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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Radical Dehydroxylative Alkylation of Tertiary Alcohols by Ti Catalysis.

Deoxygenative radical C-C bond-forming reactions of alcohols are a long-standing challenge in synthetic chemistry, and the current methods rely on multistep procedures. Herein, we report a direct dehydroxylative radical alkylation reaction of tertiary alcohols. This new protocol shows the feasibility of generating tertiary carbon radicals from alcohols and offers an approach for the facile and precise construction of all-carbon quaternary centers. The reaction proceeds with a broad substrate scope of alcohols and activated alkenes. It can tolerate a wide range of electrophilic coupling partners, including allylic carboxylates, aryl and vinyl electrophiles, and primary alkyl chlorides/bromides, making the method complementary to the cross-coupling procedures. The method is highly selective for the alkylation of tertiary alcohols, leaving secondary/primary alcohols (benzyl alcohols included) and phenols intact. The synthetic utility of the method is highlighted by its 10-g-scale reaction and the late-stage modification of complex molecules. A combination of experiments and density functional theory calculations establishes a plausible mechanism implicating a tertiary carbon radical generated via Ti-catalyzed homolysis of the C-OH bond.

Highly Enantioselective Cross-Electrophile Aryl-Alkenylation of Unactivated Alkenes.

Enantioselective cross-electrophile reactions remain a challenging subject in metal catalysis, and with respect to data, studies have mainly focused on stereoconvergent reactions of racemic alkyl electrophiles. Here, we report an enantioselective cross-electrophile aryl-alkenylation reaction of unactivated alkenes. This method provides access to a number of biologically important chiral molecules such as dihydrobenzofurans, indolines, and indanes. The incorporated alkenyl group is suitable for further reactions that can lead to an increase in molecular diversity and complexity. The reaction proceeds under mild conditions at room temperature, and an easily accessible chiral pyrox ligand is used to afford products with high enantioselectivity. The synthetic utility of this method is demonstrated by enabling the modification of complex molecules such as peptides, indometacin, and steroids.

Energy decomposition analysis based on broken symmetry unrestricted density functional theory.

In this paper, the generalized Kohn-Sham energy decomposition analysis (GKS-EDA) scheme is extended to molecular interactions in open shell singlet states, which is a challenge for many popular EDA methods due to the multireference character. Based on broken symmetry (BS) unrestricted density functional theory with a spin projection approximation, the extension scheme, named GKS-EDA(BS) in this paper, divides the total interaction energy into electrostatic, exchange-repulsion, polarization, correlation, and dispersion terms. Test examples include the pancake bond in the phenalenyl dimer, the ligand interactions in the Fe(ii)-porphyrin complexes, and the radical interactions in dehydrogenated guanine-cytosine base pairs and show that GKS-EDA(BS) is a practical EDA tool for open shell singlet systems.

What kind of neutral halogen bonds can be modulated by solvent effects?

The response of a series of neutral halogen bonds X'-XY (X'-X = BrF, ClF, I2, Br2 and Cl2; Y = pyridine, NH3, H2S, HCN, H2O and dimethyl ether) to solvent effects is investigated using quantum theory of atoms in molecules (AIM), molecular electrostatic potential (MESP) and generalized Kohn-Sham energy decomposition analysis (GKS-EDA). The physical origin of the halogen bonds in various environments is explored. It is shown that halogen bonds in the gas phase are indeed governed by electrostatic interactions. A linear correlation between the magnitude of the σ hole and the electrostatic interaction is established. If the local softness of the donor or the acceptor is large, the polarization of the corresponding XB complex is large. Otherwise, the polarization is small. From gas phase to solvent environments, polarization is more sensitive to the solvent effects than the other interaction terms. For the strong XBs in a polar solvent environment, polarization is even larger than the electrostatic interaction. Our study shows that a halogen bond with a large portion of polarization can be modulated by solvent effects. If the contribution of polarization is small, the corresponding halogen bond is insensitive to solvent effects.

Infrared spectroscopy of gas phase alpha hydroxy carboxylic acid homo and hetero dimers.

New gas phase infrared spectroscopy is reported for an aromatic alpha hydroxy carboxylic acid homo dimer of 9-hydroxy-9-fluorene carboxylic acid (9HFCA)2, and the hetero dimer of 9HFCA with glycolic acid. In terms of the 9-hydroxy stretching frequency, the 16 cm-1 blue-shift in the homo dimer and the 17 cm-1 blue-shift in the hetero dimer, relative to that in 9HFCA monomer, are attributed to collective effects with anti-cooperativity stronger than cooperativity. Furthermore, for the hetero dimer, the two alpha hydroxy groups' stretching frequencies are clearly resolved, and differ by 30 cm-1. This difference represents a modest, quantitative enhancement of the intramolecular H-bond by the fluorene moiety in 9HFCA monomer, as opposed to that in glycolic acid. Accurate vibrational frequencies of the alpha OH, 3568 cm-1 in the bare glycolic acid, and 3584 cm-1 in the glycolic acid homo dimer are determined for the first time by comparison to 9HFCA monomer, homo and hetero dimers. The quantitative studies by infrared spectroscopy reveal subtle interactions among intra- and intermolecular H-bonds in the alpha hydroxyl acid dimers, which are also uniquely extended to probe each monomer's subtle intramolecular interactions.

Valence Bond Based Energy Decomposition Analysis Scheme and Its Application to Cation-π Interactions.

A new energy decomposition analysis (EDA) scheme based on valence bond (VB) wave function, called VB-EDA, is presented. In VB-EDA, the total interaction energy is decomposed into frozen, charge transfer, polarization and dynamic correlation terms based on valence bond calculations. The frozen term is the energy variation of the unrelaxed VB wave function according to the change of an interaction distance. The charge transfer term is the contribution of the additional VB structures while the polarization term is due to the relaxation of VB orbitals. Dynamic correlation term is computed by post-VBSCF methods. Different from other existing VB based EDA schemes, which were used to analyze noncovalent interactions for some specific complexes, the newly developed VB-EDA is designed for the general use. Using VB-EDA, the bonding nature of cation-π interactions in a series of cation-π complexes (cations = Li+, Na+, K+, Mg2+, and Ca2+; π systems = ethylene and benzene) is explored. Furthermore, a new covalency index, which demonstrates the covalency of cation-π interactions, is presented based on the VB-EDA results. The VB-EDA analysis reveals that the cation-π interactions in the Li+, Na+, and K+ complexes belong to the typical ionic bonds while the Mg2+ and Ca2+ complexes have the relatively large covalent characteristics. However, only the C2H4-Mg2+ complex can be regarded as a covalent bonding complex while the other complexes belong to the typical ionic complexes. Thereupon, it must be careful in the cognition for the covalency of intermolecular interaction. Large nonelectrostatic interaction component does not always correspond to a covalent bond.

Unravelling hydrogen bonding interactions of tryptamine-water dimer from neutral to cation.

The neutral and cationic forms of tryptamine-water dimer present a variety of noncovalent interactions. To characterize these interactions, a series of complementary methods, including the quantum theory of atoms in molecules, noncovalent interaction plots, natural bond orbital analysis, and energy decomposition analysis, were used. For the first time, the existence of the three intermolecular H-bonds in the conformer-locked tryptamine-water dimer A-H2O are identified, highlighting a single water's role as one proton donor and two proton acceptors as it binds to tryptamine. Furthermore, upon threshold ionization of the A-H2O dimer, the network of the three intermolecular H-bonds is indeed preserved while the individual H-bonds' binding strengths are subject to change; this is attributed to the existence of the optically accessible minimum energy isomer A+-H2O in the cation. In addition, it is found that the global minimum energy isomer H+-H2O contains a single intermolecular H-bond, but is more stable, by ca. 3 kcal mol-1, than the local minimum energy isomer A+-H2O; this is due to the stronger intramolecular interaction of H+-H2O as opposed to A+-H2O.