Ab Initio Valence Bond Research Articles

Exploring the Bonding Nature of Iron(IV)-Oxo Species through Valence Bond Calculations and Electron Density Analysis.

Compound I (Cpd I) plays a pivotal role in substrate transformations within the catalytic cycle of cytochrome P450 enzymes (P450s). A key constituent of Cpd I is the iron(IV)-oxo unit, a structural motif also found in other heme enzymes and nonheme enzymes. In this study, we performed ab initio valence bond (VB) calculations, employing the valence bond self-consistent field (VBSCF) and breathing orbital valence bond (BOVB) methods, to unveil the bonding nature of this vital "Fe(IV)═O″ unit in bioinorganic chemistry. Comparisons were drawn with the triplet O2 molecule, which shares some electronic characteristics with iron(IV)-oxo. Additionally, Cpd I models of horseradish peroxidase (HRP) and catalase (CAT) were analyzed to assess the proximal ligand effect on the electronic structure of iron(IV)-oxo. Our VB analysis underscores the significant role of noncovalent resonance effects in shaping the iron(IV)-oxo bonding. The resonance stabilization within the π and σ frameworks occurs to comparable degrees, with additional stabilization resulting from resonance between VB structures from these frameworks. Furthermore, we elucidated the substantial influence of proximal and equatorial ligands in modulating the relative significance of different VB structures. Notably, in the presence of these ligands, iron(IV)-oxo is better described as iron(III)-oxyl or iron(II)-oxygen, displaying weak covalent character but enhanced by resonance effects. Although both species exhibit diradicaloid characters, resonance stabilization in iron(IV)-oxo is weaker than in O2. Further exploration using the Laplacian of electron density shows that, unlike O2, which exhibits a charge concentration region between its two oxygen atoms, iron(IV)-oxo species display a charge depletion region.

Synergistic Charge Transfer Effect in Ferrous Heme-CO Bonding within Cytochrome P450.

We conducted ab initio valence bond (VB) calculations employing the valence bond self-consistent field (VBSCF) and breathing orbital valence bond (BOVB) methods to investigate the nature of the coordination bonding between ferrous heme and carbon monoxide (CO) within cytochrome P450. These calculations revealed the significant influence exerted by both proximal and equatorial ligands on the π-backdonation effect from the heme to the CO. Moreover, our VB calculations unveiled a phenomenon of synergistic charge transfer (sCT). In the case of ferrous heme-CO bonding, the significant stabilization in this sCT arises from cooperative resonance between the VB structures associated with σ donation and π backdonation. Unlike many other ligands, CO possesses the unique ability to establish two mutually perpendicular π-backdonation orbital interaction pairs, leading to an intensified stabilization attributed to σ-π resonance. Furthermore, while of a smaller energy magnitude, sCT due to one π-π pair is also present, contributing to the differential stabilization of ferrous heme-CO bonding.

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.

Bonding and the role of electrostatics in driving C-C bond formation in high valent organocopper compounds.

The electronic structures and contrasting reactivity of [Cu(CF3)4]- and [Cu(CF3)3(CH3)]- were probed using coupled cluster and ab initio valence bond calculations. The Cu-C bonds in these complexes were found to be charge shift bonds. A key finding is that electrostatics likely prevent [Cu(CF3)4]- from accessing a productive transition state for C-C bond formation while promote one for [Cu(CF3)3(CH3)]-. These results therefore highlight essential design criteria for Cu-mediated C-C/C-heteroatom bond formation.

Implementation of molecular symmetry in valence bond calculation

AbstractA novel strategy for the construction of many‐electron symmetry‐adapted wave function is proposed for ab initio valence bond (VB) calculations and is implemented for valence bond self‐consistent filed (VBSCF) and breathing orbital valence bond (BOVB) methods with various orbital optimization algorithms. Symmetry‐adapted VB functions are constructed by the projection operator of symmetry group. The many‐electron symmetry‐adapted wave function is expressed in terms of symmetry‐adapted VB functions, and thus the VB calculations can be performed with the molecular symmetry restriction. Test results show that molecular symmetry reduces the computational cost of both the iteration numbers and CPU time. Furthermore, excited states with specific symmetry can be conveniently obtained in VB calculations by using symmetry‐adapted VB functions.

The roles of charge transfer and polarization in non-covalent interactions: a perspective from ab initio valence bond methods.

Noncovalent interactions are ubiquitous and have been well recognized in chemistry, biology and material science. Yet, there are still recurring controversies over their natures, due to the wide range of noncovalent interaction terms. In this Essay, we employed the Valence Bond (VB) methods to address two types of interactions which recently have drawn intensive attention, i.e., the halogen bonding and the CH‧‧‧HC dihydrogen bonding. The VB methods have the advantage of interpreting molecular structures and properties in the term of electron-localized Lewis (resonance) states (structures), which thereby shed specific light on the alteration of the bonding patterns. Due to the electron localization nature of Lewis states, it is possible to define individually and measure both polarization and charge transfer effects which have different physical origins. We demonstrated that both the ab initio VB method and the block-localized wavefunction (BLW) method can provide consistent pictures for halogen bonding systems, where strong Lewis bases NH3, H2O and NMe3 partake as the halogen bond acceptors, and the halogen bond donors include dihalogen molecules and XNO2 (X = Cl, Br, I). Based on the structural, spectral, and energetic changes, we confirm the remarkable roles of charge transfer in these halogen bonding complexes. Although the weak C-H∙∙∙H-C interactions in alkane dimers and graphene sheets are thought to involve dispersion only, we show that this term embeds delicate yet important charge transfer, bond reorganization and polarization interactions.

On the Bonding Nature in the Crystalline Tri-Thorium Cluster: Core-Shell Syngenetic σ-Aromaticity.

A unique thorium‐thorium bond was observed in the crystalline tri‐thorium cluster [{Th(η8‐C8H8)(μ3‐Cl)2}3{K(THF)2}2]∞, though the claim of σ‐aromaticity for Th3 bond has been questioned. Herein, a new type of core–shell syngenetic bonding model is proposed to describe the stability of this tri‐thorium cluster. The model involves a 3c–2e bond in the Th3 core and a multicentered (ThCl2)3 charge‐shift bond with 12 electrons scattering along the outer shell. To differentiate the strengths of the 3c–2e bond and the charge‐shift bond, the block‐localized wavefunction (BLW) method which falls into the ab initio valence bond (VB) theory is employed to construct a strictly core/shell localized state and its contributing covalent resonance structure for the Th3 core bond. By comparing with the σ‐aromatic H3 + and nonaromatic Li3 +, the computed resonance energies and extra cyclic resonance energies confirm that this Th3 core bond is truly delocalized and σ‐aromatic.

On the Bonding Nature in the Crystalline Tri‐Thorium Cluster: Core‐Shell Syngenetic σ‐Aromaticity

AbstractA unique thorium‐thorium bond was observed in the crystalline tri‐thorium cluster [{Th(η8‐C8H8)(μ3‐Cl)2}3{K(THF)2}2]∞, though the claim of σ‐aromaticity for Th3 bond has been questioned. Herein, a new type of core–shell syngenetic bonding model is proposed to describe the stability of this tri‐thorium cluster. The model involves a 3c–2e bond in the Th3 core and a multicentered (ThCl2)3 charge‐shift bond with 12 electrons scattering along the outer shell. To differentiate the strengths of the 3c–2e bond and the charge‐shift bond, the block‐localized wavefunction (BLW) method which falls into the ab initio valence bond (VB) theory is employed to construct a strictly core/shell localized state and its contributing covalent resonance structure for the Th3 core bond. By comparing with the σ‐aromatic H3+ and nonaromatic Li3+, the computed resonance energies and extra cyclic resonance energies confirm that this Th3 core bond is truly delocalized and σ‐aromatic.

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.

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.

Partial Double Metal-Carbon Bonding Model in Transition Metal Methyl Compounds.

The chemical bond between a transition metal and a methyl group (M-CH3) is typically defined as a single covalent bond, which is of fundamental significance and general interest in understanding the structural properties and reactivity of transition metal alkyl compounds. Herein, we demonstrate that the M-CH3 bonding involves varying σ and π components and thus should be best described in terms of the partial double M═CH3 bond. The often-neglected π bonding stems from an occupied π-symmetric orbital of the methyl group comprising all three C-H σ bonds (but one C-H' contributes more than the other two) and a vacant low-lying metal d(π) orbital, and is associated with the intramolecular C-H'···M agostic effect (i.e., an acute M-C-H' angle and a short H'···M distance), whose origin is still controversial. We quantify the geometric and energetic impacts of the π interaction involved in the M-CH3 bond by explicitly computing the intramolecular πCH' → dM interaction with the ab initio valence bond (VB) theory. Our computations of the ligand-free [TiCH3]3+ and a series of metallocene catalysts provide a direct proof for the presence of the π bonding in M-CH3 bonds, which is the cause for the agostic effect. The partial double M═CH3 bonding model is not only validated by a range of bonding analyses including VB self-consistent field (VBSCF)-based energy decomposition and quantum theory of atoms in molecules (QTAIM) but also authenticated by the specific activity of double M═CH3 bonds in the C-H activation and olefin insertion. More importantly, the σ bond gradually switches from a classical covalent bond to a novel charge-shift bond with the π bonding becoming increasingly significant. We anticipate that the recognition of the π interaction between electrophilic metal centers and C-H bonds can benefit the understanding of the nature of metal-carbon bonds in transition metal ethyl, alkyl, and carbene compounds.

On the Nature of the Bonding in Coinage Metal Halides.

This article analyzes the nature of the chemical bond in coinage metal halides using high-level ab initio Valence Bond (VB) theory. It is shown that these bonds display a large Charge-Shift Bonding character, which is traced back to the large Pauli pressure arising from the interaction between the bond pair with the filled semicore d shell of the metal. The gold-halide bonds turn out to be pure Charge-Shift Bonds (CSBs), while the copper halides are polar-covalent bonds and silver halides borderline cases. Among the different halogens, the largest CSB character is found for fluorine, which experiences the largest Pauli pressure from its σ lone pair. Additionally, all these bonds display a secondary but non-negligible π bonding character, which is also quantified in the VB calculations.

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.

Anti-Electrostatic Main Group Metal–Metal Bonds That Activate CO2

There has been growing interest in the CO2 capture and reduction by transition-metal-free catalysts. Here we performed a proof-of-concept study using an ab initio valence bond method called the block-localized wave function (BLW) method. The integrated BLW and density function theory (DFT) computations demonstrated that heterobimetallic Ae+/Al(I) (Ae represents alkaline earth metals Mg and Ca) Lewis acid/base combinations without transition metals can facilely capture and activate CO2. There are two remarkable findings in this study. The first concerns the ionic nature of the metal-metal bonds. The experimentally synthesized low valent aluminum compound with a bidentate β-diketiminate (BDI) ligand, or (BDI)Al(I) in brief, is a Lewis base due to the lone pair on the aluminum cation though overall Al(I) is positively charged. Al(I) can form ionic metal-metal bonds with the alkaline earth metals of the positively charged Lewis acids (BDI)Ae+. This type of ionic metal-metal bonds is counterintuitive and antielectrostatic as both metals carry positive charges. The second finding is the CO2 activation mechanism. (BDI)Al(I) can effectively bind and activate CO2 by transferring one electron to CO2, and the resulting complex can be best expressed as [(BDI)Al(I)]+[CO2]-. The participation of (BDI)Ae+ further enhances the capture and activation of CO2 by (BDI)Al(I).

Role of Charge Transfer in Halogen Bonding.

Halogen bonding has received intensive attention recently for its applications in the construction of supramolecular assemblies and crystal engineering and its implications and potentials in chemical and biological processes and rational drug design. Peculiarly, in intermolecular interactions, halogen atoms are known as electron-donating groups carrying partial negative charges in molecules due to its high electronegativity, but they can counterintuitively act as Lewis acids and bind with Lewis bases in the form of a halogen bond. The unsettling issue regarding the nature of the halogen bonding is whether the electrostatics or charge transfer interaction dominates. The recently proposed σ-hole concept nicely reinforces the role of electrostatic attraction. Also, good correlations between the halogen bonding strength and the interaction energy from the simple point-charge model have been found. This leads to the claim that there is no need to invoke the charge transfer concept in the halogen bond. But there is alternative evidence supporting the importance of charge transfer interaction. Here, we visited a series of prominent halogen bonded complexes of the types Y3C-X···Z (X = Br, I; Y = F, Cl, Br; Z = F-, Cl-, Br-, I-, NMe3) with the block-localized wave function (BLW) method at the M06-2X-D3/6-311+G(d,p) (def2-SVP for iodine) level of theory. As the simplest variant of ab initio valence bond (VB) theory, the BLW method is unique in the strict localization of electrons within interacting moieties, allowing for quantitative evaluation of the charge transfer effect on geometries, spectral properties, and energetics in halogen bonding complexes. By comparing the halogen bonding complexes with and without the charge transfer interaction, we proved that the charge transfer interaction significantly shortens the X···Z bonding distance and stretches the C-X bonds. But the shortening of the halogen bonding results in the less favorable steric effect, which is composed of Pauli repulsion, electrostatics, and electron correlation. There are approximate linear correlations between the charge transfer effect and binding energy and between bonding distance and binding energy. These correlations may lead to the illusion that the charge transfer interaction is unimportant or irrelevant, but further analyses showed that the inclusion of charge transfer is critical for the proper description of the halogen bonding, as considering only electrostatics and polarization leads to only about 45-60% of the binding strengths and much elongated bonding distances.

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.

Resonance-Assisted but Antielectrostatic Intramolecular Au···H-O Hydrogen Bonding in Gold(I) Complexes: A Computational Verification.

The peculiar Au···H hydrogen bonding has garnered significant interests, but its existence and nature remain an open question in gold chemistry. In this paper, we established and authenticated the first intramolecular Au···H-O hydrogen bonding in gold(I) complexes. Our computational results based on an ab initio valence bond (VB) method, namely the block-localized wave function (BLW) method, clarified that this Au···H-O hydrogen bonding is a new type of resonance-assisted hydrogen bond (RAHB). In this RAHB, π conjugation in the hydrogen bond donor has the capability to modulate the Au···H-O hydrogen bonding. In contrast to conventional RAHBs, however, the Au···H-O hydrogen bonding is antielectrostatic and is dominated by the charge transfer interaction including cooperative σ electron donation from the d orbital of the metal center to the antibonding orbital of the hydroxyl group and π conjugation from the hydroxyl group to adjacent π deficient or strong π electron withdrawing groups. This novel theoretical perspective not only confirms the existence and reveals the nature of intramolecular Au···H hydrogen bonding but also provides a promising strategy to rationally design strong gold hydrogen bonds.

Ab initio valence bond theory: A brief history, recent developments, and near future.

This Perspective presents a survey of several issues in ab initio valence bond (VB) theory with a primary focus on recent advances made by the Xiamen VB group, including a brief review of the earlier history of the ab initio VB methods, in-depth discussion of algorithms for nonorthogonal orbital optimization in the VB self-consistent field method and VB methods incorporating dynamic electron correlation, along with a concise overview of VB methods for complex systems and VB models for chemical bonding and reactivity, and an outlook of opportunities and challenges for the near future of the VB theory.

Novel implementation of seniority number truncated valence bond methods with applications to H22 chain.

Both the efficiency and capability of the seniority number truncated valence bond (VB) methods are highly improved by using our recently proposed extension of Malmqvist's algorithm for the reciprocal transformation of many-electron bases constructed by nonorthogonal orbitals [Zhou, Chen, and Wu, J. Chem. Phys. 149(4), 044111 (2018)] and by the adoption of the direct technique in solving the generalized eigenvalue problem. Due to the compactness of the wave function that benefited from seniority number restriction, the memory need and computational cost for energy evaluation and orbital optimization in valence bond self-consistent field calculation are largely reduced. The last obstacle in nonorthogonal orbital based ab initio VB calculation is thus removed. Consequently, we can accomplish seniority number truncated VB calculation at the same computational scaling as that of the most general configuration selected multiconfigurational self-consistent field with a memory cost much less than the corresponding complete active space self-consistent field (CASSCF). Test on Hn string molecules shows that the seniority number truncated VB calculation maintains the majority of static correlation by using a more compact wave function than CASSCF.

How Resonance Modulates Multiple Hydrogen Bonding in Self-Assembled Systems.

The secondary electrostatic interaction (SEI) has been regarded as the fundamental cause for the relative strengths of multiple hydrogen bonds for decades, though recent studies challenged its validation. Here, we used our developed block-localized wave function (BLW) method, which is a variant of ab initio valence bond (VB) theory and can self-consistently derive the wave function for a strictly electron-localized state, to study a series of exemplary multiply hydrogen-bonded complexes and critically examine the role of SEI in the binding. Our computations show that the multiple hydrogen bond in self-assembled complexes is a kind of resonance-assisted hydrogen bond (RAHB) in nature, and the π resonance which moves electron density from the hydrogen bond donor to the acceptor is the true origin of the different hydrogen bond strengths. By quenching the π resonance effect, the hydrogen bond strengths become nearly identical for various neutral doubly, triply, and quadruply hydrogen-bonded dimers where in general the SEI model works. In other words, the SEI plays only a minor role in multiply hydrogen-bonded complexes, and the π resonance, which changes not only electron densities but also molecular polarities (dipole moments), is the major force.