the birefringence of a magnetite colloidal solution in kerosene subjected to constant and pulsed electric fields. A possible mechanism of generating an induced dipole moment in the aggregates is analyzed. The moment is characterized by a long relaxation time and, according to the results of optical experiments, is interpreted as permanent. The calculated dipole moments are consistent with the experimental data in the order of magnitude.     

Front Cover: Understanding Local-Field Correction Factors in the Framework of the Onsager−Böttcher Model (ChemPhysChem 3/2019)

The determination of the appropriate local-field factor for quantifying the response of a molecule to an external electric field is of major importance in optical spectroscopy. Although numerous studies have dealt with the evolution of the optical properties of emitters as a function of their environment, the choice of the model used to quantify local fields is still ambiguous, and sometimes even arbitrary. In this paper, we review the Onsager–Böttcher model, which introduces the polarizability of the probe molecule as the determinant parameter for the local field factor, and we establish a simple conceptual framework encompassing all commonly used models. Finally, a discussion of published experimental research illustrates the potential of the measurement of local electric fields in dense dielectric media, as well as the subtleties involved in their interpretation.     

Quantum-chemical method for determination of effective structure-energy parameters of multiparticle interaction in solutions of polar substances

A new method is developed for the determination of equilibrium value of effective structure-energy parameter of multiparticle interaction (Onsager radius of a molecule) in solutions of polar compounds. The method is based on the results of quantum-chemical calculations of the dependence of an electric dipole moment of the studied molecule in the ground state on the dielectric properties of the individual solvents that are applied. Additinal data were obtained that confirmed an opinion that by its physical sense the Onsager radius of a molecule was a value close to van der Waals radius of the same molecule which can be found using known methods of quantum chemistry and structural chemistry for isolated molecules (gas phase). It was shown by an example of solutions of 4-dimethylaminochalcone and several phthalimide and N-methylphthalimide derivatives that the results of determination of Onsager and van der Waals radii of all the studied molecules using three independent methods are in good quantitative agreement confirming their validity.     

外部电场下水分子间静电相互作用的分子动力学研究

本文利用分子动力学模拟探讨了不同外电场下,液态水的分子间作用及分子排布的变化. 在不同外电场下,O…O原子间的径向分布函数差别很小,但是单个水分子的偶极矩的取向变化却很大. 当外电场为0时,单个水分子偶极取向的范围很宽（30-150度）. 与此同时,本文给出了局域诱导电场随着位置的变化关系图. 当外加电场增强时,局域的诱导电场强度也随之增加. 由于电场下偶极矩有序性的增加,局域诱导的静电相互作用能显著增加. 计算结果表明,相对介电常数随着电场强度的增加而呈现指数衰减的变化形式. 这一变化趋势可以用来理解不同电化学环境下,静电相互作用和局域诱导电场的变化.     

Electric parameters of photosystem II particles — electric light scattering study

Electric light scattering and microelectrophoresis were applied to investigate the electric moments (permanent dipole moment and electric polarizability and electrophoretic mobility of envelope-free chloroplasts and photosystem II (PS II particles. The effect of the removal of the extrinsic polypeptides (18, 24 and 33 kDa) on the electric moments was also studied. A significant difference was observed between the orientation behaviour of chloroplasts and PS II preparations. The data indicate that the permanent and induced dipole moments contribute to the orientation of the PS II particles, whereas chloroplasts possess induced dipole moment only.

NaCl and Tris treatments of PS II preparations influence both the transverse permanent dipole moment and the electric polarizability of PS II particles. The increase in the electrophoretic mobility of PS II particles on removal of the extrinsic proteins corresponds to an increase in the electric polarizability value, demonstrating its interfacial nature.     

Electrochromism and Solvatochromism

The position and the intensity of electronic bands are influenced by an electric field. Pronounced changes in the position of absorption bands are mainly due to the dipole moment of the molecule in the ground state and the change in the dipole moment during the excitation process, and pronounced changes in intensity are due to the field dependence of the transition moment, which can be described by the transition polarizability. The effect of an external electric field on the optical absorption (electrochromism) of suitable molecules can be used to determine the dipole moment in the ground state, the change in dipole moment during the excitation process, the direction of the transition moment of the electronic band, and certain components of the transition polarizability tensor. These data largely determine the strong solvatochromism (solvent-dependence of the position and intensity of electronic bands), which is observed in particular with molecules having large dipole moments. Smaller contributions to solvatochromism result from dispersion interactions, which predominate in the case of nonpolar molecules. The models developed have been experimentally checked and verified by a combination of electro-optical absorption measurements (influence of an external electric field on absorption) and investigation of the solvent-dependence of the electronic bands.     

Solvatochromic behavior of donor-acceptor-polyenes: dimethylamino-cyano-diphenylbutadiene

4-(Dimethylamino)-4'-cyano-1,4-diphenylbutadiene (DCB) and 4-(dimethylamino)-2,6-dimethyl-4'-cyano-1,4-diphenylbutadiene (DMDCB) have been characterized spectroscopically. Quantum chemical calculations were performed for comparison. Solvatochromic shifts of the fluorescence were strong and showed a linear dependence on the solvent polarity parameters, whereas shifts in the absorption spectra are very weak only correlate better with the polarizability of the solvents. Excited state dipole moments derived from fluorescence using the Onsager model are very large and similar for both compounds. It is concluded that a strongly allowed and highly dipolar pi, pi* state is the lowest excited state in polar solvents. The strong difference in absorption and fluorescence solvatochromic slopes suggests that the simple Onsager model with a point dipole approximation is not sufficient here.     

Reduced-size polarized basis sets for calculations of molecular electric properties. I. The basis set generation

Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).     

Building cavities in a fluid of spherical or rod-like particles: a contribution to the solvation free energy in isotropic and anisotropic polarizable continuum model

A general formalism for the calculation of cavitation energies in the framework of the scaled particle theory has been implemented in the Polarizable Continuum Model (PCM), contributing to the nonelectrostatic part of the molecular free energy in solution. The solute cavity and the solvent molecules are described as hard spherocylinders, whose radius and length are related to the actual molecular shape, while the solvent density is estimated from experimental data, or from the solvent molecular volume, suitably scaled. The present model can describe isotropic solutions of spherical and rod-like molecules in spherical or rod-like solvents, and also anisotropic solutions in which the solvent molecules are oriented in space: in this case, the cavitation energy also depends on the relative orientation of solute and solvent molecules. Test calculations have been performed on simple systems to evaluate the accuracy of the present approach, in comparison with other methods and with the available experimental estimates of the cavitation energy, giving encouraging results.     

Polarizable atomic multipole solutes in a Poisson-Boltzmann continuum

Modeling the change in the electrostatics of organic molecules upon moving from vacuum into solvent, due to polarization, has long been an interesting problem. In vacuum, experimental values for the dipole moments and polarizabilities of small, rigid molecules are known to high accuracy; however, it has generally been difficult to determine these quantities for a polar molecule in water. A theoretical approach introduced by Onsager [J. Am. Chem. Soc. 58, 1486 (1936)] used vacuum properties of small molecules, including polarizability, dipole moment, and size, to predict experimentally known permittivities of neat liquids via the Poisson equation. Since this important advance in understanding the condensed phase, a large number of computational methods have been developed to study solutes embedded in a continuum via numerical solutions to the Poisson-Boltzmann equation. Only recently have the classical force fields used for studying biomolecules begun to include explicit polarization in their functional forms. Here the authors describe the theory underlying a newly developed polarizable multipole Poisson-Boltzmann (PMPB) continuum electrostatics model, which builds on the atomic multipole optimized energetics for biomolecular applications (AMOEBA) force field. As an application of the PMPB methodology, results are presented for several small folded proteins studied by molecular dynamics in explicit water as well as embedded in the PMPB continuum. The dipole moment of each protein increased on average by a factor of 1.27 in explicit AMOEBA water and 1.26 in continuum solvent. The essentially identical electrostatic response in both models suggests that PMPB electrostatics offers an efficient alternative to sampling explicit solvent molecules for a variety of interesting applications, including binding energies, conformational analysis, and pK(a) prediction. Introduction of 150 mM salt lowered the electrostatic solvation energy between 2 and 13 kcalmole, depending on the formal charge of the protein, but had only a small influence on dipole moments.     

An intramolecular induction correction model of the molecular dipole moment

A model for intramolecular polarization is presented. It is used to describe the changes in the molecular charge distribution occurring as a response to changes of dihedral angles in the molecule. The model is based on a multicenter multipole distribution of the molecular charge distribution. The electric field from this charge distribution induce dipole moments in the same molecule. The model contains atom type parameters to describe the damping of the electric field. A total of four atom types are used. The parameters are fitted to a calibration set with various functional groups, and tested against a validation set. The error obtained for the calibration set is reduced by 92% and by 88% for the validation set, if compared to an accurate state-of-the-art force field. It is shown that rotating the non-polarizable multicenter multipole distribution for the equilibrium geometry gives too large dipole moments for dihedral angles deviating from the equilibrium geometry. This will lead to too large long-range attractions in simulations. This problem is overcome by using the dipole polarizability correction suggested here, which gives dipole moments very close to the Hartree-Fock dipole moments obtained from reference calculations.     

Calculations of static dipole polarizabilities of alkali dimers: prospects for alignment of ultracold molecules

The rapid development of experimental techniques to produce ultracold alkali molecules opens the ways to manipulate them and to control their dynamics using external electric fields. A prerequisite quantity for such studies is the knowledge of their static dipole polarizability. In this paper, we computed the variations with internuclear distance and with vibrational index of the static dipole polarizability components of all homonuclear alkali dimers including Fr(2), and of all heteronuclear alkali dimers involving Li to Cs, in their electronic ground state and in their lowest triplet state. We use the same quantum chemistry approach as in our work on dipole moments [Aymar and Dulieu, J. Chem. Phys. 122, 204302 (2005)], based on pseudopotentials for atomic core representation, Gaussian basis sets, and effective potentials for core polarization. Polarizabilities are extracted from electronic energies using the finite-field method. For the heaviest species Rb(2), Cs(2), and Fr(2) and for all heteronuclear alkali dimers, such results are presented for the first time. The accuracy of our results on atomic and molecular static dipole polarizabilities is discussed by comparing our values with the few available experimental data and elaborate calculations. We found that for all alkali pairs, the parallel and perpendicular components of the ground state polarizabilities at the equilibrium distance R(e) scale as (R(e))(3), which can be related to a simple electrostatic model of an ellipsoidal charge distribution. Prospects for possible alignment and orientation effects with these molecules in forthcoming experiments are discussed.     

Theory of the dielectric constant of ice

The first result of this paper is to show that the Onsager—Slater theory of the dielectric constant is consistent for some reasoable model of ice in the limit of no intrinsic defects. Accordingly, a model is presented, called the unit model, which has unit cells with no dipole moments for which the Onsager—Slater theory is exact. The second result of this paper is to show that the unit model is physically and chemically realistic. Bjerrum defects are introduced into the model and the relation between the dielectric constant and the Bjerrum defect charge found by Onsager and Dupuis for a less realistic model continues to hold and is satisfied by the experimental values. In a simple point charge approximation the charge distribution determined by the model requirements and the experimentally determined Bjerrum fault charge are found and seem reasonble. Higher order multipole interaction energies are consistent with eviations from pure 1/T dependence of the dielectric constant of real ice with intrinsic defects, can be derived in the context of the unit model. This formula interpolates between the Onsager—Slater formula in the limit of no intrinsic defects and the Kirkwood—Frohlich formula in the limit of many intrinsic defects. For the concentration of defects in real ice the interpolation formula is practically the same as the Onsager—Slater formula and differs from the Kirkwood—Frohlich formula by a factor of nearly $\text{3}\text{2}$.     

Excited state polarizabilities from solvatochromic shifts

A new method is proposed to estimate the polarizability (α_e) of a molecule in an excited state using solvatochromic shift measurements and McRae's equation. In the earlier methods the contribution due to polarizability was not considered. In view of this, the proposed method is also expected to give a better estimation of excited state electric dipole moment (μ_e) and the (θ) angle between excited and ground state electric dipole moments, μ_e and μ_g apart from giving values of polarizability of the molecules in the excited state. This method has been applied in the case of the La band of p-nitro aniline and the results for all the parameters are found to be satisfactory and of right order in comparison with that reported in literature.     

Thermodynamical study of the thermoelectric effect for magnesium silicide

The thermoelectric effect of magnesium silicide is studied by using a thermodynamical method in the presence of an electric field. The thermoelectric potential is evaluated from the partial derivative of free energy with respect to charge in which the free energy is calculated at the B3LYP/6-31G(d,p) level of density functional theory. This free energy is also utilized to determine the average dipole moment from which the polarizability, alpha; molar polarization, Psi; and dielectric constant can be computed. The present calculation for the dielectric constant (approximately 24-20) is in very good agreement with the experimental value (20). This accurate dielectric constant can be used to derive the relation of the thermoelectric potential with respect to temperature, from which the thermoelectric power or the Seebeck coefficients are calculated. The present result shows good agreement with experiment measurement for the Seebeck coefficients. In comparison, that calculation from the energy band structure theory is far off from the experimental values.