We describe an implementation of the cluster-in-molecule （CIM） resolution of the identity （RI） approximation second-order Moller-Plesset perturbation theory （CIM-RI-MP2）, with the purpose of extending RI-MP2 calculations to very large systems. For typical conformers of several large polypeptides, we calculated their conformational energy differences with the CIM-RI-MP2 and the generalized energy-based fragmentation MP2 （GEBF-MP2） methods, and compared these results with the density functional theory （DFT） results obtained with several popular functionals. Our calculations show that the conformational energy differences obtained with CIM-RI-MP2 and GEBF-MP2 are very close to each other. In comparison with the GEBF-MP2 and CIM-RI-MP2 relative energies, we found that the DFT functionals （CAM-B3LYP-D3, LC-ωPBE-D3, M05-2X, M06-2X and coB97XD） can give quite accurate conformational energy differences for structurally similar conformers, but provide less-accurate results for structurally very different conformers.
We review our recent work on the methodology development of the excited-state properties for the molecules in vacuum and liquid solution.The general algorithms of analytical energy derivatives for the specific properties such as the first and second geometrical derivatives and IR/Raman intensities are demonstrated in the framework of the time-dependent density functional theory(TDDFT).The performance of the analytical approaches on the calculation of excited-state energy Hessian has also been shown.It is found that the analytical approaches are superior to the finite-difference method on the computational accuracy and efficiency.The computational cost for a TDDFT excited-state Hessian calculation is only 2–3 times as that for the DFT ground-state Hessian calculation.With the low computational complexity of the developed analytical approaches,it becomes feasible to realize the large-scale numerical calculations on the excited-state vibrational frequencies,vibrational spectroscopies and the electronic-structure parameters which enter the spectrum calculations of electronic absorption and emission,and resonance Raman spectroscopies for medium-to large-sized systems.
A linear scaling local correlation method,cluster-in-molecule(CIM)method,was developed in the last decade for large systems.The basic idea of the CIM method is that the electron correlation energy of a large system,within the M ller-Plesset perturbation theory(MP)or coupled cluster(CC)theory,can be approximately obtained from solving the corresponding MP or CC equations of various clusters.Each of such clusters consists of a subset of localized molecular orbitals(LMOs)of the target system,and can be treated independently at various theory levels.In the present article,the main idea of the CIM method is reviewed,followed by brief descriptions of some recent developments,including its multilevel extension and different ways of constructing clusters.Then,some applications for large systems are illustrated.The CIM method is shown to be an efficient and reliable method for electron correlation calculations of large systems,including biomolecules and supramolecular complexes.
