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Wang Y, Lin Z, Ouyang R, Jiang B, Zhang IY, Xu X. Toward Efficient and Unified Treatment of Static and Dynamic Correlations in Generalized Kohn-Sham Density Functional Theory. JACS AU 2024; 4:3205-3216. [PMID: 39211596 PMCID: PMC11350721 DOI: 10.1021/jacsau.4c00488] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/10/2024] [Revised: 07/26/2024] [Accepted: 08/06/2024] [Indexed: 09/04/2024]
Abstract
Accurate description of the static correlation poses a persistent challenge in electronic structure theory, particularly when it has to be concurrently considered with the dynamic correlation. We develop here a method in the generalized Kohn-Sham density functional theory (DFT) framework, named R-xDH7-SCC15, which achieves an unprecedented accuracy in capturing the static correlation, while maintaining a good description of the dynamic correlation on par with the state-of-the-art DFT and wave function theory methods, all grounded in the same single-reference black-box methodology. Central to R-xDH7-SCC15 is a general-purpose static correlation correction (SCC) model applied to the renormalized XYG3-type doubly hybrid method (R-xDH7). The SCC model development involves a hybrid machine learning strategy that integrates symbolic regression with nonlinear parameter optimization, aiming to achieve a balance between generalization capability, numerical accuracy, and interpretability. Extensive benchmark studies confirm the robustness and broad applicability of R-xDH7-SCC15 across a diverse array of main-group chemical scenarios. Notably, it displays exceptional aptitude in accurately characterizing intricate reaction kinetics and dynamic processes in regions distant from equilibrium, where the influence of static correlation is most profound. Its capability to consistently and efficiently predict the whole energy profiles, activation barriers, and reaction pathways within a user-friendly "black-box" framework represents an important advance in the field of electronic structure theory.
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Affiliation(s)
- Yizhen Wang
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
| | - Zihan Lin
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
| | - Runhai Ouyang
- Materials
Genome Institute, Shanghai University, Shanghai 200444, China
| | - Bin Jiang
- Key
Laboratory of Precision and Intelligent Chemistry, Department of Chemical
Physics, University of Science and Technology
of China, Hefei, Anhui 230026, China
- Hefei
National Laboratory, Hefei 230088, China
| | - Igor Ying Zhang
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
- Hefei
National Laboratory, Hefei 230088, China
- Shanghai
Key Laboratory of Bioactive Small Molecules, Shanghai200032, China
| | - Xin Xu
- Shanghai
Key Laboratory of Molecular Catalysis and Innovation Materials, Collaborative
Innovation Centre of Chemistry for Energy Materials, MOE Laboratory
for Computational Physical Science, Department of Chemistry, Fudan University, Shanghai 200438, China
- Hefei
National Laboratory, Hefei 230088, China
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2
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Hoja J, List A, Boese AD. Multimer Embedding Approach for Molecular Crystals up to Harmonic Vibrational Properties. J Chem Theory Comput 2024; 20:357-367. [PMID: 38109226 PMCID: PMC10782452 DOI: 10.1021/acs.jctc.3c01082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Revised: 11/16/2023] [Accepted: 11/20/2023] [Indexed: 12/20/2023]
Abstract
Accurate calculations of molecular crystals are crucial for drug design and crystal engineering. However, periodic high-level density functional calculations using hybrid functionals are often prohibitively expensive for the relevant systems. These expensive periodic calculations can be circumvented by the usage of embedding methods in which, for instance, the periodic calculation is only performed at a lower-cost level and then monomer energies and dimer interactions are replaced by those of the higher-level method. Herein, we extend such a multimer embedding approach to enable energy corrections for trimer interactions and the calculation of harmonic vibrational properties up to the dimer level. We evaluate this approach for the X23 benchmark set of molecular crystals by approximating a periodic hybrid density functional (PBE0+MBD) by embedding multimers into less expensive calculations using a generalized-gradient approximation functional (PBE+MBD). We show that trimer interactions are crucial for accurately approximating lattice energies within 1 kJ/mol and might also be needed for further improvement of lattice constants and hence cell volumes. Finally, the vibrational properties are already very well captured at the monomer and dimer level, making it possible to approximate vibrational free energies at room temperature within 1 kJ/mol.
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Affiliation(s)
- Johannes Hoja
- Department of Chemistry, University
of Graz, Heinrichstraße 28/IV, Graz 8010, Austria
| | - Alexander List
- Department of Chemistry, University
of Graz, Heinrichstraße 28/IV, Graz 8010, Austria
| | - A. Daniel Boese
- Department of Chemistry, University
of Graz, Heinrichstraße 28/IV, Graz 8010, Austria
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3
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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; 56:3462-3474. [PMID: 37991873 DOI: 10.1021/acs.accounts.3c00538] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2023]
Abstract
ConspectusThe noncovalent interactions, including dispersion interactions, control the structures and stabilities of complex chemical systems, including host-guest complexes and the adsorption process of molecules on the solid surfaces. The density functional theory (DFT) with empirical dispersion correction is now the working horse in many areas of applications. Post-Hartree-Fock (post-HF) methods have been well recognized to provide more accurate descriptions in a systematic way. However, traditional post-HF methods are mainly limited to small- or medium-sized systems, and their applications to periodic condensed phase systems are still very limited due to their expensive computational costs.To extend post-HF calculations to large molecules, the cluster-in-molecule (CIM) local correlation approach has been established, allowing highly accurate electron correlation calculations that are routinely available for very large systems. In the CIM approach, the electron correlation energy of a large molecule could be obtained from electron correlation calculations on a series of clusters, each of which contains a subset of occupied and virtual localized molecular orbitals. The CIM method could be massively and efficiently parallelized on general computer clusters. The CIM method has been implemented at various electron correlation levels, including second-order Mo̷ller-Plesset perturbation theory (MP2), coupled cluster singles and doubles (CCSD), CCSD with perturbative triples correction [CCSD(T)], etc. The CIM-MP2 energy gradient algorithm was developed and applied to the geometry optimizations of large systems. The CIM method has also been extended to condensed-phase systems under periodic boundary conditions (PBC-CIM). For periodic systems, the correlation energy per unit cell could be evaluated with correlation energy contributions from a series of clusters that are built with localized Wannier functions.CIM-based electron correlation calculations have been employed to investigate a number of chemical problems in which the dispersion interaction is important. CIM-based post-HF methods including CIM domain-based local pair natural orbital (DLPNO) CCSD(T) are applied to compute the relative or binding energies of biological systems or supramolecular complexes, the reaction barrier in a relatively complex chemical reaction. The CIM-MP2 method is used to obtain the optimized geometry of large systems. CIM-based post-HF calculations have also been used to compute the cohesive energies of molecular crystals and adsorption energies of molecules on the solid surfaces. The CIM and its PBC variant are expected to become a powerful theoretical tool for accurate calculations of the energies and structures for a broad range of large systems and condensed-phase systems with significant dispersion interactions.
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Affiliation(s)
- Wei Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Yuqi Wang
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
| | - Zhigang Ni
- College of Material, Chemistry and Chemical Engineering, Hangzhou Normal University, Hangzhou 311121, People's Republic of China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, New Cornerstone Science Laboratory, School of Chemistry and Chemical Engineering, Nanjing University, Nanjing 210023, People's Republic of China
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4
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Chen B, Xu X. Discriminating and understanding molecular crystal polymorphism. J Comput Chem 2023; 44:969-979. [PMID: 36585855 DOI: 10.1002/jcc.27057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2022] [Revised: 11/01/2022] [Accepted: 11/30/2022] [Indexed: 01/01/2023]
Abstract
Polymorph discrimination for a molecular crystal has long been a challenging task, which, nonetheless, is a major concern in the pharmaceutical industry. In this work, we have investigated polymorph discrimination on three different molecular crystals, tetrolic acid, oxalic acid, and oxalyl dihydrazide, covering both packing polymorphism and conformational polymorphism. To gain more understanding, we have performed energy decomposition analysis based on many-body expansion, and have compared the results from the XO-PBC method, that is, the eXtended ONIOM method (XO) with the periodic boundary condition (PBC), with those from some commonly used dispersion corrected density functional theory (DFT-D) methods. It is shown here that, with the XYG3 doubly hybrid functional chosen as the target high level to capture the intra- and short-range intermolecular interactions, and the periodic PBE as the basic low level to take long range interactions into account, the XO-PBC(XYG3:PBE) method not only obtains the correct experimental stability orderings, but also predicts reasonable polymorph energy ranges for all three cases. Our results have demonstrated the usefulness of the present theoretical methods, in particular XO-PBC, while highlighted the importance of a better treatment of different kinds of interactions to be beneficial to polymorph control.
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Affiliation(s)
- Bozhu Chen
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Fudan University, Shanghai, China
| | - Xin Xu
- Department of Chemistry, Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Fudan University, Shanghai, China.,Hefei National Laboratory, Hefei, China
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5
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Chen Z, Liu Z, Xu X. Accurate descriptions of molecule-surface interactions in electrocatalytic CO 2 reduction on the copper surfaces. Nat Commun 2023; 14:936. [PMID: 36807556 PMCID: PMC9941474 DOI: 10.1038/s41467-023-36695-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2022] [Accepted: 02/14/2023] [Indexed: 02/22/2023] Open
Abstract
Copper-based catalysts play a pivotal role in many industrial processes and hold a great promise for electrocatalytic CO2 reduction reaction into valuable chemicals and fuels. Towards the rational design of catalysts, the growing demand on theoretical study is seriously at odds with the low accuracy of the most widely used functionals of generalized gradient approximation. Here, we present results using a hybrid scheme that combines the doubly hybrid XYG3 functional and the periodic generalized gradient approximation, whose accuracy is validated against an experimental set on copper surfaces. A near chemical accuracy is established for this set, which, in turn, leads to a substantial improvement for the calculated equilibrium and onset potentials as against the experimental values for CO2 reduction to CO on Cu(111) and Cu(100) electrodes. We anticipate that the easy use of the hybrid scheme will boost the predictive power for accurate descriptions of molecule-surface interactions in heterogeneous catalysis.
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Affiliation(s)
- Zheng Chen
- grid.8547.e0000 0001 0125 2443Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, 200433 Shanghai, People’s Republic of China
| | - Zhangyun Liu
- grid.8547.e0000 0001 0125 2443Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, 200433 Shanghai, People’s Republic of China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, 200433, Shanghai, People's Republic of China. .,Hefei National Laboratory, 230088, Hefei, P. R. China.
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6
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Chen WK, Fang WH, Cui G. Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems. J Chem Phys 2023; 158:044110. [PMID: 36725521 DOI: 10.1063/5.0129458] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023] Open
Abstract
Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.
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Affiliation(s)
- Wen-Kai Chen
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Wei-Hai Fang
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Ganglong Cui
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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7
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Yan W, Xu X. Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals. J Chem Theory Comput 2022; 18:2931-2946. [PMID: 35467852 DOI: 10.1021/acs.jctc.2c00055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful and versatile tools in elucidating molecular structures. To eliminate ambiguities of experimental assignments, accurate calculations of NMR spectra are of great importance. Here, a method for theoretical evaluation of the NMR shielding constants by analytic derivatives using gauge including atomic orbitals (GIAO) has been implemented for the XYG3 type of doubly hybrid density functionals (xDH), namely, the GIAO-xDH method. Benchmark calculations on shielding constants and chemical shifts demonstrate the remarkable accuracy of the GIAO-xDH method, compared to the accurate CCSD(T) references. It is shown here that the XYGJ-OS functional is able to give a mean absolute deviation (MAD) of ∼3.0 ppm in the calculated shielding constants for 13C, 15N, 17O, 19F, while both XYGJ-OS and xDH-PBE0 functionals are able to provide a satisfactory estimation of chemical shifts with MADs of ∼0.03 and 1.0 ppm for 1H and 13C, respectively. The basis set influence upon the method has been examined and a computational scheme considering both accuracy and efficiency has been proposed and tested to predict the experimental 13C chemical shifts of five medium-sized natural product molecules, yielding a MAD of ∼1.0 ppm, which demonstrates the practical feasibility of the GIAO-xDH method.
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Affiliation(s)
- Wenjie Yan
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
| | - Xin Xu
- Collaborative Innovation Center of Chemistry for Energy Materials, Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, Ministry of Education Key Laboratory of Computational Physical Sciences, Department of Chemistry, Fudan University, Shanghai, 200433, China
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8
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Li Y, Wang D, Fu F, Xia Q, Li W, Li S. Structures and properties of ionic crystals and condensed phase ionic liquids predicted with the generalized energy-based fragmentation method. J Comput Chem 2022; 43:704-716. [PMID: 35213748 DOI: 10.1002/jcc.26828] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2021] [Revised: 01/20/2022] [Accepted: 01/21/2022] [Indexed: 11/11/2022]
Abstract
The generalized energy-based fragmentation (GEBF) approach is extended to facilitate ab initio investigations of structures, lattice energies, vibrational spectra and 1 H NMR chemical shifts of ionic crystals and condensed-phase ionic liquids (ILs) with the periodic boundary conditions (PBC). For selected periodic systems, our results demonstrate that the so-called PBC-GEBF approach can provide satisfactory descriptions on ground-state energies, structures, and vibrational spectra of ionic crystals and IL crystals. The PBC-GEBF approach is then applied to three realistic condensed phase systems. For three ionic crystals (LiCl, NaCl, and KCl), we apply the PBC-GEBF approach with MP2 theory as well as some popular DFT methods to investigate their crystal structures and lattice energies. Our calculations indicate that the crystal structures obtained with PBC-GEBF-MP2/6-311 + G** are very close to the corresponding X-ray structures, while PBC-GEBF-ωB97X-D/6-311 + G** provides satisfactory prediction for crystal structures and lattice energies. For two polymorphs of [n-C4 mim][Cl] crystals, we find that the PBC-GEBF approach at the M06-2X/6-311 + G** level can give a satisfactory descriptions on structures and Raman spectra of these two crystals. Furthermore, for [C2 mim][BF4 ] ILs, we demonstrate that their 1 H NMR chemical shifts can be estimated from averaging over 5 typical snapshots (extracted from MD simulations) with the PBC-GEBF approach at the B97-2/pcSseg-2 level. The calculated results account for the observed experimental data quite well. Therefore, we expect that the PBC-GEBF approach, combined with various quantum chemistry methods, will become an effective tool in predicting structures and properties of ionic crystals and condensed-phase ILs.
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Affiliation(s)
- Yunzhi Li
- School of Chemistry and Chemical Engineering, Linyi University, Linyi, China.,School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, China
| | - Dong Wang
- School of Chemistry and Chemical Engineering, Linyi University, Linyi, China
| | - Fangjia Fu
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, China
| | - Qiying Xia
- School of Chemistry and Chemical Engineering, Linyi University, Linyi, China
| | - Wei Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, China
| | - Shuhua Li
- School of Chemistry and Chemical Engineering, Key Laboratory of Mesoscopic Chemistry of Ministry of Education, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing, China
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9
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Wang Y, Li Y, Chen J, Zhang IY, Xu X. Doubly Hybrid Functionals Close to Chemical Accuracy for Both Finite and Extended Systems: Implementation and Test of XYG3 and XYGJ-OS. JACS AU 2021; 1:543-549. [PMID: 34467317 PMCID: PMC8395692 DOI: 10.1021/jacsau.1c00011] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
While being widely used to understand the chemical reactions in heterogeneous catalysis or other multidisciplinary systems, a great challenge that semilocal and hybrid density functional approximations (DFAs) are facing is to deliver a uniformly accurate description for both finite and extended systems. Herein, we perform reliable and well-converged periodic calculations of two doubly hybrid approximations (DHAs), XYG3 and XYGJ-OS, and demonstrate that the good accuracy of DHAs achieved for molecules is transferable to the semiconductors and insulators. Such an accuracy is not only for energetic properties but also for the first- and second-order response properties, which is general for different kinds of chemical environments, including simple cubic bulks, perovskite-type transition metal oxides like TiO2, and heterogeneous systems like CO adsorption on the NaCl(100) surface. The present finding has strengthened the predictive power of DFT, which not only will inspire the future development of the top-rung DFAs but also will boost their applications in multidisciplinary studies with high accuracy and efficiency.
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Affiliation(s)
- Yizhen Wang
- Collaborative
Innovation Center of Chemistry for Energy Materials, Shanghai, Key
Laboratory of Molecular Catalysis and Innovative Materials, MOE Key
Laboratory of Computational Physical Sciences, Shanghai Key Laboratory
of Bioactive Small Molecules, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Yajing Li
- Collaborative
Innovation Center of Chemistry for Energy Materials, Shanghai, Key
Laboratory of Molecular Catalysis and Innovative Materials, MOE Key
Laboratory of Computational Physical Sciences, Shanghai Key Laboratory
of Bioactive Small Molecules, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Jun Chen
- State
Key Laboratory of Structural Chemistry, Fujian Institute of Research on the Structure of Matter, Chinese
Academy of Sciences, Fuzhou 350002, People’s Republic
of China
| | - Igor Ying Zhang
- Collaborative
Innovation Center of Chemistry for Energy Materials, Shanghai, Key
Laboratory of Molecular Catalysis and Innovative Materials, MOE Key
Laboratory of Computational Physical Sciences, Shanghai Key Laboratory
of Bioactive Small Molecules, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
| | - Xin Xu
- Collaborative
Innovation Center of Chemistry for Energy Materials, Shanghai, Key
Laboratory of Molecular Catalysis and Innovative Materials, MOE Key
Laboratory of Computational Physical Sciences, Shanghai Key Laboratory
of Bioactive Small Molecules, Department of Chemistry, Fudan University, Shanghai 200433, People’s Republic of China
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