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.     

Electric deflection studies on lead clusters

The dielectric response to an inhomogeneous electric field has been investigated for Pb(N) clusters (N=7-38) within a molecular beam experiment. The experiments give clear evidence that lead clusters with 12, 14, and 18 atoms possess permanent dipole moments. For these cluster sizes, the permanent electric dipole moments strongly determine the response to the electric field, leading to a significantly increased apparent polarizability. An adiabatic polarization mechanism allows a semiquantitative explanation of the observed susceptibility anomalies. The beam profiles of most of the lead clusters with N not equal12, 14, and 18 also display a small broadening induced by the electric field, indicating permanent dipole moments of about (0.01-0.02) D/atom. Nearly constant dipole moments per atom for larger lead clusters (N>20) manifest in a linear increase in the polarizability per atom. Also, for lead clusters such as Pb(25), which do exhibit almost no measurable beam broadening, the polarizabilties are increased compared to the bulk value. This could be partially explained by the electronic structure of the lead clusters but might be also a consequence of quenched permanent dipole moments because for highly flexible clusters only an increased beam deflection, but no broadening, will be observed.     

On the calculation of dipole moment and polarizability derivatives by the analytical energy gradient method: Application to the formaldehyde molecule

Following the suggestion of Komornicki and McIver we have implemented an efficient computational scheme for the evaluation of dipole moment and polarizability derivatives at the Hartree-Fock SCF level. The derivatives are obtained by utilizing the analytical gradients of the molecular energy, calculated in the presence of an external electric field, with respect to the atomic cartesian coordinates, which are differentiated numerically with respect to the field. The implementation of the method within the framework of the MOLECULE program is discussed, concentrating on such aspects as numerical accuracy, utilization of molecular symmetry and computational efficiency. As an application, the dipole moment and polarizability derivatives of the formaldehyde molecule have been calculated, yielding infrared intensities and Raman scattering activities in the double harmonic approximation. The theoretical results are compared with the available experimental data; the agreement is satisfactory given the inherent restrictions of the SCF model.     

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.     

Fundamental relationships in the theory of electric multipole moments and multipole polarizabilities in static fields

New derivations are given of equations relating molecular electric multipole moments and polarizabilities of general order to the electrostatic energy. The unabridged moment convention is shown to yield relatively simple relations between derivatives of the energy with respect to field gradients and the multipole moments and polarizabilities. Care is taken to distinguish various forms of these derivatives, and one form leads to a proof of a general symmetry of polarizability tensors with respect to permutations of rank indices. The condition of internal equilibrium is shown to be fundamental to the existence of this symmetry. The transformation of multipole moment and polarizability tensors under translation of the coordinate origin is expressed in relatively simple general form. The traceless multipole and polarizability tensors of Buckingham and McLean and Yoshimine are obtained as linear combinations of the unabridged tensors and their traces.     

MECHANISM OF ORIENTATION AND LINEAR DICHROISM OF PHOTOSYNTHETIC PARTICLES IN ELECTRIC FIELDS: CHLOROPLASTS AND CHLOROPHYLL-PROTEIN COMPLEXES

Abstract— The mechanisms of orientation in pulsed and alternating electric fields of thylakoids (derived from the sonication of spinach chloroplasts) and of light-harvesting chlorophyll a/b-protein complexes (CPII) were investigated by utilizing linear dichroism techniques. Comparisons of the linear dichroism spectra of thylakoids and CPII particles suggest that the latter are oriented with their directions of largest electronic polarizabilities (and thus probably their largest dimensions) within the thylakoid membrane planes. At low electric field strengths (< 12 V cm^?1), and at low frequencies of alternating electric fields (< 0.25 Hz), thylakoid membranes tend to align with their normals parallel to the direction of the applied electric field; the mechanism of orientation involves a permanent dipole moment of the thylakoids which is oriented perpendicular to the planes of the membranes. However, at high field strengths and high frequencies of the applied alternating electric fields, the thylakoids tend to orient with their planes parallel to the applied field, thus exhibiting an inversion of the sign of the linear dichroism as the electric field strength is increased. At the higher frequencies and at higher field strengths, the orientation mechanisms of the thylakoids involve induced dipole moments related to anisotropies in the electronic polarizabilities. The polarizability is higher within the plane than along a normal to the plane, thus accounting for the inversion of the dichroism as the electric field strength is increased. The CPII particles align with their largest dimension parallel to the applied field at all field strength, indicating that the induced dipole moment dominates the orientation mechanisms in pulsed electric fields. The magnitude of the absolute linear dichroism of CPII suspensions increases with increasing dilution, indicating that aggregates of lower symmetry are formed at higher concentrations of the CPII complexes.     

Size- and shape-dependent polarizabilities of sandwich and rice-ball Co(n)Bz(m) clusters from density functional theory

The dipole polarizabilities of Co(n)Bz(m), (n, m = 1-4, m = n, n + 1) clusters are studied by means of an all-electron gradient-corrected density functional theory and finite field method. The dipole moments are relatively large for most of the clusters, implying their asymmetric structures. The total polarizability increases rapidly as cluster size, whereas the average polarizability shows "odd-even" oscillation with relatively large values at (n, n + 1). The polarizabilities exhibit clear shape-dependent variation, and the sandwich structures have systematically larger polarizability and anisotropy than the rice-ball isomers. The dipole polarizabilities are further analyzed in terms of the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, ionization potential, and electron delocalization volume. We conclude that the polarizability variations are determined by the interplay between the geometrical and electronic properties of the clusters.     

Electric dipole (hyper)polarizabilities of spatially confined LiH molecule

In this study we report on the electronic contributions to the linear and nonlinear static electronic electric dipole properties, namely the dipole moment (μ), the polarizability (α), and the first-hyperpolarizability (β), of spatially confined LiH molecule in its ground X (1)Σ(+) state. The finite-field technique is applied to estimate the corresponding energy and dipole moment derivatives with respect to external electric field. Various forms of confining potential, of either spherical or cylindrical symmetry, are included in the Hamiltonian in the form of one-electron operator. The computations are performed at several levels of approximation including the coupled-cluster methods as well as multi-configurational (full configuration interaction) and explicitly correlated Gaussian wavefunctions. The performance of Kohn-Sham density functional theory for the selected exchange-correlation functionals is also discussed. In general, the orbital compression effects lead to a substantial reduction in all the studied properties regardless of the symmetry of confining potential, however, the rate of this reduction varies depending on the type of applied potential. Only in the case of dipole moment under a cylindrical confinement a gradual increase of its magnitude is observed.     

The Role of Computational Chemistry in the Experimental Determination of the Dipole Moment of Molecules in Solution

The methods for the experimental determination of electric dipole moment of molecules in solution from measurements of dielectric permittivity and refractive index are traditionally based on the classical Onsager model. In this model the molecular solute is approximated as a simple polarizable point dipole inside a spherical or ellipsoidal cavity of a dielectric medium representing the solvent. However, the inadequacies of the model resulting from the assumption of a simple shape of the cavity, for the evaluation of the cavity field effect, and from the uncertainty of the polarizability of the molecular solute influences the results and hampers the comparison with the electric dipole moments computed from quantum chemical solvation models. In this article we propose a new method for the experimental determination of the electric dipole moment in solution in which information from the Polarizable Continuum Model calculations are used in place of the Onsager model. The new method overcomes the limitations of this latter model regarding both the cavity field effect and the polarizability of the molecular solutes, and thus allows a coherent comparison between experimental and computed dipole moments of solvated molecules. © 2019 Wiley Periodicals, Inc.     

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.     

Nonlinear optical properties of benzofurobenzofurans

The geometric structure, dipole moment, μ, linear polarizability, α and first hyperpolarizability, β, of symmetrically substituted amino-and cyanobenzofurobenzofurans and dihydrobenzofurobenzofurans have been calculated by ab initio coupled perturbed Hartree-Fock methods. Singlet electronic transition energies and excited state dipole moments have been calculated by the AMI program. The benzofurobenzofuran derivatives are planar, while dihydrobenzofurobenzofuran derivatives have a V-shaped form, in agreement with experimental X-ray data. The molecular structure is rather unaffected by substitution. The linear polarizability is weakly sensitive to the substituent and substituent position, while β value changes over about 1 order of magnitude. Although both series of compounds have relatively modest hyperpolarizability, reaching ca. 60% β of para-nitroaniline, they have good properties for second harmonic generation devices: transparency in the visible spectral region, thermal stability and conformational rigidity.     

A density functional theory-based chemical potential equalisation approach to molecular polarizability

The electron density changes in molecular systems in the presence of external electric fields are modeled for simplicity in terms of the induced charges and dipole moments at the individual atomic sites. A chemical potential equalisation scheme is proposed for the calculation of these quantities and hence the dipole polarizability within the framework of density functional theory based linear response theory. The resulting polarizability is expressed in terms of the contributions from individual atoms in the molecule. A few illustrative numerical calculations are shown to predict the molecular polarizabilities in good agreement with available results. The usefulness of the approach to the calculation of intermolecular interaction needed for computer simulation is highlighted.     

Influence of the anisotropic polarizability on the anomalous dielectric relaxation spectra

The nonlinear dielectric response due to the application of a strong dc bias electric field superimposed on a weak ac electric field is considered in the context of the anomalous diffusion (subdiffusion). A perturbation procedure is used to derive analytical expressions for the first three harmonic components of the electric polarization of an assembly of both polar and anisotropically polarizable symmetric-top molecules. To accomplish that, an infinite hierarchy of multiterm (21) differential-recurrence equations of noninteger order for the moments is established and solved for the stationary regime. The results so obtained are illustrated in the form of Argand diagrams and three-dimensional relaxation spectra for the complex nonlinear dielectric increment extracted from the first harmonic component of the electric susceptibility. These plots show the role and importance played by the fractional exponent and the parameter P measuring the influence of the dipole moment over the permanent one.     

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.     

A second attempt to establish an analytical expression to steam-water dipole orientation parameter using the Boubaker polynomials expansion scheme

In this paper, an analytical expression to the steam-water dipole orientation parameter is proposed. The calculations have been carried out under the presumptions that: the electric properties of the water molecules are characterized completely by a permanent dipole moment and a constant scalar polarizability, that translational fluctuations may be neglected, and that the positions are orientation-free. The results are presented in the form of continuous and integrable expressions that can be easily compared to the precedent studies as well as involved in similar analytical models.     

Unified Treatment for Arbitrary-rank Cartesian Electric and Magnetic Multipole Moment Operators

In this study, the theory of cartesian electric and magnetic multipole moments is extended in a unified way. The general analytical expressions for distinct components of arbitrary rank cartesian electric and magnetic multipole moment operators are derived as linear combination of corresponding spherical operators, which can be used as interconversion between cartesian and spherical electric and magnetic multipole moment tensors. The transformation properties, such as translation and rotation of cartesian electric and magnetic multipole moments are given in a very simple general form. The relationship between distinct and linearly independent components of cartesian multipole moment tensors in system of linear symmetry is also presented. The formulae obtained in this paper can be utilized to calculate the interaction energies between charge distributions.     

A Continuum Reaction Field Theory of Polarizable, Nondipolar, Quadrupolar Solvents: Ab Initio Study of Equilibrium Solvation in Benzene

A continuum theory to describe solvation in nondipolar quadrupolar solvents is developed by accounting for electronic polarizability. A general Hamiltonian for a solute–solvent system in an arbitrary nonequilibrium configuration is obtained in terms of two field variables—densities of the solvent quadrupole and induced dipole moments. Equilibrium solvation is studied by optimizing this Hamiltonian with account of cavity boundaries. As an application, electronic structures and free energies of small molecules in benzene are examined with ab initio methods. Solvation stabilization due to solvent quadrupole moments is found to be substantial; for the solutes considered here, it is comparable to and often in excess of that arising from solvent-induced dipole moments.     

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.     

High-order field electrophoresis theory for a nonuniformly charged sphere

An electrophoresis theory is developed for a rigid sphere in a general nonuniform electric field. The zeta potential distribution and the double-layer thickness are both arbitrary. The zeta potential of the sphere is assumed to be small so that the deformation of the double layer can be neglected. Explicit expressions for the translational and rotational velocities of the sphere are derived in terms of the multipole moments of the zeta potential distribution and the tensor coefficients of the applied electric field. The presence of the kth-order component in the electrical potential field applied to the sphere results in a translation of the sphere only when the sphere possesses the (k-1)th- or (k+1)th-order multipole moments of the zeta potential distribution. In addition, the kth-order component in the electrical potential field causes a rotation of the sphere only when the sphere possesses the kth-order moment of the zeta potential distribution. As an illustrative example for the utility of our theory, we theoretically devise an electrophoresis analysis scheme for estimating the dipole moment of a dipolar sphere by observing the electrophoretic translation of the sphere in a quadratic potential field.