A new method is presented to describe deformations of an N-membered planar ring (N-ring) molecule in terms of deformation vectors that can be expressed by a set of 2N-3 deformation amplitudes and phase angles. The deformation coordinates are directly derived from the normal vibrational modes of the N-ring and referenced to a regular polygon (N-gon) of unit length. They extend the conceptual approach of the Cremer-Pople puckering coordinates (J. Am. Chem. Soc. 1975, 97, 1354) to the planar ring and make it possible to calculate, e.g., a planar ring of special deformation on a Jahn-Teller surface. It is demonstrated that the 2N-3 deformation parameters are perfectly suited to describe the pseudorotation of a bond through the ring as it is found in cyclic Jahn-Teller systems. In general, an N-membered planar ring can undergo N-2 different bond pseudorotations provided the energetics of such a process is feasible. The Jahn-Teller distortions observed in ring compounds correspond either directly to the basic pseudorotation modes or to linear combinations of them. Any deformed ring molecule can be characterized in terms of the new ring deformation coordinates, which help to identify specific electronic effects. The usefulness of the ring deformation coordinates is demonstrated by calculating the Jahn-Teller surfaces for bond pseudorotation in the case of the cyclopropyl radical cation and cyclobutadiene as well as the ring deformation surfaces of disulfur dinitride and its dianion employing multireference averaged quadratic coupled cluster (MR-AQCC) theory, equation-of-motion coupled cluster theory in form of EOMIP-CCSD, and single determinant coupled cluster theory in form of CCSD(T).

Convergence problems of meta-GGA (generalized gradient approximation) XC (exchange and correlation) functionals containing a self-interaction correction term are traced back to a singularity of the latter that occurs at critical points of the electron density. This is demonstrated for the bond critical point of equilibrium and stretched H2. A simple remedy is suggested that cures meta-XC functionals such as VSXC, TPSS, M05, M06, and their derivatives without extra cost.

The Automated Protein Structure Analysis (APSA) method, which describes the protein backbone as a smooth line in three-dimensional space and characterizes it by curvature kappa and torsion tau as a function of arc length s, was applied on 77 proteins to determine all secondary structural units via specific kappa(s) and tau(s) patterns. A total of 533 alpha-helices and 644 beta-strands were recognized by APSA, whereas DSSP gives 536 and 651 units, respectively. Kinks and distortions were quantified and the boundaries (entry and exit) of secondary structures were classified. Similarity between proteins can be easily quantified using APSA, as was demonstrated for the roll architecture of proteins ubiquitin and spinach ferridoxin. A twenty-by-twenty comparison of all alpha domains showed that the curvature-torsion patterns generated by APSA provide an accurate and meaningful similarity measurement for secondary, super secondary, and tertiary protein structure. APSA is shown to accurately reflect the conformation of the backbone effectively reducing three-dimensional structure information to two-dimensional representations that are easy to interpret and understand.

⎯The general trade effects and changes in the commodity and geographical trade structures for Russia under the condition of integrating trade with countries of the European Union, BRICS and Trans-Pacific Partnership have been estimated in the article. It has been stated that it is preferable for the Russian economy to approach European Union countries in order to obtain the maximum values of the welfare effect and trade-creation effect, and to proportionally increase the export and import volumes with the BRICS countries. Based on the prolongation of the shortterm tendencies, the long-term challenges to the Russian economy and possibilities of liberalizing trade with the mentioned trade unions have been specified.

Once at the epicenter of the original source of the coronavirus spread, the governments of China, the Republic of Korea and Japan introduced immediate administrative measures to isolate the population, which helped to effectively contain the spread of COVID-19 on their territory. The review shows that in the first half of 2020, due to policy of isolation in these Northeast Asia countries, there was a contraction of their economies. The subsequent dynamics of economic growth of the three Northeast Asia countries indicated structural differences in their economies. In the face of economic recession during a COVID-19 pandemic, the governments of Northeast Asia countries are applying stimulating economic policies, with Japan having the largest public spending with respect to its GDP, followed by the Republic of Korea and China. In China, the support for the economy is focused on fiscal policy measures, in the Republic of Korea – monetary and macro-financial policies, in Japan – a combination of policies’ various measures. In the context of a decrease in the coronavirus spread, mid-term estimates indicate that these three countries will be able to maintain positive economic growth rates while investment supporting of the green and digital technologies, including the support through the measures of economic policy. These support measures could have a short- and medium-term positive impact on the economies of the three Northeast Asia countries. However, for the purpose to localizing the pandemic in these countries large fiscal expenditures will contribute to the further growth of their public debt, thereby reducing the national savings rate, restraining the dynamics of their economic growth in the long term