Solvent Effect on Absorption and Fluorescence Spectra of Three Biologically Active Carboxamides (C<Subscript>1</Subscript>, C<Subscript>2</Subscript> and C<Subscript>3</Subscript>). Estimation of Ground and Excited State Dipole Moment from Solvatochromic Method Using Solvent Polarity Parameters

The absorption and fluorescence spectra of three Carboxamides namely (E)-2-(4-Chlorobenzylideneamino)-N-(2-chlorophenyl)-4, 5, 6, 7-tetrahydrobenzo[b]thiophene-3-carboxamide (C₁), (E)-N-(3-Chlorophenyl)-2-(3, 4-dimethoxybenzylideneamino)-4, 5, 6, 7-tetrahydrobenzo[b]thiophene-3-carboxamide (C₂) and (E)-N-(3-Chlorophenyl)-2-(3, 4, 5-trimethoxybenzylideneamino)-4, 5, 6, 7-tetrahydrobenzo[b]thiophene-3-carboxamide (C₃) have been recorded at room temperature in solvents of different polarities using dielectric constant (ε) and refractive index (n). Experimental ground (μ_g) and excited (μ_e) state dipole moments are estimated by means of solvatochromic shift method and also the excited dipole moments are estimated in combination with ground state dipole moments. It was estimated that dipole moments of the excited state were higher than those of the ground state of all three molecules. Further, the changes in dipole moment (Dm \Delta \mu ) were calculated both from solvatochromic shift method and on the basis of microscopic empirical solvent polarity parameter (E_T^N E_T^N ) and the values are compared.     

Spin–orbit coupling in biradicals. 5. Zero-field splitting in triplet dimethylnitrenium,dimethylphosphenium and dimethylarsenium cations

The spin dipole–spin dipole and spin–orbit coupling contributions to the zero-field splitting parameters D and E of [CH₃–N–CH₃]⁺, [CH₃–P–CH₃]⁺, and [CH₃–As–CH₃]⁺ have been calculated from CASSCF(14,14)/cc-pVTZ wave functions and the Breit–Pauli Hamiltonian at T₁ B3LYP/cc-pVTZ optimized geometries. The spin–orbit coupling contributions represent a minor correction for the dimethylnitrenium cation, which has a triplet ground state. They dominate the spin–spin terms by an order of magnitude in the dimethylphosphenium cation and by more than two orders of magnitude in the dimethylarsenium cation, both of which have a singlet ground state. The properties of all these biradicaloids follow expectations based on the simple algebraic 2-in-2 model of biradical structure.     

Radiative lifetimes of 7d, 8d <Superscript>1</Superscript>D<Subscript>2</Subscript> excited states of Hg I

Radiative lifetimes of 7d, 8d ¹ D ₂ excited states of Hg I are measured using pulsed two-photon excitation from the ground [Xe]5d ¹⁰6s ^{2 1} S ₀ mercury state, detecting the decay of the laser-induced fluorescence. The results are compared with theoretical values, obtained by means of a Hartree-Fock single configuration method, taking into account electron configuration interaction. The radiative lifetime value dependence on the effective principal quantum number for the nd ¹ D ₂ series is analyzed and compared with the quantum defect dependence. Received 25 February 2000 and Received in final form 26 July 2000     

Ab initio all-electron fully relativistic Dirac—Fock self-consistent field calculations for UCI6

Ab initio all-electron fully relativistic Dirac-Fock and non-relativistic Hartree-Fock self-consistent field (SCF) calculations are reported at four UCl bond distances, assuming octahedral UCl₆. The results are fitted to a polynomial, obtaining thereby the optimized values of the bond distance and the corresponding total electronic energy for the UCl₆. The nonrelativistic Hartree-Fock (HF) and Dirac-Fock (DF) SCF calculations predict UCl₆ to be bound, with a predicted dissociation (atomization) energy D _e of 11.88 eV and 17.89 eV, respectively. Relativistic effects lead to ~51% increment in the predicted atomization energy of UCl₆. The UCl bond lengths predicted for UCl₆ with the relativistic DF and non-relativistic HF wave-functions are 2.46 Å and 2.58 Å, respectively. Complete neglect in the SCF step of the two-electron [SS|SS] integrals involving the small components of the spinors (NOSS) in the DF SCF calculation for UCl₆ predicts a D _e of 18.25 eV and essentially the same bond length (2.48 Å) as that predicted with the full SCF procedure. Thus the small components contribute an antibinding relativistic effect of ~0.4 eV to the D _e of UCl₆ and have a negligible effect on the bond length. The calculations show that relativistic effects are significant for the bonding and the dissociation (atomization) energy of UCl₆, and that these may be treated accurately using Dirac's fully relativistic equation for an electron.     

N.M.R. studies of cis-1,2-difluoroethylene and vinyl fluoride in a nematic solvent

Constrained anisotropic dipole oscillator strength techniques are used to obtain reliable values for a wide range of anisotropic and isotropic dipole properties of NO, including most anisotropic components of the dipole-dipole dispersion energy coefficients for the interaction of NO with NO, O₂, H₂, N₂, CO, He, Ne, Ar, Kr and Xe. Some of the anisotropic constraints required for our calculations are obtained via dipole sum rules from ab initio, multi-reference configuration interaction wavefunctions for NO. The individual dipole properties of NO considered include the dipole oscillator strength sums S_k , k = 2,1,0(? 1/2)? 2,? 3,? 4,..., the logarithmic dipole sums L_k and mean excitation energies I_k , k = 2(? 1)? 2, and, as a function of wavelength, the dynamic polarizability and its anisotropy, the total depolarizaiton ratio, and the Rayleigh scattering cross-section. Our constrained dipole oscillator strength results are often the only reliable, and often the only available, values for many of the properties and dispersion energies considered.     

[2.2]Paracyclophane: theoretical study of its lower excited states and of the zero-field splitting parameters D

The lower excited singlet and triplet states and the zero-field splitting parameters D of [2.2]paracyclophane are studied within a semiempirical π theory which takes into account overlap effects between the two benzene rings, transanular and through-bond interaction via the methylene bridges. Whereas the singlet energies depend strongly on the through-bond interaction and the mutual polarization of σ core and π system this is not the case for the energies and zero-field splitting parameters D of the two lowest triplet states. The deformations of the benzene rings in [2.2]paracyclophane lead only to a small decrease of the excitation energies of about 0·2 eV. The D parameter can be written as a sum D = D_A + D_B + D_AB with the intrasubunit contributions D_A and D_B of the conjugated subunits A and B of the phane and an intersubunit term D_AB . We demonstrate that the deformations reduce the intrasubunit terms D_A and D_B and that they are crucial for the decrease of the D values of [2.2]paracyclophane with respect to p-xylene. The difference between the D values of the first and second triplet states is governed by the intersubunit term D_AB which has a different sign in the two states. However, this difference does not depend markedly on the transanular interaction. A further reduction of D_A and D_B in the first triplet state only is caused by transanular interaction by means of symmetrical charge-transfer terms in the wavefunction.     

Ab initio calculations of multipole moments,polarizabilities and long-range interaction coefficients for the azabenzene molecules

Using LCAO-SCF wave functions on the monomers and a non-empirical Unsöld procedure for the second-order properties we have calculated the (2 ^l ) multipole moments (up to l=6), the (l,l') multipole polarizabilities (up to l + l' = 6) and the related long-range coefficients describing the electrostatic, induction and dispersion interactions for the different azabenzene molecules. The agreement with available experimental data is good, in particular for the dipole polarizabilities. The anisotropy of the long-range interaction potential is dominated by the electrostatic contributions, although the dispersion terms, especially the mixed-pole terms (l≠l') for even n (C₈, C₁₀), also contribute significantly; the induction energy is rather small. The π contributions to the polarizabilities and the dispersion interactions are found to be larger than earlier estimates. Moreover, it is shown by calculating the dipole polarizabilities of some (aza)naphthalenes and (aza)anthracenes, that a bond polarizability model can be applied effectively only if the delocalized π electrons are considered separately from the σ electrons.     

The calculation of dynamic polarizabilities and of the dipole-dipole and dipole-quadrupole contributions to the dispersion energy

By using a single Slater-type 2p orbital with a frequency-dependent exponent in the basis set for the variation solution of the first-order time-dependent perturbation equation, good results are obtained for the dipole dynamic polarizability of the hydrogen atom. The accuracy attained has been reproduced only by variation calculations with larger basis sets. The same happens with the quadrupole dynamic polarizability: a single 3d Slater-type orbital with a similarly optimized exponent in the basis of states for the variation calculation is enough to yield results which are very close to the exact values for all frequencies. Using the frequency-dependent dipole and quadrupole polarizabilities thus obtained we have calculated the dipole and quadrupole contributions to the dispersion energy of two hydrogen atoms and found results which are within 1 per cent of the exact values.

Considering the simplicity of our wavefunction as compared with the four-term wavefunction used by Chan and Dalgarno [5] to construct the basis for their variation calculation and the excellent agreement we obtain, it is important to emphasize the value of using optimized frequency-dependent exponents in the basis of states used for the variation calculation.     

Interatomic dispersion dipole

A new formula is derived for the coefficient D ₇ of the leading term in R ^-7 for the electric dipole moment of two atoms in S-states at a large distance R apart. An approximation is proposed which leads to a simple formula for D ₇ involving mainly accessible atomic properties. The approximation is checked for scaled hydrogen atoms and is accurate to about one per cent.     

Hyperfine coupling constants of cesium 7D states using two-photon spectroscopy

Doppler-free two-photon transitions of cesium 6S_1/2→7D_{3/2, 5/2} were observed in a thermal stabilized cell. A repeated spectrum of 75 MHz introduced from the side band of an electro-optical modulator served as a frequency marker to improve the accuracy of frequency measurement. The hyperfine magnetic dipole constant A and electrical quadrupole constant B of Cs 7D_{3/2, 5/2} can be derived from the splitting intervals of the observed spectra. The results are: A=7.36(07) MHz, B=−0.88(87) MHz for the 7D_3/2 state, and A=−1.81(05) MHz, B=1.01(1.06) MHz for the 7D_5/2 state. These coefficients are improvements for testing high-precision measurements and determining fundamental physical constants.     

On a possible interpretation of the X(3872) as a 1<Superscript>1</Superscript>D<Subscript>2</Subscript> state in a constituent-quark model based on a generalized Fermi-Breit equation

A recent experimental analysis suggested to represent the X(3872) -resonance as a c [`(c)] \bar{{c}} 1¹ D ₂ state but this attribution is being hotly debated. We calculate the mass values for that state by means of a previously studied constituent-quark model. The different contributions of the model Hamiltonian to the total mass are also explicitly shown.     

High Pressure effect on fluorescence lifetime τ for magnetic dipole 5D0→5F1 transitions in YAG:Eu3+

The fluorescence lifetime for magnetic dipole ⁵D₀→⁷F₁ transition in yttrium aluminum garnet doped with Eu³⁺ (YAG:Eu³⁺) crystal was studied under the pressure of up to 10.4?GPa at room temperature. The fluorescence lifetime τ (⁵D₀→⁷F₁ transition) slowly decreased with pressure. The pressure effect on τ (⁵D₀→⁷F₁ transition) was explained with a model which considered pressure effect on line position: inter-ionic distance, ion volume, molecular volume, ion polarizability, molecular polarizability, sample refractive index, and surrounding hydrostatic medium refractive index. The fluorescence lifetime τ calculated by the presented model was in close correspondence with the experimental values.     

Lattice dynamical study of alkali metals: An unified approach based on CGW model

The phonon dispersion relations for lithium, sodium, potassium, rubidium and cesium along the principal symmetry directions as well as their lattice specific heats have been deduced using Clark, Gazis and Wallis angular force model. This model which conforms to the translational symmetry of the lattice, reproduces the observed crossover in lithium along [ζ00] direction at ζ = 0·49, without producing any crossovers in other alkali metals. Besides, the theoretical dispersion curves of all alkali metals are in excellent agreement with the corresponding experimental or homologous dispersion relations and theirϑ _D values compare well with the experimental values over a wide temperature range. It is shown that the strength of electron-ion interactions plays a significant role in the success of any unified lattice dynamical study of alkali metals while the three-body interactions of thecgw model do not. The importance of umklapp processes, failure of the earlier models to produce a crossover and the experimentalϑ _D-T curve in lithium as well as the apparent variation in the nature and range of atomic interactions of alkali metals are discussed.     

Formulae which relate pressure,activity and potentials of mean force to sums of integrals over Ursell-Mayer correlation functions of the distribution functions

The pure rotational spectrum in the far-infrared between 30 and 170 cm^-1 and its absolute intensity has been measured for CH₂D₂ in the vibrational ground state by high-resolution interferometric Fourier transform techniques. The analysis of the integrated cross-sections in the essentially water-free spectrum results in an accurate value for the permanent, vibrationally induced ground state electric dipole moment of CH₂D₂|μ₀| = (6·40±0·33) x 10^-3D.The influence of centrifugal effects on intensities and on the determination of the permanent dipole moment was investigated. Although centrifugal effects are important for the explanation of single band profiles, they appear to be of little relevance for the resulting permanent dipole moment. A new, more general 9- dimensional dipole moment function for methane is derived from ab initio calculations and experimental band strength information of CHD₃. Quantum Monte Carlo calculations using this function and a new, more general 9- dimensional analytical, anharmonic potential function for methane yield a semi-theoretical estimate μ₀ ^z = – (7·8±0·5)x10^-3D for CH₂D₂.     

钪原子的自电离里德伯能级3d4s(1D2)nf2 D3/2,3d4s(1D2)nf2 F5/2和3d4s(1D2)np2 D3/2<

在多通道量子亏损理论框架下,利用相对论多通道理论,分别在冻结实近似和考虑偶极极化下计算钪原子的J^π=(3/2)^-,(5/2)^-的三个收敛于 3d4s(¹D₂)的自电离里德伯系列的能级.对3d4s(¹D₂)np²D_3/2和3d4s(^{1 关键词： 相对论多通道理论 多通道量子亏损理论 电子-电子关联 自电离里德伯系列}     

Many-particle effects in resonant inelastic scattering of an X-ray photon by an atom

The influence of many-particle effects on the shape and values of the double differential cross section for the resonant inelastic scattering of a linearly polarized X-ray photon by a free atom near the K and KL₂₃ ionization thresholds has been theoretically analyzed for the neon atom. The calculations have been performed using the nonrelativistic Hartree-Fock approximation for single-electron wavefunctions and the dipole approximation for the anomalous dispersion component of the cross section. The analytical structure of the contact part of the scattering cross section has been obtained beyond the dipole approximation. The effects of the radial relaxation of electron shells, spin-orbit and multiplet splitting, and configuration interaction in the doubly excited atomic states, as well as the Auger and radiative decays of the produced vacancies, are taken into account. The nature and role of the effect of correlation amplitudes, which is responsible for the appearance of the nonzero amplitudes of nonradiative transitions between intermediate and final single-electron states of the same symmetry that are obtained in different Hartree-Fock fields, have been analyzed also. The calculations are predictive and, for an incident-photon energy of 5.41 keV, agree well with experimental results for the Kα X-ray emission spectrum of the neon atom.     

Approximative Berechnung von diamagnetischen Suszeptibilitäten

The Hartree-Fock perturbation method formulated in a previous paper [7] for approximate calculations of the magnetic susceptibilities of polyatomic molecules using CNDO/2 or INDO wavefunctions is reviewed. The method uses gauge-invariant atomic orbitals together with a set of approximations proposed in People's MO theory of diamagnetism. An expression is obtained for the susceptibility of a molecule involving three different parts which are referred to as intra-atomic, interatomic and cross contributions, respectively. All these contributions are used to calculate the susceptibilities of a series of hydrocarbons (CH₄, C₂H₆, C₂H₄, C₂H₂, cyclopropane). The mean values are in good agreement with experiment (except C₂H₂). Surprisingly, the interatomic and cross terms make considerable contributions to the total susceptibility. It seems justified to include the cross terms in the other terms and to define new terms which can be referred to as local or non-local contributions to the susceptibility. The local part can be divided up into a sum of atomic contributions which are comparable with the empirical Pascal constants. The numerical results reproduce very well the empirical atomic contributions and the constitutive correction for the carbon-carbon double bond. The calculations cover also the principal components of the atomic contributions. The non-local contribution may be considered as a generalization of the formula of Hall and Hardisson to all valence electrons.     

Electron resonance studies of the renner effect

The gas phase electron resonance spectra of NCO in its ground ²Π_3/2 vibronic state and in two excited vibronic states are described. Theoretical analysis of the spectra yields effective g values for the three states. In additon the ¹⁴N magnetic hyperfine and electric quadrupole coupling constants and the electric dipole moment are determined. The theory of the Renner coupling of electronic and vibrational motion is extended, and shown to account for anomalous contributions to the g values. The theory also shows that these contributions are closely related to the Renner coupling constant.     

Dispersion energy constants C 6(A,B), dipole oscillator strength sums and refractivities for Li,N, O,H2, N2, O2, NH3, H2O,NO and N2O

Accurate values for the orientation-averaged long-range dipole-dipole dispersion energy coefficients, C ₆(A, B), have been determined for all possible pair interactions involving ground state H, Li, N, O, H₂, N₂, O₂, NH₃, H₂O, NO, and N₂O. The calculations have been carried out by employing dipole oscillator strength distributions for these species that have been constructed (except in the case of H) by using discrete oscillator strength, photo-absorption, and high energy inelastic scattering data and by requiring the distributions to reproduce the Thomas-Reiche-Kuhn sum rule and, in the case of the molecules, available accurate refractivity and dispersion measurements for the relevant dilute gases. These oscillator strength distributions were also used to evaluate the refractivity R(λ), as a function of wavelength λ in the visible and ultra-violet region below the ultra-violet absorption thresholds, and the dipole oscillator strength sums S _-2l , l = 1, 2, …, 7, for each atom and molecule. The calculated values of R(λ) provide refractivities for wavelengths, especially in the ultra-violet region, for which accurate experimental data are often not available. The accurate results for C ₆(A, B) and for various dipole oscillator strength sums are used to make self-consistent tests of the adequacy of (1) the C ₆(A, A) bounds provided by Padé approximant methods and (2) various semi-empirical formulae for C ₆(A, B). Some problems that can arise in using other procedures to evaluate the S _-2l and C ₆(A, B) are discussed briefly.     

The influence of intermolecular interactions on the Kerr effect in gases

Expressions are derived for the second and third Kerr virial coefficients, B _K and C _K, of spherical top molecules in terms of irreducible cluster polarizabilities, and values are calculated using the dipole-induced dipole model for argon, krypton, xenon, methane, tetrafluoromethane, neopentane and sulphur hexafluoride. For mixtures of rare gases it is shown that the collision-induced dipole moment makes a negligible contribution to B _K. The effect of the choice of intermolecular potential function on the calculated second Kerr virial coefficients is also demonstrated. It is found that the predominant contributions to C _K arise from the pair polarizability, and that the triplet polarizability is only of minor importance.