Thermally induced polarizabilities and dipole moments of small tin clusters

We study the influence of thermal excitation on the electric susceptibilities for Sn(6) and Sn(7) clusters by molecular beam electric deflection and Monte-Carlo simulations in conjunction with quantum-chemical calculations. At low temperatures (40 K), no field-induced broadening of the Sn(6) and Sn(7) cluster beams are observed, in agreement with vanishing permanent electric dipole moments due to their centro-symmetrical ground states. The electric polarizabilities of Sn(6) and Sn(7), as inferred from the field-induced molecular beam deflection, are in good agreement with the quantum-chemical predictions. At elevated temperatures of 50-100 K, increased polarizabilities of about 2-3 ?(3) are obtained. Also, we found indications of a field-induced beam broadening which points to the existence of permanent dipole moments of about 0.01-0.02 D per atom at higher temperatures. These results cannot be explained by thermal excitations within a harmonic oscillator model, which would yield a temperature-independent polarizability and fluxional, but not permanent, dipole moments. We analyze this behavior by Monte-Carlo simulations in order to compute average temperature-induced electric dipole moments. For that purpose, we developed a novel technique for predicting observables sampled on the quantum-chemical potential energy surface by an umbrella sampling correction of Monte-Carlo results obtained from simulations utilizing an empirical potential. The calculated, fluxional dipole moments are in tune with the observed beam broadenings. The cluster dynamics underlying the polarizability appear to be intermediate between rigid and floppy molecules which leads to the conclusion that the rotational, not the vibrational temperature seems to be the key parameter that determines the temperature dependence of the polarizability.     

Electric deflection studies of rhodium clusters

The static electric dipole polarizabilities of rhodium clusters Rhn, n=5-28, have been measured via a molecular beam deflection method. Uniform high-field beam deflections, indicative of induced polarization, were observed for all Rhn except Rh7 and Rh10 which by contrast exhibited beam broadening and anomalously high effective polarizabilities. Analysis of the beam deflection profile of Rh7 indicates that it possesses a permanent dipole moment of 0.24+/-0.02 D. Unlike the other clusters in the n=5-28 size range, the polarizability of Rh10 is observed to decrease with increasing source temperature. We attribute this temperature dependence to paraelectric behavior, suggesting that Rh10 is a fluxional molecule possessing a dipole moment that spatially fluctuates, uncorrelated with overall rotation.     

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.     

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.     

DFT calculations of static dipole polarizabilities and hyperpolarizabilities for the boron clusters Bn (n=3–8,10)

The static electric dipole polarizabilities and second‐order hyperpolarizabilities of several bare boron clusters have been calculated with density functional theory. The average second‐order hyperpolarizability γ_av reaches a saturation limit of about 50,000 a.u. already with B₅ for a given type of structure. The average polarizability per atom shows overall a decrease with increasing cluster size, while the average second hyperpolarizability per atom first increases from B₃ to B₆, and then starts to decrease. For the noncentrosymmetric clusters dipole moments and first‐order hyperpolarizabilities are reported. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 131–135, 2000     

New Molecular Cage Clusters of Pb by Encapsulation of Mg

Endohedral clusters formed from the Zintl ions Pb₁₀^2? and Pb₁₂^2? are particularly stable and therefore suitable for the assembly of larger aggregates. We therefore investigate the formation of Mg‐doped lead clusters in the gas phase, and demonstrate that a whole series of new molecular cage clusters of lead can be generated by encapsulation of magnesium. Mass spectrometry reveals that some of the cluster compounds, with one and two Mg atoms attached to the lead clusters, display large intensities compared to the pure lead clusters, which indicates that the compound clusters are particularly stable. The magnesium‐doped lead‐cluster assemblies were further analyzed within a molecular‐beam electric deflection experiment. Almost vanishing permanent dipole moments for MgPb_10–16 support the idea that a single Mg atom could be encapsulated within a highly symmetric lead cage, which results in structures with not only enhanced stability but also increased symmetry compared to the pure lead clusters Pb_N.     

Bismuth-doped tin clusters: experimental and theoretical studies of neutral Zintl analogues

The electron count of gas-phase clusters is increased gradually by element substitution in order to mimic the total number of electrons of known stable closo-clusters. A combination of elements from the fourth and fifth group of the periodic table such as Sn and Bi is well-suited for this approach. Hence, these small Sn-Bi clusters are investigated by employing the electric field deflection method. For clusters in the series Sn(M-N)Bi(N) (M = 5-13, N = 1-2), the beam profiles obtained in cryogenic experiments are dominated by beam broadening, indicating the presence of a permanent electric dipole moment that is sensitive to the (rigid) cluster structure. An intensive search for the global minimum structure employing a density functional theory/genetic algorithm method is performed. Dielectric properties for the identified low-energy isomers are computed. The structural and dielectric properties are used in beam profile simulations in order to discuss the experimental data. Comparison of theoretical and experimental results enables identification of the growing pattern of these small bimetallic clusters. For multiply doped clusters, it is concluded that the dopant atoms do not form direct Bi-Bi bonds, but more interestingly, a rearrangement of the cluster skeleton becomes apparent. The structural motifs are different from pure tin clusters but rather are rationalized using the corresponding structures of tin anions or are based on the Wade-Mingos concept. Further evidence for this idea is deduced from nuclear independent chemical shift calculations, which show nearly identical behavior for negatively charged pure and neutral bimetallic clusters. All of these findings are consistent with the idea of neutral Zintl analogues in the gas phase.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Structure and electric properties of Sn(N) clusters (N = 6-20) from combined electric deflection experiments and quantum theoretical studies

Electric deflection experiments have been performed on neutral Sn(N) clusters (N = 6-20) at different nozzle temperatures in combination with a systematic search for the global minimum structures and the calculation of the dielectric properties based on density functional theory. For smaller tin clusters (N = 6-11), a good agreement between theory and experiment is found. Taking theoretically predicted moments of inertia and the body fixed dipole moment into account permits a quantitative simulation of the deflected molecular beam profiles. For larger Sn(N) clusters (N = 12-20), distinct differences between theory and experiment are observed; i.e., the predicted dipole moments from the quantum chemical calculations are significantly larger than the experimental values. The investigation of the electric susceptibilities at different nozzle temperatures indicates that this is due to the dynamical nature of the tin clusters, which increases with cluster size. As a result, even at the smallest nozzle temperature of 40 K, the dipole moments of Sn(12-20) are partially quenched. This clearly demonstrates the limits of current electric deflection experiments for structural determination and demonstrates the need for stronger cooling of the clusters in future experiments.     

Molecular geometry and polarizability of small cadmium selenide clusters from all-electron ab initio and Density Functional Theory calculations

We have calculated molecular geometries and electric polarizabilities for small cadmium selenide clusters. Our calculations were performed with conventional ab initio and density functional theory methods and Gaussian-type basis sets especially designed for (CdSe)(n). We find that the dipole polarizability per atom converges rapidly to the bulk value.     

Spatial Taming and Trapping of Molecules

Molecular beam techniques for study of collisional and spectroscopic processes have recently been enhanced by use of static electric or magnetic fields to orient or align molecules with permanent dipole moments. A more general method is now in prospect, applicable both to alignment and to spatial trapping of molecules. This exploits the anisotropic interaction of the electric field vector of intense laser radiation with the dipole moment induced in a polarizable molecule by the laser field. The interaction creates directional superpositions of field-free states that correspond to oblate spheroidal wavefunctions, with eigenenergies that decrease with increasing field strength. We suggest that this polarizability interaction produces the marked alignment found in laser-induced dissociative ionization of CO by the Saclay group. We also present calculations illustrating the feasibility of spattal trapping. In combination with supermirror focussing and buffer-gas cooling, an intense infrared laser can typically confine molecules for long-times (-hours) within a small (-picoliter) and cold (?1°K) “pocket of light.”     

Breakdown of the pseudopotential approximation for magnetizabilities and electric multipole moments: test calculations for Au, AuF, and Sn(n) cluster (n ≤ 20)

The response of the electronic wavefunction to an external electric or magnetic field is widely considered to be a typical valence property and should, therefore, be adequately described by accurately adjusted pseudopotentials, especially if a small-core definition is used within this approximation. In this paper we show for atomic Au and Au(+), as well as for the molecule AuF and tin clusters, that in contrast to the case of the static electric dipole polarizability or the electric dipole moment, core contributions to the static magnetizability are non-negligible, and can therefore lead to erroneous results within the pseudopotential approximation. This error increases with increasing size of the core chosen. For tin clusters, which are of interest in ongoing molecular beam experiments currently carried out by the Darmstadt group, the diamagnetic and paramagnetic isotropic components of the magnetizability tensor almost cancel out and large-core pseudopotentials do not even predict the correct sign for this property due to erroneous results in both the diamagnetic and (more importantly) the paramagnetic terms. Hence, all-electron calculations or pseudopotentials with very small cores are required to adequately predict magnetizabilities for atoms, molecules and the solid state, making it computationally more difficult to obtain this quantity for future investigations in heavy atom containing molecules or clusters. We also demonstrate for this property that all-electron density functional calculations are quite robust and give results close to wavefunction based methods for the atoms and molecules studied here.     

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 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.     

Magnetic moments of bare and benzene-capped cobalt clusters

Magnetic moments of bare cobalt clusters Co(n) (n=7-32) and benzene-capped cobalt clusters Co(n)(bz)(m) have been measured at temperatures ranging from 54 to 150 K using a molecular beam deflection method. It was observed that Co(12-32) produced at temperatures greater than approximately 100 K display high-field-seeking behavior at all temperatures in the range investigated, indicating that they are superparamagnetic species. At temperatures below approximately 100 K, the field-on beam profiles of Co(7-11) and some larger clusters displayed substantial symmetric broadening, indicating that some fraction of the clusters in the beam were no longer superparamagnetic, but rather were in a blocked (locked-moment) state. In the superparamagnetic regime (T=150 K) Co(n) clusters in the n=7-32 size range were found to possess per-atom moments ranging from 1.96+/-0.04 micro(b)(Co(24)) to 2.53+/-0.04 micro(b)(Co(16)), significantly above the bulk value of 1.72 micro(b). Locked-moment isomers were found to display moments of approximately 1 micro(b) per atom. Cobalt clusters containing a layer of adsorbed benzene molecules were found to possess significantly lower moments per cobalt atom than the corresponding bare cobalt clusters.     

Influence of cation binding on the electro-optically determined electric moments of purple membranes

Analysis of the elect ro-optically determined permanent dipole moment and electric polarizability of purple membrane fragments reveals the complex nature of the membrane electric moments.The problem to distinguish between the contribution of the membrane structural charges (charged groups of the polypeptide chain and polar lipid headarouos), bound cations and the electric double layer structure deserves particular attention not only because of its importance for electro-optics but also in respect to the relation of the membrane surface electric properties to the membarans transport function.The removal of divalent cations (Ca²⁺ and Mg²⁺) bound to purple membrane in the native state induces a cat ion-free species or purple membrane (deionized - blue membrane) with drastically changed spectroscopic properties and function. The preseent paper summarizes our study on the electric moments of blue membrane and their changes during the blue to purple transition. We intended to provide an insight into the possible regulation of this reversible transition (purple-to-blue and blue-to-purple) through changes of the asymmetric charge distribution and the importance of the asymmetric interfacial charge distribution for the proton transfer in purple membranes.The changes in the electric moments (permanent and induced dipole moments) of purple membrane fragments upon di- and trivalent cations binding to cation-depleted purple membranes were studied by electric light scattering (rotational electrokinetics) in d.c. and a.c. electric fields, and by electric pulses with reversing polarity, the results show a recovery of the membrane charge asymmetry (permanent dipole moment) though not of the induced dipole moment.     

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.     

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.     

The permanent electric dipole moment of chromium monodeuteride, CrD

A number of low-N lines of the X (6)Sigma(+)<--A (6)Sigma(+)(0,0) band of chromium monodeuteride, CrD, have been recorded at near the natural linewidth limit by high resolution laser excitation spectroscopy of a supersonic molecular beam sample. The shifts and splitting of these lines caused by a static electric field have been analyzed to give the permanent electric dipole moments of the X (6)Sigma(+)(upsilon=0) and A (6)Sigma(+)(upsilon=0) states as 3.510(33) and 1.153(3) D, respectively. The dipole moment of the A (6)Sigma(+)(upsilon=0) state can be measured with higher precision because of some interesting near degeneracies in its level structure. The trends in the observed dipole moments for the first-row transition metal monohydrides are rationalized and compared with theoretical predictions.     

Optical, dynamic, and electro-optical properties of poly(N-acryloyl-11-aminoundecanoic acid) in solutions

The optical, electro-optical, and dynamic characteristics of poly(N-acryloyl-11-aminoundecanoic acid) in organic solvents and of the sodium salt of its monomer in water were studied via the methods of flow birefringence, equilibrium and nonequilibrium electric birefringence, and dynamic light scattering. It is shown that, in aqueous solutions, the monomer forms coarse particles of both symmetric and asymmetric shapes. The linear dimensions of these particles are estimated from the data of translational and rotational diffusion. Polymer macromolecules in organic solvents feature negative anisotropy of optical polarizability. Contributions of optical microform and macroform effects to the observed flow birefringence are analyzed in detail. The intrinsic optical anisotropy of the monomer unit of the polymer, which correlates well with the corresponding values for comb-shaped polymers of a similar structure, is estimated. It is shown that polymer molecules lack marked intrinsic permanent macromolecular dipoles and that electric birefringence in their solutions is associated with macroscopic induced dipole moments that appear during orientation of the dipole moments of polar groups in side chains of the polymer under application of an electric field.