Application of the MuMATH computer algebra system to sets of first order kinetic equations of significance in chemistry

Analytical solutions to systems of first order differential equations have long been available; however, they become so involved that they are seldom used. Numerical simulations are preferred in practice, although they produce bulky output that is difficult to interpret. Even worse, they are occasionally seriously in error owing to “stiffness” in the equations, intrinsic instability, or other pathological behavior. Computer algebra systems can handle the complicated manipulations that make the analytical solutions of first order kinetic systems inconvenient and can serve as a check on numerical simulations. We show applications of the small MuMATH(R) computer algebra package to a variety of first-order process, including relaxation kinetics and the analysis of stability of steady states in nonlinear kinetic systems.     

Quantum statistical mechanics of closed‐ring molecular chains

A model for a closed‐ring unhindered three‐dimensional macromolecular chain, based on Quantum Mechanics, is presented. Upon starting from an exact non‐relativistic Hamiltonian operator, we integrate out all electronic degrees of freedom, in the Born‐Oppenheimer framework, giving rise to an effective vibro‐rotational Hamiltonian for the chain. Then, assuming a harmonic oscillator‐like vibrational potential between nearest‐neighbour atoms, the integration of the atomic radial degrees of freedom is carried in the limit of high frequencies. Thus, all bond lengths become fixed, including the one which makes the chain to become a closed ring. This formulation leads to a specific Hamiltonian for the remaining angular variables of the closed‐ring chain, and constitutes an alternative in comparison with standard Gaussian models, which do not. Use is made of a variational inequality by Peierls to find an approximate quantum partition function for the angular variables of the system. We then proceed to obtain approximately another representation for the angular partition function in the classical limit. Several features of the classical partition function are discussed.     

Use of a symbolic algebra program in NMR

Computer algebra (CA) on microcomputers may be used as a convenient tool to gain greater insight into the use and design of modern NMR pulse sequences and into their relation to the spin parameters. Some applications are demonstrated.     

Stereospecificity in thermal isomerization of preisocalamendiol,a ten-membered ring sesquiterpene: An application of molecular mechanics calculations

Molecular mechanics calculations were carried out to explain stereospecificity in the cyclization reaction of prisocalamendiol ($\text{1}$), a ten-membered ring sesquiterpene, suggesting that this stereospecificity does not depend on relative stabilities of the conformational isomers of $\text{1}$, but is due to those of the corresponding conformers in each transition state. Particularly, molecular mechanics calculations, which were made on the basis of such a transition state model as $\text{3}$, can explain the experimental results much well.     

Quantum statistics and classical mechanics: real time correlation functions from ring polymer molecular dynamics

We propose an approximate method for calculating Kubo-transformed real-time correlation functions involving position-dependent operators, based on path integral (Parrinello-Rahman) molecular dynamics. The method gives the exact quantum mechanical correlation function at time zero, exactly satisfies the quantum mechanical detailed balance condition, and for correlation functions of the form C(Ax)(t) and C(xB)(t) it gives the exact result for a harmonic potential. It also works reasonably well at short times for more general potentials and correlation functions, as we illustrate with some example calculations. The method provides a consistent improvement over purely classical molecular dynamics that is most apparent in the low-temperature regime.     

Atropselective macrocyclization of diaryl ether ring systems: application to the synthesis of vancomycin model systems

Vancomycin is the last line of defense available in the clinic for treating multidrug-resistant bacterial infections. Vancomycin contains two 16-membered diaryl ether macrocycles, each of which contains a stereogenic axis across the diaryl ether linkage. Since an effective total synthesis of vancomycin requires that these stereogenic axes be formed in a stereoselective manner, we have developed an atropselective variation of the triazene mediated diaryl ether forming reaction. This variation introduced an energetic penalty into the transition state of the undesired atropisomer. This reaction is used to synthesize the C-O-D diaryl ether macrocycle found in vancomycin with high diastereoselectivity (de > 90%), providing the naturally occurring atropisomeric configuration.     

An approach to the imine ring system of pinnatoxins

[reaction: see text] A concise stereoselective approach to the spirobicyclic imine fragment of pinnatoxins and pteriatoxins is described. The approach relies on a tandem reaction sequence involving consecutive sigmatropic rearrangements to build the quaternary chiral center at the core of the spirobicyclic ring system.     

Crystal structure 2,4-dideacetyldi-hydroxyinuchinenolide C. Effect of pseudorotation in the seven-membered ring of linear trans,trans-conjugated pseudoguanolides

The spatial structure of 2,4-dideacetyldihydroxyinuchinenolide C has been established by the x-ray structural method. On the basis of an analysis of known crystal structures of linear trans, trans-conjugated pseudoguanolides using the method of molecular mechanics it has been shown that a partial pseudo-rotation of the seven-membered carbocycle in these compounds is possible.Institute of Organic Synthesis and Coal Chemistry, Academy of Sciences of the Republic of Kazakhstan, Karaganda. A. N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences, Moscow. Translated from Khimiya Prirodnykh Soedinenii, No. 4, pp. 536–542, July–August, 1993.     

Crystal structure 2,4-dideacetyldi-hydroxyinuchinenolide C. Effect of pseudorotation in the seven-membered ring of linear trans,trans-conjugated pseudoguanolides

The spatial structure of 2,4-dideacetyldihydroxyinuchinenolide C has been established by the x-ray structural method. On the basis of an analysis of known crystal structures of linear trans, trans-conjugated pseudoguanolides using the method of molecular mechanics it has been shown that a partial pseudo-rotation of the seven-membered carbocycle in these compounds is possible.     

Quantum mechanics and the structure of noble-gas clusters

The importance of quantum mechanics for the thermal behaviour of Argon clusters with special respect to phase transitions is investigated applying a Path-Integral Monte-Carlo (PIMC) method. Results for the small-angle neutron scattering function (SANS) for various cluster sizes and temperatures are presented.     

Quantum delocalization of benzene in the ring puckering coordinates

The effect of quantum mechanical delocalization of atomic nuclei on the conformation of the six‐membered ring structure in two hydrocarbons, cyclohexane and benzene, is investigated using ab initio path integral approach. A striking feature of benzene species is revealed using ring puckering coordinate representation, which demonstrates that the zero point motion of the heavy atom skeleton dominates over the out‐of‐plane thermal motions of the ring. Even more unexpected is the fact, that this is true not only at low temperature of 150 K, at which such behavior would not be surprising, but also at room temperature, where the nuclear quantum effects are usually of lesser importance, especially in the case of such heavy nuclei as carbon. In view of this finding the planar conformation of benzene, whose equilibrium (T = 0 K) geometry results from the well‐known properties of the electronic structure, can be elucidated also at nonzero temperature. According to our simulations, it appears as a consequence of quantum delocalization of the carbon nuclei rather than a trivial time average over the classical configurations of the puckered ring. This interesting behavior is contrasted with the clearly nonplanar structure of cyclohexane, whose ring puckering states can be unequivocally assigned even if the nuclear delocalization is taken into account. © 2014 Wiley Periodicals, Inc.     

Approaches to dihydrooxazine ring systems and application in the synthesis of bioactive natural products

This review describes selected approaches to the synthesis of 4H-5,6-dihydro-1,2-oxazines and application of these methods to the synthesis of natural products containing this heterocyclic ring system. The focus is on applications and on interesting aspects of chemistry related to this subclass of natural products, as well as newer methods for the synthesis of oxazines.     

An intramolecular diels-alder approach to the galanthan ring system

A novel “phenylbutadiene + Δ²-pyrroline” intramolecular cycloaddition has been used to construct a functionalized galanthan.     

An oxidative entry into the amido trioxadecalin ring system

The amido trioxadecalin ring system is a key structural component of the architecturally interesting anticancer and immunosuppressive agents of the mycalamide, theopederin, and onnamide families of natural products. We report a new entry into this structure in which a mixed acetal serves as a surrogate for a formaldehyde hemiacetal in an addition to an oxidatively generated acyliminium ion. The stereochemical outcome of this process can be explained by the conformational preferences of the product ring system. [reaction: see text]