Scaled in Cartesian Coordinates Ab Initio Molecular Force Fields of DNA Bases: Application to Canonical Pairs

The model of Regularized Quantum Mechanical Force Field (RQMFF) was applied to the joint treatment of ab initio and experimental vibrational data of the four primary nucleobases using a new algorithm based on the scaling procedure in Cartesian coordinates. The matrix of scaling factors in Cartesian coordinates for the considered molecules includes diagonal elements for all atoms of the molecule and off-diagonal elements for bonded atoms and for some non-bonded atoms (1–3 and some 1–4 interactions). The choice of the model is based on the results of the second-order perturbation analysis of the Fock matrix for uncoupled interactions using the Natural Bond Orbital (NBO) analysis. The scaling factors obtained within this model as a result of solving the inverse problem (regularized Cartesian scale factors) of adenine, cytosine, guanine, and thymine molecules were used to correct the Hessians of the canonical base pairs: adenine–thymine and cytosine–guanine. The proposed procedure is based on the block structure of the scaling matrix for molecular entities with non-covalent interactions, as in the case of DNA base pairs. It allows avoiding introducing internal coordinates (or coordinates of symmetry, local symmetry, etc.) when scaling the force field of a compound of a complex structure with non-covalent H-bonds.

(ζ−m, ζm)-Type Algebraic Minimal Surfaces in Three-Dimensional Euclidean Space

We introduce the real minimal surfaces family by using the Weierstrass data (ζ−m,ζm) for ζ∈C, m∈Z≥2, then compute the irreducible algebraic surfaces of the surfaces family in three-dimensional Euclidean space E3. In addition, we propose that family has a degree number (resp., class number) 2m(m+1) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

Pengembangan Media Pembelajaran Matematika Berbasis Macromedia Flash pada materi koordinat kartesius kelas VIII SMP

The purpose of this research are to develop macromedia flash-based mathematics learning media for cartesian coordinate material for class VIII SMPN 19 Mataram. Macromedia flash-based learning media is an audio-visual media presented in the form of software consisting of basic competencies, learning objectives, materials and quizzes. This development aims to overcome the weaknesses in the learning process that have occurred due to the lack of use of media in classroom, besides that it can also assist students in learning the concept of cartesian coordinates, especially in visualizing the objects in the material. The research methodology used in developing this learning media is 4D (Define, Design, Developement, Dissemination). Data collection techniques using interview guidelines and questionnaires. The result of this research is a software product of learning media for cartesian coordinates based on macromedia flash in the CD form. The product has been declared valid with good criteria by 4 validators. Based on the limited trial, it is known that the response of class VIII students of SMPN 19 Mataram that use the macromedia flash-based learning media cartesian coordinate is good.

METHODOLOGY OF CONVERTING OF THE COORDINATES OF THE BASIS ATOMS IN A UNIT CELL OF CRYSTALLINE Β-GA2O3, SPECIFIED IN A MONOCLINIC CRYSTALLOGRAPHIC SYSTEM, IN THE LABORATORY CARTESIAN COORDINATES FOR COMPUTER APPLICATIONS

One of the most important areas of modern technology is the creation of new structural materials with predetermined properties. Along with industrial methods for their preparation and technologies associated with the artificial growth of crystalline structures, various methods of computer modeling of new materials have recently become increasingly important. Such approaches can significantly reduce the number of full-scale experiments. Many applications of the computational materials science are related to the need to establish a relationship between structure and electronic characteristics, and other physical properties of crystals. This article on the example of crystalline β-Ga2O3 presents the algorithms used in the converting of the coordinates of the basis atoms in a unit cell of crystal, specified in a crystallographic system, in the Cartesian coordinates for the computational experiment.

The Algebraic Surfaces of the Enneper Family of Maximal Surfaces in Three Dimensional Minkowski Space

We consider the Enneper family of real maximal surfaces via Weierstrass data (1,ζm) for ζ∈C, m∈Z≥1. We obtain the irreducible surfaces of the family in the three dimensional Minkowski space E2,1. Moreover, we propose that the family has degree (2m+1)2 (resp., class 2m(2m+1)) in the cartesian coordinates x,y,z (resp., in the inhomogeneous tangential coordinates a,b,c).

Modeling 13 Archimedean solids by and object-oriented language

The computational study of structures with chemical relevance is preceded by its modeling in such manner that no calculations can be submitted without the knowledge of their spatial atomic arrangement. In this regard, the use of an object-oriented language can be helpful both to generate the Cartesian coordinates (.xyz file format) and to obtain a ray-traced image. The modeling of chemical structures based on programming has some advantages with respect to other known strategies. The more important advantage is the generation of Cartesian coordinates that can be visualized easily by using free of charge software. Our approach facilitates the spatial vision of complex structures and make tangible the chemistry concepts delivered in the classroom. In this article an undergraduate project is described in which students generate the Cartesian coordinates of 13 Archimedean solids based on a geometrical/programming approach. Students were guided along the project and meetings were held to integrate their ideas in a few lines of programmed codes. They improved their decision-making process and their organization and collecting information capabilities, as much as their reasoning and spatial depth. The final products of this project are the coded algorithms and those made tangible the grade of learning/understanding derived of this activity.

Automated handling of complex chemical structures in Z-matrix coordinates - the chemcoord library

In this work, we present a fully automated method for the construction of chemically meaningful sets of non-redundant internal coordinates (also commonly denoted as Z-matrices) from the cartesian coordinates of a molecular system. Particular focus is placed on avoiding ill-definitions of angles and dihedrals due to linear arrangements of atoms, to consistently guarantee a well-defined transformation to cartesian coordinates, even after structural changes. The representations thus obtained are particularly well suited for pathway construction in double-ended methods for transition state search and optimisations with non-linear constraints. Analytical gradients for the transformation between the coordinate systems were derived for the first time, which allows analytical geometry optimizations purely in Z-matrix coordinates. The geometry optimisation was coupled with a Symbolic Algebra package to support arbitrary non-linear constraints in Z-matrix coordinates, while retaining analytical energy gradient conversion. Sample applications are provided for a number of common chemical reactions and illustrative examples where these new algorithms can be used to automatically produce chemically reasonable structure interpolations, or to perform non-linearly constrained optimisations of molecules.