Topological Symmetry of the Bosonic String

We exhibit the topological symmetry of the bosonic string in the framework ofthe BRST formalism. To get the Slavnov–Taylor symmetry independent of thediffeomorphism one, we extend the latter by introducing an antiderivation. Thenon the functional space, we establish that the antiderivation, the Slavnov–Taylor,and the extended Ward operators generate a supersymmetric invariance of thebosonic string.     

Insight and performance of LC-DFT vs DFT in the NMR shielding and chemical shift calculations: Case of CHClCH?CF3

Fifteen density functional theory (DFT) methods and fifteen long-range corrected density functional theory (LC-DFT) methods were used in the present work to assess nuclear magnetic resonance parameters such as nuclear shielding constant (NSC), nuclear chemical shift (NCS), and nuclear anisotropic shielding constant (NAS). These different methods were associated with the full basis set 6-311++G(3df,3pd). The gauge-independent atomic orbital was used for the calculation of nuclear shielding tensors of the nuclei contained in the stereoisomers cis- and trans-CHClCHCF₃. Thus, the effects of LC are clearly observed for heavy nuclei (¹³C, ¹⁹F, ³⁵Cl). The results of NSC, NCS, and NAS from DFT are better described than LC-DFT with regard to the KT3 method. Moreover, the results from the LC-DFT are better described than the standard DFT with regard to CCSD(T). Based on the latter method used as the benchmark, the NSCs of nuclei are well fitted by the competitive functionals LC-TPSSTPSS and LC-PKZBPKZB. In the particular case of the trans-isomer, mPWPKZB was found to be the best method. For the NCSs, the more accurate methods include the latter two LC functionals and the non-LC functionals TPSSTPSS and mPWPKZB. The accuracy of NAS depends strongly on the nuclei. Thus, CAM-B3LYP describes it well for ¹⁹F and LC-PKZBPKZB for ³⁵Cl. The rest of nuclei are well fitted by all the methods except ¹³C₁ and ¹³C₂, which are better reproduced by the LC-DFT except the LC-PKZBPKZB, LC-TPSSTPSS, and CAM-B3LYP functionals.     

Stability,metastability and spectroscopic constants of electronic states of NH− and CH−

Highly correlated ab initio methods were used in order to calculate potential energy curves (PECs) of the bound electronic states of CH^? and NH^? anions and the long-range parts of their excited states. The spin–orbit interaction between electronic states has been calculated for the cases in which the couplings were assumed to be responsible for perturbations. The spectroscopic constants of bound states were calculated from the PECs and compared with previous theoretical and/or available experimental values. Also, from the ground states of CH/CH^? and NH/NH^?, the adiabatic electron affinities were given and discussed.