Development Of The Cluster-in-molecule Local Correlation Method

Electron correlation methods have been widely used in describing molecular systems.However,the applicability of conventional electron correlation methods is limited to small-and medium-sized systems due to the steep computational scaling with the system size.It is well known that the dynamic correlation between electrons is a local property.To achieve lower or even linear computational scaling,local correlation methods were developed in terms of localized molecular orbitals(LMOs).The cluster-in-molecule(CIM)approach proposed by our group in 2002 has been established to be one of a few representative linear scaling local correlation methods.In this thesis,we mainly focus on further development of the CIM approach.First,a fully optimized CIM method is proposed and it is more efficient and powerful for calculations of large systems.Second,we implement analytical energy gradients of the CIM-second order M(?)ller-Plesset perturbation theory(MP2).With the analytical energy gradients,CIM method can now be used to optimize molecular geometries.In addition,the CIM program is parallelized and it is applicable for real-life chemical systems now.The main contributions and innovations are summarized as follows:In Chapter 3,a more efficient procedure for constructing virtual LMOs of clusters is proposed.In the new procedure,Boughton-Pulay projection method is employed instead of the iterative Boys localization procedure.This new procedure can also be used in other local correlation methods.In addition,basis set superposition error(BSSE)correction for binding energy calculations is implemented.Efficient two-level CIM approach is proposed to accurately calculate reaction energies.Benchmark calculations and illustrative applications at the MP2 and coupled cluster(including CCSD,and CCSD(T))levels show that this newly optimized CIM approach is a reliable theoretical tool for electron correlation calculations of various large chemical systems.In Chapter 4,an efficient analytical energy gradient algorithm for the CIM-MP2 method is presented.In our algorithm,the gradient contributions from the non-separable term of the two-body density matrix on a given atom is extracted from calculations on a cluster constructed for this atom.The other terms in the CIM-MP2 energy gradient expression are evaluated by constructing the density matrices of the whole system with the contributions from all clusters constructed.For basis sets with diffuse functions,tight CIM parameters are necessary to obtain accurate gradients.Benchmark calculations show that the CIM-MP2 method can accurately reproduce the conventional MP2 gradients and geometries for larger systems.The optimized structure of a 174-atom oligopeptide using the CIM-MP2 method with the cc-pVDZ basis set is in good agreement with the corresponding crystal structure.The present CIM-MP2 gradient program can be used for optimizing the geometries of large systems with hundreds of atoms on ordinary workstations.In Chapter 5,we parallelize the correlation energy calculations of a single cluster based on efficient electron correlation modules in PQS package.With the parallelized CIM program,a cluster of 3000 basis functions at MP2 level or 800 basis functions at CCSD(T)level is now accessible.The CIM-MP2 gradient program is partly parallelized and it can be used for gradient calculations of a system with 3000 basis functions.