Search results for "Coupling constant"
showing 10 items of 262 documents
Process-independent strong running coupling
2016
We unify two widely different approaches to understanding the infrared behaviour of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realised via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running-coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann--Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be…
The effect of interactions on Bose-Einstein condensation in a quasi two-dimensional harmonic trap
1999
A dilute bose gas in a quasi two-dimensional harmonic trap and interacting with a repulsive two-body zero-range potential of fixed coupling constant is considered. Using the Thomas-Fermi method, it is shown to remain in the same uncondensed phase as the temperature is lowered. Its density profile and energy are identical to that of an ideal gas obeying the fractional exclusion statistics of Haldane. PACS: ~03.75.Fi, 05.30.Jp, 67.40.Db, 05.30.-d
Importance of Triples Contributions to NMR Spin–Spin Coupling Constants Computed at the CC3 and CCSDT Levels
2016
We present the first analytical implementation of CC3 second derivatives using the spin-unrestricted approach. This allows, for the first time, the calculation of nuclear spin–spin coupling constants (SSCC) relevant to NMR spectroscopy at the CC3 level of theory in a fully analytical manner. CC3 results for the SSCCs of a number of small molecules and their fluorine substituted derivatives are compared with the corresponding coupled cluster singles and doubles (CCSD) results obtained using specialized basis sets. For one-bond couplings the change when going from CCSD to CC3 is typically 1–3%, but much higher corrections were found for 1JCN in FCN, 15.7%, and 1JOF in OF2, 6.4%. The changes v…
A Combined Experimental and Theoretical Study on the Magnetic Properties of a Family of Bis(μ‐phenoxido)dicopper(II) Complexes Bearing ω‐[Bis(2‐hydro…
2009
Five new neutral bis(μ-phenoxido)dicopper(II) complexes, [Cu2(μ-HL1)2]·3EtOH·H2O (1), [Cu2(μ-HL2)2]·1.65H2O (2), [Cu2(μ-HL3)2(μ-H2O)] (3), [Cu2(μ-HL4)2] (4) and [Cu2(μ-HL5)2(μ-H2O)] (5), were prepared from a family of ω-[bis(2-hydroxy-3,5-dimethylbenzyl)amino]alkan-1-ol ligands (H3L1–H3L5 derived from 2-aminoethanol, 3-aminopropanol, 4-aminobutanol, 5-aminopentanol and 6-aminohexanol, respectively) bearing a [O,N,O,O′] donor set. In complexes 3 and 5, there is also a bridging water molecule between the metallic centres. The copper(II) coordination planes of all these complexes form a roof-like structure (the bridging O atoms are located at the top of the roof). The structural differences fo…
Convergence of nuclear magnetic shieldings and one‐bond 1J(11 B 1H) indirect spin–spin coupling constants in small boron molecules
2018
Self‐consistent field Hartree–Fock (SCF‐HF), density functional theory (B3LYP, KT1, KT2, and KT3), and coupled‐cluster calculations of the nuclear magnetic shielding constants of BH and BH3 molecules have been conducted to characterize the convergence of individual results obtained with correlation‐ and polarization‐consistent basis sets. The individual 11B and 1H NMR parameters were estimated in the complete basis set limit and compared with benchmark literature results. The SCF‐HF and density functional theory B3LYP predicted boron shieldings and shielding anisotropies of BH significantly differed from the results obtained by coupled‐cluster with single, double, and perturbative treatment…
H2 O, H2 , HF, F2 and F2 O nuclear magnetic shielding constants and indirect nuclear spin-spin coupling constants (SSCCs) in the BHandH/pcJ-n and BHa…
2009
Good performance of segmented contracted basis sets XZP, where X = D, T, Q and 5, for obtaining H(2)O, H(2), HF, F(2) and F(2)O nuclear isotropic shielding constants in the BHandH Kohn-Sham basis set limit was shown. The results of two- and three-parameter complete basis set limit extrapolation schemes were compared with experimental results, earlier literature data and benchmark ab initio results. Similar convergence patterns of shieldings obtained from calculations using general purpose XZP basis sets and from polarization-consistent basis sets pcS-n and pcJ-n, where n = 0, 1, 2, 3 and 4, designed to accurately predict magnetic properties were observed. On the contrary, the SSCCs were mor…
Basis Set Convergence of Indirect Spin-Spin Coupling Constants in the Kohn-Sham Limit for Several Small Molecules
2012
The performance of more than 40 density functionals in predicting indirect spin-spin coupling constants (SSCCs) in the Kohn-Sham basis set limit was tested. For comparison, similar calculations were performed using the RHF, SOPPA, SOPPA(CC2), and SOPPA(CCSD) methods, and the results were estimated toward the complete basis set (CBS) limit. The SSCCs of nine small molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6), and C(6)H(6)) were calculated using the dedicated Jensen pcJ-n polarization-consistent basis sets and used for the CBS limit estimations within the Kohn-Sham limit. These CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the 4…
Theoretical nuclear spin-spin coupling constants using atom-atom polarizabilities.13CH and HH′ coupling constants of some [2.2.1] bicyclic compound…
1977
Synthesis, crystal structures and magnetic properties of bis(μ-dialkoxo)-bridged linear trinuclear copper(II) complexes with aminoalcohol ligands: a …
2012
The bis(μ-dialkoxo)-bridged trinuclear copper(II) complexes [Cu(3)(ap)(4)(ClO(4))(2)EtOH] (1), [Cu(3)(ap)(4)(NO(3))(2)] (2), [Cu(3)(ap)(4)Br(2)] (3) and [Cu(3)(ae)(4)(NO(3))(2)] (4) (ae = 2-aminoethanolato and ap = 3-aminopropanolato) have been synthesised via self-assembly from chelating aminoalcohol ligands with the corresponding copper(II) salts. The complexes are characterised by single-crystal X-ray diffraction analyses and variable temperature magnetic measurements. The crystal structures of complexes 1-4 consist of slightly bent linear or linear trinuclear [Cu(3)(aa)(4)](2+) (aa = aminoalcoholato) units to which the perchlorate, nitrate or bromide anions are weakly coordinated. The a…
1H and13C NMR spectroscopy of brominated diphenyl ethers. A multiple linear regression analysis
2000
The 1H and 13C NMR chemical shifts and 1H, 1H coupling constants of 27 brominated diphenyl ethers are reported. The increment models for the bromine substituent effects on the 1H and 13C NMR chemical shifts were constructed based on a multiple linear regression analysis. In addition to the single substituent effects, two particle increments and corrective terms for conformational effects are included in these models in order to obtain a reliable prediction of chemical shifts. Copyright © 2000 John Wiley & Sons, Ltd.