Dipole Expansion Research Articles

Modeling the Fluorescence Quantum Yields of Aromatic Compounds: Benchmarking the Machinery to Compute Intersystem Crossing Rates.

The from-first-principles calculation of fluorescence quantum yields (FQYs) and lifetimes of organic dyes remains very challenging. In this article, we extensively test the machinery to calculate FQYs. Specifically, we perform an extensive analysis on the parameters influencing the intersystem crossing (ISC), internal conversion (IC), and fluorescence rate constants calculations. The impact of (i) the electronic structure (chosen exchange-correlation functional and spin-orbit Hamiltonian), (ii) the vibronic parameters (coordinate system, broadening function, and dipole expansion), and (iii) the excited-state kinetic models are systematically assessed for a series of seven rigid aromatic molecules. Our studies provide more insights into the choice of parameters and the expected accuracy for the computational protocols aiming to deliver FQY values. Some challenges are highlighted, such as, on the one hand, the difficulty to benchmark against the experimental nonradiative rate constants, for which the separation between the IC and ISC contributions is often not provided in the literature and, on the other hand, the need to go beyond the harmonic approximation for the calculation of the IC rates.

Extensive Analysis of the Parameters Influencing Radiative Rates Obtained through Vibronic Calculations.

Defining a theoretical model systematically delivering accurate ab initio predictions of the fluorescence quantum yields of organic dyes is highly desirable for designing improved fluorophores in a systematic rather than trial-and-error way. To this end, the first required step is to obtain reliable radiative rates (kr), as low kr typically precludes effective emission. In the present contribution, using a series of 10 substituted phenyls with known experimental kr, we analyze the impact of the computational protocol on the kr determined through the thermal vibration correlation function (TVCF) approach on the basis of time-dependent density functional theory (TD-DFT) calculations of the energies, structures, and vibrational parameters. Both the electronic structure (selected exchange-correlation functional, application or not of the Tamm-Dancoff approximation) and the vibronic parameters (line-shape formalism, coordinate system, potential energy surface model, and dipole expansion) are tackled. Considering all possible combinations yields more than 3500 cases, allowing to extract statistically-relevant information regarding the impact of each computational parameter on the magnitude of the estimated kr. It turns out that the selected vibronic model can have a significant impact on the computed kr, especially the potential energy surface model. This effect is of the same order of magnitude as the difference noted between B3LYP and CAM-B3LYP estimates. For the treated compounds, all evaluated functionals do deliver reasonable trends, fitting the experimental values.

The influence of halides in polyoxotitanate cages; dipole moment, splitting and expansion of d-orbitals and electron–electron repulsion

Metal-doped polyoxotitanate (M-POT) cages have been shown to be efficient single-source precursors to metal-doped titania [TiO2(M)] (state-of-the-art photocatalytic materials) as well as molecular models for the behaviour of dopant metal ions in bulk titania. Here we report the influence halide ions have on the optical and electronic properties of a series of halide-only, and cobalt halide-'doped' POT cages. In this combined experimental and computational study we show that halide ions can have several effects on the band gaps of halide-containing POT cages, influencing the dipole moment (hole-electron separation) and the structure of the valance band edge. Overall, the band gap behaviour stems from the effects of increasing orbital energy moving from F to I down Group 17, as well as crystal-field splitting of the d-orbitals, the potential effects of the Nephelauxetic influence of the halides and electron-electron repulsion.

Modeling the electrostatic component of toner adhesion and detachment

In this paper, we explore both the physical and mathematical models of electrostatic adhesion. Addressed topics include, review of the dipole and analytical field expansion models of adhesion, addition of an applied field in the analytical model for electrostatic detachment, parametric studies of adhesion and detachment, and analysis of the model for non-uniform particle charge distribution.

X-ray diffraction analysis of titanium tritide film during 1600 days

The generation and accumulation of 3He by tritium decay modified the physical and chemical properties of tritides. Here the evolution of lattice defects in long-aged titanium tritide films is investigated by X-ray diffraction and changes in the positions, intensities and line shapes of diffraction peaks have been determined over a period of about 1600days (>4years). Texture effects are also observed by biased intensities in standard θ–2θ scans. The results show that the TiT1.5 film keeps an fcc structure during 1600days and reveals an hkl-dependent unit-cell expansion and line width broadening which are interpreted in terms of isolated tetrahedral interstitial 3He atoms and isolated bubble growth models by dislocation loop-punching or dislocation dipole expansion combined with Krivoglaz theory. In the first 12days of aging, isolated tetrahedral interstitial 3He atoms or 3He clusters are formed, then interstitial 3He atoms diffuse into (111) planes and precipitate into clusters. The spontaneous formation of Frenkel pairs, the self-interstitial atoms produced are built into dislocations resulting in formation platelet bubbles and dislocation dipoles between 12 and 27days. Above 27days, multiple stages of 3He bubbles growth appear: (1) between 27 and 85days platelet helium bubbles growth by dislocation dipoles expansion, (2) between 85 and 231days the transition from platelet bubbles to sphere bubbles by loop emission, (3) after 231days sphere bubbles growth by dislocation loop-punching and probably formation of sub-grain boundaries by dislocation rearrangement.

Analytical Expressions for High-Frequency VLSI Interconnect Impedance Extraction in the Presence of a Multilayer Conductive Substrate

We propose an efficient method to accurately compute the frequency-dependent impedance of VLSI interconnects in the presence of multilayer conductive substrates. The resulting accuracy (errors less than 3%) and CPU time reduction (more than an order of magnitude) emerge from three different ingredients: a 2-D Green's function approach with the correct quasi-static limit, a modified discrete complex images approximation to the Green's function, and a continuous dipole expansion to evaluate the magnetic vector potential at the short distances that are relevant to VLSI interconnects. This approach permits the evaluation of the self-impedance and mutual-impedance of multi-conductor current loops, including substrate effects, in terms of easily computable analytical expressions that involve their relative separations and the electromagnetic parameters of the multilayer substrate.

Accuracy of typical approximations in classical models of intermolecular polarization

One of the largest limitations of standard molecular-mechanics force fields is the neglect of intermolecular polarization. Several attempts to cure this problem have been made, but the results have not always been fully satisfactory. In this paper, we present a quantitative study of the fundamental approximations that underlie polarization models for classical force fields. The induced charge density of a large set of molecular dimers is compared to supermolecular calculations for a hierarchy of simplified models. We study the effect of the Pauli principle, the local inhomogeneity of the electric field, the intramolecular coupling of the polarization response, and the fact that the induced density is a continuous function. We show that standard point-polarizability models work rather well, despite their lack of all these effects, because (1) there is a systematic error cancellation between the neglect of effects of the Pauli principle and the locally inhomogeneous electric field, and (2) the lack of intramolecular coupling and the use of a dipole expansion of the induced density have only minor effects on the polarization. However, the cancellation in (1) is not perfect, and therefore polarizable force-fields could be improved if both effects are explicitly treated.

Dominance of shear elastic energy far from a point defect in a solid

It is shown that the elastic energy far from a point defect in an isotropic solid is mainly shear elastic energy. The calculation, which is based on a standard dipole expansion, shows that no matter how large or small the bulk modulus is compared to the shear modulus, less than 10% of the distant point defect energy is associated with volume changes.

A molecular analysis of the vibrational energy relaxation mechanism of the CN − ion in water based upon path integral influence functional theory combined with a dipole expansion of the solute–solvent interaction

The molecular mechanism of vibrational energy relaxation of the CN − ion in water has been investigated using path integral influence functional theory combined with a dipole expansion of the solute–solvent interaction. First, in order to find out which solvent water molecules contribute most to the absorbtion of the solute excess vibrational energy, the normal modes of the solution, adopted for the harmonic oscillators bath approximation in the influence functional theory, have been back-transferred to the molecular coordinates and a contribution to the relaxation has been assigned to each water molecule according to the transformation matrix. Then, the coupling intensity C ( i)2 between solute and solvent molecules playing a major role in the relaxation, has been analyzed by dipole expansion of the solute–solvent interaction, where bending, rotational and translational degrees of freedom were all represented by the standard variables μ 1, μ 2, R, θ 1, θ 2, and ϕ for the dipole expansion. From these analyses, it is clarified that (1) the contribution of the solvent water to the relaxation decreases rapidly in proportion to 1 / R 6, such that only water molecules in the first hydration shell take part in the relaxation, (2) water molecules located in the direction of C–N bond contribute much to the relaxation, and (3) the excess energy is transferred to the bending of the relevant water molecule and its rotational libration represented by the variable θ 2.

Structure and Dynamics of the Aqueous Liquid−Vapor Interface: A Comprehensive Particle-Based Simulation Study

This research addresses a comprehensive particle-based simulation study of the structural, dynamic, and electronic properties of the liquid-vapor interface of water utilizing both ab initio (based on density functional theory) and empirical (fixed charge and polarizable) models. Numerous properties such as interfacial width, hydrogen bond populations, dipole moments, and correlation times will be characterized with identical schemes to draw useful conclusions on the strengths and weakness of the proposed models for interfacial water. Our findings indicate that all models considered in this study yield similar results for the radial distribution functions, hydrogen bond populations, and orientational relaxation times. Significant differences in the models appear when examining both the dipole moments and surface relaxation near the aqueous liquid-vapor interface. Here, the ab initio interaction potential predicts a significant decrease in the molecular dipole moment and expansion in the oxygen-oxygen distance as one approaches the interface in accordance with recent experiments. All classical polarizable interaction potentials show a less dramatic drop in the molecular dipole moment, and all empirical interaction potentials studied yield an oxygen-oxygen contraction as the interface is approached.

Space-time evolution of ultrarelativistic quantum dipoles in quantum electrodynamics

We discuss space-time evolution of ultrarelativistic quantum dipole in QED. We show that the space-time evolution can be described, in a certain approximation, by means of a regularized wave function, whose parameters are determined by the process of the dipole creation by a local current. We derive using these wave functions the dipole expansion law, that is found to coincide parametrically in the leading order with the one suggested by Farrar, Frankfurt,Liu and Strikman.

On the consequences of the violation of the Hellmann–Feynman theorem in calculations of electric properties of molecules

The general relation between one-electron electric properties ε (dipole moment, polarizability, hyperpolarizability, etc.) of molecules calculated as energy derivatives (E) and as dipole expansion (D) is derived: ε E= ε D+ ε NHF, where ε NHF represents the non-Hellmann–Feynman correction, which vanishes for wave functions satisfying the Hellmann–Feynman theorem. It is shown that in cases when the wave function does not satisfy the Hellmann–Feynman theorem (e.g., limited CI) not only the NHF correction may be very large, but what is more important, the elements of static polarizability tensors ( α, β, γ, etc.) obtained via the dipole expansion are non-physical because they do not satisfy the Kleinman symmetry, and for example α ij D≠ α ji D, β ijj D≠ β jji D or γ iijj D= γ ijji D≠ γ jjii D (for i≠j, i=x,y,z ). Finally, it is concluded that in the case of wave functions which do not satisfy the Hellmann–Feynman theorem only energy derivative methods are the correct way for calculations of one-electron electric properties of molecules.

Calculation of the fine structure of oxygen-like ions using polarization potential function

We have calculated the forbidden transition energies and magnetic dipole transition probabilities of 2s22p4(3P1-3P2) and 2s22p4 (3P0-3P1) of oxygen-like isoelectronic sequences (Z=10-32) by a method of polarization potential correction. The transition energies show good agreement with experiment and are much better than the calculations in literature. These results also illustrate that it is feasible by using the dipole expansion of polarization potential to deal with some dynamic and non-dynamic effects in the central field approach. The relation of polarizability and cut-off radius with atomic number is discussed. We also give the fitted formula between the polarizability α1 and atomic number Z as α1=0.73429-9.56644×10-4Z+7.43016×10-5Z2 -2.53298×10-6Z3+2.08306×10-8Z4.

Character of dislocations at the γ/ γ′ interfaces and internal stresses in nickel-base superalloys

It is experimentally observed in Ni-based superalloys that the dislocation substructure after deformation at elevated temperatures is different on horizontal and vertical γ/ γ′ interfaces. Edge dislocation networks are predominantly observed at horizontal interfaces while screw dislocation segments are seen mostly on the vertical interfaces. A crystallographic model of the critical shear stress for dipole expansion for screw and 60° dislocation segments in the γ/ γ′ interfaces is used to explain the observations in high γ′ volume fraction (∼70%) alloys. However, the same model is found to be inadequate in explaining the substructure observations in those alloys with lower γ′ volume fraction (∼40%) which have wider matrix ( γ) channels ( ≈180 nm ). It is shown by superimposition of the dislocation's stress field, the internal coherency stresses and the externally applied stress that between 60° and screw dislocation segments the former increase the internal stresses in vertical interfaces more than the latter.

ISOLATED PERIODIC ORBITS AND STABILITY IN SEPARABLE POTENTIALS

A method for determining the main families of isolated periodic orbits and their characteristic exponents in planar potentials which are separated by a point transformation is proposed. Since these orbits are continued analytically with the same stability, these results are persistent under small perturbations. The method is applied to the two fixed centers problem, the Paul trap and the dipole expansion of an electrostatic potential.

How to run the coupling in the dipole approach to the BFKL equation

We use the dipole expansion to provide a systematic way of including the running coupling in the BFKL equation. In terms of a Borel representation, we obtain an expression for the kernel of the BFKL equation.

Temperature dependence of deformation mechanisms in a single crystal nickel-base alloy with high volume fraction of γ′ phase

The temperature dependence of the yield stress was analyzed in SRR99. High and low temperature regimes can be distinguished. TEM studies show that in the low-temperature regime paired loops expand from the γ′ phase leading to high dislocation densities in matrix channels. At high temperatures deformation starts by expansion of dislocation dipoles in the matrix. The experimental results are compared with the temperature dependence of CRSS values calculated for dipole expansion in narrow matrix channels.

RCS measurement of small circular holes

The Rayleigh scattering from small circular holes in a thin screen was studied. The backscattered fields calculated from a dipole expansion were compared those from an exact solution and measurements for a single, electrically small hole. The backscatter from the holes is given by rather simple expansion where the first term is adequate for a good engineering solution. These expressions are within 1 dB of the exact solution for ka<or=0.96 for E-plane scattering and ka<or=0.69 for H-plane scattering when a is the hole's radius and k is the propagation constant.<<ETX>>

ChemInform Abstract: The Torsional Dependence of the Dipole Moment Operator in Methyl Silane.

Abstract The torsional dependence of the dipole moment operator μ in methyl silane has been in vestigated in detail. To represent the dependence of μ on torsional state to the order corresponding to quadratic distortion, four torsion or torsion-rotation operators enter involving four dipole distortion parameters: μ0T, μ2T, μ|T, and (μ|T - μ⊥T). The Stark effect has been studied for the microwave transitions (J = 1 ← 0) for states with torsional quantum number v = 0 and 2. From the differences in the effective dipole moments, determinations were made of μ0T and of an upper limit to μ2T. The weak, perturbation-allowed torsional absorption spectrum has been observed from 150 to 380 cm−1 at a resolution of 0.15 cm−1 using Fourier transform spectroscopy. The spectrum was dominated by five bands for which the torsion-rotation structure was largely resolved: v = 1 ← 0, 2 ← 1, 2 ← 0, 3 ← 1, and 4 ← 2. An intensity analysis yielded values for μ⊥T, (μ|T - μ⊥T), and a linear combination of μ0T and μ2T. By comparing the present results with earlier precision molecular beam measurements of the effective constants μ ∼ K and μ ∼ J Q that characterize the rotational dependence of the dipole moment for matrix elements diagonal in J, it has been shown that these two constants arise from torsional effects, rather than centrifugal distortion. Only three dipole expansion parameters are required to account for the molecular beam measurements in the ground torsional state, the microwave Stark shifts, and the far-infrared torsional intensities. These are: μ0T = 0.0297(10) D, μ⊥T = 25.1(1.0) μD, and (μ|T - μ⊥T) = −93.3(1.1) μD.

The torsional dependence of the dipole moment operator in methyl silane

The torsional dependence of the dipole moment operator μ in methyl silane has been in vestigated in detail. To represent the dependence of μ on torsional state to the order corresponding to quadratic distortion, four torsion or torsion-rotation operators enter involving four dipole distortion parameters: μ 0 T , μ 2 T , μ | T , and ( μ | T - μ ⊥ T ). The Stark effect has been studied for the microwave transitions ( J = 1 ← 0) for states with torsional quantum number v = 0 and 2. From the differences in the effective dipole moments, determinations were made of μ 0 T and of an upper limit to μ 2 T . The weak, perturbation-allowed torsional absorption spectrum has been observed from 150 to 380 cm −1 at a resolution of 0.15 cm −1 using Fourier transform spectroscopy. The spectrum was dominated by five bands for which the torsion-rotation structure was largely resolved: v = 1 ← 0, 2 ← 1, 2 ← 0, 3 ← 1, and 4 ← 2. An intensity analysis yielded values for μ ⊥ T , ( μ | T - μ ⊥ T ), and a linear combination of μ 0 T and μ 2 T . By comparing the present results with earlier precision molecular beam measurements of the effective constants μ ∼ K and μ ∼ J Q that characterize the rotational dependence of the dipole moment for matrix elements diagonal in J, it has been shown that these two constants arise from torsional effects, rather than centrifugal distortion. Only three dipole expansion parameters are required to account for the molecular beam measurements in the ground torsional state, the microwave Stark shifts, and the far-infrared torsional intensities. These are: μ 0 T = 0.0297(10) D, μ ⊥ T = 25.1(1.0) μD, and ( μ | T - μ ⊥ T ) = −93.3(1.1) μD.