Negative Quadrupole Moment Research Articles

Periodic DFT computation of rotational barriers for linear molecules in zeolites: Validation via zero-point energies and isotopic heat difference values of adsorbed H2/D2

A climbing image nudged elastic band (cNEB) algorithm was applied on the basis of density functional theory (DFT) calculations of the rotational barriers of eight linear molecules (H2, N2, O2, CO, CO2, NO, N2O, C2H2) adsorbed in NaY and NaCaY periodic zeolite models at the MeII cation sites (the Na or Ca metal cation in the SII site) located near the 6R windows. A specific approach is applied for molecules with positive quadrupole (H2, C2H2) and small negative quadrupole (3O2) moments while applying cNEB. The obtained T-geometry relative to the cation is the most frequent case for H2 adsorption in cationic form sieves and metalorganic frameworks (MOFs). The computed barriers for the T- and other linear (L) orientations are in good correlation with the quadrupole moments taken from literature irrespective of the dipole values (CO, NO, N2O). In the case of NaY, the Al distribution per 6R sites is also discussed which allowed finding particular favorite adsorption sites. The calculated zero-point energies relative to the obtained rotational barriers regarding the H2 - D2 pair result in a qualitative agreement with the experimental isotopic difference in the H2/D2 adsorption heats in NaY which ultimately lead to the H2/D2 separation coefficient.

The Effect of the Molecular Dipole and Quadrupole moments on Ion-Molecule Reaction Rates near 0 K

We review the results of our recent experimental and theoretical studies of gas-phase ion-molecule reactions involving the He+ ion at low collision energies (Ecoll), in the kB⋅(0 – 40) K range. To avoid heating of the ions by stray electric fields, the reactions are studied within the orbit of a Rydberg electron. We reach collision energies down to ~0 K by employing a merged-beam setup. In the case of a molecule with a dipole moment (e.g., ammonia), we observe a strong enhancement of the measured reaction yield with decreasing Ecoll. This enhancement is attributed to rotational states which experience linear negative Stark shifts in the electric field of the ion. When the molecule has no dipole moment but a negative quadrupole moment (e.g., N2), we observe a suppression of the total reaction yield at the lowest collision energy. Our results are interpreted with the aid of an adiabatic-channel model.

Multipole-moment effects in ion-molecule reactions at low temperatures: part II - charge-quadrupole-interaction-induced suppression of the He+ + N2 reaction at collision energies below kB·10 K.

We report on an experimental and theoretical investigation of the He+ + N2 reaction at collision energies in the range between 0 and kB·10 K. The reaction is studied within the orbit of a highly excited Rydberg electron after merging a beam of He Rydberg atoms (He(n), n is the principal quantum number), with a supersonic beam of ground-state N2 molecules using a surface-electrode Rydberg–Stark decelerator and deflector. The collision energy Ecoll is varied by changing the velocity of the He(n) atoms for a fixed velocity of the N2 beam and the relative yields of the ionic reaction products N+ and N2+ are monitored in a time-of-flight mass spectrometer. We observe a reduction of the total reaction-product yield of ∼30% as Ecoll is reduced from ≈kB·10 K to zero. An adiabatic capture model is used to calculate the rotational-state-dependent interaction potentials experienced by the N2 molecules in the electric field of the He+ ion and the corresponding collision-energy-dependent capture rate coefficients. The total collision-energy-dependent capture rate coefficient is then determined by summing over the contributions of the N2 rotational states populated at the 7.0 K rotational temperature of the supersonic beam. The measured and calculated rate coefficients are in good agreement, which enables us to attribute the observed reduction of the reaction rate at low collision energies to the negative quadrupole moment, Qzz, of the N2 molecules. The effect of the sign of the quadrupole moment is illustrated by calculations of the rotational-state-dependent capture rate coefficients for ion–molecule reactions involving N2 (negative Qzz value) and H2 (positive Qzz value) for |J, M〉 rotational states with J ≤ 5 (M is the quantum number associated with the projection of the rotational angular momentum vector J⃑ on the collision axis). With decreasing value of |M|, J⃑ gradually aligns perpendicularly to the collision axis, leading to increasingly repulsive (attractive) interaction potentials for diatomic molecules with positive (negative) Qzz values and to reaction rate coefficients that decrease (increase) with decreasing collision energies.

Localizing the Shape Transition in Neutron-Deficient Selenium.

Neutron-deficient selenium isotopes are thought to undergo a rapid shape change from a prolate deformation near the line of beta stability towards oblate deformation around the line of N=Z. The point at which this shape change occurs is unknown, with inconsistent predictions from available theoretical models. A common feature in the models is the delicate nature of the point of transition, with the introduction of even a modest spin to the system sufficient to change the ordering of the prolate and oblate configurations. We present a measurement of the quadrupole moment of the first-excited state in radioactive ^{72}Se-a potential point of transition-by safe Coulomb excitation. This is the first low-energy Coulomb excitation to be performed with a rare-isotope beam at the reaccelerated beam facility at the National Superconducting Cyclotron Laboratory. By demonstrating a negative spectroscopic quadrupole moment for the first-excited 2^{+} state, it is found that any low-spin shape change in neutron-deficient selenium does not occur until ^{70}Se.

Multiple shadows from distorted static black holes

We study the local shadow of the Schwarzschild black hole with a quadrupole distortion and the influence of the external gravitational field on the photon dynamics. The external matter sources modify the light ring structure and lead to the appearance of multiple shadow images. In the case of negative quadrupole moments we identify the most prominent mechanism causing multiple shadow formation. Furthermore, we obtain a condition under which this mechanism can be realized. This condition depends on the quadrupole moment, but also on the position of the observer and the celestial sphere.

Reorientation-effect measurement of the〈21+∥E2̂∥21+〉matrix element in10Be

The highly-efficient and segmented TIGRESS gamma-ray spectrometer at TRIUMF has been used to perform a reorientation-effect Coulomb-excitation study of the 2(1)(+) state at 3.368 MeV in Be-10. This is the first Coulomb-excitation measurement that enables one to obtain information on diagonal matrix elements for such a high-lying first excited state from gamma-ray data. With the availability of accurate lifetime data, a value of -0.110 +/- 0.087 eb is determined for the diagonal matrix element, which assuming the rotor model, leads to a negative spectroscopic quadrupole moment of Q(S)(2(1)(+)) = -0.083 +/- 0.066 eb. This result is in agreement with both no-core shell-model calculations performed in this work with the CD-Bonn 2000 two-nucleon potential and large shell-model spaces, and Green's function Monte Carlo predictions with two-plus three-nucleon potentials.

A Hirshfeld-I interpretation of the local moment composition of the quadrupole moments of the halogenated acetylenes FCCF, ClCCCl, BrCCBr, and ICCI

We have interpreted the molecular quadrupole moments of the di-halogenated acetylenes, XCCX, where X=F, Cl, Br, and I as well as the parent HCCH in terms of the in situ atomic moments (charge, dipole and quadrupole) calculated with the Hirshfeld-I partitioning of the electron density. The conclusion from this analysis is that the SCF and CCSD molecular densities are similar and predict comparable atomic densities and in situ moments. We find that the σ charge on carbon decreases monotonically with the electronegativity difference between carbon and the substituent X, being positive for X=F, Cl and Br and going negative for X=I and H. The π charge on carbon is negative for all of the halogens and positive for H, reflecting the opportunity for back donation in the halogens and the lack thereof in H. The contribution of the three localized moments to the molecular quadrupole moments of ClCCCl, HCCH, BrCCBr and ICCI are all positive resulting in positive quadrupole moments while the negative quadrupole moment of FCCF is due to cancelation between the large negative contribution of the charge and the positive induced dipole, quadrupole terms. The HI charges are significantly different from the point charges obtained from fitting the molecular quadrupole moments. Additionally we show that the computed in situ atomic quadrupoles may be used to assign an electronic configuration to the in situ atoms.

Quadrupole-bound anions: Efficacy of positive versus negative quadrupole moments

A pseudopotential method is utilized to study the critical stability of model anions formed by long-range quadrupolar molecular potentials. Results indicate that critical quadrupole moments of simple point-charge triads do not serve well as predictors of real quadrupole-bound anions of systems with negative moments.

Can Electron-Rich π Systems Bind Anions?

In general, anion-π interactions exist between anions and aromatics with a positive quadrupole moment. The interaction between anions and aromatics with a negative quadrupole moment is expected to be unstable due to Coulombic repulsion. However, here we investigated the cases of aromatics with a negative quadrupole moment such as electron-rich alkyl/alkenyl/alkynyl-substituted benzenes and triphenylene, which interact with halides. Favorable binding was demonstrated with coupled cluster theory with singles, doubles, and perturbative triples excitations [CCSD(T)] at the complete basis set (CBS) limit. Stability increases with chain length, unsaturation, and halogenation. Energy decomposition analysis based on symmetry adapted perturbation theory (SAPT) shows that electrostatic repulsion is overcome by induction effects arising from the alkyl substituents.

Arene−Cation Interactions of Positive Quadrupole Moment Aromatics and Arene−Anion Interactions of Negative Quadrupole Moment Aromatics

Arene−Cation Interactions of Positive Quadrupole Moment Aromatics and Arene−Anion Interactions of Negative Quadrupole Moment Aromatics

Pseudoscalar and vector meson form factors from lattice QCD

We present a study of the pseudoscalar and vector meson form factors, calculated using the fat-link irrelevant clover (FLIC) action in the framework of quenched lattice QCD. Of particular interest is the determination of a negative quadrupole moment, indicating that the $\ensuremath{\rho}$ meson is not spherically symmetric.

Van der Waals Complexes of Small Molecules with Benzenoid Rings: Influence of Multipole Moments on Their Mutual Orientation

Intermolecular interaction between some small molecules (HF, H2O, NH3, and CH4) and certain benzenoid ring systems (benzene, hexafluorobenzene, and 1,3,5-trifluorobenzene) has been investigated in detail at MP2 level of theory using 6-311++G** basis set, and the results are corrected for basis set superposition error (BSSE). Vibrational frequencies were calculated for all the geometries at the same level of theory and basis sets to ensure that the geometries obtained correspond to true minima. In the complexes with benzene, which has a large negative quadrupole moment, the preferred geometry has the electropositive end of the small molecule (HF, H2O, and NH3) pointing toward the ring and the corresponding interaction energies are -3.24, -2.43, and -1.57 kcal/mol, respectively. For the complexes with hexafluorobenzene which has a large positive quadrupole moment, the most stable geometries are those in which the electropositive end of HF, H2O, and NH3 points away from the ring and the corresponding interaction energies are -1.59, -2.73, and -3.14 kcal/mol, respectively. Methane, which has neither a dipole nor a quadrupole moment, is weakly bound and is oriented differently in different systems. 1,3,5-Trifluorobenzene has a negligible quadrupole moment, and the complexes with small molecules are stabilized by cyclic hydrogen bonding. Although the point dipole-quadrupole and point quadrupole-quadrupole interactions present in these complexes account qualitatively for the preferred orientations, distributed multipole moments of the constituent atoms are found to give a quantitative description of the interaction in such complexes.

Arene−Cation Interactions of Positive Quadrupole Moment Aromatics and Arene−Anion Interactions of Negative Quadrupole Moment Aromatics

Intermolecular interactions involving aromatic pi-electron density are widely believed to be governed by the aromatic molecular quadrupole moment, Theta(zz). Arene-cation binding is believed to occur primarily with negative Theta(zz) aromatics, and arene-anion binding is believed to occur largely with positive Theta(zz) aromatics. We have performed quantum mechanical computations that show the cation binding of positive Theta(zz) aromatics and the anion binding of negative Theta(zz) aromatics is quite common in the gas phase. The pi-electron density of hexafluorobenzene, the prototypical positive Theta(zz ) aromatic (experimental Theta(zz) = 9.5 +/- 0.5 DA), has a Li+ binding enthalpy of -4.37 kcal/mol at the MP2(full)/6-311G**level of theory. The RHF/6-311G** calculated Theta(zz) value of 1,4-dicyanobenzene is +11.81 DA, yet it has an MP2(full)/6-311G** Li+ binding enthalpy of -12.65 kcal/mol and a Na+ binding enthalpy of -3.72 kcal/mol. The pi-electron density of benzene, the prototypical negative Theta(zz) aromatic (experimental Theta(zz) = -8.7 +/- 0.5 DA), has a F- binding enthalpy of -5.51 kcal/mol. The RHF/6-311G** calculated Theta(zz) of C6H2I4 is -10.45 DA, yet it has an MP2(full)/6-311++G** calculated F- binding enthalpy of -20.13 kcal/mol. Our results show that as the aromatic Theta(zz) value increases the cation binding enthalpy decreases; a plot of cation binding enthalpies versus aromatic Theta(zz) gives a line of best of fit with R2 = 0.778. No such correlation exists between the aromatic Theta(zz) value and the anion binding enthalpy; the line of best fit has R2 = 0.297. These results are discussed in terms of electrostatic and polarizability contributions to the overall binding enthalpies.

Predicted electric field near small superconducting ellipsoids.

We predict the existence of large electric fields near the surface of superconducting bodies of ellipsoidal shape of dimensions comparable to the penetration depth. The electric field is quadrupolar in nature with significant corrections from higher order multipoles. Prolate (oblate) superconducting ellipsoids are predicted to exhibit fields consistent with negative (positive) quadrupole moments, reflecting the fundamental charge asymmetry of matter.

Linear Dichroism in X-Ray Absorption and Orbital Orderings

Linear Dichroism in X-Ray Absorption and Orbital Orderings

Intrinsic quadrupole moment of the nucleon

We address the question of the intrinsic quadrupole moment Q_0 of the nucleon in various models. All models give a positive intrinsic quadrupole moment for the proton. This corresponds to a prolate deformation. We also calculate the intrinsic quadrupole moment of the Delta(1232). All our models lead to a negative intrinsic quadrupole moment of the Delta corresponding to an oblate deformation.

Excitation of nuclear anharmonic vibrations in heavy-ion fusion reactions

We discuss the effects of multi-phonon excitations on heavy-ion fusion reactions at energies near and below the Coulomb barrier, focusing especially on the role of anharmonicities. We carry out a systematic study of those effects on the excitation function of the fusion cross section and on the fusion barrier distribution, by using the vibrational limit of the interacting boson model. We also analyze the recently measured high-precision data of the $^{16}$O + $^{148}$Sm fusion reaction with this model and discuss the anharmonic properties of the quadrupole as well as the octupole vibrations in $^{148}$Sm. Negative and positive static quadrupole moments are deduced for the first 2$^+$ and 3$^-$ states in $^{148}$Sm, respectively. It is shown that the fusion barrier distribution strongly depends on the sign of the quadrupole moments, suggesting that subbarrier fusion reactions offer an alternative method to extract the static quadrupole moments of phonon states in spherical nuclei.

Role of Anharmonicities of Nuclear Vibrations in Fusion Reactions at Sub-barrier Energies

We discuss the effects of double octupole and quadrupole phonon excitations in $^{144}$Sm on fusion reactions between $^{16}$O and $^{144}$Sm at subbarrier energies. The effects of anharmonicities of the vibrational states are taken into account by using the $sdf$-interacting boson model. We compare the results with those in the harmonic limit to show that anharmonicities play an essential role in reproducing the experimental fusion barrier distribution. From the analysis of the high quality fusion data available for this system, we deduce negative static quadrupole moments for both the first 2$^{+}$ and 3$^{-}$ states in $^{144}$Sm. This is the first time that the sign of static quadrupole moments of phonon states in a spherical nucleus is determined from the data of subbarrier fusion reactions.

Comment on "Large-space shell-model calculations for light nuclei"

In a recent publication Zheng, Vary, and Barrett reproduced the negative quadrupole moment of Li-6 and the low-lying positive-parity states of He-5 by using a no-core shell model. In this Comment we question the meaning of these results by pointing out that the model used is inadequate for the reproduction of these properties.

Particle-octupole coupling in N=83 nuclei from neutron transfer studies with polarized deuterons

Neutron pick-up measurements have identified the s 1 2 and d 3 2 holes states in 147Gd, 145Sm, and 143Nd. The results also locate the 1 2 + and 3 2 + members of the v f 7 2 ×3 − septuplet via their admixtures from these hole states. Additional energy perturbations of the septuplet result largely from a negative quadrupole moment of the octupole phonon, with a Z-dependence consistent with the microscopic structure of the 3 − excitation in the N=82 nuclei.