Block-localized Wave Function Method Research Articles

Metastability of π-π stacking between the closed-shell ions of like charges

Planar cations or anions can form stacks in crystals or solutions, where the surrounding or environment plays a decisive role as demonstrated in previous studies. However, it remains unclear whether these counterintuitive interactions possess any inherent stability or are thoroughly repulsive if the constraint of environment is removed. In this work, we explored the inherent stability of π-π stacking between closed-shell ions of like charges with prototypes derived from experimental studies. The inherent metastability was identified by the characteristic local minima and the transition states preventing their dissociation and verified by ab initio molecular dynamics (AIMD) simulations. The nature of involved interactions was deciphered with the energy decomposition approach based on the block-localized wavefunction method (BLW-ED). Like the conventional neutral π-π stacking interactions, electron correlation is the most attractive energy component. But it is overturned by the Coulombic repulsion between net charges for all modes of dimerization, resulting in the overall repulsive inter-cation or anion interactions. Contributions from van der Waals interactions were also observed in the reduced density gradient analysis. The origin of the metastability was elucidated by examining the contributions of individual physical factors to the well-depths. The inherent metastability originates from the electron correlation, which dramatically increases due to the enhanced overlap between ions from a transition state to its corresponding minimum.

Planar Four-Membered Diboron Actinide Compound with Double Möbius Aromaticity.

The Möbius rule predicts that a planar four-membered metallacycle can be aromatic with four mobile electrons, but such a simple ring has escaped recognition because it usually favors Hückel anti-aromaticity. Here, we report that a quasi-square four-membered actinide compound (Pa2B2) is doubly Möbius aromatic. Chemical bonding analyses reveal that this diboron protactinium molecule has four delocalized π electrons in addition to four delocalized σ electrons, satisfying the 4n Möbius rule for both σ and π components. Energetically, the block-localized wavefunction method, which is the simplest variant of ab initio valence bond theory, shows that the delocalization energy for the π and σ electrons reaches up to 65.0 and 72.3 kcal/mol, respectively, while the extra cyclic resonance energy (ECRE) amounts to 45 kcal/mol. The large positive ECRE values strongly confirm the unprecedented double Möbius aromaticity in Pa2B2. We anticipate that this new type of aromatic molecule can enrich the concept of Möbius aromaticity and open a new avenue for actinide compounds.

Selectivity Rule of Cryptands for Anions: Molecular Rigidity and Bonding Site.

Cryptands utilize inside CH or NH groups as hydrogen bond (H-bond) donors to capture anions such as halides. In this work, the nature and selectivity of confined hydrogen bonds inside cryptands were computationally analyzed with the energy decomposition scheme based on the block-localized wavefunction method (BLW-ED), aiming at an elucidation of governing factors in the binding between cryptands and anions. It was revealed that the intrinsic strengths of inward hydrogen bonds are dominated by the electrostatic attraction, while the anion preferences (selectivity) of inner CH and NH hydrogen bonds are governed by the Pauli exchange repulsion and electrostatic interaction, respectively. Typical conformers of cages are classified into two groups, including the C3(h) -symmetrical conformers, in which all halide anions are located near the centroids of cages, and the "semi-open" conformers, which exhibit shifted bonding sites for different halide anions. Accordingly, the difference in governing factors of selectivity is attributed to either the rigidity of cages or the binding site of anions for these two groups. In details, the C3 conformers of NH cryptands can be enlarged more remarkably than the C3(h) -symmetrical conformers of CH cryptands as the size of anion (ionic radius) increases, resulting in the relaxation of the Pauli repulsion and a dramatic reduction in electrostatic attraction, which eventually rules the selectivity of NH cryptands for halide anions. By contrary, the CH cryptands are more rigid and cannot effectively reduce the Pauli repulsion, which subsequently governs the anion preference. Unlike C3 conformers whose rigidity determines the selectivity, semi-open conformers exhibit different binding sites for different anions. From F- to I- , the bonding site shifts toward the outside end of the pocket inside the semi-open NH cryptand, leading to the significant reduction of the electrostatic interaction that dominates the anion preference. Differently, binding sites are much less affected by the size of anion inside the semi-open CH cryptand, in which the Pauli exchange repulsion remains the key factor for the selectivity of inner hydrogen bonds.

The strength and selectivity of perfluorinated nano-hoops and buckybowls for anion binding and the nature of anion-π interactions.

Perfluorinated cycloparaphenylenes (F-[n]CPP, n= 5-8), boron nitride nanohoop (F-[5]BNNH), and buckybowls (F-BBs) were proposed as anion receptors via anion-π interactions with halide anions (Cl- , Br- and I- ), and remarkable binding strengths up to -294.8kJ/mol were computationally verified. The energy decomposition approach based on the block-localized wavefunction method, which combines the computational efficiency of molecular orbital theory and the chemical intuition of ab initio valence bond theory, was applied to the above anion-π complexes, in order to elucidate the nature and selectivity of these interactions. The overall attraction is mainly governed by the frozen energy component, in which the electrostatic interaction is included. Remarkable binding strengths with F-[n]CPPs can be attributed to the accumulated anion-π interactions between the anion and each conjugated ring on the hoop, while for F-BBs, additional stability results from the curved frameworks, which distribute electron densities unequally on π-faces. Interestingly, the strongest host was proved to be the F-[5]BNNH, which exhibits the most significant anisotropy of the electrostatic potential surface due to the difference in the electronegativities of nitrogen and boron. The selectivity of each host for anions was explored and the importance of the often-overlooked Pauli exchange repulsion was illustrated. Chloride anion turns out to be the most favorable anion for all receptors, due to the smallest ionic radius and the weakest destabilizing Pauli exchange repulsion.

Classical Electrostatics Remains the Driving Force for Interanion Hydrogen and Halogen Bonding.

Interanion hydrogen bonding (IAHB) and halogen bonding (IAXB) have emerged as a counterintuitive linker in a range of fascinating applications. Despite the overall repulsive (positive) binding energy, anions are trapped in a local minimum with its corresponding transition state (TS) preventing dissociation. In other words, the adduct of anions is metastable. Seemingly, the electrostatic paradigm and force field description of hydrogen/halogen bonding (HB/XB) are challenged, because of the preconceived Coulombic repulsion. Aiming at an insightful understanding of these interanion phenomena, we employed the energy decomposition approach based on the block-localized wavefunction method (BLW-ED) to investigate a series of exemplary interanion complexes. As expected, the key distinction from the conventional HB/XB lies in the electrostatic interaction, which is not increasingly repulsive as anions gradually approach to each other. Rather, there is a Coulombic barrier at a certain point. After this point, the electrostatic repulsion diminishes with the decreasing distance between anions. Differently, other energy components vary monotonically just like in conventional cases. The nonmonotonic characteristic of the electrostatic interaction in interanion complexes was reproduced using the multipole expansion in AMOEBA polarizable force field in which the state-specified atomic multipoles were adopted. This suggests that the nonmonotonicity can be well interpreted by classical electrostatic theory and there is no conceptual difference between conventional HB/XB and IAHB/IAXB. The stability of IAHB/IAXB depends on the competition between the local attractive HB/XB and the global Coulombic repulsion of net charges, though there is cooperativity between these two contrasting forces. This concise model was supported by the attractive IAHB/IAXB in modified molecular capsules, which exhibit strong quadruple HB/XBs and a considerable distance between charged substituents.

Generalization of Block-Localized Wave Function for Constrained Optimization of Excited Determinants.

The block-localized wave function method is useful to provide insights on chemical bonding and intermolecular interactions through energy decomposition analysis. The method relies on block localization of molecular orbitals (MOs) by constraining the orbitals to basis functions within given blocks. Here, a generalized block-localized orbital (GBLO) method is described to allow both physically localized and delocalized MOs to be constrained in orbital-block definitions. Consequently, GBLO optimization can be conveniently tailored by imposing specific constraints. The GBLO method is illustrated by three examples: (1) constrained polarization response orbitals through dipole and quadrupole perturbation in a water dimer complex, (2) the ground and first excited-state potential energy curves of ethene about its C-C bond rotation, and (3) excitation energies of double electron excited states. Multistate density functional theory is used to determine the energies of the adiabatic ground and excited states using a minimal active space (MAS) comprising specifically charge-constrained and excited determinant configurations that are variationally optimized by the GBLO method. We find that the GBLO expansion that includes delocalized MOs in configurational blocks significantly reduces computational errors in comparison with physical block localization, and the computed ground- and excited-state energies are in good accordance with experiments and results obtained from multireference configuration interaction calculations.

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.

Induction, Resonance, and Secondary Electrostatic Interaction on Hydrogen Bonding in the Association of Amides and Imides.

Both computations and experiments have confirmed that amides have stronger self-associations than imides. While this intriguing phenomenon is usually explained in the term of secondary electrostatic repulsion from the additional spectator carbonyl groups in imides, recently it was proposed that the π resonance effect from the spectator carbonyl which alters the balance between the acidity of the hydrogen-bond (H-bond) donor and the basicity of the H-bond acceptor is the major cause. In this work, we examined the roles of π resonance and the secondary electrostatic interaction in the formation of amide and imide dimers by deactivating the π conjugation from the spectator carbonyl and flipping the spectator carbonyl using the block-localized wave function method which is the simplest variant of valence bond theory. Energetic, geometrical, and spectral results show that three major forces, namely the σ induction effect (IE), π resonance effect (RE), and secondary electrostatic interaction (SEI), contribute to the different binding energies in the dimers of amides and imides. Whereas IE favors stronger binding among imides, both RE and SEI diminish the self-association of imides. Obviously, the negative force from RE and SEI exceeds the positive force from IE. Relatively, SEI plays a little bigger role than RE.

Hydrogen- and Halogen-Bonds between Ions of like Charges: Are They Anti-Electrostatic in Nature?

Recent theoretical studies suggested that hydrogen bonds between ions of like charges are of a covalent nature due to the dominating nD →σ*H-A charge-transfer (CT) interaction. In this work, energy profiles of typical hydrogen (H) and halogen (X) bonding systems formed from ions of like charges are explored using the block-localized wavefunction (BLW) method, which can derive optimal geometries and wave functions with the CT interaction "turned off." The results demonstrate that the kinetic stability, albeit reduced, is maintained for most investigated systems even after the intermolecular CT interaction is quenched. Further energy decomposition analyses based on the BLW method reveal that, despite a net repulsive Coulomb repulsion, a stabilizing component exists due to the polarization effect that plays significant role in the kinetic stability of all systems. Moreover, the fingerprints of the augmented electrostatic interaction due to polarization are apparent in the variation patterns of the electron density. All in all, much like in standard H- and X-bonds, the stability of such bonds between ions of like charges is governed by the competition between the stabilizing electrostatic and charge transfer interactions and the destabilizing deformation energy and Pauli exchange repulsion. While in most cases of "anti-electrostatic" bonds the CT interaction is of a secondary importance, we also find cases where CT is decisive. As such, this work validates the existence of anti-electrostatic H- and X-bonds. © 2017 Wiley Periodicals, Inc.

Study of proton-coupled electron transfer (PCET) with four explicit diabatic states at the ab initio level

Proton-coupled electron transfer (PCET) broadly exists in chemical and biological processes and can be intuitively described in terms of diabatic (resonance) states. The conventional molecular orbital (MO) based methods, however, have the difficulty in rationally defining diabatic states which are strictly electron-localized. Here we used the block-localized wavefunction (BLW) method, which is the simplest variant of valence bond (VB) theory, to define four major diabatic states and compare the concerted and the sequential transfers of electron and proton between formamide and its radical form. Our preliminary computations with partial breathing orbitals (BOs) show that the BLW method can locate the intermediate state in the stepwise mechanism, though the barriers are overestimated with references to high-level MO results, indicating the importance of dynamical electron correlation at transition states and the need for full BOs. But all computations at all levels concur that the concerted mechanism is preferred over the stepwise mechanism in the system studied in this work.

The origins of the directionality of noncovalent intermolecular interactions.

The recent σ-hole concept emphasizes the contribution of electrostatic attraction to noncovalent bonds, and implies that the electrostatic force has an angular dependency. Here a set of clusters, which includes hydrogen bonding, halogen bonding, chalcogen bonding, and pnicogen bonding systems, is investigated to probe the magnitude of covalency and its contribution to the directionality in noncovalent bonding. The study is based on the block-localized wavefunction (BLW) method that decomposes the binding energy into the steric and the charge transfer (CT) (hyperconjugation) contributions. One unique feature of the BLW method is its capability to derive optimal geometries with only steric effect taken into account, while excluding the CT interaction. The results reveal that the overall steric energy exhibits angular dependency notably in halogen bonding, chalcogen bonding, and pnicogen bonding systems. Turning on the CT interactions further shortens the intermolecular distances. This bond shortening enhances the Pauli repulsion, which in turn offsets the electrostatic attraction, such that in the final sum, the contribution of the steric effect to bonding is diminished, leaving the CT to dominate the binding energy. In several other systems particularly hydrogen bonding systems, the steric effect nevertheless still plays the major role whereas the CT interaction is minor. However, in all cases, the CT exhibits strong directionality, suggesting that the linearity or near linearity of noncovalent bonds is largely governed by the charge-transfer interaction whose magnitude determines the covalency in noncovalent bonds.

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.

Aromaticity in Group 14 Homologues of the Cyclopropenylium Cation

The nature of the bonding and the aromaticity of the heavy Group 14 homologues of cyclopropenylium cations E3H3+ and E2H2E'H+ (E, E' = C-Pb) have been investigated systematically at the BP86/TZ2P DFT level by using several methods. Aromatic stabilization energies (ASE) were evaluated from the values obtained from energy decomposition analysis (EDA) of charged acyclic reference molecules. The EDA-ASE results compare well with the extra cyclic resonance energy (ECRE) values given by the block localized wavefunction (BLW) method. Although all compounds investigated are Hückel 4n+2 π electron species, their ASEs indicate that the inclusion of Group 14 elements heavier than carbon reduces the aromaticity; the parent C3H3+ ion and Si2H2CH+ are the most aromatic, and Pb3H3+ is the least so. The higher energies for the cyclopropenium analogues reported in 1995 employed an isodesmic scheme, and are reinterpreted by using the BLW method. The decrease in the strength of both the π cyclic conjugation and the aromaticity in the order C ≫ Si>Ge>Sn>Pb agrees reasonably well with the trends given by the refined nucleus-independent chemical shift NICS(0)πzz index.

New procedure to evaluate aromaticity at the density functional theory, Hartree-Fock, and post-self-consistent field levels

The spatial exchange interaction, arising from the exchange-type two-electron integrals (i(p)j(q)/i'(p)j'(q)) between two different groups P and Q, is another driving force for the delocalization of π-electrons besides orbital charge-transfer and exchange interactions. We have developed a new combination program for restricted geometry optimization, in which all of the orbital and spatial interactions among isolated groups were excluded from the localized geometry of a conjugated molecule. This was achieved by deleting particular Fock elements and the 15 types of exchange-type two-electron integrals, ensuring that the corresponding π-electrons are completely localized within their respective groups and the π-orbitals are fully localized. The extra stabilization energy (ESE) of benzene is -36.3 kcal/mol (B3LYP/6-31G*), and the level of density functional theory, Hartree-Fock, and post-self-consistent field (Møller-Plesset 2, configuration interaction singles and doubles, and singles and doubles coupled-cluster) and the basis sets have slight effect on the ESE. Based on the comparisons between our procedure, Morokuma's energy decomposition analysis and the block-localized wave function method, it was confirmed that our program calculates reliable results. The nonaromaticity of acyclic polyenes and antiaromaticity of cyclobutadiene and planar cyclooctatetraene were also estimated. Comparison of the CC single bond lengths in the ground state with its π-localized geometries showed that shortening of the single bonds in acyclic polyenes and butadiyne should be attributed to different hybridization, demonstrating that the effect of π-delocalization on single bonds is so small as to be negligible.

Consistent Aromaticity Evaluations of Methylenecyclopropene Analogues

Quantitative evaluations of the aromaticity (antiaromaticity) of neutral exocyclic substituted cyclopropenes (HC)(2)C=X (X = BH to InH (group 13), CH(2) to SnH(2) (group 14), NH to SbH (group 15), O to Te (group 16)) by their computed extra cyclic resonance energies (ECRE, via the block-localized wave function method) and by their aromatic stabilization energies (ASEs, via energy decomposition analyses) correlate satisfactorily (R(2) = 0.974). Electronegative X-based substituents increase the aromaticity of the cyclopropene rings, whereas electropositive substituents have the opposite effect. For example, (HC)(2)C=O is the most aromatic (ECRE = 10.3 kcal/mol), and (HC)(2)C=InH is the most antiaromatic (ECRE = -15.0 kcal/mol). The most refined dissected nucleus-independent chemical shift magnetic aromaticity index, NICS(0)(πzz), also agrees with both energetic indexes (R(2) = 0.968, for ECRE; R(2) = 0.974, for ASE), as do anisotropy of the induced current density plots.

BLOCK-LOCALIZED WAVEFUNCTION ENERGY DECOMPOSITION (BLW-ED) ANALYSIS OF σ/π INTERACTIONS IN METAL-CARBONYL BONDING

The bonding features in metal-carbonyls including neutral M CO (M = Ni , Pd , Pt ) and M CO + (M+ = Cu +, Ag +, Au +) complexes have been elucidated at the DFT level with relativistic compact effective potentials for transition metals and 6-311+G(d) basis sets for C and O by the block-localized wavefunction (BLW) method. The BLW method can decompose the intermolecular interactions in terms of Heitler–London, polarization, and charge transfer energy contributions. Since the metal– CO bonding involves two synergic interactions, namely the σ-dative bond from the carbon lone electron pair to an empty d σ orbital on the metal, and the π back-donation from filled d π orbitals to the empty 2π* orbital on CO , the present BLW-ED analyses quantitatively demonstrated that in neutral M CO complexes the π-bonding dominates over the σ-bonding, whereas in cationic M CO + complexes, the σ-bonding plays a major role. But in both neutral and cationic species, the CO polarization induced by the metals enhances the C–O bond and increases the C–O vibrational frequencies, while the π back-donation tends to weaken the C–O bond and decrease the C–O vibrational frequencies. For neutral complexes, the latter is more prominent than the former, and consequently, there is a red-shifting of the C–O vibrational frequencies. In contrast, the π back-donation is insignificant in M CO + cations, and the C–O eventually vibrates at higher frequencies than the free CO frequency.

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.

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).

Solvent Effects, Reaction Coordinates, and Reorganization Energies on Nucleophilic Substitution Reactions in Aqueous Solution

AbstractFor Abstract see ChemInform Abstract in Full Text.

Importance of Electronic Delocalization on the C−N Bond Rotation in HCX(NH2) (X = O, NH, CH2, S, and Se)

A block-localized wave function method, which in effect can switch off conventional conjugation and hyperconjugation effects, is employed to investigate the origin of the rotational barriers in formamide and its analogues. It is found that the resonance between the π electrons on the CX double bond and the nitrogen lone pair significantly stabilizes the planar conformation in HCXNH2 (X = O, NH, CH2, S, and Se). The absolute resonance energy follows the order of formamide < thioformamide < selenoformamide, with predicted vertical resonance energies of −25.5, −35.7, and −37.6 kcal/mol, respectively. The computed vertical resonance energies for X = O, NH, and CH2 are −25.5, −22.5, and −19.1 kcal/mol, respectively, which follow the decreasing trend of electronegativity. Although the rotational barrier about the C−N bond in vinylamine (4.5 kcal/mol) is much smaller than that of formamide (15.7 kcal/mol), the resonance energy in vinylamine is of the same order as that of formamide (−19.1 versus −25.5 kcal/mol)....