The Clarity Evaluation Function And Algorithm Of Charge Density Map

The physical and chemical properties of materials depend on its chemical composition and crystal structure.Therefore,the determination of the composition and crystal structure of a material is the first step in the study of the properties of materials.X-ray light is a kind of light source which is suitable for studying crystal structure because its wavelength is equal to the atomic distance of the crystal.The X-ray single crystal diffraction experiment(XRD)becomes the standard method to measure the crystal structure.In this thesis,we mainly study the crystal structure analysis in crystallography.The experimental data of single crystal XRD consist the diffraction intensity and position information.After the index and correction,the diffraction intensity information of each diffraction point can be obtained.The modulus of structure factor is proportional to the diffraction intensity.The structure factor is an imaginary number which contains the amplitude and phase information.The measured XRD experimental data is only the amplitude information and the phase information cannot be determined.This leads crystal structure analysis to the "phase problem".By analogy the imaging process of X light with natural light,this thesis pointed out that the loss of phase information resulting the unknown quantity is two times the number of equations in equations represented by the Patterson diagram with the help of the convolution principle.The crystal analytical problem is an inverse problem.Two kinds of crystal structure analysis method(the Error Reduction and the Charge Flipping algorithm)are discussed and compared with the conventional direct method.These novel algorithm has a great advantage that its iterative algorithm of the real space and reciprocal space is simple and efficient.In this paper,we further analyze the X-ray diffraction process with optical imaging(photography)process,and propose the concept of the clarity definition of the charge density map in XRD for the first time by means of the clarity definition in image.It is pointed out that the higher the clarity of the charge density map,the closer the crystal structure is to the real situation.In this conclusion and the analogy sharpness function in the image,the clarity definition function Tian1 of the charge density map is constructed,based on the nature of the charge density map obtained from the Fourier transformation of the structure factors.Drawing on the idea of the density modification method in Error Reduction and Charge Flipping iterative algorithm,the Tian1 algorithm of crystal structure analysis algorithm suitable for the Tian1 function calculation is established.This algorithm not only eliminates the artificial charge density threshold parameters in Charge Flipping algorithm,but also fundamentally reveals the Tian1 function value maximum for the correct structure and corresponding to the essence of the success of the Charge Flipping algorithm.Although the three algorithms of Error Reduction,Charge Flipping and Tian1 are different,the ultimate goal of the three algorithms is essentially same,that is,the maximum value of the Tian1 function is achieved by adjusting the charge density.Therefore,it can be said that the Tian1 function value is a good criterion for the correctness of the crystal structure.In view of the Tian1 algorithm proposed in this thesis,the code is written and tested.The first test is the analysis of the feasibility of the algorithm including the convergence and the complexity.A variety of crystals were tested to explore the universality of the Tian1 algorithm.And to verify the applicability of Tian1 algorithm by testing different resolution of XRD data.Finally,in the actual experiment data of XRD for structure analysis,real test Tian1 algorithm.Tian1 algorithm has high efficiency of the Error Reduction algorithm and the Charge Flipping algorithm at the same time more concise than both,and a solid mathematical prove is given.The good agreement between the structure models analyzed by the Tian1 algorithm and the standard SHELX program shows that the Tian1 algorithm can be used as a practical analytical method of crystal structure.