The (φ 4)3 + 1 theory with infinitesimal bare coupling constants

1987 ◽  
Vol 35 (4) ◽  
pp. 453-459 ◽  
Author(s):  
I. Yotsuyanagi
1961 ◽  
Vol 123 (3) ◽  
pp. 1065-1071 ◽  
Author(s):  
Murray Gell-Mann ◽  
Fredrik Zachariasen

1997 ◽  
Vol 91 (5) ◽  
pp. 897-907 ◽  
Author(s):  
SHEELA KIRPEKAR ◽  
THOMAS ENEVOLDSEN ◽  
JENS ODDERSHEDE ◽  
WILLIAM RAYNES

1997 ◽  
Vol 7 (11) ◽  
pp. 1299-1304 ◽  
Author(s):  
P. Weinberger ◽  
C. Sommers ◽  
U. Pustogowa ◽  
L. Szunyogh ◽  
B. Újfalussy

2019 ◽  
Author(s):  
Xianghai Sheng ◽  
Lee Thompson ◽  
Hrant Hratchian

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the Approximate Projection model. Results show that improvements using the Approximate Projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin-projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin-projection can be important for both geometry optimization and energy evaluations. The Approximate Project model provides an affordable and practical approach for effectively correcting spin-contamination errors in molecular exchange coupling constant and spin crossover gap calculations.


2020 ◽  
Vol 24 (10) ◽  
pp. 1139-1147
Author(s):  
Yang Mingyan ◽  
Wang Daoquan ◽  
Wang Mingan

2-Phenylcyclododecanone and 2-cyclohexylcyclododecanone derivatives were synthesized and characterized by 1H NMR, 13C NMR, HR-ESI-MS and X-ray diffraction. Their preferred conformations were analyzed by the coupling constants in the 1H NMR spectra and X-ray diffraction, which showed the skeleton ring of these derivatives containing [3333]-2-one conformation, and the phenyl groups were located at the side-exo position of [3333]-2-one conformation due to the strong π-π repulsive interaction between the π- electron of benzene ring and π-electron of carbonyl group. The cyclohexyl groups were located at the corner-syn or the side-exo position of [3333]-2-one conformation depending on the hindrance of the other substituted groups. The π-π electron effect played a crucial role in efficiently controlling the preferred conformation of 2-aromatic cyclododecanone and the other 2-aromatic macrocyclic derivatives with the similar preferred square and rectangular conformations.


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