A Software Tool(VMF)for Visualization Of Molecular Face And Topological Analysis Of The Potential Acting On An Electron Within A Molecule(PAEM)Based On Linux Platform

To elucidate and predict structures and properties of the molecular system based on the state of electrons and nuclei at the microscopic level are important basic content of theoretical and computational chemistry.With the development of quantum chemical theory,space model for characterizing molecular shape has become more real but it comes with large masses of data from computer.It is imperative to develop visualization software tool in order to get useful information quickly and show molecular model more vividly by graphic image.In terms of molecular face theory(MFT),combined with molecular shape and structural characteristics,a software tool for visualization of molecular face(VMF)is achieved on the Linux platform by adopting C language programming and OpenGL graphics standards.Visualization of both molecular entity and topological structure are designed in the VMF.Visualizations of molecular face in three-dimensional(3-D)and two-dimensional(2-D)space,paths of the force acting on an electron within a molecule(FAEM)and topological analysis of some representative molecules are realized in VMF.Basic theory and implementation process of VMF are explored comprehensively and systematically in this thesis.The main contents are summarized as follows:1.Interpolation of 3-D regular data setsAccording to the definition of the potential acting on an electron within a molecule(PAEM),PAEM and electron density at each point on a regular grid of 3-D with fixed interval are calculated by the ab initio MELD program and our own program.It will take a significant amount of time when MELD program is used to calculate high-resolution grid data.Given this,an incomplete interpolation method(IIM)is provided to improve the computation efficiency of the initial data.In the final high resolution grid data,the region with PAEM changed obviously such as nucleus and chemical bonds are obtained in the high-resolution setting by MELD.Other data regions are obtained by using cubic linear interpolation method in the low resolution grid data.The results show that IIM has higher linear correlation compared with MELD program.Meanwhile,IIM reduces the time overhead substantially and improves the computational efficiency obviously.2.Realization of visualization of molecular face in 3-D by improving marching cubes methodUnder the MFT,all the classical turning points of the electron in a molecule where PAEM equals the negative value of ionization energy(-IE)constitute the molecular face.We are dedicated to improving the MC algorithm so as to better meet the characteristics of molecular shape,and further realize the construction of the isosurface of molecular face from 3-D regular data sets.The improving process of MC algorithm is as follows:(1)Relationships of conversion between decimal digits and binary digits are used to denote vertices of cell(the cell is the smallest unit in the 3-D regular data sets).Position relations(edge,face diagonal,body diagonal)for two vertices can be determined by doing XOR operations for two binary indexes of vertices in the cell.Indexes of vertices are used to mark the index of edge and face.(2)Cells which intersect the isosurface are classified into 16 configurations by the signs of the vertices and its position relations.These 16 distinct configurations are further classified into three types.Shared positive vertex,group order ranking and mixed method are presented and applied to different types during triangulation.Finally,a set of non-overlapping triangles is obtained and formed a triangulated irregular network(TIN).The vertex index of TIN and the topological relations of face to face,edge to face and vertex to face are also constructed.(3)Mapping the electron density of each vertex to color table.This would make MF not only can represent molecular sizes,but also can reflect the distribution of electron density values on the iso-surface.During the implementation process,an extended sub-case LUT method is used to solve the topological inconsistency.Moreover,redundancy calculations are avoided by using the adjacent relation of the neighbor cells.And hence improve the efficiency of the algorithm and save time.In order to optimize storage structure,a method based on the combination of 3-D index array with one-dimensional(1-D)array was used to store attributes of the cell.The molecular faces of some typical molecules are depicted through the visual module of VMF.The shape features of molecule are showed from the molecular face.VMF can not only display molecular face based on the MF theory,but also render molecular shape in terms of molecular isodensity contour theory(MIDCT).Furthermore,molecular surface area and volume are calculated by VMF.3.Obtaining isoline model of molecule in 2-DOn the basis of TIN,the 2-D isoline model can be obtained by the projection of MF isosurface model onto a plane.Linear interpolation method is applied to calculate the coordinates and electron densities of intersection points of TIN and plane.The intersection points are connected in sequence according to the topological relations between face and face,face and edge,face and vector of TIN.Then the whole isoline contour of the molecule is generated.There is a collection of disjoint isolines located in a given projection plane when change the threshold of isoline.We can discuss the change rule of PAEM and attribute characteristic of each critical point from the projected image.When set the projection plane to chemical bond or nucleus plane,the coordinates,PAEM and electron density of the critical point can be calculated.By the signature of PAEM curvatures,the critical points can be classified into four types:a critical point in the nucleus,saddle point in the chemical bond,critical point in the interior ring,and critical point in the interior cage.4.Trajectories of the gradient vector field of PAEM and topological analysis of molecular structureTopological properties of PAEM are investigated by its gradient vector field trajectory,the number and kind of the critical points.Then the structural feature of molecules can be further studies.Starting at critical points,moving a distance away from this point in the direction indicated by the gradient vector and repeating this procedure until the path generate terminates.Since the gradient vector field of PAEM in the direction of fastest change in the threshold of isoline,its trajectories are perpendicular to the isolines of PAEM.FAEM represents the minus of the gradient of PAEM at each position.The directions of FAEM path are opposite to the gradient vector field of PAEM.Any two FAEM paths do not intersect and perpendicular to the isolines of PAEM.FAEM determines the speed and direction of electronic motions.The FAEM paths can be classified into three types according to its different starting and ending positions.Type one:The paths originate at infinity and terminate at nuclei,the nuclei act as attractors.The basin of an attractor is a region of 3-D space which meets conditions of type one.An atom is defined as the union of an attractor and its associated basin.Type two:The paths originate at the saddle points and terminate at the nuclei.Join these paths associated with the same saddle point will generate a bond path.The bond path connects two bonded atoms by a saddle point.Type three:The paths originate at infinity and terminate at the saddle point.These paths are perpendicular to the associated chemical bond.Join these paths associated with the same saddle point will generate a 2-D boundary or 3-D interatomic surface.By using VMF,the FAEM paths of H2,hydrogen halide,lithium halide and a series of typical organic molecules are described.The molecular structure feature is discussed in terms of the number and kind of critical points,the boundaries between the basins of neighboring atoms and the number of electrons in each atomic region.Based on the least square method,fitting method of a parabola combined with exponential is presented to obtain the expression of interatomic surface in the diatomic molecule.The interatomic surface of the water molecule is fitted by TableCurve 3D software.The numbers of electrons in each atomic region of a diatomic molecule and a water molecule are calculated by adding the number of electrons of the cell at each side of the interatomic surface.The results provide a basis for recognizing electron transfer and micro mechanics of chemical reactions.