Long-range Region Research Articles

Electrostatic potentials and fields from density expansions of deformed atoms in molecules.

The exact representation of the molecular density by means of atomic expansions, consisting in spherical harmonics times analytical radial factors, is employed for the calculation of electrostatic potentials, fields, and forces. The resulting procedure is equivalent to an atomic multipolar expansion in the long-range regions, but works with similar efficiency and accuracy in the short-range region, where multipolar expansions are not valid. The performances of this procedure are tested on the calculation of the electrostatic potential contour maps and electrostatic field flux lines of water and nitrobenzene, computed from high-quality molecular electron densities obtained with Slater basis sets.

Description of Dynamic Dielectric Response in Poly(vinylidene Fluoride-Trifluoroethylene) Copolymers

We propose a theory of dynamic dielectric response in organic ferroelectrics PVDF, P(VDF/TrFE) copolymer before and after irradiation by fast electrons. For this purpose, we use random field formalism. In the adopted model we consider above polymers as disordered ferroelectrics in mixed ferroglass phase (FG) with a coexistence of polar short- and long-range order regions. Short-range order regions correspond to amorphous layers, while long-range order regions appears in the crystalline phase of all-trans conformation. In our formalism, we account for change of VDF content as well as for the influence of irradiation, by variation of content of electric dipoles and other random field sources. The downward shift of para-ferroelectric phase transition temperature and gradual transformation of mixed FG phase into dipole glass state with the increase of the irradiation dose was shown to be related to the self-consistent change of parameters of random field distribution function. We were able to fit the low-temperature dynamic dielectric response related to amorphous phase by Vogel-Fulcher (V-F) law with parameters close enough to those observed in the experiment. The coincidence between calculated and measured behaviour (namely, almost complete disappearance of high-temperature maxima, corresponding to ferroelectric phase transition, their submergence into low-temperature maxima and V-F law for low-temperature maxima of absorption) of irradiated samples speaks in favour of irradiation induced relaxor behaviour of P(VDF/TrFE) copolymers. We also discuss the physical reasons for choice of parameters necessary to fit our theory to the experiment.

Theory of radiation induced relaxor behavior of poly(vinylidene fluoride-trifluoroethylene) copolymers

We propose a theory of the dynamic dielectric response in the organic ferroelectrics polyvinylidene fluoride (PVDF), poly(vinylidene fluoride/trifluoroethylene) [P(VDF/TrFE)] copolymer before and after irradiation by fast electrons. For this purpose, we use our random field formalism. In the adopted model we consider the earlier polymers as the disordered ferroelectrics in a mixed ferroglass phase (FG) with a coexistence of polar short- and long-range order regions. Short-range order regions correspond to amorphous layers, while long-range order regions appears in the crystalline phase of all-trans conformation. In our formalism, we account for the change of VDF content as well as for the influence of the irradiation, by variation of the content of electric dipoles and other random field sources. The downward shift of the paraferroelectric phase transition temperature and gradual transformation of the mixed FG phase into a dipole glass state with the increase of the irradiation dose was shown to be related to the self-consistent change of parameters of random field distribution function. We were able to fit the low-temperature dynamic dielectric response related to the amorphous phase by Vogel–Fulcher (V–F) law with parameters close enough to those observed in the experiment. The coincidence between calculated and measured behavior (namely, almost complete disappearance of high-temperature maxima, corresponding to the ferroelectric phase transition, their submergence into low-temperature maxima and V–F law for the low-temperature maxima of absorption) of the irradiated samples speaks in favor of irradiation induced relaxor behavior of P(VDF/TrFE) copolymers. We also discuss the physical reasons for the choice of the parameters of material necessary to fit our theory to the experiment.

H2AX is required for recombination between immunoglobulin switch regions but not for intra-switch region recombination or somatic hypermutation.

Changes in chromatin structure induced by posttranslational modifications of histones are important regulators of genomic function. Phosphorylation of histone H2AX promotes DNA repair and helps maintain genomic stability. Although B cells lacking H2AX show impaired class switch recombination (CSR), the precise role of H2AX in CSR and somatic hypermutation (SHM) has not been defined. We show that H2AX is not required for SHM, suggesting that the processing of DNA lesions leading to SHM is fundamentally different from CSR. Impaired CSR in H2AX−/− B cells is not due to alterations in switch region transcription, accessibility, or aberrant joining. In the absence of H2AX, short-range intra-switch region recombination proceeds normally while long-range inter-switch region recombination is impaired. Our results suggest a role for H2AX in regulating the higher order chromatin remodeling that facilitates switch region synapsis.

Screening and confinement in U(1)N−1 Abelian effective theories

We discuss the effect of dynamical charged particles in U(1)N−1 Abelian effective theories of QCD. Screening and confinement at zero temperature are explained qualitatively. The effect of dynamically charged particle is expressed in terms of an effective action of integer electric currents. When a screening is expected, the static potential shows a flattening in the long-range region and a linear behavior in the intermediate region. We show why the screening is better observed in the Polyakov-loop correlators than in the Wilson loops. The breaking of the adjoint string is explained without the Z(N) picture.

The application of direct potential fitting to the X1∑ + ground electronic states of LiCl, TlCl, RbF and CsF

A procedure for directly fitting the potential energy curve of a diatomic molecule has been applied to the X 1∑ + ground states of LiCl, TlCl, RbF and CsF. Extensive, high-precision infrared and pure-rotational data sets for all isotopomers of the aforementioned molecules have been employed in direct least-squares fits of a radially dependent Hamiltonian operator. The Born–Oppenheimer potentials are represented by a modified Lennard–Jones function that is shown to be flexible and provide the proper behavior in the long-range region of the potential. While the potential fits of LiCl and TlCl required the inclusion of Born–Oppenheimer breakdown functions, no such functions were necessary for either RbF or CsF.

Evolution of the periodicity and the self-similarity in DNA sequence: a Fourier transform analysis.

Fourier transform analysis was applied to elucidate the periodical and self-similar properties in the DNA sequences mainly of beta-globin genes in different species, and the evolutionary change in those properties was then investigated. Map patterns of a two-dimensional DNA walk showed that the stretches of exons are significantly shorter than those of introns, suggesting that the evolution of exons is driven by natural selection, whereas that of introns is generated by unknown internal rules. Using a monomer analysis, we obtained the power spectra of four different bases, A, G, C, and T, in DNA sequences. Periodicities in the short- (2 to 10 base pairs [bp]), medium- (10 to 50 bp) and long-range order (50 to 300 bp) of beta-globin gene sequences could be observed, and power spectral densities of these periodicities were increased with evolution. These results suggest the existence of the internal rules in the occurrence of the synonymous and nonsynonymous substitutions in the sequences, the destabilization of the interaction between DNA and histone protein, and the stabilization of the chromatin structure, respectively. Moreover, 1/f(alpha) analysis of the power spectra (log-log plot) in the far long-range region (160 to 16,000 bp) suggested the increase in the self-similarity (the fractal structure) of DNA sequences with evolution. A general trend of the increase in a 3 bp periodicity with evolution might be functionally related to the CAG trinucleotide repeat diseases such as Huntington chorea, where a marked periodicity of 3 bp could be observed. Fourier transform analysis applied to a DNA sequence offers a great new avenue for extracting information on the evolution of a DNA sequence.

Theoretical calculations of thermal rate constants for the N( [formula omitted])+acetylene reaction

Variational transition-state theory calculations have been carried out for the N( 2 D )+C 2H 2 and C 2D 2 reactions using the results of ab initio molecular orbital calculations. Comparison between the calculated and experimental rate constants indicates that multiple surface coefficient is much larger than the value predicted from electronic degeneracy, meaning that non-adiabatic transitions are important for these reactions. We have calculated five doublet potential energy curves that asymptotically correlate to the N( 2 D )+C 2H 2 reactants in the long-range Van der Waals region, where the potential curves are close in energy. This result qualitatively suggests that non-adiabatic transitions effectively take place in the long-range region.

Experimental Born–Oppenheimer Potential for theX1Σ+Ground State of HeH+: Comparison with theAb InitioPotential

All literature on vibration–rotational and pure rotational transition energies for theX1Σ+state of4HeH+,3HeH+,4HeD+, and3HeD+have been employed in a direct least-squares fit of the radially dependent Hamiltonian. The Born–Oppenheimer potential is represented by a modified Lennard–Jones function that provides for correct behavior in the near dissociation long-range region. Only 19 adjustable parameters were required to represent the 166 measured transition energies, which are reproduced almost to within the measurement accuracies. The fitted potential and Born–Oppenheimer breakdown functions are shown to be in good agreement with the results ofab initiocalculations. The results are used to obtain high-order centrifugal distortion constants as well as level widths for quasi-bound levels.

Wave-packet dynamics of resonant x-ray Raman scattering: Excitation near the ClLII,IIIedge of HCl

A theory of radiative and nonradiative x-ray Raman scattering based on nuclear wave-packet dynamics is presented. The theory is evaluated with special emphasis on the cases when the intermediate and/or final state potentials are dissociative. Different ``one-step'' and ``two-step'' time-dependent wave-packet formalisms are proposed and evaluated, giving different interpretational content and computational efficiency. An interference between the molecular background and the narrow atomiclike contributions is predicted and evaluated. Due to this interference the atomiclike spectral feature manifests itself as a peak or as a spectral hole depending on the circumstances in terms of excitation energy, spectral width of incident radiation, and the form of the interatomic potentials. The counterintuitive situation may even arise that a narrow peak is formed by increasing the spectral photon width. The duration of the resonant x-ray Raman scattering influences in a qualitatively different manner the space distributions of the wave packets in the molecular and the dissociative domains, something that is crucial for the formation of the cross section profile. It is shown that the scattering cross section is proportional to the square of the core excited wave packet and inversely proportional to the derivative of the difference between core excited and final state potentials. The atomiclike profile is shown to consist of a Lorentzian inner part and red or blue wings which give direct information about the long-range regions of the potentials; red wings for diverging potentials, and blue for converging. A technique of mapping of the space distribution of the squared core excited wave packet and the interatomic potentials is suggested. The various features are demonstrated by an ab initio computational study of the resonant Auger spectra of the HCl molecule close to the Cl ${L}_{\mathrm{I}\mathrm{I},\mathrm{I}\mathrm{I}\mathrm{I}}$ edge.

The haplolethal region at the 16F gene cluster of Drosophila melanogaster: structure and function.

Extensive aneuploid analyses had shown the existence of a few haplolethal (HL) regions and one triplolethal region in the genome of Drosophila melanogaster. Since then, only two haplolethals, 22F1-2 and 16F, have been directly linked to identified genes, dpp and wupA, respectively. However, with the possible exception of dpp, the actual bases for this dosage sensitivity remain unknown. We have generated and characterized dominant-lethal mutations and chromosomal rearrangements in 16F and studied them in relation to the genes in the region. This region extends along 100 kb and includes at least 14 genes. The normal HL function depends on the integrity of a critical 4-kb window of mostly noncoding sequences within the wupA transcription unit that encodes the muscle protein troponin I (TNI). All dominant lethals are breakpoints within that window, which prevent the functional expression of TNI and other adjacent genes in the proximal direction. However, independent mutations in these genes result in recessive lethal phenotypes only. We propose that the HL at 16F represents a long-range cis regulatory region that acts upon a number of functionally related genes whose combined haploidy would yield the dominant-lethal effect.

From Long-Range Interaction to Solid-Body Contact Between Colloidal Surfaces During Forming

A simulation method based on the discrete element method (DEM) has been developed for studying the particle packing dynamics and for optimizing the colloidal forming processes. The DEM needs explicit functions for the computation. The explicit van der Waals interaction functions derived by Hamaker between two surfaces (or spheres) become infinite if the surface distance approach zero. This is a numerical singularity problem due to the continuum assumption in the Hamaker theory and is inconsistent with the physical reality. The analytical solutions obtained by using the modern Lifshitz’s theory and solution by incorporating the non-continuum theories (e.g. Lennard–Jones potential) are too complex to be applied for the DEM process simulation. During consolidation processes, the colloids move from the long-range interaction region into the solid-body contact with other colloids or with the boundaries. The long-range interaction were described by the DLVO theory. Meanwhile, the Johnson–Kendall–Roberts (JKR) theory took the adhesion energy (or surface energy) into account for describing the elastic solid-body contact. Both the Derjaguin approximation and the JKR theory based on the continuum assumption have been successfully applied to solve the transition (or numerical singularity) problem from the DLVO long-range interaction to the elastic JKR solid-body contact for the DEM simulation. Solving the transition/singularity problem is the first step for simulating the consolidation processes. In this numerical model, the adhesion energy, the elastic deformation, the hard sphere diameter and the compact Stern layer were considered. The shortest surface distance (without external load) is calculated at a distance where the JKR adhesion force is equal to the DLVO interaction force. The interactions between two spheres, between sphere and surface plane and between two different materials were shown. The DEM simulation results show that the particle-pile-up is an essential mechanism for the particles to get into solid-body contact in stabilized suspensions.

Analytical Hartree-Fock electron densities for singly charged cations and anions

The Hartree-Fock (HF) electron density has an important property that it is identical to the unknown exact density to the first order in the perturbation theory. We generate the spherically averaged HF electron density ρ(r) by using the numerical HF method for the singly charged 53 cations from Li+ to Cs+ and 43 anions from H− to I− in their ground state. The resultant density is then accurately fitted into an analytical function F(r), which is expressed by a linear combination of basis functions rniexp(−ζir). The present analytical approximation F(r) has the following properties: (1) F(r) is nonnegative, (2) F(r) is normalized, (3) F(r) reproduces the HF moments (k=−2 to +6), (4) F(0) is equal to ρ(0), (5) F′(0) satisfies the cusp condition and (6) F(r) has the correct exponential decay in the long-range asymptotic region. The present results together with our previous ones for neutral atoms provide a compilation of accurate analytical approximations of the HF electron densities for all the neutral and singly charged atoms with the number of electrons N≤54.

Exchange Energy on Alkali Diatomic Molecules: Period Effects

The exchange energy in the long-range near-dissociation region is analyzed for the ground electronic states of homo- and heteronuclear alkali diatomic molecules. The analysis is based on the use of the functional formAe−arto represent this exchange term. A period effect is observed in the values of both parameters and the exponent parameteraappears to approach an asymptotic limit for the heavier molecules. The results obtained in this study also suggest that some care must be taken in using even this function to represent the exchange energy.

Analytical Hartree-Fock electron densities for atoms He through Lr

The Hartree–Fock electron density has an important property that it is identical to the exact density to first order in the perturbation theory. For the neutral atoms from He (Z=2) to Lr (Z=103) in their ground state, we report an accurate analytical approximation F(r) to the spherically averaged electron density ρ(r) obtained by the numerical Hartree–Fock method. The present density function F(r) is expressed by a linear combination of reasonable number (not more than 30) of basis functions rni exp(−ζir), and has the following properties: (i) F(r) is nonnegative, (ii) F(r) is normalized, (iii) F(r) reproduces the Hartree–Fock moments (k=−2 to +6), (iv) F(0) is equal to ρ(0), (v) F′(0) satisfies the cusp condition, and (vi) F(r) has the correct exponential decay in the long-range asymptotic region.

Magnetic properties and magnetic phase diagram of the frustrated Co1-xFexPt3 compounds.

The investigation of the magnetic properties of the pseudobinary ${\mathrm{Co}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Pt}}_{3}$ L${1}_{2}$ ordered compounds resulting from alloying the ferromagnet ${\mathrm{CoPt}}_{3}$ and the frustrated antiferromagnet ${\mathrm{FePt}}_{3}$ is reported. dc susceptibilities and zero field cooled and field cooled magnetizations as a function of temperature and field (0--35 T) have been investigated. On the Co-rich side (x0.6), the compounds display a long-range ferromagnetic order characterized by the occurrence of two reentrant spin-glass phases (or mixed magnetic phases) at low temperature and magnetic field starting at very low iron concentration. This ferromagnetic region is closed by a multicritical point located around x=0.55 and T=120 K. On the iron-rich side, an antiferromagnetic region with two antiferromagnetic [1/21/20] and [1/200] structures is observed for 1\ensuremath{\ge}x\ensuremath{\gtrsim}0.8. Beyond 0.8 the basic antiferromagnetic order [1/21/20] changes progressively into a spin-glass ordering and the less stable one [1/200] persists at low temperature up to Fe concentrations as high as 0.6. Although the complex behavior of the iron-rich side in the intermediate region is not totally elucidated, a tentative phase diagram is proposed and discussed comparatively with the previously determined (Fe-Mn)${\mathrm{Pt}}_{3}$ and (Co-Mn)${\mathrm{Pt}}_{3}$ phase diagrams. The occurrence of a spin-glass phase that separates the long-range ferromagnetic region from the antiferromagnetic one is specific to the (Co-Fe)${\mathrm{Pt}}_{3}$ system in agreement with theoretical models. The (Co-Fe)${\mathrm{Pt}}_{3}$ appears as the most frustrated among the three systems considered. \textcopyright{} 1996 The American Physical Society.

Observation and Analysis of theA1[formula]State of6Li2fromv= 0 to the Dissociation Limit

Interacting rovibrational levels of theF1[formula]andE1[formula]states of6Li2have been excited via the optical–optical double-resonance process, (F,E)1[formula]←A1[formula]←X1[formula]. The resulting fluorescence in the region 7000–11000 cm−1, which has been examined at high resolution with a Fourier transform spectrometer, was found to consist of transitions to very high levels of theA1[formula]state. These are only observed when there is an interaction between theFstate level and anEstate level above the shelf in the potential curve, and occur when either level is excited. Levels up tov= 84, ∼2.5 cm−1below the dissociation limit, have been assigned and the data extend well into the long-range region, up toR∼ 51 Å. An analysis of the data in this region has yielded the following long-range parameters for theA1Σ+state:D0= 9214.68(5) cm−1,De= 9352.27(5) cm−1,C3= 3.580(10) × 105cm−1·Å3,C6= 1.0(2) × 107cm−1·Å6. Based on the results of the analysis of theA1[formula]state data, a value ofDe(X1[formula]) = 8517.03(05) cm−1has been calculated for the dissociation energy of the ground state of6Li2.

Temperature-dependent Ruderman-Kittel-Kasuya-Yosida interaction.

We develop a method that provides an analytical expression of the free-electron spin susceptibility for arbitrary temperature. The result can be further reduced by using the low-temperature approximation, which shows that the oscillation decays exponentially as exp(-\ensuremath{\pi}${\mathit{T}}^{\mathcal{'}}$${\mathit{k}}_{\mathit{Fr}}$) in the long-range limit, and the wave number of the oscillation varies as ${\mathit{k}}_{0}$\ensuremath{\sim}${\mathit{k}}_{\mathit{F}}$[1-(${\mathrm{\ensuremath{\pi}}}^{2}$/12)${\mathit{T}}^{{\mathcal{'}}^{}2}$], where ${\mathit{T}}^{\mathcal{'}}$ is the normalized temperature with respect to the Fermi energy. The result contradicts what Darby has proposed, especially in the long-range region. On the other hand, in the short-range region, where the Sommerfeld expansion method is valid, numerical study shows that Darby's result agrees with ours fairly well.

A non-directed, hydroxylamine-generated suppressor mutation in the P3 pairing region of the bacteriophage T4 td intron partially restores self-splicing capability.

Hydroxylamine (HA) mutagenesis of an HA-induced splicing-defective bacteriophage T4 td intron mutant with a mutation in the intron P3 RNA pairing region was used to generate pseudorevertants. Because HA can only cause GC to AT transitions, the original mutant (H104A) could not undergo true reversion, yet the compensatory mutation on the opposite side of the P3 helix, which was complementary to the original H104A mutation, could occur. A pseudorevertant was isolated that contained both the original H104A mutation and the compensatory mutation HS9. By phenotypic and molecular genetic criteria, this double mutant (H104A-HS9) was shown to be able to undergo significant RNA splicing, thus confirming the existence and functional importance of the long-range P3 pairing region in this phage intron. The second-site suppressor mutation (HS9) was isolated by phage cross and also exhibited some self-splicing ability. A correlation exists between the strength of P3 helix Watson-Crick base pairing and the apparent level of splicing when wild-type, H104A, HS9, and H104A-HS9 are compared. This suggests that the primary role of the P3 RNA pairing region in the T4 td intron is structural in contributing to the critical RNA secondary structure.

Natural energy decomposition analysis: An energy partitioning procedure for molecular interactions with application to weak hydrogen bonding, strong ionic, and moderate donor–acceptor interactions

We present a procedure for partitioning the Hartree–Fock self-consistent-field (SCF) interaction energy into electrostatic, charge transfer, and deformation components. The natural bond orbital (NBO) approach of Weinhold and co-workers is employed to construct intermediate supermolecule and fragment wave functions that satisfy the Pauli exclusion principle, thereby avoiding the principal deficiency of the popular Kitaura–Morokuma energy decomposition scheme. The function counterpoise method of Boys and Bernardi enters the procedure naturally, providing an estimate of basis set superposition error (BSSE). We find that the energy components exhibit little basis set dependence when BSSE is small. Applications are presented for several representative molecular and ion complexes: the weak hydrogen bond of the water dimer, the strong ionic interaction of the alkali metal hydrides, and the moderate donor–acceptor interactions of BH3NH3 and BH3CO. Electrostatic interaction dominates the long-range region of the potential energy surface and charge transfer is strongly stabilizing for fragments within van der Waals contact. The repulsive interaction in the short range region of the potential arises from deformation as the fragment wave functions distort to avoid significant interpenetration.