Development And Applications Of The Generalized Energy-based Fragmentation Method

Over the last decades,quantum chemistry has been widely used in the areas of chemistry,biology,physics,material science,and etc.However,the computational cost of the conventional quantum chemistry methods increases rapidly with the system size.In order to extend quantum chemistry calculations to very large systems,theoretical chemists have developed many low or linear scaling quantum chemistry methods.Among these methods,fragment-based methods have attracted much attention in recent years.The basic idea of fragment-based methods is to evaluate the total energy(or properties)of a large system through combining energies(or properties)of a series of small subsystems constructed according to a fragmentation scheme.A number of fragment-based methods have been designed by different research groups,and they differ from each other in the manner of constructing subsystems and recombining results.It is commonly believed that these fragment-based methods can provide satisfactory descriptions on electronic structure of large systems.The main work of this thesis focus on the development and applications of the generalized energy-based fragmentation(GEBF)method.First,we compare the performance of the GEBF method and the electrostatically embedded many-body(EE-MB)method for medium-sized water clusters with large basis sets;Second,we demonstrate that the GEBF method can provide highly accurate relative energies of large water clusters with both high-level electron correlation methods and very large basis sets;Third,the applicability of the GEBF method to various large molecular systems is examined at different theoretical levels.Main contributions of the present dissertation can be summarized as follows:In chapter 3,we systematically investigate the performance of the GEBF method and the EE-MB method for medium-sized water clusters(H2O)n(n=10,20,30),in which conventional calculations are available for comparison.The GEBF and EE-MB methods are two representative methods of two categories of fragment-based methods(based on the inclusion-exclusion principle or the many-body expansion).Our calculations demonstrate that the GEBF method provides uniformly accurate ground-state energies for 10 low-energy isomers of three water clusters under study at a series of theory levels,while the EE-MB method(with one water molecule as a fragment and without using the cutoff distance)shows a poor convergence for(H2O)20 and(H2O)30 when the basis set contains diffuse functions.Our analysis shows that the neglect of the basis set superposition error(BSSE)for each subsystem has little effect on the accuracy of the GEBF method,but leads to much less accurate results for the EE-MB method.The accuracy of the EE-MB method can be dramatically improved by using an appropriate cutoff distance and using two water molecules as a fragment.For(H2O)30,the average deviation of the EE-MB method truncated up to the three-body level calculated with this strategy(relative to the conventional energies)is about 0.003 hartree at the M06-2X/6-311++G**level,while the deviation of the GEBF method with a similar computational cost is less than 0.001 hartree.The GEBF method is demonstrated to be applicable for electronic structure calculations of water clusters at any basis set.In chapter 4,the GEBF method has been applied to investigate relative energies of large water clusters(H2O)n(n=32,64)with the coupled-cluster singles and doubles with noniterative triple excitations(CCSD(T))and second-order Moller-Plesset perturbation theory(MP2)at the complete basis set(CBS)limit.Here large water clusters are chosen to be representative structures sampled from molecular dynamics(MD)simulations of liquid water.Our calculations show that the GEBF method is capable of providing highly accurate relative energies for these water clusters in a cost-effective way.We demonstrate that the relative energies from GEBF-MP2/CBS are in excellent agreement with those from GEBF-CCSD(T)/CBS for these water clusters.With the GEBF-CCSD(T)/CBS relative energies as the benchmark results,we have assessed the performance of several theoretical methods widely used for ab initio MD simulations of liquids and aqueous solutions.These methods include density functional theory(DFT)with a number of different functionals,MP2,and density functional tight-binding(the third generation,DFTB3 in short).We find that MP2/aug-cc-pVDZ and several DFT methods(such as LC-(?PBE-D3 and ?B97XD)with the aug-cc-pVTZ basis set can provide satisfactory description for these water clusters.Some widely used functionals(such as B3LYP,PBEO)and DFTB3 are not accurate enough for describing the relative energies of large water clusters.Although the basis set dependence of DFT is less than that of ab initio electron correlation methods,we recommend the combination of a few best functionals and large basis sets(at least aug-cc-pVTZ)in theoretical studies on water clusters or aqueous solutions.In chapter 5,we evaluated the applicability of the GEBF method for three types of molecular clusters and two proteins(2RVD and TC5B)at different theoretical levels.Our calculations show that GEBF(4.0,8)-DFT can reproduce the corresponding standard DFT energies very well for all systems under study.While for GEBF-MP2 calculations,our study shows that a relatively large distance threshold(?4.5 A)and the maximum number no less than ten(??10)are essential for satisfactory results.For example,GEBF(4.5,10)-MP2 calculations can provide accurate results for(CH2OH)32 clusters,but for(HCONH2)32 clusters with more involved hydrogen bond networks,GEBF(4.5,12)-MP2 scheme is necessary for satisfactory results.To conclude,GEBF calculations with suitable parameters can provide accurate ground-state energies for various molecular systems at various theoretical levels and larger subsystems should be constructed in the GEBF-MP2 calculation than those in the GEBF-HF(or DFT)calculation.In addition,the computational time of the GEBF calculations are already considerably less than the corresponding conventional calculations for these medium-sized systems,and the cost of the GEBF method is demonstrated to increase linearly with the system size,which allows the GEBF calculations applicable for even large molecular systems.We believe this work offer some useful information for the applicability of the GEBF method for various molecular systems,which will inspire more applications of the GEBF method in the near future.