Energy decomposition analysis method using density matrix formulation.

In this work, an energy decomposition analysis (EDA) method with the strategy of density matrix, called DM-EDA, is proposed on the basis of single reference electronic structure calculations. Different from traditional EDA methods, instead of an intermediate state wave function, the EDA terms in DM-EDA are expressed in the forms of the density matrix. This method can be carried out with various kinds of density matrices. With the efficient implementation, DM-EDA not only greatly improves the computational efficiency but also provides quantitative knowledge of intermolecular interactions with a large number of monomers.

QM/MM-Based Energy Decomposition Analysis Method for Large Systems.

In this work, a QM/MM-based EDA method, called GKS-EDA(QM/MM), is proposed. As an extension of GKS-EDA, this scheme divides the total interaction energy into electrostatic, exchange-repulsion, polarization, and correlation/dispersion terms. GKS-EDA(QM/MM) can be applied to describe the interactions of large-scale systems combined with various QM/MM platforms. By using the examples of a hydrated hydronium ion complex in water solution, the barnase-barstar complex, and MMP-13-pyrimidinetrione in a metalloprotein, the capability of GKS-EDA(QM/MM) for various interactions in large systems is validated.

The Influence of Hydrogen Bonds on the Roaming Reaction.

Roaming bypasses the conventional transition state and is a significant reaction pathway due to the unusual energy distributions of its products; however, its reaction pathway under external environmental interactions remains unclear. Herein, we report for the first time the roaming process of nitrobenzene, which is influenced by the hydrogen bonds (H-bonds) between nitro- and phenyl radicals and water molecules in the gas phase. Notably, despite the fact that the single water structure produces a higher but narrower barrier, whereas the double water structure leads to a lower but wider barrier, the roaming reaction still occurs. The underlying mechanism responsible for these influences of H-bonds is ascribed to the dramatically changed polarization and correlation interactions between the roaming radicals. The reaction rates and thermal perturbation probabilities are also remarkably influenced due to the presence of the H-bonds, by approximately 2 orders of magnitude. It is anticipated that this work will encourage the promising feasibility of introducing environmental molecules to modulate the roaming reaction.

Energy decomposition analysis methods for intermolecular interactions with excited states.

Intermolecular interactions with excited states play important roles in various photochemical and photophysical processes. In this work, an energy decomposition analysis (EDA) method of intermolecular interactions for systems in which one monomer is in a singly excited state while others are in their ground states, called GKS-EDA(TD), is proposed. Based on the computational results of time-dependent density functional theory (TD-DFT), GKS-EDA(TD) divides the total interaction energy with excited states into electrostatic, exchange-repulsion, polarization, correlation and dispersion. The nature of intermolecular interactions in test examples with their low-lying singly excited states is investigated, which shows that GKS-EDA(TD) can be used for various intermolecular interactions with different excitation modes. Furthermore, GKS-EDA(TD) is employed to explore the non-covalent interactions in a series of C60⋯ nucleic acid base complexes with the decomposition of excitation energy contribution.

Assessments of DFT-based energy decomposition analysis methods for intermolecular interactions.

In this work, the analysis results of three energy decomposition analysis (EDA) methods, namely, generalized Kohn-Sham (GKS) EDA, extended transition state EDA, and density functional theory symmetry-adapted perturbation theory (DFT-SAPT), were extensively assessed for various intermolecular interactions. According to the physical meanings of their definitions, the EDA terms in the three methods can be grouped into four categories: electrostatics, exchange-repulsion/Pauli/exchange, polarization/orbital/induction, and CD (correlation/dispersion/dispersion) terms. Test examples include 1092 non-covalent interaction complexes in the standard sets (S66, PNICO23, HAL59, IL16, S66 × 8, and X40 × 10). It is concluded that despite the different basis sets and different running platforms (programs), the results of the three EDA methods are comparable. In general, except the dispersion term, all the EDA terms in the three methods are in excellent agreement. The CD term in GKS-EDA is comparable with the dispersion term in the DFT-SAPT. GKS-EDA provides another way to explore the role of electronic correlations from DFT calculations.

Radical Pairing Interactions and Donor-Acceptor Interactions in Cyclobis(paraquat-p-phenylene) Inclusion Complexes.

Understanding molecular interactions in mechanically interlocked molecules (MIMs) is challenging because they can be either donor-acceptor interactions or radical pairing interactions, depending on the charge states and multiplicities in the different components of the MIMs. In this work, for the first time, the interactions between cyclobis(paraquat-p-phenylene) (abbreviated as CBPQTn+ (n = 0-4)) and a series of recognition units (RUs) were investigated using the energy decomposition analysis approach (EDA). These RUs include bipyridinium radical cation (BIPY•+), naphthalene-1,8:4,5-bis(dicarboximide) radical anion (NDI•-), their oxidized states (BIPY2+ and NDI), neutral electron-rich tetrathiafulvalene (TTF) and neutral bis-dithiazolyl radical (BTA•). The results of generalized Kohn-Sham energy decomposition analysis (GKS-EDA) reveal that for the CBPQTn+···RU interactions, correlation/dispersion terms always have large contributions, while electrostatic and desolvation terms are sensitive to the variation in charge states in CBPQTn+ and RU. For all the CBPQTn+···RU interactions, desolvation terms always tend to overcome the repulsive electrostatic interactions between the CBPQT cation and RU cation. Electrostatic interaction is important when RU has the negative charge. Moreover, the different physical origins of donor-acceptor interactions and radical pairing interactions are compared and discussed. Compared to donor-acceptor interactions, in radical pairing interactions, the polarization term is always small, while the correlation/dispersion term is important. With regard to donor-acceptor interactions, in some cases, polarization terms could be quite large due to the electron transfer between the CBPQT ring and RU, which responds to the large geometrical relaxation of the whole systems.

Reductive Cross-Coupling of Unreactive Electrophiles.

Transition-metal-catalyzed reductive coupling of electrophiles has emerged as a powerful tool for the construction of molecules. While major achievements have been made in the field of cross-couplings between organic halides and pseudohalides, an increasing number of reports demonstrates reactions involving more readily available, low-cost, and stable, but unreactive electrophiles. This account summarizes the recent results in our laboratory focusing on this topic. These findings typically include deoxygenative C-C coupling of alcohols, reductive alkylation of alkenyl acetates, reductive C-Si coupling of chlorosilanes, and reductive C-Ge coupling of chlorogermanes.The reductive deoxygenative coupling of alcohols with electrophiles is synthetically appealing, but the potential of this chemistry remains to be disclosed. Our initial study focused on the reaction of allylic alcohols and aryl bromides by the combination of nickel and Lewis acid catalysis. This method offers a selectivity that is opposite to that of the classic Tsuji-Trost reactions. Further investigation on the reaction of benzylic alcohols led to the foundation of a dynamic kinetic cross-coupling strategy with applications in the nickel-catalyzed reductive arylation of benzylic alcohols and cobalt-catalyzed enantiospecific reductive alkenylation of allylic alcohols. The titanium catalysis was later established to produce carbon radicals directly from unactivated tertiary alcohols via C-OH cleavage. The development of their coupling reactions with carbon fragments delivers new methods for the construction of all-carbon quaternary centers. These reactions have shown high selectivity for the functionalization of tertiary alcohols, leaving primary and secondary alcohols intact. Alkenyl acetates are inexpensive, stable, and environmentally friendly and are considered the most attractive alkenyl reagents. The development of reductive alkylation of alkenyl acetates with benzyl ammoniums and alkyl bromides offers mild approaches for the conversion of ketones into aliphatic alkenes.Extensive studies in this field have enabled us to extend the cross-electrophile coupling from carbon to silicon and germanium chemistry. These reactions harness the ready availability of chlorosilanes and chlorogermanes but suffer from the challenge of their low reactivity toward transition metals. Under reductive nickel catalysis, a broad range of alkenyl and aryl electrophiles couple well with vinyl- and hydrochlorosilanes. The use of alkyl halides as coupling partners led to the formation of functionalized alkylsilanes. The C-Ge coupling seems less substrate-dependent, and various common chlorogermanes couple well with aryl, alkenyl, and alkyl electrophiles. In general, functionalities such as Grignard-sensitive groups (e.g., acid, amide, alcohol, ketone, and ester), acid-sensitive groups (e.g., ketal and THP protection), alkyl fluoride and chloride, aryl bromide, alkyl tosylate and mesylate, silyl ether, and amine are tolerated. These methods provide new access to organosilicon and organogermanium compounds, some of which are challenging to obtain otherwise.

A general tight-binding based energy decomposition analysis scheme for intermolecular interactions in large molecules.

In this work, a general tight-binding based energy decomposition analysis (EDA) scheme for intermolecular interactions is proposed. Different from the earlier version [Xu et al., J. Chem. Phys. 154, 194106 (2021)], the current tight-binding based density functional theory (DFTB)-EDA is capable of performing interaction analysis with all the self-consistent charge (SCC) type DFTB methods, including SCC-DFTB2/3 and GFN1/2-xTB, despite their different formulas and parameterization schemes. In DFTB-EDA, the total interaction energy is divided into frozen, polarization, and dispersion terms. The performance of DFTB-EDA with SCC-DFTB2/3 and GFN1/2-xTB for various interaction systems is discussed and assessed.

λ-DFVB(U): A hybrid density functional valence bond method based on unpaired electron density.

In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn-Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron-electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF.

Metal-Ligand Bonds in Rare Earth Metal-Biphenyl Complexes.

A series of theoretical methods, including density functional theory, multiconfiguration molecular orbital theory, and ab initio valence bond theory, are devoted to understanding the metal-ligand bonds in M-BP (BP = biphenyl; M = Sc, Y, or La) complexes. Different from most transition metal-BP complexes, the most stable metal-biphenyl conformers are not half-sandwich but clamshell. Energy decomposition analysis results reveal that the M-BP bonds in the clamshell conformers possess extra-large orbital relaxation. According to the wave function analysis, 2-fold donations and 2-fold back-donations exist in the clamshell M-BP bonds. The back-donations from M to BP are quite strong, while donations from BP to M are quite weak. Our work improves our understanding of the metal-ligand bonds, which can be considered as the "reversed" Dewar-Chatt-Duncanson model.

Exploring the nature of electron-pair bonds: an energy decomposition analysis perspective.

In this paper, the nature of electron-pair bonds is explored from an energy decomposition perspective. The recently developed valence bond energy decomposition analysis (VB-EDA) scheme is extended for the classification of electron-pair bonds, which divides the bond dissociation energy into frozen, reference state switch, quasi-resonance and polarization terms. VB-EDA investigations are devoted to a series of electron-pair bonds, including the covalent bonds (H-H, H3C-CH3, H3C-H, and H2N-NH2), the ionic bonds (Na-Cl, Li-F), the charge-shift (CS) bonds (HO-OH, F-F, Cl-Cl, Br-Br, H-F, F-Cl, H3Si-F and H3Si-Cl), and the inverted central carbon-carbon bond in [1.1.1] propallene. It is shown that the VB-EDA approach at the VBSCF level is capable of predicting the characters of the electron-pair bonds. The perspective from VB-EDA illustrates that a relatively high value of quasi-resonance term indicates a CS bond while a large portion of polarization term suggests a classical covalent bond.

Reliable Prediction of the Protein-Ligand Binding Affinity Using a Charge Penetration Corrected AMOEBA Force Field: A Case Study of Drug Resistance Mutations in Abl Kinase.

Protein mutations that directly impair drug binding are related to therapeutic resistance, and accurate prediction of their impact on drug binding would benefit drug design and clinical practice. Here, we have developed a scoring strategy that predicts the effect of the mutations on the protein-ligand binding affinity. In view of the critical importance of electrostatics in protein-ligand interactions, the charge penetration corrected AMOEBA force field (AMOEBA_CP model) was employed to improve the accuracy of the calculated electrostatic energy. We calculated the electrostatic energy using an energy decomposition analysis scheme based on the generalized Kohn-Sham (GKS-EDA). The AMOEBA_CP model was validated by a protein-fragment-ligand complex data set (Abl236) constructed from the co-crystal structures of the cancer target Abl kinase with six inhibitors. To predict ligand binding affinity changes upon protein mutation of Abl kinase, we used sampling protocol with multistep simulated annealing to search conformations of mutant proteins. The scoring strategy based on AMOEBA_CP model has achieved considerable performance in predicting resistance for 8 kinase inhibitors across 144 clinically identified point mutations. Overall, this study illustrates that the AMOEBA_CP model, which accurately treats electrostatics through penetration correction, enables the accurate prediction of the mutation-induced variation of protein-ligand binding affinity.

Nickel-Catalyzed Reductive Csp3-Ge Coupling of Alkyl Bromides with Chlorogermanes.

Reductive cross-coupling provides facile access to organogermanes, but it remains largely unexplored. Herein we report a nickel-catalyzed reductive Csp3-Ge coupling of alkyl bromides with chlorogermanes. This work has established a new method for producing alkylgermanes. The reaction proceeds under very mild conditions and tolerates various functionalities including ether, alcohol, alkene, nitrile, amine, ester, phosphonates, amides, ketone, and aldehyde. The application of this method to the modification of bioactive molecules is demonstrated.

Nickel-Catalyzed Reductive C-Ge Coupling of Aryl/Alkenyl Electrophiles with Chlorogermanes.

Cross-electrophile coupling has emerged as a promising tool for molecular synthesis; however, current studies have focused mainly on forging C-C bonds. We report a cross-electrophile C-Ge coupling reaction and thereby demonstrate the possibility of constructing organogermanes from carbon electrophiles and chlorogermanes. The reaction proceeds under mild conditions and offers access to both aryl and alkenyl germanes. Electron-rich, electron-poor, and ortho-/meta-/para-substituted (hetero)aryl electrophiles, as well as cyclic and acyclic alkenyl electrophiles, were coupled. Gram-scale reaction, incorporation of the -GeR3 moiety into complex biologically active molecules, and derivatization of formed organogermanes are demonstrated.

XEDA, a fast and multipurpose energy decomposition analysis program.

A fast and multipurpose energy decomposition analysis (EDA) program, called XEDA, is introduced for quantitative analysis of intermolecular interactions. This program contains a series of variational EDA methods, including LMO-EDA, GKS-EDA and their extensions, to analyze non-covalent interactions and strong chemical bonds in various environments. XEDA is highly efficient with a similar computational scaling of single point energy calculations. Its efficiency and universality are validated by a series of test examples including van der Waals interactions, hydrogen bonds, radical-radical interactions and strong covalent bonds.

Metal Effect Meets Volcano Plots: A DFT Study on Tris(phosphino)borane-Transition Metal Complexes Catalyzed H2 Activation.

Bifunctional transition metal complexes are of particular interest in metal-ligand cooperative activation of small molecules. As a novel type of bifunctional catalyst, Lewis acid transition metal (LA-TM) complexes have attracted increasing interest in hydrogen activation and storage. To advance the catalyst design, herein the metal effect of LA-TM complexes on the hydrogen activation has been systematically studied with a series of tris(phosphino)borane (TPB) complexes with V, Cr, Mn, Fe, Co, and Ni as metal centers. The metal effect not only influences the mechanism of hydrogen activation, but also notably casts a volcano plot for the activity. TPB complexes of V, Cr, Mn, Fe, and Co tend to activate H2 through a stepwise mechanism, while TPB-Ni prefers a synergetic mechanism for H2 activation. More importantly, the metal effect significantly influences the activity of H2 activation and the formation of the LA-H-TM bridging hydride. The trend of changes in the LA-H-TM structures, the second-order perturbation stabilization energies, and the Laplacian bond orders, along with different metals (from V to Ni), are all interestingly constitute volcano plots for the performance of TPB-TM complexes catalyzed H2 activation. TPB-Mn and TPB-Fe are found to be the optimal catalysts among the discussed TPB-TM complexes. The volcano plots disclosed for the metal effects should be informative and instructive for homogeneous and heterogeneous LA-TM catalysts development.

Understanding intermolecular interactions of large systems in ground state and excited state by using density functional based tight binding methods.

A novel energy decomposition analysis scheme, named DFTB-EDA, is proposed based on the density functional based tight-binding method (DFTB/TD-DFTB), which is a semi-empirical quantum mechanical method based on Kohn-Sham-DFT for large-scale calculations. In DFTB-EDA, the total interaction energy is divided into three terms: frozen density, polarization, and dispersion. Owing to the small cost of DFTB/TD-DFTB, DFTB-EDA is capable of analyzing intermolecular interactions in large molecular systems containing several thousand atoms with high computational efficiency. It can be used not only for ground states but also for excited states. Test calculations, involving the S66 and L7 databases, several large molecules, and non-covalent bonding complexes in their lowest excited states, demonstrate the efficiency, usefulness, and capabilities of DFTB-EDA. Finally, the limits of DFTB-EDA are pointed out.

Diabatization around Conical Intersections with a New Phase-Corrected Valence-Bond-Based Compression Approach.

In the present work, the valence-bond-based compression approach for diabatization (VBCAD), previously presented in the literature [J. Phys. Chem. Lett. 2020, 11, 5295-5301] in the case of avoided crossings, is extended to the more general situation of conical intersections and their vicinity. A pointwise phase-correction scheme for diabatic states is proposed, based on the explicit use of the peculiarities of the nonorthogonality of ab initio valence bond (VB) theory. Rather than fitting or propagating nonadiabatic couplings, it allows us to determine the phase of diabatic states consistently and automatically at each geometry point. Moreover, it is shown that the undetermination of degenerate states around a conical intersection can be fixed naturally from a straightforward classical VB picture. These are illustrated with two prototypical symmetry-induced (Jahn-Teller) conical intersection models.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited.

A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.