Related papers: Structures of Molecules at the Atomic Level: Caffe…
We continue our study of the quantum optics of a single photon interacting with a system of two level atoms. In this work we investigate the case of a periodic arrangement of atoms. We provide a general structure theorem characterizing the…
Empirical scoring functions based on either molecular force fields or cheminformatics descriptors are widely used, in conjunction with molecular docking, during the early stages of drug discovery to predict potency and binding affinity of a…
The correlations of primary and secondary structures were analyzed using proteins with known structure from Protein Data Bank. The correlation values of amino acid type and the eight secondary structure types at distant position were…
The "chemical bond" is a central concept in molecular sciences, but there is no consensus as to what a bond actually is. Therefore, a variety of bonding models have been developed, each defining the structure of molecules in a different…
We assess the predictive accuracy of perturbation theory based estimates of changes in covalent bonding due to linear alchemical interpolations among molecules. We have investigated $\sigma$ bonding to hydrogen, as well as $\sigma$ and…
The MCAS Way extends the MCAS concept of atomic orbitals to molecular bonding. There are many examples given for each bonding type. Part I: The MCAS atomic orbital concept. There are no spherical orbitals and spin pairing does not occur…
A new approach for describing the effective electronic states of "atoms in compounds" to study the properties of molecules and condensed matter which are circumscribed by the operators heavily concentrated in atomic cores is proposed. Among…
We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of properties of the atomic length which are reminiscent of the…
Along with recent progress in structural biology and genome biology, structural dynamics of molecular systems including nucleic acids has attracted attention in the context of gene regulation. Structure-function relationship is an important…
Using first-principles total-energy pseudopotential calculations, we have studied the properties of chains of potassium and aluminum in nanotubes. For BN tubes, there is little interaction between the metal chains and the tubes, and the…
Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born--Oppenheimer and…
We present a geometrical analysis of the protrusion statistics of side chains in more than 4,000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of C{\alpha}…
Newly discovered carbon nanotubes provide an environment in which small atoms move relatively freely. An assembly of such atoms provides a realization of a quasi-one dimensional system which is an ideal testing ground for concepts and…
Proteins are linear chain molecules that play a central role in life and health. Protein native state folds are modular assemblies of space-filling building blocks of {\alpha}-helices, \{beta}-sheets and tight turns. Here we deduce the…
Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical…
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We…
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,…
It is expected that atomic vacancies or nanometric cavities reduce the number of chemical bonds of nearby atoms and hence the strength of a voided solid. However, the hardness of a porous specimen does not always follow this simple picture…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
Chemical graphs are simple undirected connected graphs, where vertices represent atoms in a molecule and edges represent chemical bonds. A degree-based topological index is a molecular descriptor used to study specific physicochemical…