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The soft function in non-abelian gauge theories exponentiate, and their logarithms can be organised in terms of the collections of Feynman diagrams called Cwebs. The colour factors that appear in the logarithm are controlled by the web mixing matrices. Direct construction of the diagonal blocks of Cwebs using the new concepts of Normal ordering, basis Cweb and Fused-Web was recently carried out in [1]. In this article we establish correspondence between the boomerang webs introduced in [2] and non-boomerang Cwebs. We use this correspondence together with Uniqueness theorem and Fused web formalism introduced in [1] to obtain the diagonal blocks of four general classes of Cwebs to all orders in perturbation theory which also cover all the four loop Boomerang Cwebs connecting four Wilson lines. We also fully construct the mixing matrix of a special Cweb to all orders in perturbation theory. [ABSTRACT FROM AUTHOR]

The correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of the collections of Feynman diagrams called Cwebs. The colour factors that appear in the logarithm correspond to completely connected diagrams and are determined by the web mixing matrices. In this article we introduce several new concepts: (a) Normal ordering of the diagrams of a Cweb, (b) Fused-Webs (c) Basis and Family of Cwebs. We use these ideas together with a Uniqueness theorem that we prove to arrive at an understanding of the diagonal blocks, and several null matrices that appear in the mixing matrices. We demonstrate using our formalism that, once the basis Cwebs present upto order α s n are determined, the number of exponentiated colour factors for several classes of Cwebs starting at order α s n + 1 can be predicted. We further provide complete results for the mixing matrices, to all orders in perturbation theory, for two special classes of Cwebs using our framework. [ABSTRACT FROM AUTHOR]

More than 47,000 articles have been published in the area of Metal-Organic Framework since its seminal discovery in 1995, exemplifying the intense research carried out in this short span of time. Among other applications, gas adsorption and storage are perceived as central to the MOFs research, and more than 10,000 MOFs structures are reported to date to utilize them for various gas storage/separation applications. Molecular modeling, particularly based on density functional theory, played a key role in (i) understanding the nature of interactions between the gas and the MOFs geometry (ii) establishing various binding pockets and relative binding energies, and (iii) offering design clues to improve the gas uptake capacity of existing MOF architectures. In this review, we have looked at various MOFs that are studied thoroughly using DFT/periodic DFT (pDFT) methods for CO2, H2, O2, and CH4 gases to provide a birds-eye-view on how various exchange-correlation functionals perform in estimating the binding energy for various gases and how factors such as nature of the (i) metal ion, (ii) linkers, (iii) ligand, (iv) spin state and (v) spin-couplings play a role in this process with selected examples. While there is still room for improvement, the rewards offered by the molecular modelling of MOFs were already substantial that we advocate experimental and theoretical studies to go hand-in-hand to undercut the trial-and-error approach that is often perceived in the selection of MOFs and gas partners in this area. The importance of density functional theory-based molecular modeling studies in offering design clues to improve the gas adsorption and storage capacity of existing MOF architectures is discussed here. The use of DFT-based investigation in conjunction with experimental synthesis is an imperative tool in designing new-generation MOFs with enhanced uptake capacity. [ABSTRACT FROM AUTHOR]

SrF, being a laser-coolable molecule, can be an interesting system for spectroscopic tests of fundamental physics. We present an electronic structure study of this molecule within the four-component relativistic coupled-cluster singles and doubles (RCCSD) framework and employ the RCCSD-based methods to compute its molecular-frame dipole moment and core properties such as hyperfine structure coupling constant and molecular P, T-odd electronic structure parameters that are of great importance for the high-precision tests of fundamental physics. The impact of basis set size, Hamiltonian and nuclear model on the property calculation of SrF is also investigated. The computed results are in good agreement with the available experimental values. The present study shows that the SrF molecule could be useful for high-precision molecular experiments to explore physics beyond the Standard Model of elementary particles. [ABSTRACT FROM AUTHOR]