Traditional quantum chemistry methods are only applicable to medium-sized systems, due to the fact that their computational cost increases rapidly with the system size. We have developed two efficient linear scaling methods, which can extend ab initio quantum chemistry calculations to large systems and periodic condensed phase systems. 
     (1) The cluster-in-molecule (CIM) local correlation approach. The main idea of this approach is to decouple the electron correlation equations of the whole system into a series of electron correlation equations corresponding to small clusters with a subset of orthonormal localized molecular orbitals [1,2]. The total correlation energy is then obtained as a sum of the individual contributions from calculations of various cluster. The most important advantage of this approach is that electron correlation calculations on different clusters can be carried out independently on different computer nodes. This feature allows the CIM method to be applicable to much larger systems than other local correlation methods [3,4]. The analytical energy gradient of the CIM-MP2 method has been implemented and the CIM-MP2 method is now applicable for obtaining optimized structures of systems with hundreds of atoms [5]. The extension of the CIM approach to periodic crystals has been achieved, which can provide accurate descriptions on the lattice energies of various crystals at post-Hartree-Fock levels [6,7]. The CIM method has been recognized to be one of the most promising local correlation approaches for large systems and periodic crystals [8].  
     (2) The energy-based fragmentation approach.In this approach, the ground-state energy of a large molecule can be evaluated as linear combination of ground-state energies of a series of small subsystems [9] or “electrostatically embedded” subsystems [10]. The latter approach, named as the generalized energy-based fragmentation (GEBF) approach, can be easily implemented at various theoretical levels with existing quantum chemistry programs. With this approach, one can now perform full ab initio calculations for large molecules with thousands of atoms on ordinary workstations, providing accurate descriptions on ground-state energies and properties, optimized geometries, vibrational spectra and other properties [11, 12]. The GEBF approach was extended to molecular crystals and other condensed phase systems [13] under periodic boundary condition (PBC). The PBC-GEBF method with advanced quantum chemistry methods is capable of providing accurate descriptions on the lattice energies, crystal structures, vibrational and NMR spectra for various types of condensed phase systems [14].

Representative Publications
[1] Li, S.*, Ma J. and Jiang Y. "Linear scaling local correlation approach for solving the coupled cluster equations of large systems" J. Comput. Chem. 2002, 23, 237. (Times cited: 171)
[2] Li, S.*, Shen, J., Li, W., Jiang Y. “An efficient implementation of the ‘cluster-in-molecule’ approach for local electron correlation calculations” J. Chem. Phys. 2006, 125, 074109. (Times cited: 121)
[3] Guo, Y., Li W., Li S.* "Improved cluster-in-molecule local correlation approach for electron correlation calculation of large systems" J. Phys. Chem. A, 2014, 118, 8996. (Times cited: 39)
[4] Ni, Z., Guo, Y., Neese, F., Li, W., and Li, S.* "Cluster-in-molecule local correlation method with an accurate distant pair correction for large systems", J. Chem. Theory Comput. 2021, 17, 756(Times cited: 24)
[5] Ni, Z., Wang, Y., Li, W., Pulay, P.*, and Li, S.* "Analytical energy gradients for the cluster-in-molecule MP2 method and its application to geometry optimizations of large systems" J. Chem. Theory Comput. 2019, 15, 3623 (Times cited: 7)
[6] Wang, Y., Ni, Z., Li, W.* and Li, S.*, "Cluster-in-molecule local correlation approach for periodic systems", J. Chem. Theory Comput., 2019,15,2933 (Times cited: 11)
[7] Wang, Y., Ni, Z., Neese, F., Li, W., Guo, Y.* and Li, S.* “Cluster-in-Molecule Method Combined with the Domain-Based Local Pair Natural Orbital Approach for Electron Correlation Calculations of Periodic Systems ” J. Chem. Theory Comput., 2022, 18, 6510.
[8] Li, W., Wang, Y., Ni, Z., Li, S.* “Cluster-in-Molecule Local Correlation Method for Dispersion Interactions in Large Systems and Periodic Systems” Acc. Chem. Res. 2023, Accepted.
[9] Li, S.*, Li, W. and Fang, T. “An efficient fragment-based approach for predicting the ground-state energies and structures of large molecules” J. Am. Chem. Soc. 2005, 127, 7215.(Times cited: 215)
[10] Li, W., Li, S.*, Jiang Y. “Generalized energy-based fragmentation approach for computing the ground-state energies and properties of large molecules” J. Phys. Chem. A 2007, 111, 2193. (Times cited: 260)
[11] Hua, W., Fang, T., Li, W., Yu, J.G., Li, S.* “Geometry optimizations and vibrational spectra of large molecules from a generalized energy-based fragmentation approach” J. Phys. Chem. A 2008, 112, 10864. (Times cited: 120)
[12] Li S.*; Li W.; Ma J. "Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates" Acc. Chem. Res. 2014, 47, 2712 (Times cited: 141)
[13] Fang, T.; Li, W.; Gu, F.; Li, S.* "Accurate Prediction of Lattice Energies and Structures of Molecular Crystals with Molecular Quantum Chemistry Methods" J. Chem. Theory Comput. 2015, 11, 91 (Times cited:45).
[14] Li, W.; Dong, H.; Ma, J., and Li, S.* "Structures and spectroscopic properties of large molecules and condensed-phase systems predicted by generalized energy-based fragmentation approach" Acc. Chem. Res. 2021, 54, 169 (Times cited:32).

   We have proposed a block-correlated electron correlation framework for strongly correlated systems, which cannot be accurately described by traditional single-reference electron correlation methods. Block-correlated electron correlation methods are defined in terms of block states and orbitals, different from traditional orbital-based electron correlation methods. Here all orbitals in a system are divided into blocks and the tensor products of block states are used as N-electron basis sets. Depending on how blocks are defined, block-correlated coupled cluster (BCCC) method [1] can have different variants, including CAS-BCCC, GVB-BCCC, etc. With the CASSCF wave function as the reference function, the CAS-BCCC method can provide accurate descriptions for bond-breaking processes and reaction barriers in systems with small active spaces [2,3]. The block correlated second-order perturbation theory based on the GVB reference function has been developed and implemented [4], which has noticeably better performance than MP2 for strongly correlated systems. The GVB-BCCC method is defined with the generalized valence bond (GVB) wave function as the reference function, which is now easily available with our new algorithm [5]. The GVB-BCCC method can provide highly comparable results as the density matrix renormalization group method for systems with large active spaces [6,7], which are beyond the capability of existing multi-reference methods.
     An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems [8]. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. This new method was demonstrated to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.

Representative Publications
[1] Li, S. “Block-correlated coupled cluster theory: The general formulation and its application to the antiferromagnetic Heisenberg model” J. Chem. Phys. 2004, 120, 5017. (Times cited: 61)
[2] Fang, T., Li, S.* “Block correlated coupled cluster theory with a CASSCF reference function: The formulation and test applications for single bond breaking” J. Chem. Phys. 2007, 127, 204108. (Times cited: 57)
[3] Fang, T., Shen, J., Li, S.* “Block correlated coupled cluster method with a complete active-space self-consistent-field reference function: the formula for general active spaces and its applications for multi-bond breaking systems”. J. Chem. Phys. 2008, 128, 224107. (Times cited: 41)
[4] Xu, E.; Li, S.* "Block correlated second order perturbation theory with a generalized valence bond reference function.", J. Chem. Phys. 2013, 139, 174111. (Times cited: 43)
[5] Wang, Q.; Zou, J.; Xu, E.; Pulay, P.*; Li, S. * "Automatic construction of the initial orbitals for efficient generalized valence bond calculations of large systems ", J. Chem. Theory Comput. 2019, 15, 141 (Times cited: 16)
[6] Wang, Q.; Duan, M,; Xu, E.; Zou, J.; Li, S.*"Describing Strong Correlation with Block-Correlated Coupled Cluster Theory ", J. Phys. Chem. Lett. 2020, 11, 7536(Times cited: 12)
[7] Zou, J., Wang, Q., Ren, X., Wang, Y., Zhang, H., Li, S.* "Efficient Implementation of Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Strongly Correlated Systems" J. Chem. Theory Comput. 2022, 18, 5276.
[8] Zhang, H., Zou, J., Ren, X., Li, S.* “Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems” J. Phys. Chem. Lett. 2023, 14, 6792.

   We have carried out a series of computational investigations on mechanisms of important chemical reactions reported experimentally. Our studies on activation of alkanes, H₂ and N₂ have provided important insights for understanding these activation processes. For N₂ reduction at a mononuclear surface Ta center, our calculations show that a rare side-on mode of N₂ coordination to the TaIII center of [(≡SiO)₂TaH] is critical for the subsequent hydride-transfer steps in the cleavage of N₂[1]. For the dihydrogen activation by a phosphine-borane compound, our calculations indicate that an unusual concerted Lewis acid-Lewis base mechanism is responsible for the observed H₂ activation [2]. This mechanism is now well accepted for understanding the activation of small molecules by “frustrated Lewis pairs”.
     On the other hand, we have explored the possibility of designing new chemical reactions based on predicted reaction mechanisms via a combined use of theoretical and experimental approaches. With this research mode, we have found a new B-B bond activation mode and explored its synthetic applications. In this new activation mode, the B-B bond of B₂(pin)₂ can be homolytically cleaved via the cooperative catalysis of two 4-cyanopyridine molecules to generate two persistent pyridine-boryl radicals [3]. With the unique reactivity of such radicals, we have experimentally established several new C-C coupling reactions [4-8]. For example, 4-substituted pyridine derivatives could be synthesized using α, β-unsaturated ketones and 4-cyanopyridine via a radical migration/C-C coupling mechanism [4]. The readily available pyridine-boryl radicals may continue to provide opportunities for developing more diborane involved reactions. With B(C₆F₅)₃ as catalyst, we have developed a hydroarylation of 1,3-dienes with phenols [9], and an OH-assisted propargylation of phenols via sequential additions of aryl terminal alkynes to phenols [10]. We also established a B(C₆F₅)₃-catalyzed mono- and dihydrosilylation of terminal alkynes by using a silane-tuned chemoselectivity strategy [11].
     To facilitate the design of new reactions, we have developed a combined molecular dynamics and coordinate driving (MD/CD) method for automatically searching reaction pathways of chemical reactions [12]. The refined MD/CD algorithm could allow pathways of chemical reactions in solution to be explored [13]. This method is expected to be an efficient tool for design of new reactions and catalysts.

Representative Publications
[1] J. Li, S. Li* "Energetics and Mechanism of Dinitrogen Cleavage at a Mononuclear Surface Tantalum Center: A New Way of Dinitrogen Reduction" Angew. Chem. Int. Ed. 2008, 47, 8040.
[2] Y. Guo, S. Li* "Unusual Concerted Lewis Acid-Lewis Base Mechanism for Hydrogen Activation by a Phosphine-Borane Compound " Inorg. Chem. 2008, 47, 6212.
[3] G. Wang, H. Zhang, J. Zhao, W. Li, J. Cao, C. Zhu*, and S. Li* "Homolytic Cleavage of a B−B Bond by the Cooperative Catalysis of Two Lewis Bases: Computational Design and Experimental Verification ",Angew. Chem. Int. Ed. 2016, 55, 5985.
[4] G. Wang, J. Cao, L. Gao, W. Chen, W. Huang, X. Cheng,* S. Li* "Metal-Free Synthesis of C-4 Substituted Pyridine Derivatives Using Pyridine-boryl Radicals via a Radical Addition/Coupling Mechanism: A Combined Computational and Experimental Study" J. Am. Chem. Soc., 2017, 139, 3904.
[5] J. Cao, G. Wang, L. Gao, X. Cheng, and S. Li* “Organocatalytic reductive coupling of aldehydes with 1,1-diarylethylenes using an in situ generated pyridine-boryl radical", Chem. Sci. 2018, 9, 3664
[6] J. Cao, G. Wang, L. Gao, H. Chen, X. Liu, X. Cheng and S. Li* “Perfluoroalkylative pyridylation of alkenes via 4-cyanopyridine-boryl radicals” Chem. Sci. ,2019, 10, 2767.
[7] L. Gao, G. Wang, J. Cao, D. Yuan, X. Cheng, X. Guo, and S. Li* “Organocatalytic decarboxylative alkylation of N-hydroxy-phthalimide esters enabled by pyridine-boryl radicals” Chem. Commun. 2018, 54, 11534.
[8] L. Gao, G. Wang, J. Cao, H. Chen, Y. Gu, X. Liu, X. Cheng, J. Ma, and S. Li*, “Lewis Acid-Catalyzed Selective Reductive Decarboxylative Pyridylation of N-Hydroxyphthalimide Esters: Synthesis of Congested Pyridine-Substituted Quaternary Carbons” ACS Catal. 2019, 9, 10142.
[9] G. Wang, L. Gao, H. Chen, X. Liu, J. Cao, S. Chen, X. Cheng, and S. Li*, “Chemoselective Borane-Catalyzed Hydroarylation of 1,3-Dienes with Phenols”, Angew. Chem. Int. Ed. 2019, 58, 1694.
[10] H. Chen, M. Yang, G. Wang*, L. Gao, Z. Ni, J. Zou, and S. Li*, “B(C6F5)3 Catalyzed Sequential Additions of Terminal Alkynes to para-Substituted Phenols: Selective Construction of Congested Phenol-Substituted Quaternary Carbons” Org. Lett. 2021, 23, 5533
[11] G. Wang, X. Su, L. Gao, X. Liu, G. Li and S. Li*, “Borane-catalyzed selective dihydrosilylation of terminal alkynes: reaction development and mechanistic insight” Chem. Sci. 2021, 12, 10883
[12] M. Yang, J. Zou, G. Wang, S. Li,* “Automatic Reaction Pathway Search via Combined Molecular Dynamics and Coordinate Driving Method” J. Phys. Chem. A 2017, 121, 1351.
[13] M. Yang, L. Yang, G. Wang, Y. Zhou,* D. Xie, S. Li,* “Combined Molecular Dynamics and Coordinate Driving Method for Automatic Reaction Pathway Search of Reactions in Solution” J. Chem. Theory Comput. 2018, 14, 5787.

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