Exact renormalization group and Φ-derivable approximations

We show that the so-called Φ-derivable approximations can be combined with the exact renormalization group to provide efficient non-perturbative approximation schemes. On the one hand, the Φ-derivable approximations allow for a simple truncation of the infinite hierarchy of the renormalization group flow equations. On the other hand, the flow equations turn the non-linear equations that derive from the Φ-derivable approximations into an initial value problem, offering new practical ways to solve these equations.     

Application of solid-state 35Cl NMR to the structural characterization of hydrochloride pharmaceuticals and their polymorphs

Solid-state (35)Cl NMR (SSNMR) spectroscopy is shown to be a useful probe of structure and polymorphism in HCl pharmaceuticals, which constitute ca. 50% of known pharmaceutical salts. Chlorine NMR spectra, single-crystal and powder X-ray diffraction data, and complementary ab initio calculations are presented for a series of HCl local anesthetic (LA) pharmaceuticals and some of their polymorphs. (35)Cl MAS SSNMR spectra acquired at 21.1 T and spectra of stationary samples at 9.4 and 21.1 T allow for extraction of chlorine electric field gradient (EFG) and chemical shift (CS) parameters. The sensitivity of the (35)Cl EFG and CS tensors to subtle changes in the chlorine environments is reflected in the (35)Cl SSNMR powder patterns. The (35)Cl SSNMR spectra are shown to serve as a rapid fingerprint for identifying and distinguishing polymorphs, as well as a useful tool for structural interpretation. First principles calculations of (35)Cl EFG and CS tensor parameters are in good agreement with the experimental values. The sensitivity of the chlorine NMR interaction tensor parameters to the chlorine chemical environment and the potential for modeling these sites with ab initio calculations hold much promise for application to polymorph screening for a wide variety of HCl pharmaceuticals.