XMVB: a program for ab initio nonorthogonal valence bond computations

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.

Identifying a real space measure of charge-shift bonding with probability density analysis

Charge-shift bonds have been hypothesized as a third type of chemical bonds in addition to covalent and ionic bonds. They have first been described with valence bond theory where they are identified by the resonance energy resulting from ionic contributions. While other indicators have been described, a clear real space fingerprint for charge-shift bonding is still lacking. Probability density analysis has been developed as a real space method, allowing chemical bonding to be identified from the many-electron probability density |Ψ|2 where the wave function Ψ can be obtained from any quantum chemical method. Recently, barriers of a probability potential, which depends on this density, have proven to be good measures for delocalization and covalent bonding. In this work, we employ many examples to demonstrate that a well-suited measure for charge-shift bonding can be defined within the framework of probability density analysis. This measure correlates well with the charge-shift resonance energy from valence bond theory and thus strongly supports the charge-shift bonding concept. It is, unlike the charge-shift resonance energy, not dependent on a reference state. Moreover, it is independent of the polarity of the bond, suggesting to characterize bonds in molecules by both their polarity and their charge-shift character.

Multiconfigurational actinide nitrides assisted by double Möbius aromaticity

Understanding the bonding nature between actinides and main-group elements remains a key challenge in actinide chemistry due to the involvement of f orbitals. Herein, we propose a unique "aromaticity-assisted multiconfiguration" (AAM) model to elucidate the bonding nature in actinide nitrides (An2N2, An = Ac, Th, Pa, U). Each planar four-membered An2N2 with equivalent An-N bonds possesses four delocalized π electrons and four delocalized σ electrons, forming a new family of double Möbius aromaticity that contributes to the molecular stability. The unprecedented aromaticity further supports actinide nitrides to exhibit multiconfigurational characters, where the unpaired electrons (2, 4 or 6 in naked Th2N2, Pa2N2 or U2N2, respectively) either are spin-free and localized on metal centres or form metal-ligand bonds. High-level multiconfigurational computations confirm an open-shell singlet ground state for actinide nitrides, with small energy gaps to high spin states. This is consistent with the antiferromagnetic nature observed experimentally in uranium nitrides. The novel AAM bonding model can be authenticated in both experimentally identified compounds containing a U2N2 motif and other theoretically modelled An2N2 clusters and is thus expected to be a general chemical bonding pattern between actinides and main-group elements.

3,4-Dimethylenecyclobutene: A Building Block for Design of Macrocycles with Excited State Aromatic Low-Lying High-Spin States

3,4-Dimethylenecyclobutene (DMCB) is an unusual isomer of benzene. Motivated by recent synthetic progress to substituted derivatives of this scaffold, we carried out a theoretical and computational analysis with a particular focus on the extent of (anti)aromatic character in the lowest excited states of different multiplicities. We found that the parent DMCB is non-aromatic in its singlet ground state (S0), lowest triplet state (T1), and lowest singlet excited state (S1), while it is aromatic in its lowest quintet state (Q1) as this state is represented by a triplet multiplicity cyclobutadiene (CBD) ring and two uncoupled same-spin methylene radicals. Interestingly, the Q1 state, despite having four unpaired electrons, is placed merely 4.8 eV above S0, and there is a corresponding singlet tetraradical 0.16 eV above. The DMCB is potentially a highly useful structural motif for the design of larger molecular entities with interesting optoelectronic properties. Here, we designed macrocycles composed of fused DMCB units, and according to our computations, two of these have low-lying nonet states (i. e., octaradical states) at energies merely 2.40 and 0.37 eV above their S0 states as a result of local Hückel- and Baird-aromatic character of individual 6π- and 4π-electron monocycles.

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.

Hybrid Density Functional Valence Bond Method with Multistate Treatment

Recently, a hybrid density functional valence bond (VB) method, λ-DFVB(U), has been proposed and shown to give accuracy that is comparable to that of CASPT2 in calculations of atomization energies, atomic excitation energies, and reaction barriers, while its computational cost is approximately the same as the valence bond self-consistent-field (VBSCF) method. However, the interaction between electronic states is not included in λ-DFVB(U) since the last step of λ-DFVB(U) is not a diagonalization of the Hamiltonian matrix on the electronic state basis. Therefore, λ-DFVB(U) gives the wrong topology of the potential energy surfaces (PESs) near the conical intersection region. In the present paper, we propose a novel hybrid density functional VB method with multistate treatment, named λ-DFVB(MS), in which an effective Hamiltonian matrix is constructed on the basis of the diabatic states obtained by the valence-bond-based compression approach for the diabatization scheme, and the interaction between electronic states can be included through the diagonalization of the effective Hamiltonian matrix. Test calculations show that λ-DFVB(MS) gives the correct topology of the PESs near the conical intersection region. We also show that the VBSCF wave function with selected VB structures can be applied as a reference in λ-DFVB(MS).

Valence Bond Theory Allows a Generalized Description of Hydrogen Bonding

This paper describes the nature of the hydrogen bond (HB), B:---H-A, using valence bond theory (VBT). Our analysis shows that the most important HB interactions are polarization and charge transfer, and their corresponding sum displays a pattern that is identical for a variety of energy decomposition analysis (EDA) methods. Furthermore, the sum terms obtained with the different EDA methods correlate linearly with the corresponding VB quantities. The VBT analysis demonstrates that the total covalent-ionic resonance energy (RECS) of the HB portion (B---H in B:---H-A) correlates linearly with the dissociation energy of the HB, ΔEdiss. In principle, therefore, RECS(HB) can be determined by experiment. The VBT wavefunction reveals that the contributions of ionic structures to the HB increase the positive charge on the hydrogen of the corresponding external/free O-H bonds in, for example, the water dimer compared with a free water molecule. This increases the electric field of the external O-H bonds of water clusters and contributes to bringing about catalysis of reactions by water droplets and in water-hydrophobic interfaces.

New Methodology to Produce Sets of Valence Bond Structures with Enhanced Chemical Insights

The valence bond (VB) theory uses localized orbitals, and its wave function is composed of a linear combination of various VB structures which are based on sets of spin functions. The VB structures are not unique, and different sets are used, Rumer sets being the most common for classical VB due to their advantage as being both easily obtained as linearly independent and meaningful. Yet, Rumer rules, which are responsible for the simplified process of obtaining the Rumer sets, are very restrictive. Furthermore, Rumer sets are best suited for cyclic systems; however, in noncyclic systems, structures resulting from Rumer rules are often not the most intuitive/suitable structures for these systems. We have developed a method to obtain chemically insightful structures, which is based on concepts of chemical bonding. The method provides sets of VB structures with improved chemical insight, which can also be controlled. Parallel to the Rumer structures, the chemical insight sets of structures are based on electron pair coupling, and hence, pictorially can be drawn similarly to the Lewis structures. Yet, different from Rumer rules, the chemical insight method, being more flexible, allows larger combinations of bonds as well as larger combinations of structures in the sets it offers, resulting in many more possible sets that are better adapted to the systems studied.

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.

Captodative Effect Facilitates the Excitation in Diboron Molecule (CAAC)2 B2 (SH)2

Given the extraordinary versatility in chemical reactions and applications, boron compounds have gained increasing attentions in the past two decades. One of the remarkable advances is the unprecedented preparation of unsaturated boron species. Notably, Braunschweig et al. found that the cyclic (alkyl)(amino) carbenes (CAACs) stabilized diboron molecules (CAAC)₂ B₂ (SR)₂ host unpaired electrons and exist in the 90°-twisted diradical form, while other analogues, such as N-heterocyclic carbenes (NHCs), stabilized diboron molecules prefer a conventional B=B double bond. Since previous studies recognized the differences in the steric effect between CAAC and NHC carbenes, here we focused on the role of thiol substituents in (CAAC)₂ B₂ (SR)₂ by gradually localizing involved electrons. The co-planarity of the thiol groups and the consequent captodative effect were found to be the culprit for the 90°-twisted diradical form of (CAAC)₂ B₂ (SR)₂ . Computational analyses identified two forces contributing to the π electron movements. One is the "push" effect of lone pairs on the sulfur atoms which boosts the π electron delocalization between the BB center and CAACs. The other is the π electron delocalization within each (CAAC)B(SR) fragment where the pull effect originates from the π electron withdrawal by CAACs. There are two such independent and orthogonal push-pull channels which function mainly in individual (CAAC)B(SR) fragments. This enhanced π push-pull effect in the triplet state facilitates the electronic excitation in (CAAC)₂ B₂ (SR)₂ by reducing the singlet-triplet gap.

The effect of immediate environment on bond strength of different bond types-A valence bond study

The ability to design catalysis largely depends on our understanding of the electrostatic effect of the surrounding on the bonds participating in the reaction. Here, we used a simplistic model of point charges (PCs) to determine a set of rules guiding how to construct PC-bond arrangement that can strengthen or weaken different chemical bonds. Using valence bond theory to calculate the in situ bond energies, we show that the effect of the PC mainly depends on the bond's dipole moment irrespective of its type (being covalent or charge shift). That is, polar bonds are getting stronger or weaker depending on the sign and location of the PC, whereas non- or weakly polar bonds become stronger or weaker depending only on the location of the PC and to a smaller extent compared with polar bonds. We also show that for polar bonds, the maximal bond strengthening and weakening effect can be achieved when the PC is placed along the bond axis, as close as possible to the more and less polarizable atom/fragment, respectively. Finally, due to the stabilizing effects of polarizability, we show that, overall, it is easier to cause bond strengthening compared with bond weakening. Particularly, for polar bonds, bond strengthening is larger than bond weakening obtained by an oppositely signed PC. These rules should be useful in the future design of catalysis in, e.g., enzyme active sites.

Multi-center bonds as resonance hybrids: A real space perspective

The concept of distinct bonds within molecules has proven to be successful in rationalizing chemical reactivity. However, bonds are not a well-defined physical concept, but rather vague entities, described by different and often contradicting models. With probability density analysis, which can-in principle-be applied to any wave function, bonds are recovered as spin-coupled positions within most likely electron arrangements in coordinate space. While the wave functions of many systems are dominated by a single electron arrangement that is built from two-center two-electron bonds, some systems require several different arrangements to be well described. In this work, a range of these multi-center bonded molecules are classified and investigated with probability density analysis. The results are compared with valence bond theory calculations and data from collision-induced dissociation experiments.

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.

Electronic densities and valence bond wave functions

Valence bond (VB) wave functions are studied from the density point of view. The density is plotted as a difference with the quasi-state built on the same orbitals. The densities of the components of the VB wave function are also shown. The breathing orbital effect leads to small modifications of the density. It is shown that while the densities of ionic and covalent components are the same, their coupling ends-up in modifications of the electronic density.

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.

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 π_CH' → d_M 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.

Nature of the Trigger Linkage in Explosive Materials Is a Charge-Shift Bond

Explosion begins by rupture of a specific bond, in the explosive, called a trigger linkage. We characterize this bond in nitro-containing explosives. Valence-bond (VB) investigations of X-NO₂ linkages in alkyl nitrates, nitramines, and nitro esters establish the existence of Pauli repulsion that destabilizes the covalent structure of these bonds. The trigger linkages are mainly stabilized by covalent-ionic resonance and are therefore charge-shift bonds (CSBs). The source of Pauli repulsion in nitro explosives is unique. It is traced to the hyperconjugative interaction from the oxygen lone pairs of NO₂ into the σ_(X-N)^* orbital, which thereby weakens the X-NO₂ bond, and depletes its electron density as X becomes more electronegative. Weaker trigger bonds have higher CSB characters. In turn, weaker bonds increase the sensitivity of the explosive to impacts/shocks which lead to detonation. Application of the analysis to realistic explosives supports the CSB character of their X-NO₂ bonds by independent criteria. Furthermore, other families of explosives also involve CSBs as trigger linkages (O-O, N-O, Cl-O, N-I, etc. bonds). In all of these, detonation is initiated selectively at the CSB of the molecule. A connection is made between the CSB bond-weakening and the surface-electrostatic potential diagnosis in the trigger bonds.

N-Body Reduced Density Matrix-Based Valence Bond Theory and Its Applications in Diabatic Electronic-Structure Computations

Valence bond (VB) theory, as a helpful complement to the more popular molecular orbital theory, is a fundamental electronic-structure theory that aims at interpreting molecular structure and chemical reactions in a lucid way. Both theoretical and experimental chemists have shown great interest in VB theory because of its capability of providing intuitive insight into the nature of chemical bonding and the mechanism of chemical reaction in a clear and comprehensible language rooted in Lewis structure. Therefore, there is a great call for the renaissance of VB theory. Nevertheless, this is possible only after a series of methods and algorithms were developed and efficiently implemented in user-friendly programs so as to serve computational chemists for general applications. In the past three decades, we have devoted a great amount of scientific enthusiasm toward this goal. In this Account, we will concisely summarize and briefly but insightfully discuss recent developments in ab initio VB theory, especially the N-body reduced density matrices (RDM)-based approach and its applications in diabatic electronic-structure computations, which is very useful for the vivid interpretation of many fundamental chemical processes such as electron and energy transfers. Furthermore, because of the fundamentally important role that the diabatic state plays in electron and energy transfers, which are two frontier research topics in both molecular and biochemical sciences, there are a broad range of applications that VB theory can handle.We start by briefly reviewing the general feature of ab initio VB wave functions. In particular, we focus on the multistructural ab initio VB theory that uses strictly localized orbitals, including the fundamental VB self-consistent field (VBSCF) and two post-SCF methods, VBCI and VBPT2, that use the VBSCF wave function as reference. We then allot a section to describing the recent developments of the RDM-based VB approach in the second quantization language. In this section, the enhanced Wick theorem is first outlined, followed by a brief discussion of its applications in evaluating VBSCF energy gradients and a Hessian with respect to the orbital expansion coefficients, together with a short review of the implementation of an automatic formula and code generator (AFCG) designed for many-body methods with nonorthogonal orbitals. Then, we introduce the application of the RDM-based approach in implementing the post-SCF method that addresses dynamic electronic correlation via perturbation theory, viz., the icVBPT2 method that adopts an internal contraction technique naturally. We finish this section by incorporating VB theory with the concept of seniority number, in which the tensor analysis technique is carefully exploited with the RDM-based approach, resulting in significant improvements in both the number of the active electrons/orbitals and in the speedup of the computational efficiency, thus pushing VB theory to its new limit. With these achievements available, we present the applications of VB theory in diabatic electronic-structure computations by using the intuitive insight rendered by VB theory. Therefore, we believe that there is a bright future in VB theory with true opportunities and new challenges coexisting both for theoretical developments and computational applications.

Real space electron delocalization, resonance, and aromaticity in chemistry

Chemists explaining a molecule’s stability and reactivity often refer to the concepts of delocalization, resonance, and aromaticity. Resonance is commonly discussed within valence bond theory as the stabilizing effect of mixing different Lewis structures. Yet, most computational chemists work with delocalized molecular orbitals, which are also usually employed to explain the concept of aromaticity, a ring delocalization in cyclic planar systems which abide certain number rules. However, all three concepts lack a real space definition, that is not reliant on orbitals or specific wave function expansions. Here, we outline a redefinition from first principles: delocalization means that likely electron arrangements are connected via paths of high probability density in the many-electron real space. In this picture, resonance is the consideration of additional electron arrangements, which offer alternative paths. Most notably, the famous 4n + 2 Hückel rule is generalized and derived from nothing but the antisymmetry of fermionic wave functions.

The concept of delocalization, resonance and aromaticity are commonly discussed within electronic structure frameworks relying on specific wave function expansions. Here the authors propose a redefinition of these concepts from first-principles by investigating saddle points of the all-electron probability density.

Valence Bond Theory-Its Birth, Struggles with Molecular Orbital Theory, Its Present State and Future Prospects

This essay describes the successive births of valence bond (VB) theory during 1916–1931. The alternative molecular orbital (MO) theory was born in the late 1920s. The presence of two seemingly different descriptions of molecules by the two theories led to struggles between the main proponents, Linus Pauling and Robert Mulliken, and their supporters. Until the 1950s, VB theory was dominant, and then it was eclipsed by MO theory. The struggles will be discussed, as well as the new dawn of VB theory, and its future.

Revealing the biradicaloid nature inherited in the derivatives of thieno[3,4-c][1,2,5]thiadiazole: a computational study

Computational studies were performed on non-classical thieno[3,4-c][1,2,5] thiadiazole and its pi donor derivatives (TT dyes) so as to delineate the factors responsible for their near-infrared (NIR) absorption. For all dyes except the unsubstituted bare dye, adiabatic singlet-triplet energy gaps (estimated through the ΔSCF procedure using the B3LYP and M062X DFT methods and SFTDDFT with the 5050 functional) were less than 1eV. Percentage calculations of the biradicaloid character suggested a moderate biradicaloid nature in all derivatives. There was a resemblance between the frontier molecular orbital (MO) picture of the TT bicyclic ring and the degenerate non-bonding molecular orbitals of Trimethyleneethane (TME, a known biradical). Inter-fragment charge transfer analysis revealed not only a considerable donation of charge to the central ring (Acceptor, TT part) but also substantial charge redistribution within the ring itself. From these results, it was inferred that NIR absorption, in these dyes, was due to: (1) a reduced HOMO-LUMO gap (HLG) as a TME biradical substructure forms its chromophoric part; and (2) charge transfer from the donor substituents. The non-bonding nature of the S atom, in the bare dye, with its neighbouring N/C atom (of the highest occupied π-MOs), led to an examination of its electronic structure using the ab initio valence bond method. The relatively large weight and energetic stability of the biradicaloid VB structures compared to those of the ylidic structures clearly disclosed the importance of biradicaloid structures in the overall resonance of the bare dye. Their utility as singlet fission materials was screened using singlet and triplet energy-based molecular structure activity criteria. The results were encouraging, demanding experiments to reaffirm the materials' usefulness.

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.

Valence Bond Alternative Yielding Compact and Accurate Wave Functions for Challenging Excited States. Application to Ozone and Sulfur Dioxide

A novel state-averaged version of ab initio nonorthogonal valence bond method is described, for the sake of accurate theoretical studies of excited states in the valence bond framework. With respect to standard calculations in the molecular orbital framework, the state-averaged breathing-orbital valence bond (BOVB) method has the advantage to be free from the penalizing constraint for the ground and excited state(s) to share the same unique set of orbitals. The ability of the BOVB method to faithfully describe excited states and to compute accurate transition energies from the ground state is tested on the five lowest-lying singlet electronic states of ozone and sulfur dioxide, among which 1¹B₂ and 2¹A₁ are the challenging ones. As the 1¹A₂, 1¹B₁, and 1¹B₂ states are of different symmetries than the ground state, they can be calculated at the state-specific BOVB level. On the other hand, the 2¹A₁ states and the 1¹A₁ ground states, which are of like symmetry, are calculated with the state-averaged BOVB technique. In all cases, the calculated vertical energies are close to the experimental values when available, and at par with the most sophisticated calculations in the molecular framework, despite the extreme compactness of the BOVB wave functions, made of no more than 5-9 valence bond structures in all cases. The features that allow the combination of compactness and accuracy in challenging cases are analyzed. For the "ionic" 1¹B₂ states, which are the site of important charge fluctuations, it is because of the built-in dynamic correlation inherent to the BOVB method. For the 2¹A₁ ones, this is the fact that these states have the degree of freedom of having different orbitals than the ground states, even though they are of like symmetry and calculated simultaneously using the newly implemented state-average BOVB algorithm. Finally, the description of the excited states in terms of Lewis structures is insightful, rationalizing the fast ring closure for the 2¹A₁ state of ozone and predicting some diradical character in the so-called "ionic" 1¹B₂ states.

Unifying Conceptual Density Functional and Valence Bond Theory: The Hardness-Softness Conundrum Associated with Protonation Reactions and Uncovering Complementary Reactivity Modes

In this study, we address the long-standing issue-arising prominently from conceptual density functional theory (CDFT)-of the relative importance of electrostatic, i.e., "hard-hard", versus spin-pairing, i.e., "soft-soft", interactions in determining regiochemical preferences. We do so from a valence bond (VB) perspective and demonstrate that VB theory readily enables a clear-cut resolution of both of these contributions to the bond formation/breaking process. Our calculations indicate that appropriate local reactivity descriptors can be used to gauge the magnitude of both interactions individually, e.g., Fukui functions or HOMO/LUMO orbitals for the spin-pairing/(frontier) orbital interactions and molecular electrostatic potentials (and/or partial charges) for the electrostatic interactions. In contrast to previous reports, we find that protonation reactions cannot generally be classified as either charge- or frontier orbital-controlled; instead, our results indicate that these two bonding contributions generally interplay in more subtle patterns, only giving the impression of a clear-cut dichotomy. Finally, we demonstrate that important covalent, i.e., spin pairing, reactivity modes can be missed when only a single spin-pairing/orbital interaction descriptor is considered. This study constitutes an important step in the unification of CDFT and VB theory.

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.

Covalent vs Charge-Shift Nature of the Metal-Metal Bond in Transition Metal Complexes: A Unified Understanding

We present here a general conceptualization of the nature of metal-metal (M-M) bonding in transition-metal (TM) complexes across the periods of TM elements, by use of ab initio valence-bond theory. The calculations reveal a dual-trend: For M-M bonds in groups 7 and 9, the 3d-series forms charge-shift bonds (CSB), while upon moving down to the 5d-series, the bonds become gradually covalent. In contrast, M-M bonds of metals having filled d-orbitals (groups 11 and 12) behave oppositely; initially the M-M bond is covalent, but upon moving down the Periodic Table, the CSB character increases. These trends originate in the radial-distribution-functions of the atomic orbitals, which determine the compactness of the valence-orbitals vis-à-vis the filled semicore orbitals. Key factors that gauge this compactness are the presence/absence of a radial-node in the valence-orbital and relativistic contraction/expansion of the valence/semicore orbitals. Whenever these orbital-types are spatially coincident, the covalent bond-pairing is weakened by Pauli-repulsion with the semicore electrons, and CSB takes over. Thus, for groups 3-10, which possess (n - 1)s²(n - 1)p⁶ semicores, this spatial-coincidence is maximal at the 3d-transition-metals which consequently form charge-shift M-M bonds. However, in groups 11 and 12, the relativistic effects maximize spatial-coincidence in the third series, wherein the 5d¹⁰ core approaches the valence 6s orbital, and the respective Pauli repulsion generates M-M bonds with CSB character. These considerations create a generalized paradigm for M-M bonding in the transition-elements periods, and Pauli repulsion emerges as the factor that unifies CSB over the periods of main-group and transition elements.

How Do Local Reactivity Descriptors Shape the Potential Energy Surface Associated with Chemical Reactions? The Valence Bond Delocalization Perspective

How do local reactivity descriptors, such as the Fukui function and the local spin density distribution, shape the potential energy surface (PES) associated with chemical reactions and thus govern reactivity trends and regioselective preferences? This is the question that is addressed here through a qualitative valence bond (VB) analysis. We demonstrate that common density functional theory (DFT)-based local reactivity descriptors can essentially be regarded-in one way or another-as indirect measures of delocalization, i.e., resonance stabilization, of the reactants within VB theory. The inherent connection between (spatial) delocalization and (energetic) resonance stabilization embedded in VB theory provides a natural and elegant framework for analyzing and comprehending the impact of individual local reactivity descriptors on the global PES. Our analysis provides new insights into the role played by local reactivity descriptors and illustrates under which conditions they can sometimes fail to predict reactivity trends and regioselective preferences, e.g., in the case of ambident reactivity. This treatment constitutes a first step toward a unification of VB theory and conceptual DFT.

Revealing a Decisive Role for Secondary Coordination Sphere Nucleophiles on Methane Activation

Density functional theory and ab initio calculations indicate that nucleophiles can significantly reduce enthalpic barriers to methane C-H bond activation. Valence bond analysis suggests the formation of a two-center three-electron bond as the origin for the catalytic nucleophile effect. A predictive model for methane activation catalysis follows, which suggests that strongly electron-attracting and electron-rich radicals, together with both a negatively charged and strongly electron-donating outer sphere nucleophile, result in the lowest reaction barriers. It is corroborated by the sensitivity of the calculated C-H activation barriers to the external nucleophile and to continuum solvent polarity. More generally, from the present studies, one may propose proteins with hydrophobic active sites, available strong nucleophiles, and hydrogen bond donors as attractive targets for engineering novel methane functionalizing enzymes.

Coupled electron and proton transfer in the piperidine drug metabolism pathway by the active species of cytochromes P450

KS-DFT and MSDFT studies reveal a novel CEPT step that triggers ring contraction of piperidines by P450.

On the connection between probability density analysis, QTAIM, and VB theory

Classification of bonds is essential for understanding and predicting the reactivity of chemical compounds. This classification mainly manifests in the bond order and the contribution of different Lewis resonance structures. Here, we outline a first principles approach to obtain these orders and contributions for arbitrary wave functions in a manner that is both, related to the quantum theory of atoms in molecules and consistent with valence bond theory insight: the Lewis structures arise naturally as attractors of the all-electron probability density |Ψ|2. Doing so, we introduce a valence bond weight definition that does not collapse in the basis set limit.

Captodative Substitution Enhances the Diradical Character of Compounds, Reduces Aromaticity, and Controls Single-Molecule Conductivity Patterns: A Valence Bond Study

The present contribution uses a valence bond (VB) perspective to consider the captodative substitution strategy, a method to enhance the diradical character of (potentially aromatic) compounds. We confirm the qualitative reasoning that has generally been used to rationalize the diradical-character-enhancing effect of captodative substitution: this type of substitution scheme disproportionally stabilizes specific Dewar/diradical(oid) VB structures, thus increasing their weight in the full ground-state wave function. Furthermore, we assess the effect of captodative substitution on the aromaticity of the considered compound. We observe a clear trade-off between diradical character and aromaticity for our model systems: as one of these properties increases, the other decreases. This finding is especially significant within the field of single-molecule electronics because it enables unification of the previously observed inverse proportionality between the aromaticity of a compound and the magnitude of conductance through that molecule, with the observed proportionality between diradical character and the magnitude of conductance associated with a compound. To some extent, both properties, i.e., aromaticity and diradical character, appear to be the flip-sides of the same coin.

Agostic Interactions in Early Transition-Metal Complexes: Roles of Hyperconjugation, Dispersion, and Steric Effect

The agostic interaction is a ubiquitous phenomenon in catalytic processes and transition-metal complexes, and hyperconjugation has been well recognized as its origin. Yet, recent studies showed that either short-range London dispersion or structural constraints could be the driving force, although proper evaluation of the role of hyperconjugation therein is needed. Herein, a simple variant of valence bond theory was employed to study a few exemplary Ti complexes with α- or β-agostic interactions and interpret the agostic effect in terms of the steric effect, hyperconjugation, and dispersion. For the complexes [MeTiCl₃ (dmpe)] and [MeTiCl₃ (dhpe)] with α-agostic interactions, hyperconjugation plays the dominant role with comparable magnitudes in both systems, but dispersion is solely responsible for the stronger agostic interaction in the former compared with the latter. For the complexes [EtTiCl₃ (dmpe)] and [EtTiCl₃ (dhpe)] with β-agostic interactions, however, hyperconjugation and dispersion play comparable roles, and the weaker steric repulsion leads to a stronger agostic effect in the former than in the latter. Thus, the present study clarifies the variable and sensitive roles of steric, hyperconjugative, and dispersion interactions in the agostic interaction.

Oriented External Electric Fields: Tweezers and Catalysts for Reactivity in Halogen-Bond Complexes

This theoretical study establishes ways of controlling and enabling an uncommon chemical reaction, the displacement reaction, B:---(X-Y) → (B-X)⁺ + :Y^-, which is nascent from a B:---(X-Y) halogen bond (XB) by nucleophilic attack of the base, B:, on the halogen, X. In most of the 14 cases examined, these reactions possess high barriers either in the gas phase (where the X-Y bond dissociates to radicals) or in solvents such as CH₂Cl₂ and CH₃CN (which lead to endothermic processes). Thus, generally, the XB species are trapped in deep minima, and their reactions are not allowed without catalysis. However, when an oriented-external electric field (OEEF) is directed along the B---X---Y reaction axis, the field acts as electric tweezers that orient the XB along the field's axis, and intensely catalyze the process, by tens of kcal/mol, thus rendering the reaction allowed. Flipping the OEEF along the reaction axis inhibits the reaction and weakens the interaction of the XB. Furthermore, at a critical OEEF, each XB undergoes spontaneous and barrier-free reaction. As such, OEEF achieves quite tight control of the structure and reactivity of XB species. Valence bond modeling is used to elucidate the means whereby OEEFs exert their control.

Valence : A Massively Parallel Implementation of the Variational Subspace Valence Bond Method

This work describes the software package, Valence, for the calculation of molecular energies using the variational subspace valence bond (VSVB) method. VSVB is an ab initio electronic structure method based on nonorthogonal orbitals. Important features of practical value include high parallel scalability, wave functions that can be constructed automatically by combining orbitals from previous calculations, and ground and excited states that can be modeled with a single configuration or determinant. The open-source software package includes tools to generate wave functions, a database of generic orbitals, example input files, and a library build intended for integration with other packages. We also describe the interface to an external software package, enabling the computation of optimized molecular geometries and vibrational frequencies. © 2019 Wiley Periodicals, Inc.

Insights into the Trends in the Acidity Strength of Organic and Inorganic Compounds: A Valence-Bond Perspective

Few concepts are more familiar to chemists than the concept of acidity strength. In almost any undergraduate chemistry textbook, one can find lists of factors affecting the acidities of organic and inorganic molecules. The factors, invoked to explain trends in the acidity strength through series of compounds, rely on concepts such as hybridization, delocalization, inductive effects, and electronegativity. Some of these concepts could be considered somewhat fuzzy, whereas others have a rigorous physical definition, yet together they shape the traditional framework used by chemists for the qualitative assessment of acidity strengths. At the same time, a thermodynamic cycle reveals that the acidity of a H-A bond is dependent on only three unequivocally definable quantities: the bond dissociation energy, the electron affinity of A, and the solvent effects. Here we attempt to answer the following questions: "How are the qualitative factors, found in textbooks, related to these quantities?" and "How can we connect this plethora of factors to the nature of the acidic H-A bond being cleaved heterolytically in an acidic dissociation process?" To do so, we turn to valence bond theory and model a generic acidic dissociation process. Within this model, the quantities, determining the acidity strength of an H-A compound (as revealed through the thermodynamic cycling process), arise naturally and lucidly, thus enabling the evaluation of the effects of the different qualitative factors found in the literature on the bonding situation. Our analysis projects surprising and thought-provoking anomalies, which challenge common chemical knowledge.

Resonance Theory Reboot

What is now called "resonance theory" has a long and conflicted history. We first sketch the early roots of resonance theory, its heritage of diverse physics and chemistry conceptions, and its subsequent rise to reigning chemical bonding paradigm of the mid-20th century. We then outline the alternative "natural" pathway to localized Lewis- and resonance-structural conceptions that was initiated in the 1950s, given semi-empirical formulation in the 1970s, recast in ab initio form in the 1980s, and successfully generalized to multi-structural "natural resonance theory" (NRT) form in the 1990s. Although earlier numerical applications were often frustrated by the ineptness of then-available numerical solvers, the NRT variational problem was recently shown to be amenable to highly efficient convex programming methods that yield provably optimal resonance weightings at a small fraction of previous computational costs. Such convexity-based algorithms now allow a full "reboot" of NRT methodology for tackling a broad range of chemical applications, including the many familiar resonance phenomena of organic and biochemistry as well as the still broader range of resonance attraction effects in the inorganic domain. We illustrate these advances for prototype chemical applications, including (i) stable near-equilibrium species, where resonance mixing typically provides only small corrections to a dominant Lewis-structural picture, (ii) reactive transition-state species, where strong resonance mixing of reactant and product bonding patterns is inherent, (iii) coordinative and related supramolecular interactions of the inorganic domain, where sub-integer resonance bond orders are the essential origin of intermolecular attraction, and (iv) exotic long-bonding and metallic delocalization phenomena, where no single "parent" Lewis-structural pattern gains pre-eminent weighting in the overall resonance hybrid.

σ-Aromaticity in a Fully Unsaturated Ring

Aromaticity is one of the most fundamental and fascinating chemical topics, attracting both experimental and theoretical chemists owing to its many manifestations. Both σ- and π-aromaticity can be classified depending on the character of the cyclic electron delocalization. In general, σ-aromaticity stabilizes fully saturated rings with σ-electron delocalization whereas the traditional π-aromaticity describes the π-conjugation in fully unsaturated rings. Here, we demonstrate a strong correlation between nucleus-independent chemical shift (NICS) values and extra cyclic resonance energies (ECREs), which are used to evaluate the σ-aromaticity in an unsaturated three-membered ring (3MR) of cyclopropene, which were computed by molecular orbital (MO) theory and valence bond (VB) theory, respectively. Further study shows that the fully unsaturated ring in methylenecyclopropene and its metallic analogy is σ-aromatic. Our findings revolutionize the fundamental knowledge of the concept of σ-aromaticity, thus opening an avenue to design σ-aromaticity in other fully unsaturated systems, which are traditionally reserved as the domain of π-aromaticity.

Combined Multistate and Kohn-Sham Density Functional Theory Studies of the Elusive Mechanism of N-Dealkylation of N,N-Dimethylanilines Mediated by the Biomimetic Nonheme Oxidant FeIV(O)(N4Py)(ClO4)2

The oxidative C-H bond activation mediated by heme and nonheme enzymes and related biomimetics is one of the most interesting processes in bioinorganic and oxidative chemistry. However, the mechanisms of these reactions are still elusive and controversy due to the involvement of highly reactive metal-oxo intermediates with multiple spin states, despite extensive experimental efforts, especially for the N-dealkylation of N,N-dialkyalinines. In this work, we employed multistate density functional theory (MSDFT) and the Kohn-Sham DFT to investigate the mechanism of N-demethylation of N,N-dimethyalinines oxidized by the reaction intermediate Fe^IV(O)(N4Py)(ClO₄)₂. The Kohn-Sham DFT study demonstrated that the reaction proceeds via a rate-limiting hydrogen atom transfer (HAT) step and a subsequent barrier-free oxygen rebound step to form the carbinol product. The MSDFT investigation on the first C-H activation further showed that this step is an initial hydrogen atom abstraction that is highly correlated between CEPT and HAT, i.e., both CEPT and HAT processes make significant contributions to the mechanism before reaching the diabatic crossing point, then the valence bond character of the adiabatic ground state is switched to the CEPT product configuration. The findings from this work may be applicable to other hydrogen abstraction process.