Charge-Transfer-Induced <i>para</i>-Selective sp² C–H Bond Activation of Arenes by Use of a Hypervalent Iodine Compound: A Theoretical Study

The reaction mechanism of the C–H bond activation of toluene promoted by the hypervalent iodine compound TIPP-I­(OH)­OTs was investigated in detail by density functional theory calculations. Our calculations show that a plausible reaction pathway of the C–H bond activation of toluene contains two stages: (1) the ligand exchange process on TIPP-I­(OH)­OTs, involving the substitution of the hydroxyl group and tosyloxyl group with TfOH, and (2) the C–H bond activation of toluene promoted by the hypervalent iodine center with the assistance of the triflate anion. The second step is the rate-limiting step with a relatively low free energy barrier of 19.6 kcal mol^–1 in acetonitrile, which is in accord with the experimental fact that the reaction takes place at room temperature. Frontier molecular orbits and natural population analysis show that partial electron transfer from the toluene to the hypervalent iodine moiety occurs in the charge-transfer complex, resulting in the activation of the C–H bond at the para position of toluene. Further calculations show that this hypervalent iodine compound promoted C–H bond activation reaction will be effective if the substrate is electron-rich and a strong Brønsted acid is used

Generalized Energy-Based Fragmentation Approach and Its Applications to Macromolecules and Molecular Aggregates

ConspectusThe generalized energy-based fragmentation (GEBF) approach provides a very simple way of approximately evaluating the ground-state energy or properties of a large system in terms of ground-state energies of various small “electrostatically embedded” subsystems, which can be calculated with any traditional <i>ab initio</i> quantum chemistry (X) method (X = Hartree–Fock, density functional theory, and so on). Due to its excellent parallel efficiency, the GEBF approach at the X theory level (GEBF-X) allows full quantum mechanical (QM) calculations to be accessible for systems with hundreds and even thousands of atoms on ordinary workstations. The implementation of the GEBF approach at various theoretical levels can be easily done with existing quantum chemistry programs.This Account reviews the methodology, implementation, and applications of the GEBF-X approach. This method has been successfully applied to optimize the structures of various large systems including molecular clusters, polypeptides, proteins, and foldamers. Such investigations could allow us to elucidate the origin and nature of the cooperative interaction in secondary structures of long peptides or the driving force of the self-assembly processes of aromatic oligoamides. These GEBF-based QM calculations reveal that the structures and stability of various complex systems result from a subtle balance of many types of noncovalent interactions such as hydrogen bonding and van der Waals interactions. The GEBF-based <i>ab initio</i> molecular dynamics (AIMD) method also allows the investigation of dynamic behaviors of large systems on the order of tens of picoseconds. It was demonstrated that the conformational dynamics of two model peptides predicted by GEBF-based AIMD are noticeably different from those predicted by the classical force field MD method.With the target of extending QM calculations to molecular aggregates in the condensed phase, we have implemented the GEBF-based multilayer hybrid models, which could provide satisfactory descriptions of the binding energies between a solute molecule and its surrounding waters and the chain-length dependence of the conformational changes of oligomers in aqueous solutions. A coarse-grained polarizable molecular mechanics model, furnished with GEBF-X dipole moments of subsystems, exhibits some advantages of treating the electrostatic polarization with reduced computational costs. We anticipate that the GEBF approach will continue to develop with the ultimate goal of studying complicated phenomena at mesoscopic scales and serve as a practical tool to elucidate the structure and dynamics of chemical and biological systems

Generalized Energy-Based Fragmentation CCSD(T)-F12a Method and Application to the Relative Energies of Water Clusters (H₂O)₂₀

The generalized energy-based fragmentation (GEBF) approach has been implemented for the explicitly correlated F12a of coupled-cluster with the noniterative triples corrections [CCSD­(T)-F12a] method for medium- and large-sized systems. By combining the canonical Hartree–Fock (HF) total energies and the GEBF-X correlation energies, the GEBF-X/HF method is illustrated to be more accurate than the origin GEBF-X method, where X could be any electron correlation method, such as second-order Møller–Plesset perturbation theory (MP2), MP2-F12, CCSD­(T), and CCSD­(T)-F12a. By combining the GEBF-X/HF results at the MP2-F12 and CCSD­(T)-F12a levels, we can approximately achieve the CCSD­(T) complete basis set (CBS) limit. Our test calculations for 10 low-energy isomers of water 20-mers show that for the relative energies of large water clusters, both the basis set and high-level electron correlation effects should be taken into account, in which the former is even more important. In addition, the GEBF-CCSD­(T)/HF method at the CBS limit is used to evaluate 32 levels of density functional theory (DFT) methods. The results show that the DFT methods are difficult to predict the relative energies between the isomers of water 20-mers. The GEBF-CCSD­(T)/HF method at the CBS limit is expected to be a benchmark for DFT and other electron correlation methods for medium- and large-sized systems with complex structures, in which both the basis set and electron correlation effects are important

Improved Cluster-in-Molecule Local Correlation Approach for Electron Correlation Calculation of Large Systems

An improved cluster-in-molecule (CIM) local correlation approach is developed to allow electron correlation calculations of large systems more accurate and faster. We have proposed a refined strategy of constructing virtual LMOs of various clusters, which is suitable for basis sets of various types. To recover medium-range electron correlation, which is important for quantitative descriptions of large systems, we find that a larger distance threshold (ξ) is necessary for highly accurate results. Our illustrative calculations show that the present CIM-MP2 (second-order Møller-Plesser perturbation theory, MP2) or CIM-CCSD (coupled cluster singles and doubles, CCSD) scheme with a suitable ξ value is capable of recovering more than 99.8% correlation energies for a wide range of systems at different basis sets. Furthermore, the present CIM-MP2 scheme can provide reliable relative energy differences as the conventional MP2 method for secondary structures of polypeptides

Generalized Energy-Based Fragmentation Approach for Localized Excited States of Large Systems

We have extended the generalized energy-based fragmentation (GEBF) approach to localized excited states of large systems. In this approach, the excited-state energy of a large system could be expressed as the combination of the excited-state energies of “active subsystems”, which contains the chromophore center, and the ground-state energies of “inactive subsystems”. The GEBF approach has been implemented at the levels of time-dependent density functional theory (TDDFT) and approximate coupled cluster singles and doubles (CC2) method. Our results show that GEBF-TDDFT can reproduce the TDDFT excitation energies and solvatochromic shifts for large systems and that GEBF-CC2 could be used to validate GEBF-TDDFT result (with different functionals). The GEBF-TDDFT method is found to be able to provide satisfactory or reasonable descriptions on the experimental solvatochromic shifts for the <i>n</i> → π* transitions of acetone in various solutions, and the lowest π → π* transitions of pyridine and uracil in aqueous solutions

Accurate Relative Energies and Binding Energies of Large Ice–Liquid Water Clusters and Periodic Structures

Relative energies and binding energies are crucial quantities that determine various molecular properties of ice and water. We developed a new effective method to compute those energies of bulk ice–liquid water systems. In this work, ten ice–liquid 144-mers and ten periodic ice–liquid (H₂O)₆₄ systems are taken from the molecular dynamics simulations in the melting process of ice-Ih crystals. They are investigated at the levels of density functional theory (DFT), explicitly correlated second-order Møller–Plesset perturbation theory (MP2-F12), and coupled-cluster singles and doubles with noniterative triples corrections [CCSD­(T)-F12b] in the framework of generalized energy-based fragmentation approach. Our results show that the changing of noncovalent interactions significantly influences the performances of DFT and electron correlation methods for those systems in the melting process of ice. Various DFT methods predict quite different results for ice and mixed ice–liquid structures but give similar results for pure liquid ones. It also explains why many DFT-based simulations lead to inaccurate densities of ice and liquid water. The CCSD­(T)-F12b results suggest that the MP2-F12 method provides satisfactory results and is expected to be employed to simulate the phase transitions of ice crystal

Accurate Prediction of Lattice Energies and Structures of Molecular Crystals with Molecular Quantum Chemistry Methods

We extend the generalized energy-based fragmentation (GEBF) approach to molecular crystals under periodic boundary conditions (PBC), and we demonstrate the performance of the method for a variety of molecular crystals. With this approach, the lattice energy of a molecular crystal can be obtained from the energies of a series of embedded subsystems, which can be computed with existing advanced molecular quantum chemistry methods. The use of the field compensation method allows the method to take long-range electrostatic interaction of the infinite crystal environment into account and make the method almost translationally invariant. The computational cost of the present method scales linearly with the number of molecules in the unit cell. Illustrative applications demonstrate that the PBC-GEBF method with explicitly correlated quantum chemistry methods is capable of providing accurate descriptions on the lattice energies and structures for various types of molecular crystals. In addition, this approach can be employed to quantify the contributions of various intermolecular interactions to the theoretical lattice energy. Such qualitative understanding is very useful for rational design of molecular crystals

Generalized Energy-Based Fragmentation Approach for the Electronic Emission Spectra of Large Systems

The excited-state (ES) geometry optimization and electronic emission (fluorescence and phosphorescence) spectra and the ES vibrational spectra of large systems are great challenges in quantum chemistry. In this work, we develop a generalized energy-based fragmentation (GEBF) approach to compute the localized ES structures and vibrational frequencies of large systems. In this approach, the ES energy derivatives (gradients or Hessians) for a localized ES of a large system can be obtained by combining the ES energy derivatives of the corresponding active subsystems (including local excitation center) and the ground-state energy derivatives of inactive subsystems. Two strategies are adopted to overcome two difficulties from state-classification and state-tracking for treating specific ESs. First, for state-classification, we develop an improved density-based spatial clustering applied with noise algorithm with a modified transition orbital projection (TOP) algorithm, which allow a certain ES energy and energy derivatives of the whole system to be calculated with different ES energies and energy derivatives of active subsystems. Furthermore, we also employ the TOP algorithm for tracking the ESs in their geometry optimizations at the time-dependent density functional theory (TDDFT) level. Then, the GEBF approach is applied to investigate the optimized ES geometries or ES vibrational frequencies for two typical systems. Our results show that the cost-effective GEBF approach can accurately reproduce the TDDFT fluorescence spectra of the cytosine derivative and the experimental phosphorescence spectra of the β-cyclodextrin derivative. The GEBF approach is expected to be routinely applied to investigate the electronic emission spectra of very large systems with local chromophores

Block-Correlated Coupled Cluster Theory with up to Four-Pair Correlation for Accurate Static Correlation of Strongly Correlated Systems

A block-correlated coupled cluster method with up to four-pair correlation based on the generalized valence bond wave function (GVB-BCCC4) is first implemented, which offers an alternative method for electronic structure calculations of strongly correlated systems. We developed some techniques to derive a set of compact and cost-effective equations for GVB-BCCC4, which include the definition of n-block (n = 1–4) Hamiltonian matrices, the combination of excitation operators, and the definition of independent amplitudes. We then applied the GVB-BCCC4 method to investigate several potential energy surfaces of strongly correlated systems with singlet ground states. Our calculations demonstrate that the GVB-BCCC4 method can provide nearly exact static correlation energies as the density matrix renormalization group method (on the basis of the same GVB orbitals). This work highlights the significance of four-pair correlation in quantitative descriptions of static correlation energy for strongly correlated systems

Automatic Reaction Pathway Search via Combined Molecular Dynamics and Coordinate Driving Method

We proposed and implemented a combined molecular dynamics and coordinate driving (MD/CD) method for automatically searching multistep reaction pathways of chemical reactions. In this approach, the molecular dynamic (MD) method at the molecular mechanics (MM) or semiempirical quantum mechanical (QM) level is employed to explore the conformational space of the minimum structures, and the modified coordinate driving (CD) method is used to build reaction pathways for representative conformers. The MD/CD method is first applied to two model reactions (the Claisen rearrangement and the intermolecular aldol reaction). By comparing the obtained results with those of the existing methods, we found that the MD/CD method has a comparable performance in searching low-energy reaction pathways. Then, the MD/CD method is further applied to investigate two reactions: the electrocyclic reaction of benzocyclobutene-7-carboxaldehyde and the intramolecular Diels–Alder reaction of ketothioester with 11 effectively rotatable single bonds. For the first reaction, our results can correctly account for its torquoselectivity. For the second one, our method predicts eight reaction channels, leading to eight different stereo- and regioselective products. The MD/CD method is expected to become an efficient and cost-effective theoretical tool for automatically searching low-energy reaction pathways for relatively complex chemical reactions