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New content is now available online. Please follow the links to view the content.Electric and Magnetic Properties of Atoms and Molecules: A special issue in honour of <b xmlns="http://pub2web.metastore.ingenta.com/ns/">Professor A.D.Buckingham</b>
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913264
<div><strong> Source: </strong>Volume 3, Issue 2, pp i - iv</div><div></div>M.G. Papadopoulos, G. Maroulis and B. Champagne2007-11-01T12:00:00ZHartree-Fock limit values of multipole moments, polarizabilities and hyperpolarizabilities for atoms and diatomic molecules
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913408
<div><strong> Source: </strong>Volume 3, Issue 2, pp 71 - 113</div><div>This article presents the numerical, finite difference, Hartree-Fock method as a source of reference values of total energies, multipole moments, static polarizabilities and hyperpolarizabilities (<i xmlns="http://pub2web.metastore.ingenta.com/ns/">α<sub>zz</sub>, β<sub>zzz</sub>, γ<sub>zzzz</sub>, A<sub>z,zz</sub></i> and <i xmlns="http://pub2web.metastore.ingenta.com/ns/">B<sub>zz,zz</sub></i>) for atoms and diatomic molecules. The finite field method is used to evaluate polarizabilities and hyperpolarizabilities as derivatives of the dipole and quadrupole moments with respect to the field. The finite difference calculations are compared with other numerical and finite basis set results. Since the finite difference Hartree-Fock method is capable of producing multipole moments with 10-12 significant figure accuracy the high quality of (hyper)polarizability values can be guaranteed.</div>J. Kobus2007-11-01T12:00:00ZDynamic Polarizability Functions of the Hydrogen Molecule
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913282
<div><strong> Source: </strong>Volume 3, Issue 2, pp 115 - 130</div><div>An analytical method to describe tensor components of the dynamic electronic polarizability <i xmlns="http://pub2web.metastore.ingenta.com/ns/">α<sub>ii</sub></i>(<i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i>,ω) of diatomic molecules as a function of internuclear distance <i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i> and the frequency ω of external electromagnetic field is proposed. The method is based on calculations of upper and lower bounds for <i xmlns="http://pub2web.metastore.ingenta.com/ns/">α<sub>ii</sub></i>(<i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i>,ω). The bounds are calculated using the known functions of static polarizability <i xmlns="http://pub2web.metastore.ingenta.com/ns/">α<sub>ii</sub></i>(<i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i>,0) of a molecule, the limited number of energy levels <i xmlns="http://pub2web.metastore.ingenta.com/ns/">E<sub>m</sub></i>(<i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i>) of its excited electronic states, and the electric dipole transition moments (<i xmlns="http://pub2web.metastore.ingenta.com/ns/">d<sub>i</sub></i>)<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">0<i>m</i></sub>(<i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i>). The method has been applied to calculate the dynamic electronic polarizability of H<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sub> molecule over wide ranges of <i xmlns="http://pub2web.metastore.ingenta.com/ns/">R</i> and ω values.</div>M.A. Buldakov, V.N. Cherepanov and N.S. Nagornova2007-11-01T12:00:00ZComputation of Optical Rotation using Time–Dependent Density Functional Theory
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913327
<div><strong> Source: </strong>Volume 3, Issue 2, pp 131 - 150</div><div>A short overview of the time–dependent density–functional theory (TD–DFT) based formalism to compute the optical rotation of chiral molecules is given. Some computational data obtained with a new TD–DFT linear response implementation in the NWChem program package are reported. A selection of available computational studies is reviewed where TD–DFT methods were used for the computation of optical rotation and optical rotatory dispersion of molecules.</div>J. Autschbach2007-11-01T12:00:00ZThe Account of Molecular Multipole Moments in the Study of the Effect of Locally Anisotropic Polarizable Deformable Medium on the Nonlinear Optical Response of Incorporated Chromophore
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913183
<div><strong> Source: </strong>Volume 3, Issue 2, pp 151 - 162</div><div>The model suggested earlier by the author and allowing to describe the effect of locally anisotropic polarizable polymer matrix on the nonlinear optical response of incorporated chromophore is generalized to the case when a chromophore charge distribution is approximated by the multipole expansion including the terms up to octupole. The analytical formula for the local electric field, affecting the chromophore in a polymer electret, is obtained as a solution of electrostatic problem for a molecule in an ellipsoidal cavity, with corresponding boundary conditions taken into account. The approach exploits the special cavity ansatz according to which the cavity ellipsoid is chosen to be conformal to the characteristic ellipsoid of the generalized permittivity tensor of the medium. Using a self-consistent procedure, analytical formulas for induced dipole and quadrupole moments and the macroscopic frozen-in polarization are obtained. The relashionship of the microscopic molecular characteristics (electric moments and polarizabilities) with macroscopic electret polarization, as well as with external macroscopic parameters (applied electric field and permittivity of the medium) is established.</div>Marina Yu. Balakina2007-11-01T12:00:00ZFirst-Principles Langevin Molecular Dynamics Studies of Metallic and Semiconductor Clusters: GGA versus LDA Results
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913273
<div><strong> Source: </strong>Volume 3, Issue 2, pp 163 - 174</div><div>The combination of Langevin molecular dynamics for simulated annealing with realistic quantum-mechanical interactions obtained from first principles supercell calculations within the pseudo potential plane-wave method are applied to examine the structural and electronic properties of the following systems i) pure and mixed Ge<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">n</sub>Te<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">m</sub> (n, m = 0 - 2), Ge<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">3</sub>, Te<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">3</sub> and Ge<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">3</sub>Te<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">3</sub> semiconductor clusters, and ii) bimetallic PbNa<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">n</sub> (n ≤ 7) clusters. Results using the local density approximation (LDA) and the generalized gradient approximation (GGA) for the exchange correlation functional are compared with available experimental data. It is found that the GGA leads to larger bond lengths and smaller binding energies than the LDA, but both approximations lead to the same group symmetry for the ground state of these clusters. Two isomeric configurations for PbNa<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">6</sub>, having C<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">3v</sub> and O<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">h</sub> symmetries, respectively, are found. The dipole moments of semiconductor clusters are compared with those estimated from recent experiments at room temperature. The dipole moments from GGA calculations are, on average, in better agreement with experiments than those calculated with the LDA.</div>L. C. Balbás2007-11-01T12:00:00ZOn the Many-Body Components of Interaction-Induced Electric Properties: Linear Fluoroacetylene Trimer as a Case Study.
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913462
<div><strong> Source: </strong>Volume 3, Issue 2, pp 175 - 182</div><div>Results of many-body analysis of interaction-induced linear and non-linear optical properties are discussed. In particular the size of the basis set superposition error in many-body components of interaction-induced electric properties is examined. In order to eliminate the basis set superposition error the site-site function counterpoise method has been incorporated. The linear fluoroacetylene trimer has been chosen as a model system. In addition the results for two types of geometries (fixed and relaxed one) have been compared in order to determine whether the structural changes influence strongly the components of interaction-induced electric properties.</div>B. Skwara, A. Zawada and W. Bartkowiak2007-11-01T12:00:00ZResponse Properties of 2-Electron 2-D Quantum Dots: Triplet Versus Singlet.
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913444
<div><strong> Source: </strong>Volume 3, Issue 2, pp 183 - 191</div><div>The linear and non-linear optical response properties of 2-D quantum dots with two interacting carrier electrons having triplet coupling of spins are computed and compared with their singlet counterparts. The significant dependence of the response properties on the spin multiplicity in the high and low field regimes are sought to be rationalized.</div>Manas Ghosh, Ram Kuntal Hazra and S. P. Bhattacharyya2007-11-01T12:00:00ZTheoretical Evaluation of the Faraday Effect in Organic Compounds
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913156
<div><strong> Source: </strong>Volume 3, Issue 2, pp 193 - 200</div><div>Using hybrid exchange correlation functional and a basis set including diffuse functions, the Verdet constants of mono-substituted benzenes and oligothiophenes have been evaluated at DFT level using the quadratic response formalism in order to assess the effects of substitution and of chain size on this magneto-optical property. The amplitudes of the Verdet constant are nicely ordered as a function of increasing donor/acceptor character, as estimated using the Hammett's σ parameters, and present substantial exaltation for strong donor groups like the dimethylamino moiety. When available, experimental data supports these conclusions. From calculations on increasingly large oligothiophenes, the Verdet constant appears to evolve almost linearly with the number of thiophene units. Basis set investigations have highlighted the key role of diffuse functions and in particular <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i> and <i xmlns="http://pub2web.metastore.ingenta.com/ns/">d</i> functions on the C and S atoms.</div>Edith Botek, Benoît Champagne, Palash Gangopadhyay, André Persoons and Thierry Verbiest2007-11-01T12:00:00ZDFT Optimized All-Electron Basis Sets for Gradient Corrected Functionals: 4<i xmlns="http://pub2web.metastore.ingenta.com/ns/">d</i> Transition Metals
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913318
<div><strong> Source: </strong>Volume 3, Issue 2, pp 201 - 213</div><div>Density functional theory optimized all-electron basis sets for gradient corrected functionals for 4<i xmlns="http://pub2web.metastore.ingenta.com/ns/">d</i> transition metal atoms are presented. Double Zeta Valence Polarization (DZVP) basis sets were optimized with the PW86 functional. The performance of the newly generalized gradient approximation (GGA) optimized basis sets was tested with atomic and molecular properties calculations. Excitation energies of 4<i xmlns="http://pub2web.metastore.ingenta.com/ns/">d</i> transition metal atoms, as well as electronic configurations, structural parameters and harmonic vibrational frequencies of homonuclear 4<i xmlns="http://pub2web.metastore.ingenta.com/ns/">d</i> transition metal dimers are presented. The obtained results are compared with available experimental data as well as with theoretical data obtained by using analogous basis sets optimized for local functionals or with theoretical values from the literature.</div>Patrizia Calaminici and Roberto Mejia-Olvera2007-11-01T12:00:00ZThe Dipole Polarizability of Uracil in Aqueous Solution. A Sequential Monte Carlo/Quantum Mechanics Study
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913138
<div><strong> Source: </strong>Volume 3, Issue 2, pp 215 - 222</div><div>A combined and sequential Monte Carlo/quantum mechanics methodology is used to estimate the dipole polarizability of uracil in aqueous solution in normal thermodynamic conditions. Using the structures generated by the MC simulation, statistically uncorrelated configurations are sampled for subsequent quantum mechanical calculations using the central uracil molecule surrounded by the first solvation shell composed of 26 explicit water molecules. The dipole polarizability is obtained as an average value obtained from density-functional-theory calculations, using the B3P86 functional with varying basis sets. Statistically convergent result for the dipole polarizability of uracil in aqueous solution gives the average value of 100.1 ± 10.4 a<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">0</sub><sup xmlns="http://pub2web.metastore.ingenta.com/ns/">3</sup>, indicating an increase of about 50% compared to the gas phase result.</div>V. Ludwig and S. Canuto2007-11-01T12:00:00ZElectronic Structure Principles in Static and Dynamic Situations
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913336
<div><strong> Source: </strong>Volume 3, Issue 2, pp 223 - 230</div><div>Various electronic structure principles are analyzed in time-independent and time-dependent situations. Periodicity and chemical reactions have been studied as representative static cases. A generalized nonlinear Schrödinger equation has been solved in gaining insights into the reactivity dynamics associated with ion-atom collisions and atom-field interactions. Dynamical variants of various electronic structure principles reveal themselves.</div>P. K. Chattaraj, D. R. Roy and S. Giri2007-11-01T12:00:00ZParallelization Efficiency of the Elongation Method and its Application to NLO Design for Urea Crystal
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913363
<div><strong> Source: </strong>Volume 3, Issue 2, pp 231 - 241</div><div>The elongation method designed for calculating the electronic structures of aperiodic polymers has been investigated in parallelization efficiency. The elongation finite-field method for determining (hypper)polarizabilities has been successfully applied to the three-dimensional urea crystal and its derivatives. It is shown that the elongation-FF method is suitable to large-scale calculations with parallelization and a powerful tool for nonlinear optical material designing.</div>Shin-ichi Ohnishi, Feng Long Gu, Kazunari Naka and Yuriko Aoki2007-11-01T12:00:00Z<i xmlns="http://pub2web.metastore.ingenta.com/ns/">Ab Initio</i> Studies of the Dipole Moments and Polarizabilities of <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i>-nitroaniline and Related Molecules in their Ground and Excited States.
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913255
<div><strong> Source: </strong>Volume 3, Issue 2, pp 243 - 249</div><div>We report <i xmlns="http://pub2web.metastore.ingenta.com/ns/">Ab Initio</i> energies, dipole moments and mean dipole polarizabilities <α> for the ground and five lowest electronic excited singlet states of nitromethane, methylamine, nitromethylamine, nitrobenzene, aniline and <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i>-nitroaniline, together with ground state data for methane and benzene. Ground state properties were calculated using the HF/6-311++G(2d,1p) model whilst excited states were modelled using CIS and CIS(D). Our ground state results are consistent with available experimental data and other advanced literature calculations. The XCH<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sub>Y calculations give group <α> contributions of 13.6 atomic units (au) for NO<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sub> and 7.7 au for NH<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">2</sub>. The XC<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">6</sub>H<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">4</sub>Y <α>'s suggest 14.4 and 10.8 au, but there is no evidence of a contribution from the push-pull mechanism. The excited state dipole moments and <α>'s are consistent with the sparse experimental data, and we predict immensely enhanced values for these properties in many of the excited states.</div>Alan Hinchliffe, Mohamed Efhil and Humberto J Soscún2007-11-01T12:00:00ZStatic Polarizabilities (α) and Second Hyperpolarizabilities (γ) of One-Dimensional Hydrogen-Bonded Formamides
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913165
<div><strong> Source: </strong>Volume 3, Issue 2, pp 251 - 256</div><div>We investigate the chain length dependences of static polarizabilities (α) and second hyperpolarizabilities (γ) for one-dimensional hydrogen (H)-bonded chains composed of formamide from the viewpoint of cooperative effect of H-bonds. The α and γ values are calculated by the finite-field approach using the Hartree-Fock (HF), Møller-Presset perturbation theory (MP) and density functional theory (DFT) methods in order to clarify the electron correlation effects on the α and γ values of the H-bonded systems. The increase ratio of γ values per monomer for the increase of the number of monomers is found to be significantly enhanced compared to that of α values per monomer. This feature suggests the strong cooperative effects on γ originating in the interaction between the H-bonds and π-electrons of the monomers in the high-lying excited states mainly contributing to γ.</div>Ryohei Kishi, Shin-Ya Umezaki, Akihito Takebe, Masahito Nate, Hideaki Takahashi and Masayoshi Nakano2007-11-01T12:00:00ZTheoretical Modeling of Cation-π interactions in Various Environments: Case Study Using Benzene…Ammonium and Benzene…Tetramethyl- Ammonium Ion Interactions as Model Systems
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913246
<div><strong> Source: </strong>Volume 3, Issue 2, pp 257 - 265</div><div>State of the art theoretical calculations have been carried out to understand cation-π interactions in different environments. Benzene…ammonium (C<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">6</sub>H<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">6</sub>…NH<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">4</sub><sup xmlns="http://pub2web.metastore.ingenta.com/ns/">+</sup>) and benzene…tetramethylammonium (C<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">6</sub>H<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">6</sub>…N(CH<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">3</sub>)<sub xmlns="http://pub2web.metastore.ingenta.com/ns/">4</sub><sup xmlns="http://pub2web.metastore.ingenta.com/ns/">+</sup>) complexes are used as model systems and cation-π interactions in these complexes has been evaluated for their gas phase, partially hydrated and fully solvated (using continuum model) structures. The extent of utility of these model calculations has been discussed in the context of different biological environments.</div>D. Majumdar and J. Leszczynski2007-11-01T12:00:00ZPartial Least Squares Prediction of the Hyperpolarizabilities of Aniline Octamer Derivatives
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913228
<div><strong> Source: </strong>Volume 3, Issue 2, pp 267 - 276</div><div>Partial least squares (PLS) predictions for the first and second static hyperpolarizabilities (β and γ) of aniline octamer derivatives were calculated from AM1 values of the Homo-Lumo energy gap, the ground state dipole moment, the ionization potential, and the number of π-electrons. The calculations were performed for oligomers of the neutral forms of polyaniline (leucoemeraldine, emeraldine and pernigraniline) having donor (D) and/or acceptor (A) groups incorporated into their structure. The PLS estimated values are in good agreement with the β and γ values calculated at the AM1/CPHF level.</div>M.B. da S. Costa, A.E. de A. Machado and B. Barros Neto2007-11-01T12:00:00ZOn the Efficient Selection of Frequencies for Interpolating Dynamic Multipole Polarizabilities
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913417
<div><strong> Source: </strong>Volume 3, Issue 2, pp 277 - 284</div><div>We improve a previously reported technique for interpolating available values of atomic or molecular frequency-dependent multipole polarizabilities and calculating the related dispersion constants. The improvement is provided by a simple formula allowing for an efficient selection of the frequencies involved (i.e. the frequencies implying numerical evaluations performed on the interpolated polarizability). It is shown that sensibly lower interpolative errors are obtained, so giving an enhanced accuracy in the subsequent calculation of the related dispersion constants.</div>G. Figari and V. Magnasco2007-11-01T12:00:00ZOrigin of the Bulk Effect on the NLO Property of P-terphenyl Microcrystalline Structure – Computer Simulations
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913129
<div><strong> Source: </strong>Volume 3, Issue 2, pp 285 - 293</div><div>The effect of environment on the nonlinear optical (NLO) property of p-terphenyl is discussed. The performed study is mainly devoted to the simulations of the photoinduced optical second harmonic generation (SHG) and comparison of the obtained data to the literature experimental results. The structure of the investigated system has been modeled by molecular dynamic simulations. Three equivalent structures of the investigated system were built to minimize the statistical structural error. Then the averaged structural data were taken into account to compute the macroscopic optical property. Quantum chemical time-dependent density functional theory (TDDFT) calculations of the first-order nonlinear optical properties were performed. The first-order hyperpolarizability of the isolated molecule was calculated, under the influence of a polarized pumping beam. To evaluate the role of amorphous and crystalline environment the permanent local field in the bulk system was calculated. The obtained results are small; however, their effects on the first hyperpolarizabilities are large in comparison to changes in the linear optical property. Using a rigorous local field approach and the molecular dynamic modeled structure the photoinduced NLO property of p-terphenyl may be reproduced for the high power density laser beam. The obtained results are in good agreement to the experimental data.</div>M. Makowska-Janusik2007-11-01T12:00:00ZAverage Low and High Momenta in Singly-Excited 1<i xmlns="http://pub2web.metastore.ingenta.com/ns/">snl</i> States of the He Atom
http://booksandjournals.brillonline.com/content/journals/10.1163/157404007782913426
<div><strong> Source: </strong>Volume 3, Issue 2, pp 295 - 300</div><div>Average low < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i><sub xmlns="http://pub2web.metastore.ingenta.com/ns/"><</sub> > and high < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i><sub xmlns="http://pub2web.metastore.ingenta.com/ns/">></sub> > momenta are examined for 28 singly-excited 1<i xmlns="http://pub2web.metastore.ingenta.com/ns/">snl</i> singlet and triplet states (0 ≤ <i xmlns="http://pub2web.metastore.ingenta.com/ns/">l</i> < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">n</i> ≤ 5) of the He atom. The low momentum < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i><sub xmlns="http://pub2web.metastore.ingenta.com/ns/"><</sub> > decreases with increasing <i xmlns="http://pub2web.metastore.ingenta.com/ns/">n</i> and decreasing <i xmlns="http://pub2web.metastore.ingenta.com/ns/">l</i>, while the high momentum < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i><sub xmlns="http://pub2web.metastore.ingenta.com/ns/">></sub> > is nearly equal to 16/(3<i xmlns="http://pub2web.metastore.ingenta.com/ns/">π</i>)≅1.698, independent of <i xmlns="http://pub2web.metastore.ingenta.com/ns/">n</i> and <i xmlns="http://pub2web.metastore.ingenta.com/ns/">l</i>. Comparing the low < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i><sub xmlns="http://pub2web.metastore.ingenta.com/ns/"><</sub> > and high < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i><sub xmlns="http://pub2web.metastore.ingenta.com/ns/">></sub> > momenta with the average electron momentum of a hydrogenlike atom, we show that an electron with a lower momentum behaves like an <i xmlns="http://pub2web.metastore.ingenta.com/ns/">nl</i> electron of the hydrogen atom and another electron with a higher momentum behaves like the 1<i xmlns="http://pub2web.metastore.ingenta.com/ns/">s</i> electron of the helium cation. A decomposition of an uncertainty product < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">r</i> >< <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i> > finds that the largest contribution to < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">r</i> >< <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i> > comes from an outer electron and a high momentum electron, where < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">r</i> > and < <i xmlns="http://pub2web.metastore.ingenta.com/ns/">p</i> > are the usual average electron radius and momentum, respectively.</div>Hisashi Matsuyama and Toshikatsu Koga2007-11-01T12:00:00Z