Ab initio investigation of intermolecular interactions in solid benzene

A computational strategy for the evaluation of the crystal lattice constants and cohesive energy of the weakly bound molecular solids is proposed. The strategy is based on the high level ab initio coupled-cluster determination of the pairwise additive contribution to the interaction energy. The zero-point-energy correction and non-additive contributions to the interaction energy are treated using density functional methods. The experimental crystal lattice constants of the solid benzene are reproduced, and the value of 480 meV/molecule is calculated for its cohesive energy

Three-point functions of conserved currents in 3D CFT: general formalism for arbitrary spins

We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we use a computational formalism to analyse the general structure of $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where $J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ are conserved currents with spins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent even structures, and one odd structure, subject to a set of triangle inequalities. We also analyse the structure of three-point functions involving higher-spin currents and fundamental scalars and spinors.Comment: 56 pages; v2: minor edits, references adde

Three-point functions of conserved currents in 4D CFT: general formalism for arbitrary spins

We analyse the general structure of the three-point functions involving conserved higher-spin currents $J_{s} := J_{\alpha(i) \dot{\alpha}(j)}$ belonging to any Lorentz representation in four-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we computationally analyse the general structure of three-point functions $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$ for arbitrary spins and propose a classification of the results. For bosonic vector-like currents with $i=j$, it is known that the number of independent conserved structures is $2 \min (s_{i}) + 1$. For the three-point functions of conserved currents with arbitrarily many dotted and undotted indices, we show that in many cases the number of structures deviates from $2 \min (s_{i}) + 1$.Comment: 40 pages. arXiv admin note: text overlap with arXiv:2210.1313

Three-point functions of conserved supercurrents in 3D N=1\mathcal{N}=1 SCFT: general formalism for arbitrary superspins

We analyse the general structure of the three-point functions of conserved higher-spin supercurrents in 3D, $\mathcal{N}=1$ superconformal field theory. It is shown that supersymmetry imposes additional restrictions on correlation functions of conserved higher-spin currents. We develop a manifestly supersymmetric formalism to compute the three-point function $\langle \mathbf{J}^{}_{s_{1}} \mathbf{J}'_{s_{2}} \mathbf{J}''_{s_{3}} \rangle$, where $\mathbf{J}^{}_{s_{1}}$, $\mathbf{J}'_{s_{2}}$ and $\mathbf{J}''_{s_{3}}$ are conserved higher-spin supercurrents with superspins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). Using a computational approach limited only by computer power, we analytically impose the constraints arising from the superfield conservation equations and symmetries under permutations of superspace points. Explicit solutions for three-point functions are presented and we provide a complete classification of the results for $s_{i} \leq 20$; the pattern is very clear, and we propose that our classification holds for arbitrary superspins. We demonstrate that Grassmann-even three-point functions are fixed up to one parity-even structure and one parity-odd structure, while Grassmann-odd three-point functions are fixed up to a single parity-even structure. The existence of the parity-odd structure in the Grassmann-even correlation functions is subject to a set of triangle inequalities in the superspins. For completeness, we also analyse the structure of three-point functions involving conserved higher-spin supercurrents and scalar superfields.Comment: 54 pages; v2: minor corrections, references added. arXiv admin note: substantial text overlap with arXiv:2210.1313

Grassmann-odd three-point functions of conserved supercurrents in 3D N=1\mathcal{N}=1 SCFT

We consider the analytic construction of three-point functions of conserved higher-spin supercurrents in three-dimensional $\mathcal{N}=1$ superconformal field theory which are Grassmann-odd in superspace. In particular, these include the three-point functions of the supercurrent and flavour currents, which contain the three-point functions of the energy-momentum tensor and conserved vector currents at the component level. We present an analytic proof for arbitrary superspins that these correlators do not possess a parity-violating contribution. We also prove that the parity-even contribution is unique, and exists (under an assumption that is well supported by the computational approach of arXiv:2302.00593) for arbitrary superspins. The construction of the parity-even sector is shown to reduce to solving a system of linear homogeneous equations with a tri-diagonal matrix of co-rank one, which we solve explicitly for arbitrary superspins.Comment: 33 page

Time-dependent density functional theory calculation of van der Waals coefficient of sodium clusters

In this paper we employ all-electron \textit{ab-initio} time-dependent density functional theory based method to calculate the long range dipole-dipole dispersion coefficient (van der Waals coefficient) $C_{6}$ of sodium atom clusters containing even number of atoms ranging from 2 to 20 atoms. The dispersion coefficients are obtained via Casimir-Polder relation. The calculations are carried out with two different exchange-correlation potentials: (i) the asymptotically correct statistical average of orbital potential (SAOP) and (ii) Vosko-Wilk-Nusair representation of exchange-correlation potential within local density approximation. A comparison with the other theoretical results has been performed. We also present the results for the static polarizabilities of sodium clusters and also compare them with other theoretical and experimental results. These comparisons reveal that the SAOP results for C_{6} and static polarizability are quite accurate and very close to the experimental results. We examine the relationship between volume of the cluster and van der Waals coefficient and find that to a very high degree of correlation C_{6} scales as square of the volume. We also present the results for van der Waals coefficient corresponding to cluster-Ar atom and cluster-N_{2} molecule interactions.Comment: 22 pages including 6 figures. To be published in Journal of Chemical Physic

Are There Any Type 2 QSOs? The Case of AXJ0341.4-4453

The X-ray source AXJ0341.4-4453 was described by Boyle et al. as a Type 2 AGN at z = 0.672 based on the absence of broad emission lines in the observed wavelength range 4000-7000 Angstroms. We obtained a new spectrum of AXJ0341.4-4453 extending to 9600 Angstroms which reveals broad Balmer lines and other characteristics of Seyfert 1 galaxies. The FWHM of broad H-beta is at least 1600 km/s, while [O III]5007 has FWHM = 730 km/s. The flux ratio [O III]5007/H-beta = 1. Thus, AXJ0341.4-4453 is by definition a narrow-line Seyfert 1 galaxy, or perhaps a moderately reddened Seyfert 1 galaxy, but it is not a Type 2 QSO. Although examples of the latter have long been sought, particularly in connection with the problem of the X-ray background, there is still virtually no evidence for the existence of any Type 2 QSO among X-ray selected samples.Comment: 4 pages, 3 figures, to appear in MNRA