An Evolution Algorithm For Electron Wave Function Based On Hamiltonian Matrix

Electron evolution is widespread both in natural world and technology applications.The earliest recorded discovery of electron-related phenomena in ancient time was the charging of some specific objects after their friction with animal fur.Many centuries after that,due to accumulation of life experience and scientific knowledge,human species started to realize the positive and negative nature of charge,the different distribution of electrons and protons inside atoms,diffraction of electron beams and so on,getting better understanding of electrons.Nowadays,People has gone so far in electron-related science and technology that we are now exploring quantum effects of electron in many areas such as chemical reaction,molecular spectrum,molecular conductance,photo catalysis,material design etc.Electron evolution is deeply involved in these fields.Research work related to electron evolution rely both on experimental and computational data,both of which are irreplaceable.Experimental data usually originates from wet experiments based on technologies like pump-probe spectroscopy,sum-frequency spectroscopy,and multi-dimensional spectroscopy.The newest ultra-fast spectroscopy technology with highest accuracy has reached the time scale of attosecond.These spectroscopy technologies have been widely used for electron evolution measurement.They are extremely important for rigorous research.Computational data is generally produced with a set of computational methods in which TDHF and TDDFT are the most-known ones.Theoretical and computational simulations based on fundamental physical theories are used for computation of physical and chemical properties of objects.Comparing with experimental measurement,theoretical simulations provide us with more details on investigated objects,deepening our understanding towards them.This graduation thesis focus on development and application of electron evolution algorithms in theoretical and computational area.Traditional electron evolution algorithms have made great achievements in computing electronical structure and electron evolution properties of small-scale systems.However,as the length scale of investigated systems researchers are interested in grows larger and larger,these traditional methods start to suffer from huge computational resource demanding,which prevent further applications of these methods in large scale systems.Considering that electron moves much faster than nuclear and in some cases impact of perturbations on overall Hamiltonian of system can be ignored,we proposed a new easy and effective electron wave function evolution algorithm based on Hamiltonian matrix.This new algorithm is much faster than most traditional ones,allowing us to deal with electron evolution in larger scale systems.After implementation of this large-scale electron evolution algorithm,we keep doing two things:applying the new algorithm to computing physical and chemical properties of large-scale system,improving the new algorithm based on feedbacks from its application activities.In the first chapter we reviewed current research progress on electron evolution,usual factors that affect electron evolution,means of regulating electron evolution,and some specific examples of electron evolution.Besides,we also talked about challenges in electron evolution of large scale systems.In the second chapter we introduced traditional electron evolution theories and methods,mainly the theoretical foundations of HF and TDDFT.When dealing with electron evolution of small scale system,TDDFT works pretty well.But when it comes to large scale system,both TDHF and TDDFT are too costive.Faster and cheaper computational methods are required.In the third chapter we at first analyzed the details why in some cases traditional electron evolution algorithms are in trouble.Then,based on adiabatic approximation and perturbation approximation,we proposed a new easy but effective electron evolution algorithm in large scale system and gave the mathematical expression of it.User's guidance,scope of application and tips were also providedIn the fourth chapter we applied the fresh electron evolution algorithm onto rectangular graphene stripe.Several stripe structures were designed for investigation of key factors that determine time scale of electron evolution.Nitrogen and Boron atoms were doped into to investigate their impact on the time scale.By analyzing the generated simulation data,we came to the view point that non-local conjugate ?bond in system plays a vital role in long range electron transportation.More data in the following chapters support this view point.In the fifth chapter we conducted electron evolution in multi-layer graphene based sandwich structure.It was reported that this sandwich structure can work as photocatalyst in water decomposing and container for hydrogen storage.After comparing our results with data from literature,we found to some degree they disagreed with each other.Then we realized that interaction between electrons and holes are not included in our new algorithm,which caused inevitable errors in such processes,inspiring us to improve the algorithm in a new aspect.In the sixth chapter we tested our new algorithm in a complex molecule composed of carotenoid,porphyrin and fullerene.This kind of complex molecules have been used for charge transfer and artificial photosynthesis research.During the process of electron evolution in this system,both transitions between electronic states and charge diffusion play important roles.Traditional TDDFT cannot deal with this system easily due to its relatively large scale which our new algorithm can handle.The final results supports two conclusion.First,non-local conjugate ? bond makes it convenient for electron evolution.Second,support for transitions between electron evolution should be added into the algorithm in order to get better electron evolution results,which is another way of improvements.