Parametrization And Applications Of The DFTB Method

Computational simulation of materials at microscale is an important means of researches in physics,chemistry and material science,and play an important role in interpreting phenomena,properties and predicting functional materials.Although strict in theory and reliable in results,with a tremendous amount of CPU time,the application of first-principles calculations is limited.In comparison,the amount of calculations are relatively too small when parameterized empirical force field is used,and simulations for large systems and long time scales are enabled.However,electronic structure is unavailable in such method and transferability is limited for the parameters.As a compromise,semiempirical calculations retain the disposal of electronic structure and introduce empirical parameters to reduce the amount of computation.Therefore,it is useful in simulations of systems with medium spatial and time scales and forecasting trends qualitatively,etc.Density-functional tight-binding(DFTB),with tight-binding introduced into the framework of density functional theory,is one of the semiempirical methods,which is able to run electronic structure analysis,geometry optimization,spectrum simulation and molecular dynamics,etc.In this dissertation,a detailed discussion of DFTB will be launched,including methodology,applications and parametrization of atoms.In the first chapter,electronic structure calculation as well as its functions,applications and advantages compared with experiment will be introduced briefly.Then,we will summarize three common calculation methods including first-principles calculation,semiempirical calculation and empirical force field which does not belong to electronic structure calculation.Applications as well as advantages and disadvantages of these methods will be listed and a comparison will be made.Methodology of DFTB will be introduced systematically in the second chapter.According to the expansion of the energy functional,zero-order DFTB ignores the second order and the terms higher,then the total energy can be divided into two parts,band-structure energy and repulsive energy.The band-structure energy is a generalized eigenvalue problem which comes from Hamiltonian and overlap matrices,construction of the matrices and parametrization of the elements will be discussed in detail.Self-consistent-charge density-functional tight-binding(SCC-DFTB),with the second order term in the expansion of the energy functional included,solve the eigenvalue problem iteratively with Hamiltonian matrix modified by charge transfer,therefore,more accurate results will be obtained for the systems with considerable charge transfer.As an example of application of DFTB in material calculations,in the third chapter,simulation of infrared spectroscopy of graphene oxide(GO)will be performed at SCC-DFTB level.As the key intermediate for solution-based massive production of graphene from graphite,GO attracts an intense research interest.Also,there are a lot of potential applications by itself,including hydrogen storage,chemical/bio-sensor,and electronic devices.Infrared spectroscopy is an important means to study the atomic structure of GO.Due to the nonstoichiometry and amorphousness,structure of GO has still not been fully understood.The widely accepted Lerf model gives most experimental infrared characteristics correctly except the strong C=O stretching peak.This is a result of the absence of carbonyl groups in the interior part of GO.Defects or small oxidative debris should thus be introduced into the models to accommodate more carbonyl groups.Unfortunately,even for those with defects or oxidative debris included,most previous models in the literature still fail to give a correct infrared response.Actually,the C=O stretching frequency is found to be very sensitive to local chemical environment.Therefore,to introduce defects or oxidative debris into GO models,certain constrains apply.The rest part of this dissertation will focus on parametrization of atoms in DFTB.Many parameter files cannot be found due to the incompleteness of the parameter library,for example,the C-Cu and Cu-C parameter files.Therefore,a set of parameter files for the corresponding systems must be developed before DFTB calculations.The band-structure energy is the primary part in the total energy in DFTB,therefore,parameters of electronic part play a decisive role in the final results.In the fourth chapter,we will discuss the calculation of integral tables for copper and carbon using SIESTA(Spanish Initiative for Electronic Simulations with Thousands of Atoms)package.The two center integrals are found to be sensitive to range and shape of atomic wave functions.Since there are several parameters which control the atomic wave functions implemented in SIESTA,many different integral tables are obtained by adjusting such parameters.The integral tables are finally judged by the calculation of band structures of the corresponding systems.The repulsive energy is the difference between total energy and energy from electronic part.Compared with the electronic part,the repulsive energy is really small,its parametrization strongly depends on the actual systems,and play an important part in systems with different chemical environments.In the fifth chapter,the two center parameters will be recalculated using Hotbit package first.Then,the repulsive parameters will be fitted to the training set containing different surface systems and finally certain parameter files will be assembled.Tests show that the parameter files are suitable for surface configurations containing copper and carbon.