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*exact*

, 2007

"... algorithms for rigid body integration using optimized splitting methods and ..."

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algorithms for rigid body integration using optimized splitting methods and

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*Fi* *Fi* *Fi* *Fi*

"... > 0 (\Gamma1) k n p1 + \Delta \Delta \Delta + n p k j p 1 \Delta \Delta \Delta p k j ; (H.21) the mean cycle displacement squared by \Omega n 2 ff i = @ 2 @fi 2 1 i(fi; 1) fi fi fi fi fi=0 = \Gamma X 0 (\Gamma1) k (n p1 + \Delta \Delta \Delta + n p k ) 2 j p1 \Delta \D ..."

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> 0 (\Gamma1) k n p1 + \Delta \Delta \Delta + n p k j p 1 \Delta \Delta \Delta p k j ; (H.21) the mean cycle displacement squared by \Omega n 2 ff i = @ 2 @

*fi*2 1 i(*fi*; 1)*fi**fi**fi**fi**fi*=0 = \Gamma X 0 (\Gamma1) k (n p1 + \Delta \Delta \Delta + n p k ) 2 j p1 \Delta###
; in *fi*

"... line 1 n fu coup lding B3LYP. For 11 other molecules, they provide spin–spin coupling constants that are of variable quality. The spin–spin results ory (DFT) [1], shielding constants and chemical shifts nisms (diamagnetic spin–orbit, paramagnetic spin–orbit, spin–dipole, and Fermi-contact) are inclu ..."

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line 1 n fu coup lding B3LYP. For 11 other molecules, they provide spin–spin coupling constants that are of variable quality. The spin–spin results ory (DFT) [1], shielding constants and chemical shifts nisms (diamagnetic spin–orbit, paramagnetic spin–orbit, spin–dipole, and Fermi-contact) are included. For examples, see [4,8–13]. In a recent study [14], we developed two new GGAs, designed specifically to provide high-quality shielding noted KT1, satisfies the uniform electron gas condition, used the CADPAC [18] implementation of the localised-orbital/local-origin (LORG) formalism [19] for the lo-cation of the gauge origin, which imposes a limit on the size of system that can be studied when there is an ex-ternal magnetic field perturbation. To resolve this, we have implemented the functionals in the DALTON [20] program, which uses the gauge including atomic orbital 391*are relatively easy to compute, particularly for general-ised gradient approximation (GGA) functionals where an uncoupled formalism is appropriate. For light, main-group nuclei, shielding constants from conventional GGAs and hybrid exchange-correlation functionals tend to be significantly too deshielded [2]. A number of ap-proaches have been developed to try to improve shielding accuracy [3–7]. Calculations of indirect spin– spin coupling constants are somewhat less common. In part, this can be attributed to the complexity of the calculations, particularly when all four Ramsey mecha-whilst the second, denoted KT2, relaxes this condition through a fit to thermochemical data. The preliminary study [14] demonstrated that both functionals can pro-vide isotropic and anisotropic shieldings of light, main-group nuclei that are 2–3 times more accurate than those of conventional GGAs and hybrid functionals. The re-sults approach correlated ab initio quality. The KT2 functional has also been shown [17] to provide high-quality chemical shifts (shielding constants relative to reference nuclei). To date, our investigations of KT1 and KT2 havehighlight the sensitivity of the Fermi-contact term to exchange-correlation functional and are consistent with previous observations using a self-interaction corrected functional. 2004 Elsevier B.V. All rights reserved. 1.