Conventional quantum chemistry methods face significant limitations in modeling large systems. Since their computational cost increases steeply with the system size, they are usually limited to molecules with several hundreds of atoms. To address this challenge, we have developed two novel linear-scaling algorithms that enable accurate ab initio quantum chemistry calculations for complex molecular systems with thousands of atoms and periodic condensed-phase materials with large unit cells. 
      The cluster-in-molecule (CIM) local correlation approach. The core concept of the CIM method involves decoupling the electron correlation equations of a large system into a series of electron correlation equations corresponding to smaller, computationally manageable clusters defined by subsets of orthonormal localized molecular orbitals [1,2]. The total correlation energy is calculated as the sum of contributions from individual clusters, enabling efficient parallelization by distributing independent cluster calculations across multiple computer nodes. This parallelization capability distinguishes CIM from other local correlation methods, allowing it to treat effectively systems with thousands of atoms [3,4]. The analytical energy gradient for the CIM-MP2 (second-order Møller-Plesset perturbation theory) method has been developed, facilitating geometry optimizations for large molecular systems [5-6]. The CIM framework has also been extended to periodic crystals, achieving high accuracy in calculating lattice energies at post-Hartree–Fock levels, a critical advancement for solid-state and materials science applications [7,8]. Due to its scalability, parallel efficiency, and successful applications to both molecular and crystalline systems, the CIM approach is widely regarded as a leading-edge methodology for large-scale and periodic electron correlation studies [9]. 
      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 [10] or “electrostatically embedded” subsystems [11]. The latter, termed the generalized energy-based fragmentation (GEBF) approach, is readily implemented at various levels of theory using existing quantum chemistry software. This method enables full ab initio calculations for molecules with thousands of atoms on standard workstations, yielding accurate predictions of ground-state energies, molecular properties, optimized geometries, vibrational spectra, and related characteristics [12, 13]. The GEBF framework has been extended to molecular crystals and condensed-phase systems under periodic boundary conditions (PBC) [14]. By integrating the PBC-GEBF method with advanced quantum chemistry techniques, researchers can precisely model lattice energies, crystal structures, vibrational spectra, and NMR spectra for diverse condensed-phase materials [15]. This approach provides a powerful tool for studying complex systems in both molecular and solid-state chemistry.

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: 200)
[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: 148)
[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: 48)
[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: 44)
[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: 18)
[6] Wang, Y., Ni, Z., Li, W.* and Li, S.*, "Analytical Gradient Using Cluster-in-Molecule RI-MP2 Method for the Geometry Optimizations of Large Systems.", J. Chem. Theory Comput., 2024,20,3626 (Times cited: 3)
[7] Zheng, Y.，Ni, Z.，Wang, Y.，Li, W.*，Li, S.*, "Cluster-in-molecule local correlation approach for periodic systems", J. Chem. Theory Comput., 2019,15,2933 (Times cited: 20)
[8] 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.(Times cited: 9)
[9] 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, 56, 3462. (Times cited: 10)
[10] 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: 229)
[11] 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: 298)
[12] 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: 131)
[13] 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: 176)
[14] 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:47).
[15] 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:57).

   Correlated Systems
     Traditional single-reference electron correlation methods, such as coupled cluster theory, often fail to accurately describe strongly correlated systems including bond dissociation processes and transition metal complexes, due to their inherent multi-configurational nature. To address this limitation, we have developed a block-correlated electron correlation framework that is defined in terms of many-orbital blocks instead of orbitals only [1]. In this framework, orbitals are partitioned into chemically intuitive blocks (e.g., bonding pairs, lone pairs), and the total wavefunction is expanded using tensor products of many-electron block states as the N-electron basis. This strategy inherently captures both static and dynamic correlations while avoiding the exponential scaling of traditional multi-reference methods. The framework supports multiple variants depending on block definitions and reference states:
     CAS-BCCC: Using a CASSCF reference, this method delivers precise descriptions of bond-breaking processes and reaction barriers in systems with small active spaces, outperforming conventional multi-reference coupled cluster methods in accuracy [2,3].
     GVB-BCPT2: A second-order perturbation theory built on the GVB reference demonstrates superior performance over MP2 for strongly correlated systems, enabling reasonable descriptions of both weak and strong correlation effects [4].
     GVB-BCCC: By adopting a generalized valence bond (GVB) reference, this approach enables accurate and scalable treatments of systems with large active spaces. GVB calculations of general molecules are now easily available with our new algorithm [5]. With up to three- or four-block correlations, GVB-BCCC achieves accuracy comparable to the density matrix renormalization group (DMRG) method [6-9]. The unitary BCCC ansatz based on the GVB state (GVB-UBCCC) was proposed for simulating strongly correlate systems on quantum computers [10].
     To extend the framework to excited states, we propose the equation-of-motion block-correlated coupled cluster method (EOM-GVB-BCCC). The EOM-GVB-BCCC3 method, with up to three-block correlation, has shown promise in predicting low-lying excited states for systems with large active spaces, offering a cost-effective alternative to DMRG [11,12].
     In summary, these block-correlated methods are expected to become standard theoretical tools for ground- and excited-state structures and properties of strongly correlated systems.
     

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: 72)
[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: 60)
[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: 44)
[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: 53)
[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: 28)
[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: 28)
[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.(Times cited: 13)
[8] Ren, X., Zou, J., Zhang, H., Li, W.,* Li, S.* "Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems." J. Phys. Chem. Lett. 2024, 15, 693 (Times cited: 10).
[9] Ren, X., Zou, J., Li, W.*, Li, S.* "Block-Correlated Coupled Cluster Theory Based on the Generalized Valence Bond Reference for Singlet–Triplet Energy Gaps of Strongly Correlated Systems" J. Phys. Chem. Lett. 2024, 15, 11342.
[10] Hu, J., Wang, Q.*, Li, S.* "Unitary Block-Correlated Coupled Cluster Ansatz based on the Generalized Valence Bond Wave Function for Quantum Simulation " J. Chem. Theory Comput. 2025, 21, 4579.
[11] 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 (Times cited: 3)
[12] Zhang, H., Zou, J., Ren, X., Li, S.* “Equation-of-Motion Block-Correlated Coupled Cluster Method with up to Three-Block Correlation for Excited Electronic States of Strongly Correlated Systems” J. Phys. Chem. Lett. 2025, 16, 4635.

  Theoretical calculations serve as a cornerstone in modern chemical research. A primary focus of our work involves elucidating reaction mechanisms underlying pivotal chemical transformations, providing atomistic insights into experimentally observed phenomena. Concurrently, we pursue the computational design and virtual screening of novel chemical reactions and catalytic systems, rigorously validated through experimental studies. To accelerate reaction discovery, we have developed advanced methodologies for automated reaction pathway exploration and systematic mechanistic analysis.
     Novel Mechanisms for Small-Molecule Activation Our research on the activation of inert molecules—including alkanes, H₂, and N₂—has uncovered fundamental mechanistic principles governing these challenging transformations. In the case of N₂ reduction mediated by a mononuclear surface Ta(III) center, computational studies reveal that a rare side-on coordination of N₂ to the [(≡SiO)₂TaH] complex is crucial for stabilizing transition states in subsequent hydride transfer steps, ultimately enabling N≡N bond cleavage [1]. Furthermore, our theoretical investigations into H₂ activation by a phosphine-borane frustrated Lewis pair (FLP) demonstrate a concerted mechanism driven by Lewis acid-base cooperation [2]. This paradigm, now broadly recognized in the field, has informed the rational design of FLP-based catalysts for activating recalcitrant substrates such as CO₂ and alkanes under mild conditions.
    Discovery of New Reactions via Computation-Driven Design Our computational studies revealed that cooperative catalysis involving two 4-cyanopyridine molecules facilitates the homolytic cleavage of the B–B bond in B₂(pin)₂, generating persistent pyridine-boryl radical intermediates [3]. This prediction is validated by experimental studies. This new B-B activation mode laid the foundation for subsequent diverse catalytic transformations [4-7]. Guided by mechanistic insights, we expanded the scope of boron-mediated catalysis. Using B(C₆F₅)₃ as a catalyst, we developed a regioselective hydroarylation of 1,3-dienes with phenols [8], and a silane-tuned chemoselectivity strategy enabling mono- and dihydrosilylation of terminal alkynes [9]. In addition, we established a silyl-directed ortho C(sp²)–H borylation protocol for substituted arenes using a Ni(cod)₂/PMe₃/KHMDS catalyst system [10]. In the realm of asymmetric catalysis, our computational and experimental studies on BINOL-aluminum-catalyzed hydroboration of heteroaryl ketones uncovered a chiral-at-metal stereoinduction mechanism [11]. This discovery challenges conventional models and establishes a new paradigm for stereochemical control in BINOL-metal catalysis.
    Computational Tools for 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 in gas phase and solution [12-14]. The method is expected to offer a platform for de novo design of new homogeneous 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, 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.
[8] 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.
[9] 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
[10] X. Su, G. Li, L. He, S. Chen, X. Yang, G. Wang*, S. Li*, “Nickel-Catalyzed, Silyl-Directed, Ortho-Borylation of Arenes via an Unusual Ni(II)/Ni(IV) Catalytic Cycle” Nat. Commun. 2024, 15 , 7549.
[11] Z. Li, P. Chen, Z. Ni, L. Gao, Y. Zhao, R. Wang, C. Zhu, G. Wang*, S. Li*, “NAn Unusual Chiral-at-Metal Mechanism for BINOL-Metal Asymmetric Catalysis” Nat. Commun. 2025, 16, 735.
[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.
[14] G. Li, Z. Li, L. Gao, S. Chen, G. Wang* and S. Li* “Combined molecular dynamics and coordinate driving method for automatically searching complicated reaction pathways”Phys. Chem. Chem. Phys. 2023, 25, 23696.

                                                                                                                                                                 Top