Dispersion-corrected energy decomposition analysis for intermolecular interactions based on the BLW and dDXDM methods

As the simplest variant of the valence bond (VB) theory, the block-localized wave function (BLW) method defines the intermediate electron-localized state self-consistently at the DFT level and can be used to explore the nature of intermolecular interactions in terms of several physically intuitive energy components. Yet, it is unclear how the dispersion interaction affects such a kind of energy decomposition analysis (EDA) as standard density functional approximations neglect the long-range dispersion attractive interactions. Three electron densities corresponding to the initial electron-localized state, optimal electron-localized state, and final electron-delocalized state are involved in the BLW-ED approach; a density-dependent dispersion correction, such as the recently proposed dDXDM approach, can thus uniquely probe the impact of the long-range dispersion effect on EDA results computed at the DFT level. In this paper, we incorporate the dDXDM dispersion corrections into the BLW-ED approach and investigate a range of representative systems such as hydrogen-bonding systems, acid-base pairs, and van der Waals complexes. Results show that both the polarization and charge-transfer energies are little affected by the inclusion of the long-range dispersion effect, which thus can be regarded as an independent energy component in EDA.     

Attraction between electrophilic caps: A counterintuitive case of noncovalent interactions

Intermolecular attractive interaction between electrophilic sites is a counterintuitive phenomenon, as the electrostatic interaction therein is repulsive and destabilizing. Here, we confirm this phenomenon in four representative complexes, using state-of-the-art quantum mechanical methods. By employing the block-localized wavefunction (BLW) method, which can turn off intermolecular charge transfer interactions, we profoundly demonstrated the significance of charge transfer interactions in these seemingly counterintuitive complexes. Indeed, after being “turned off” the intermolecular charge transfer interaction in, for example, the FNSi···BrF complex, the originally attractive intermolecular interaction turns to be repulsive. The energy decomposition approach based on the BLW method (BLW-ED) can partition the overall stability gained on the formation of intermolecular noncovalent interaction into several physically meaningful components. According to the BLW-ED analysis, the electrostatic repulsion in these counterintuitive cases is overwhelmed by the stabilizing polarization, dispersion interaction, and most importantly, the charge transfer interaction, resulting in the eventual counterintuitive overall attraction. The present study suggests that, predicting bonding sites of noncovalent interactions using only the “hole” concept may be not universally sufficient, because other significant stabilizing factors will contribute to the stability and sometimes, play even bigger roles than the electrostatic interaction and consequently govern the complex structures. © 2018 Wiley Periodicals, Inc.     

Block-localized wavefunction (BLW) method at the density functional theory (DFT) level

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.     

Polarization and charge-transfer effects in aqueous solution via ab initio QM/MM simulations

Combined ab initio quantum mechanical and molecular mechanical (QM/MM) simulations coupled with the block-localized wave function energy decomposition (BLW-ED) method have been conducted to study the solvation of two prototypical ionic systems, acetate and methylammonium ions in aqueous solution. Calculations reveal that the electronic polarization between the targeted solutes and water is the primary many-body effect, whereas the charge-transfer term only makes a small fraction of the total solute-solvent interaction energy. In particular, the polarization effect is dominated by the solvent (water) polarization.     

Hydrogen and Halogen Bonding in Homogeneous External Electric Fields: Modulating the Bond Strengths

Recent years have witnessed various fascinating phenomena arising from the interactions of noncovalent bonds with homogeneous external electric fields (EEFs). Here we performed a computational study to interpret the sensitivity of intrinsic bond strengths to EEFs in terms of steric effect and orbital interactions. The block-localized wavefunction (BLW) method, which combines the advantages of both ab initio valence bond (VB) theory and molecular orbital (MO) theory, and the subsequent energy decomposition (BLW-ED) approach were adopted. The sensitivity was monitored and analyzed using the induced energy term, which is the variation in each energy component along the EEF strength. Systems with single or multiple hydrogen (H) or halogen (X) bond(s) were also examined. It was found that the X-bond strength change to EEFs mainly stems from the covalency change, while generally the steric effect rules the response of H-bonds to EEFs. Furthermore, X-bonds are more sensitive to EEFs, with the key difference between H- and X-bonds lying in the charge transfer interaction. Since phenylboronic acid has been experimentally used as a smart linker in EEFs, switchable sensitivity was scrutinized with the example of the phenylboronic acid dimer, which exhibits two conformations with either antiparallel or parallel H-bonds, thereby, opposite or consistent responses to EEFs. Among the studied systems, the quadruple X-bonds in molecular capsules exhibit remarkable sensitivity, with its interaction energy increased by −95.2 kJ mol⁻¹ at the EEF strength 0.005 a.u.     

Spectroscopic identification towards tunable mesoscale aggregates of zinc tetraphenylporphyrin for materials

We present a study of spectroscopic identification towards the molecular aggregates of zinc tetraphenylporphyrin(ZnTPP) illustrating how the energy states and intermolecular interactions determine the tunable properties of functional materials in condensation processes. Distinguishable fingerprints of ZnTPP nanorods and nanosheets are addressed utilizing X-ray diffraction(XRD), Raman and UV-vis absorption spectroscopies. Although these ZnTPPs are assigned to J-aggregation at different extent, the spectral analysis reveals a significant role of the intermolecular interactions associated with varying mesoscale architectures. Energy decomposition analysis(EDA) revealed that the varied ZnTPP aggregates are stabilized by altered dispersion interactions due to the dominant π…π stacking between the monomers.     

Theoretical investigation of the interactions between the π‐systems of molecular organic semiconductors and an analysis of the contributions of repulsion and electrostatics

A concept for the interactions between π‐systems is necessary to understand a number of phenomena in modern material sciences such as supramolecular properties and self‐assembly. In the present article, we investigate the intermolecular interaction energies between organic semiconductors with extended π‐systems using SAPT (symmetry‐adapted perturbation theory), LMO‐EDA (localized molecular orbital energy decomposition analysis), DFT‐D (density functional theory including dispersion corrections), and force‐field approaches. Both apolar organic molecules such as acenes and highly polarized π‐systems of merocyanines and squaraines were used to probe the influence of electrostatics on the shape of the potential energy surfaces (PES) governing the geometric structures of aggregates. Our results reveal that the shapes of the PESs result from variations in the short‐range, highly specific repulsion forces even for highly polar molecules. Using distributed quadrupoles, we show that it is nevertheless possible to mimic the intermolecular potentials with electrostatics. This is also possible with van‐der‐Waals potentials and a simple overlap‐based force‐field ansatz based on the overlap between p‐orbitals. © 2016 Wiley Periodicals, Inc.     

三核金配合物分子间Au-Au相互作用及其发光性质的含时密度泛函理论研究

使用混合密度泛函方法(MPW1PW91交换相关势), 对Au₃(HOC＝NH)₃分子进行了几何构型全优化, 在此基础上构建了Au₃(HOC＝NH)₃二聚体和三聚体模型, 采用含时密度泛函方法研究了单体和低聚体模型的分子间Au-Au相互作用与其发光性质的关系. 计算结果表明: 此d¹⁰亚金化合物低能激发态的主要成分是反键或非键的Au(5d)电子轨道到前线附近Au(6p)空轨道的跃迁, 并且这种激发大大加强了分子间Au-Au相互作用, 从而形成激发多聚体, 导致这类化合物溶液或固体发射谱红移.     

Unraveling weak interactions in aniline-pyrrole dimer clusters

Weak intermolecular interactions in aniline-pyrrole dimer clusters have been studied by the dispersion-corrected density functional theory(DFT) calculations. Two distinct types of hydrogen bonds are demonstrated with optimized geometric structures and largest interaction energy moduli. Comprehensive spectroscopic analysis is also addressed revealing the orientation-dependent interactions by noting the altered red-shifts of the infrared and Raman activities. Then we employ natural bond orbital(NBO)analysis and atom in molecules(AIM) theory to have determined the origin and relative energetic contributions of the weak interactions in these systems. NBO and AIM calculations confirm the V-shaped dimer cluster is dominated by N.H···N and C.H···π hydrogen bonds, while the J-aggregated isomer is stabilized by N.H···π, n→π* and weak π···π* stacking interactions.The noncovalent interactions are also demonstrated via energy decomposition analysis associated with electrostatic and dispersion contributions.     

Effects of intermolecular interaction on the energy distribution of valance electronic states of a carbazole-based material in amorphous thin films

Effects of intermolecular interactions on the occupied electronic structure of amorphous solid of a carbazole-based material were investigated under an assumption that the organic solid consists of randomly oriented assemblies of dimers. The electronic energy states were calculated on the ensemble of large number of random dimers, of which geometries are relaxed using semiempirical van der Waals density functional theory. Intermolecular interactions result in splitting of energy level, and further disorders occur by aggregation of randomly orientated molecules. As a result, frontier occupied energy states can be represented by a superposition of Gaussian distributions, including (i) a main distribution with full width at half maximum of 80-110 meV, depending on the methods of relaxation and (ii) shoulders separated from the center of the main distribution with a value as large as 150 meV. A possible origin for the appearance of these shoulders was ascribed to the presence of molecular assemblies consisting of more tightly bound dimers compared with the others.     

Estimation of the barrier to rotation of benzene in the (eta 6-C6H6)2Cr crystal via topological analysis of the electron density distribution function

The high-resolution X-ray diffraction analysis of the electron density distribution and plane-wave density functional theory has been applied to estimate the lattice energy and barrier to rotation of a benzene ring in the crystal of (eta(6)-C(6)H(6))(2)Cr. Experimental data made it possible to perform analysis of the metal-(pi-ligand) bond and estimate the nature and energy of weak H...H and H...C intermolecular interactions in the crystal. Summation of the intermolecular H...H and H...C interaction energies makes it possible to reproduce the experimental sublimation enthalpy value with high accuracy.     

Theoretical study on stabilities of multiple hydrogen bonded dimers

A series of self-constituted multiple hydrogen bonded (MHB) complexes has been investigated systematically by density functional theory (PBE1PBE /6-31G**), the Morokuma energy decomposition method (HF/6-31G**) and MP2 (6-31G** and 6-311++G**) calculation. We have discovered that (i) for doubly hydrogen bonded (DHB) complexes, both the interaction energy and stability increase with the charge transfer energy; (ii) for quadruple hydrogen bonded (QHB) complexes, cooperativity is the most important factor determining stability of the complex: stronger cooperative energy correlates well with larger interaction energy and thus more stable complex and vice versa; (iii) correlation energy plays an important role in intermolecular interactions. The correlation energy, mainly consisting of dispersive energy, also exhibits cooperativity in MHB dimers: positive for M-aadd and generally negative for other complexes.     

Quantitative analysis of intermolecular forces for hydrogen bond driven self-assembly of resorcinol and bis(pyridine) substituted ethylene cocrystals, before and after [2 + 2] dimerization

The long-range and dispersion corrected density functional theory (DFT + Disp), and Møller–Plesset second-order perturbation theory (MP2) were used for describing the intermolecular interactions between hydrogen bond driven self-assembly of 2(5-CN-res) … 2(4,4′-bpe) and 2(4,6-diCl-res) … 2(4,4′-bpe) cocrystals [where 5-CN-res = 5-cyanoresorcinol, 4,6-diCl-res = 4,6-dichlororesorcinol, and 4,4′-bpe = trans-1,2-bis(4-pyridyl)ethylene], before and after [2 + 2] dimerization to 2(5-CN-res) … (4,4′-tpcb) and 2(4,6-diCl-res) … (4,4′-tpcb), respectively [where 4,4′-tpcb = 1,2,3,4-tetra(4-pyridyl)cyclobutane]. The nature and strength of intermolecular forces were studied using the absolutely localized molecular orbitals energy decomposition analysis, and the plot of reduced density gradient versus the electron density multiplied by the sign of the second Hessian eigenvalue [sign(λ₂)ρ]. The results show that the interaction of 2(4,4′-bpe) is basically dispersive nature, while all of the electrostatic, dispersion, polarization and charge-transfer interactions are largely contributed to the interaction energy of 2(4,4′-bpe) with 5-CN-res and 4,6-diCl-res molecules. The total interaction energy of complexes before dimerization is greater than that after dimerization. Since the contribution of polarization and charge-transfer interactions after dimerization are nearly unchanged, the main difference in the interaction energy of complexes is due to the weaker contribution of van der Waals and electrostatic forces in the products.     

Analysis of the structures,energetics, and vibrational frequencies for the hydrogen-bonded interaction of nucleic acid bases with Carmustine pharmaceutical agent: a detailed computational approach

In the present study, it is attempted to scrutinize the hydrogen bonding interaction between Carmustine drug and DNA pyrimidine bases by means of density functional theory calculations regarding their geometries, binding energies, vibrational frequencies, and topological features of the electron density in the gas phase and the water solution. Based on the density functional theory results, it is found that the process of intermolecular interaction between Carmustine drug and nucleobases is exothermic and all of the optimized configurations are stable. Furthermore, the negative stability energy represented by a polarizable continuum model shows the significant increase in the solubility of the nucleobase after hydrogen bonding intermolecular interaction in the presence of water solvent. It is also found that the intermolecular hydrogen bonds between drug and the nucleobases play the significant role in the stability of the physisorption configurations. Hydrogen bond energies for hydrogen-bonded complexes are obtained from Espinosa method and the atoms-in-molecules theory are also applied to get a more precise insight into the nature of the intermolecular hydrogen bond interactions.     

Explorations of the nature of the coupling interactions between vitamin C and methylglyoxal: a DFT study

As the first step toward understanding the augment role of vitamin C (Vc) for the anticancer effect of methylglyoxal (MG), the nature of the coupling interactions between Vc and MG has been systematically investigated at the B3LYP/6-311++G** level of theory in combination with the atoms in molecules (AIM) theory, natural bond orbital (NBO) method, and energy decomposition analysis (EDA). The possible stable complexes have been located on their potential energy surface (PES). Most of them are characterized by one or two intermolecular H-bonds with the binding energies varying from −11.1 to −2.0 kcal/mol. AIM analyses suggest that all the intermolecular H-bonds have been predominated by the electrostatic interaction. A good linear correlation between the intermolecular H-bond distance and the electron density as well as its Laplacian at the bond critical point of the intermolecular H-bond has been observed. Depending on the selected coupling modes between Vc and MG, the origin of the blue-shifts of the stretching vibrational frequencies of different C–H bonds has been elucidated. Additionally, the inherent reason for the positive role of Vc in the anticancer process for MG has been verified through the investigation of the one-electron oxidation behaviors of the most stable complex.     

The generalized block-localized wavefunction method: a case study on the conformational preference and C-O rotational barrier of formic acid

A Lewis structure corresponding to the most stable electron-localized state is often used as a reference for the measure of electron delocalization effect in the valence bond (VB) theory. As the simplest variant of ab initio VB theory, the generalized block-localized wavefunction (BLW) method defines the wavefunction for an electron-localized state with block-localized orbitals without the orthogonalization constraint on different blocks. The validity of the method can be critically examined with experimental evidences. Here the BLW method has been applied to the investigation of the roles of both the π conjugation and σ hyperconjugation effects in the conformational preference of formic acid for the trans (Z) conformer over the cis (E) conformer. On one hand, our computations showed that the deactivation of the π conjugation or σ hyperconjugation has little impact on the Z-E energy gap, thus neither is decisive and instead the local dipole-dipole electrostatic interaction between the carbonyl and hydroxyl groups is the key factor determining the Z-E energy gap. On the other hand, the present study supported the conventional view that π conjugation is largely responsible for the C-O rotation barrier in formic acid, though the existence of hyperconjugative interactions in the perpendicular structure lowers the barrier considerably.     

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).