MOLPIPx:一个端到端可微分包,用于Python和Rust中的 permutationally不变的多项式

The Frost circle or the inscribed polygon method is a graphical method for determining the relative energies of π molecular orbitals (MOs) for planar, fully conjugated, and monocyclic compounds. This method was first described by A. A. Frost and Boris Musulin in 1953.
A Frost circle is constructed by drawing a polygon whose number of edges is equal to the number of carbons of the given cyclic system, with one of the vertices pointing down. Then, a circle is drawn enclosing the polygon so...

Ring-opening metathesis polymerization or ROMP involves strained cycloalkenes as starting materials. The mechanism of ROMP proceeds by reacting cycloalkene with Grubbs catalyst to give metallacyclobutane intermediate which undergoes a ring-opening reaction to form new carbene. The new carbene reacts with another molecule of cycloalkene. Repetition of these steps leads to the formation of an unsaturated open-chain polymer product. All these steps are reversible, however, relieving the ring...

Electrocyclic reactions, cycloadditions, and sigmatropic rearrangements are concerted pericyclic reactions that proceed via a cyclic transition state. These reactions are stereospecific and regioselective. The stereochemistry of the products depends on the symmetry characteristics of the interacting orbitals and the reaction conditions. Accordingly, pericyclic reactions are classified as either symmetry-allowed or symmetry-forbidden. Woodward and Hoffmann presented the selection criteria for...

Depending upon the different spatial orientation of the substituents, the disubstituted cycloalkanes exhibit two types of stereoisomers. The cis isomers have the substituents on the same side of the ring, whereas the trans isomers have the substituents on the opposite sides. These stereoisomers exhibit different physical properties and cannot be interconverted without breaking the carbon-carbon bonds.
In cyclohexane, the substituents can occupy different positions generating distinct isomers....

Recently, the development of olefin metathesis polymerization advanced the field of polymer synthesis. Simply put, the reorganization of substituents on their double bonds between two olefins in the presence of a catalyst is known as the olefin metathesis reaction. The use of metathesis reaction for polymer synthesis is called olefin metathesis polymerization.
Ruthenium-based Grubbs catalyst is the most commonly used catalyst for olefin metathesis polymerization. Grubbs catalyst consists...

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.