Related papers: Quaternions in molecular modeling
We introduce a four-dimensional quantum model for describing the torsional control of $\rm G_{16}$-type molecules in the electronic ground state, based on the symmetry-adapted variational method. We define conditions for which…
Since their first applications, Convolutional Neural Networks (CNNs) have solved problems that have advanced the state-of-the-art in several domains. CNNs represent information using real numbers. Despite encouraging results, theoretical…
In the model every quark or lepton is identified with a quartet of four "more elementary" particles. One particle in a quartet is a massive spin-0 boson and other three particles are massless spin-1/2 fermions.
In this paper, we give several matrix representations for the Horadam quaternions. We derive several identities related to these quaternions by using the matrix method. Since quaternion multiplication is not commutative, some of our results…
Cramer's rules for some left, right and two-sided quaternion matrix equations are obtained within the framework of the theory of the column and row determinants.
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
We present a quaternion-inspired formalism specifically developed to evaluate the electric current that traverses a single molecule subjected to an externally applied voltage. The molecule of interest is covalently connected to two small…
Motivated by a model in quantum computation we study orthogonal sets of integral vectors of the same norm that can be extended with new vectors keeping the norm and the orthogonality. Our approach involves some arithmetic properties of the…
Quaternion-valued differential equations (QDEs) is a new kind of differential equations which have many applications in physics and life sciences. The largest difference between QDEs and ODEs is the algebraic structure. On the…
Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for a machine learning revolution and have already been profoundly impacted by the…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
Understanding the geometry and topology of configuration or conformational spaces of molecules has relevant applications in chemistry and biology such as the proteins folding problem, drug design and the structure activity relationship…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
In the field of molecular electronics, particularly in quantum transport studies, the orientation of molecules plays a crucial role. This orientation, with respect to the electrodes, can be defined through the cavity of ring-shaped…
Binding energy is a fundamental thermodynamic property that governs molecular interactions, playing a crucial role in fields such as healthcare and the natural sciences. It is particularly relevant in drug development, vaccine design, and…
The quaternion Fourier transform (qFT) is an important tool in multi-dimensional data analysis, in particular for the study of color images. An important problem when applying the qFT is the mismatch between the spatial and frequency…
Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as…
A comprehensive analysis of the morphology of the solution space for a special type of quadratic quaternion equation is presented. This equation, which arises in a surface construction problem, incorporates linear terms in a quaternion…
In this paper, we considered the theory of quasideterminants and row and column determinants. We considered the application of this theory to the solving of a system of linear equations in quaternion algebra. We established correspondence…
A revised version of the quaternion approach for numerical integration of the equations of motion for rigid polyatomic molecules is proposed. The modified approach is based on a formulation of the quaternion dynamics with constraints. This…