Related papers: Enumeration of saturated and unsaturated substitut…
Combinatorial introduction of heteroatoms in the two-dimensional framework of aromatic hydrocarbons opens up possibilities to design compound libraries exhibiting desirable photovoltaic and photochemical properties. Exhaustive enumeration…
Determinants of structured matrices play a fundamental role in both pure and applied mathematics, with wide-ranging applications in linear algebra, combinatorics, coding theory, and numerical analysis. In this work, the enumeration of…
The study is aimed at revealing the most important substructures (fragments) of polyenes with heteroatoms determining the alteration in the conjugation energy of the whole compound due to substitution and the relevant charge redistribution.…
A nonhomogeneous system of linear recurrence equations can be recognized by an automaton $\mathcal{A}$ over a one-letter alphabet $A = \{z\}$. Conversely, the automaton $\mathcal{A}$ generates precisely this nonhomogeneous system of linear…
A derivative structure is a nonequivalent substitutional atomic configuration derived from a given primitive cell. The enumeration of derivative structures plays an essential role in searching for the ground states in multicomponent…
Arrow diagram (AD) method (L. Kantorovich and B. Zapol, J. Chem. Phys. \textbf{96}, 8420 (1992); \emph{ibid}, 8427) provides a convenient means of systematic calculation of arbitrary matrix elements, $<\Psi|\hat{O}|\Psi>$, of symmetrical…
This paper is devoted to a new classification of the twenty amino acids based on the heronian (integer) tetrahedron.
One-dimensional NMR spectroscopy is one of the most widely used techniques for the characterization of organic compounds and natural products. For molecules with up to 36 non-hydrogen atoms, the number of possible structures has been…
Atom tracing is essential for understanding the fate of labeled atoms in biochemical reaction networks, yet existing computational methods either simplify label correlations or suffer from combinatorial explosion. We introduce a…
This article presents the results of a study concerning interstellar molecules which are useful for the bookkeeping of the organic content of the universe and for providing a glimpse into prebiotic conditions on Earth and in other…
We give recurrence relations for the enumeration of symmetric elements within four classes of arc diagrams corresponding to certain involutions and set partitions whose blocks contain no consecutive integers. These arc diagrams are…
Enumerating chemical graphs satisfying given constraints is a fundamental problem in mathematical and computational chemistry, and plays an essential part in a recently proposed framework for the inverse QSAR/QSPR. In this paper,…
A systematics of the atomic nuclei in the frame of the nucleon number $A = Z + N$ and the proton-neutron difference $F = Z - N$ is considered. The classification scheme is provided by means of the non-compact algebra $sp(4,R)$. In this…
Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…
Structures of chemical compounds can be synthesized and categorized through mathematical means. Organic compounds are suitable targets because of their simple valences. Acyclic organic compounds made of hydrogen and second-row elements C,…
Measurements of the isotopic abundances in meteoritic amino acids have found enhancements of $^2$H/H, $^{15}$N/$^{14}$N, and $^{13}$C/$^{12}$C in the amino acids in the meteorites studied. We show that they are consistent with the…
Modeling potential alloys requires the exploration of all possible configurations of atoms. Additionally, modeling the thermal properties of materials requires knowledge of the possible ways of displacing the atoms. One solution to finding…
The determination of chemical mixture components is vital to a multitude of scientific fields. Oftentimes spectroscopic methods are employed to decipher the composition of these mixtures. However, the sheer density of spectral features…
Retrosynthesis is essential for designing synthetic pathways for complex molecules and can be revolutionized by AI to automate and accelerate chemical synthesis planning for drug discovery and materials science. Here, we propose a…
Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic…