Insights into the Electronic Structure of Molecules from Generalized Valence Bond Theory

Dynamical electron correlation and the chemical bond. III. Covalent bonds in the A2 molecules (A = C-F)

For most molecules the spin-coupled generalized valence bond (SCGVB) wavefunction accounts for the effects of non-dynamical electron correlation. The remaining errors in the prediction of molecular properties and the outcomes of molecular processes are then solely due to dynamical electron correlation. In this article we extend our previous studies of the effects of dynamical electron correlation on the potential energy curves and spectroscopic constants of the AH and AF (A = B-F) molecules to the homonuclear diatomic molecules, A2 (A = C-F). At large R the magnitude of ΔEDEC(R), the correlation energy of the molecule relative to that in the atoms, increases nearly exponentially with decreasing R, just as we found in the AH and AF molecules. But, as R continues to decrease the rate of increase in the magnitude of ΔEDEC(R) slows, eventually leading to a minimum for C2-O2. Examination of the SCGVB wavefunction for the N2 molecule around the minimum in ΔEDEC(R) did not reveal a clear cause for this puzzling behavior. As before, the changes in ΔEDEC(R) around Re were found to have an uneven effect on the spectroscopic constants of the A2 molecules.

Electronic structure of Li1,2,3 +,0,- and nature of the bonding in Li2,3 +,0,

The current study of the small lithium molecules Li2 +,0,- and Li3 +,0,- focuses on the nature of the bonding in these molecules as well as their structures and energetics (bond energies, ionization energies, and electron affinities). Valence CASSCF (2s,2p) calculations incorporate nondynamical electron correlation in the calculations, while the corresponding multireference configuration interaction and coupled cluster calculations incorporate dynamical electron correlation. Treatment of nondynamical correlation is critical for properly describing the Li2,3 +,0,- molecules as well as the Li- anion with dynamical correlation, in general, only fine-tuning the predictions. All lithium molecules and ions are bound, with the Li3 + and Li2 + ions being the most strongly bound, followed by Li3 - , Li2 , Li2 - and Li3 . The minimum energy structures of Li3 +,0,- are, respectively, an equilateral triangle, an isosceles triangle, and a linear structure. The results of SCGVB calculations are analyzed to obtain insights into the nature of the bonding in these molecules. An important finding of this work is that interstitial orbitals, a concept first put forward by McAdon and Goddard in 1985, play an essential role in the bonding of all lithium molecules considered here except for Li2 . The interstitial orbitals found in the Li3 +,0 molecules likely give rise to the non-nuclear attractors/maxima observed in these molecules.

Computational Studies of Rubber Ozonation Explain the Effectiveness of 6PPD as an Antidegradant and the Mechanism of Its Quinone Formation

The discovery that the commercial rubber antidegradant 6PPD reacts with ozone (O₃) to produce a highly toxic quinone (6PPDQ) spurred a significant research effort into nontoxic alternatives. This work has been hampered by lack of a detailed understanding of the mechanism of protection that 6PPD affords rubber compounds against ozone. Herein, we report high-level density functional theory studies into early steps of rubber and PPD (p-phenylenediamine) ozonation, identifying key steps that contribute to the antiozonant activity of PPDs. In this, we establish that our density functional theory approach can achieve chemical accuracy for many ozonation reactions, which are notoriously difficult to model. Using adiabatic energy decomposition analysis, we examine and dispel the notion that one-electron charge transfer initiates ozonation in these systems, as is sometimes argued. Instead, we find direct interaction between O₃ and the PPD aromatic ring is kinetically accessible and that this motif is more significant than interactions with PPD nitrogens. The former pathway results in a hydroxylated PPD intermediate, which reacts further with O₃ to afford 6PPD hydroquinone and, ultimately, 6PPDQ. This mechanism directly links the toxicity of 6PPDQ to the antiozonant function of 6PPD. These results have significant implications for development of alternative antiozonants, which are discussed.

Unusual In-plane Aromaticity Facilitates Intramolecular Hydrogen Transfer in Long-Bonded cis-Isonitrosyl Methoxide

The hydrogen-atom transfer from methoxy radical to nitric oxide, leading to the formation of formaldehyde and nitroxyl, represents a secondary reaction of photodissociation of methyl nitrite, which is used as rocket fuel. In this study, we explored the potential energy profile of the hydrogen-atom transfer using the electronic structure calculations at the DLPNO-CCSD(T)/aug-cc-pVTZ level of theory for two isomeric forms (cis and trans) of the pre-reaction complex. The cis-oriented pre-reaction complex has a weak elongated O─O bond, which gets further elongated in the hydrogen transfer transition state. This O─O bond stabilizes the pre-reaction complex by 32.9 kJ/mol. The O─O-induced stabilization is even greater for the transition state (48.2 kJ/mol), which was unexpected because of the larger O─O distance in the transition state structure. To address this paradox, we performed the electronic structure analysis of the reaction participants using the valence bond (VB) theory, natural resonance theory, topological analysis of the electron density and its derivatives, and analysis of the electron localization function distribution. This combined analysis led to the conclusion that the cis-transition state for hydrogen transfer, instead of being directly stabilized by the O─O interaction, gained substantial stabilization from the in-plane five-center six-electron aromaticity.

Dynamical electron correlation and the chemical bond. II. Recoupled pair bonds in the a4Σ- states of CH and CF

We extended our studies of the effect of dynamical electron correlation on the covalent bonds in the AH and AF series (A = B-F) to the recoupled pair bonds in the excited a4Σ- states of the CH and CF molecules. Dynamical correlation is energetically less important in the a4Σ- states than in the corresponding X2Π states for both molecules, which is reflected in smaller changes in the bond energies ( De). Changes in the equilibrium bond distance ( Re) and vibrational frequency (we), on the other hand, are influenced by changes in the slope and curvature of the dynamical electron correlation energy as a function of the internuclear distance R, EDEC( R). In the CH( a4-Σ) state these changes are much smaller than in the CH(X2Π) state, but in the CF( a4-Σ) state they are larger, reflecting a significant difference in shapes of the EDEC( R) curves. At large R the shape of the EDEC( R) curves for covalent and recoupled pair bonds are similar, although different in magnitude. For the CH( a4Σ-) state, EDEC( R) has a minimum at R = Re + 0.72 Å as the orbitals associated with the formation of the recoupled pair bond switch places. EDEC( R) for the CF( a4Σ-) state decreases continuously throughout the bound region of the potential energy curve because the dynamical correlation energy associated with the electrons in the lone pair orbitals is increasing. These results support our earlier conclusion that we still have much to learn about the nature of dynamical electron correlation in molecules

Dynamical electron correlation and the chemical bond. I. Covalent bonds in AH and AF (A = B-F)

Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. The present study focused on the effect of dynamical electron correlation on the spectroscopic constants, ( Re , ωe , De ) and potential energy curves, Δ E( R), of the covalently-bound AH and AF molecules, A = B-F. The changes in the spectroscopic constants, (Δ Re , Δωe , Δ De ) caused by dynamical correlation are erratic and, at times, even surprising. These changes could be understood based on the dependence of the dynamical electron correlation energies of the AH and AF molecules as a function of the bond distance, i.e., Δ EDEC( R). At large R, the magnitude of Δ EDEC( R) increases nearly exponentially with decreasing R, but this increase slows as R continues to decrease and, in many cases, even reverses at very short R. The changes in Δ EDEC( R) in the region around Re were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of Δ EDEC( R) for the most polar molecules. The variations in Δ EDEC( R) for R ≲ Re are directly correlated with major changes in the electronic structure of the molecules as revealed by a detailed analysis of the SCGVB wave function. The results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on the chemical bond and molecular properties and processes.

CH4, an ab initio story of an archetypal species

The methane molecule is an archetypal species in the whole of chemistry for its ability to form four bonds that result in a myriad of compounds of chemical and biological importance. The hybrid orbitals involved in the bonding have been scrutinized for too many decades but only lately under the ab initio microscope. In this study, we detail the formation routes CH n + (4 − n) H → CH4 ( n = 0, 1, and 2) both diabatically and adiabatically with the help of established computational techniques. The evolution of the Mulliken populations, of the non-adiabatic matrix coupling elements, and of the Kotani spin functions along the dissociation paths and finally the shape of the diabatic curves unambiguously point to a parental C atom of an excited 2 s12 p3 electronic configuration.

Dipolar 1,3-cycloaddition of thioformaldehyde S-methylide (CH2 SCH2 ) to ethylene and acetylene. A comparison with (valence) isoelectronic O3 , SO2 , CH2 OO and CH2 SO

Methods rooted in the density functional theory and in the coupled cluster ansatz were employed to investigate the cycloaddition reactions to ethylene and acetylene of 1,3-dipolar species including ozone and the derivatives issued from replacement of the central oxygen atom by the valence-isoelectronic sulfur atom, and/or of one or both terminal oxygen atoms by the isoelectronic CH₂ group. This gives rise to five different 1,3-dipolar compounds, namely ozone itself (O₃ ), sulfur dioxide (SO₂ ), the simplest Criegee intermediate (CH₂ OO), sulfine (CH₂ SO), and thioformaldehyde S-methylide (CH₂ SCH₂ , TSM). The experimental and accurate theoretical data available for some of those molecules were employed to assess the accuracy of two last-generation composite methods employing conventional or explicitly correlated post-Hartree-Fock contributions (jun-Cheap and SVECV-f12, respectively), which were then applied to investigate the reactivity of TSM. The energy barriers provided by both composite methods are very close (the average values for the two composite methods are 7.1 and 8.3 kcal mol^-1 for the addition to ethylene and acetylene, respectively) and comparable to those ruling the corresponding additions of ozone (4.0 and 7.7 kcal mol^-1 , respectively). These and other evidences strongly suggest that, at least in the case of cycloadditions, the reactivity of TSM is similar to that of O₃ and very different from that of SO₂ .

New Insights into the Remarkable Difference between CH5- and SiH5. J Phys Chem A 2021;125:7414-7424. [PMID: 34424705 DOI: 10.1021/acs.jpca.1c05357]

It has long been known that there is a fundamental difference in the electronic structures of CH₅^- and SiH₅^-, two isoelectronic molecules. The former is a saddle point for the S_N2 exchange reaction H^- + CH₄ → [CH₅^-]^‡ → CH₄ + H^-, while the latter is a stable molecule that is bound relative to SiH₄ + H^-. SCGVB calculations indicate that this difference is the result of a dramatic difference in the nature of the axial electron pairs in these anions. In SiH₅^-, the axial pairs represent two stable bonds-a weak recoupled pair bond dyad. In CH₅^-, the axial electron pairs represent an intermediate transition between the electron pairs in the reactants and those in the products. Furthermore, the axial orbitals at the saddle point in CH₅^- are highly overlapping, giving rise to strong Pauli repulsion and a high barrier for the S_N2 exchange reaction.

Spin-Coupled Generalized Valence Bond Theory: New Perspectves on the Electronic Structure of Molecules and Chemical Bonds

Spin-Coupled Generalized Valence Bond (SCGVB) theory provides the foundation for a comprehensive theory of the electronic structure of molecules. SCGVB theory offers a compelling orbital description of the electronic structure of molecules as well as an efficient and effective zero-order wave function for calculations striving for quantitative predictions of molecular structures, energetics, and other properties. The orbitals in the SCGVB wave function are usually semilocalized, and for most molecules, they can be interpreted using concepts familiar to all chemists (hybrid orbitals, localized bond pairs, lone pairs, etc.). SCGVB theory also provides new perspectives on the nature of the bonds in molecules such as C₂, Be₂ and SF₄/SF₆. SCGVB theory contributes unparalleled insights into the underlying cause of the first-row anomaly in inorganic chemistry as well as the electronic structure of organic molecules and the electronic mechanisms of organic reactions. The SCGVB wave function accounts for nondynamical correlation effects and, thus, corrects the most serious deficiency in molecular orbital (RHF) wave functions. Dynamical correlation effects, which are critical for quantitative predictions, can be taken into account using the SCGVB wave function as the zero-order wave function for multireference configuration interaction or coupled cluster calculations.

Superposition of waves or densities: Which is the nature of chemical resonance?

Resonance is a fundamental and widely used concept in chemistry, but there exist two distinct theories of chemical resonance, based on quite different and incompatible premises: the wave-function-based resonance theory (WFRT), assuming the superposition of wave functions, versus the density-matrix-based resonance theory (DMRT), which interprets the resonance phenomenon as the superposition of density matrices. The latter theory, best known to the chemistry community as the natural resonance theory (NRT), has received much more popularity than the WFRT. In this contribution, the DMRT is shown to be inherently inadequate: (i) the exact density matrix expansion is mathematically impossible unless unphysical negative weights are introduced; (ii) any approximate density matrix representing the resonance hybrid lacks the idempotent property. Therefore, the validity of the NRT ansatz should be seriously questioned. The WFRT seems the only reasonable explanation of resonance so far, and has been shown to provide valuable insights into diverse chemical problems.

Automatic Selection of Active Orbitals from Generalized Valence Bond Orbitals

The accurate multireference (MR) calculation of a strongly correlated chemical system usually relies on a correct preselection of a small number of active orbitals from numerous molecular orbitals. Currently, the active orbitals are generally determined by using a trial-and-error method. Such a preselection by chemical intuition and personal experience may be tedious or unreliable, especially for large complicated systems, and accordingly, the construction of active space becomes a bottleneck for large-scale MR calculations. In this work, we propose to automatically select the active orbitals according to the natural orbital occupation numbers by performing black box generalized valence bond calculations. We demonstrate the accuracy of this method through testing calculations of the ground states in various systems, ranging from bond dissociation of diatomic molecules (N₂, C₂, Cr₂) to conjugated molecules (pentacene, hexacene, and heptacene) as well as a binuclear transition-metal complex [Mn₂O₂(H₂O)₂(terpy)₂]³⁺ (terpy = 2,2':6,2″-terpyridine) with active spaces up to (30e, 30o) and comparing with the complete active space self-consistent field (CASSCF), density matrix renormalization group (DMRG)-CASSCF references, and other recently proposed inexpensive strategies for constructing active spaces. The results indicate that our method is among the most successful ones within our comparison, providing high-quality initial active orbitals very close to the finally optimized (DMRG-)CASSCF orbitals. The method proposed here is expected to greatly benefit the practical implementation of large active space ground-state MR calculations, for example, large-scale DMRG calculations.

The Basics of Covalent Bonding in Terms of Energy and Dynamics

We address the paradoxical fact that the concept of a covalent bond, a cornerstone of chemistry which is well resolved computationally by the methods of quantum chemistry, is still the subject of debate, disagreement, and ignorance with respect to its physical origin. Our aim here is to unify two seemingly different explanations: one in terms of energy, the other dynamics. We summarize the mechanistic bonding models and the debate over the last 100 years, with specific applications to the simplest molecules: H2+ and H2. In particular, we focus on the bonding analysis of Hellmann (1933) that was brought into modern form by Ruedenberg (from 1962 on). We and many others have helped verify the validity of the Hellmann-Ruedenberg proposal that a decrease in kinetic energy associated with interatomic delocalization of electron motion is the key to covalent bonding but contrary views, confusion or lack of understanding still abound. In order to resolve this impasse we show that quantum mechanics affords us a complementary dynamical perspective on the bonding mechanism, which agrees with that of Hellmann and Ruedenberg, while providing a direct and unifying view of atomic reactivity, molecule formation and the basic role of the kinetic energy, as well as the important but secondary role of electrostatics, in covalent bonding.

Orbital Hybridization in Modern Valence Bond Wave Functions: Methane, Ethylene, and Acetylene

The concept of hybrid orbitals is one of the key theoretical concepts used by chemists to explain the structures and other properties of molecules. Recent work found that the hybrid orbitals from modern ab initio valence bond wave functions differ significantly from traditional hybrid orbitals. We report a detailed analysis of the orbitals of methane, ethylene, and acetylene from spin-coupled generalized valence bond (SCGVB) wave functions, a variationally optimized valence bond wave function that places no constraints on the orbitals and spin function. The carbon-centered orbitals in the SCGVB wave functions are found to be 2s-2p hybrid orbitals largely localized on the carbon atom and pointed directly at the hydrogen atoms to which they are bonded. However, the SCGVB orbitals for methane, ethylene, and acetylene differ markedly from the sp³, sp², and sp hybrid orbitals traditionally associated with these molecules. It is now clear that the orbitals in modern valence bond wave functions do not follow the hybridization rules of traditional valence bond theory. These findings imply that, in modern valence bond theories, other factors are responsible for the structures and properties of molecules that are traditionally attributed to orbital hybridization.

Insight into spin-orbital interaction using MCSCF method: A special analysis of the 1 Σg + electronic state in C2 and the linear polyacetylenic C4 and C6

The symmetry-broken wave function can transform the ¹ Σ_g ⁺ state of C₂ from the classic double bonding to the quadruple bonding, where the transformed wave functions of ϕ _L and ϕ _R are singly occupied by two opposite-spinning electrons. In this article, the effective bond order (EBO) contribution of the fourth bond in C₂ is assessed through the overlap integral between ϕ _L and ϕ _R , namely the value (0.60) is the EBO contribution of the fourth bond in the transformed scheme. Hence, the new EBO is 3.36, which is more equitable than the original EBO (2.15) in the traditional scheme. In addition, the singlet diradical character of the linear polyacetylenic C₄ and C₆ in the ¹ Σ_g ⁺ state is addressed for the first time. No spin-polarized bonding exists in other linear C_2n clusters, because the ionic interaction in the polyacetylenic ¹ Σ_g ⁺ state of C₄ is negligible. Moreover, the coupling energy between α and β single electrons in C₄ is only 4.0 kcal mol^-1 based on the electron spin-flip energy. © 2019 Wiley Periodicals, Inc.

Spin-Coupled Generalized Valence Bond Description of Group 14 Species: The Carbon, Silicon and Germanium Hydrides, XH n ( n = 1-4)

Although elements in the same group in the Periodic Table tend to behave similarly, the differences in the simplest Group 14 hydrides-XH _n (X = C, Si, Ge; n = 1-4)-are as pronounced as their similarities. Spin-coupled generalized valence bond (SCGVB) as well as coupled cluster [CCSD(T)] calculations are reported for all of the molecules in the CH _n/SiH _n/GeH _n series to gain insights into the factors underlying these differences. It is found that the relative weakness of the recoupled pair bonds of SiH and GeH gives rise to the observed differences in the ground state multiplicities, molecular structures, and bond energies of SiH _n and GeH _n. A number of factors that influence the strength of the recoupled pair bonds in CH, SiH, and GeH were examined. Two factors were identified as potential contributors to the decrease in the strengths of these bonds from CH to SiH and GeH: (i) a decrease in the overlap between the orbitals involved in the bond and (ii) an increase in Pauli repulsion between the electrons in the two lobe orbitals centered on the X atoms. Finally, an analysis of the hybridization of the SCGVB orbitals in XH₄ indicates that they are closer to sp hybrids than sp³ hybrids, which implies that the underlying cause of the tetrahedral structure of the XH₄ molecules is not a direct result of the hybridization of the X atom orbitals.

Electron Correlation from the Adiabatic Connection for Multireference Wave Functions

An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M^{5} scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.

Multiconfiguration Pair-Density Functional Theory and Complete Active Space Second Order Perturbation Theory. Bond Dissociation Energies of FeC, NiC, FeS, NiS, FeSe, and NiSe

We investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) and complete active space second-order perturbation theory for computing the bond dissociation energies of the diatomic molecules FeC, NiC, FeS, NiS, FeSe, and NiSe, for which accurate experimental data have become recently available [Matthew, D. J.; Tieu, E.; Morse, M. D. J. Chem. Phys. 2017, 146, 144310-144320]. We use three correlated participating orbital (CPO) schemes (nominal, moderate, and extended) to define the active spaces, and we consider both the complete active space (CAS) and the separated-pair (SP) schemes to specify the configurations included for a given active space. We found that the moderate SP-PDFT scheme with the tPBE on-top density functional has the smallest mean unsigned error (MUE) of the methods considered. This level of theory provides a balanced treatment of the static and dynamic correlation energies for the studied systems. This is encouraging because the method is low in cost even for much more complicated systems.

Predicting Bond Dissociation Energies of Transition-Metal Compounds by Multiconfiguration Pair-Density Functional Theory and Second-Order Perturbation Theory Based on Correlated Participating Orbitals and Separated Pairs

We study the performance of multiconfiguration pair-density functional theory (MC-PDFT) and multireference perturbation theory for the computation of the bond dissociation energies in 12 transition-metal-containing diatomic molecules and three small transition-metal-containing polyatomic molecules and in two transition-metal dimers. The first step is a multiconfiguration self-consistent-field calculation, for which two choices must be made: (i) the active space and (ii) its partition into subspaces, if the generalized active space formulation is used. In the present work, the active space is chosen systematically by using three correlated-participating-orbitals (CPO) schemes, and the partition is chosen by using the separated-pair (SP) approximation. Our calculations show that MC-PDFT generally has similar accuracy to CASPT2, and the active-space dependence of MC-PDFT is not very great for transition-metal-ligand bond dissociation energies. We also find that the SP approximation works very well, and in particular SP with the fully translated BLYP functional SP-ftBLYP is more accurate than CASPT2. SP greatly reduces the number of configuration state functions relative to CASSCF. For the cases of FeO and NiO with extended-CPO active space, for which complete active space calculations are unaffordable, SP calculations are not only affordable but also of satisfactory accuracy. All of the MC-PDFT results are significantly better than the corresponding results with broken-symmetry spin-unrestricted Kohn-Sham density functional theory. Finally we test a perturbation theory method based on the SP reference and find that it performs slightly worse than CASPT2 calculations, and for most cases of the nominal-CPO active space, the approximate SP perturbation theory calculations are less accurate than the much less expensive SP-PDFT calculations.

Negative hyperconjugation effect on the reactivity of phosphoramide mustard derivatives as a DNA alkylating agent: theoretical and experimental insights

In this work we suggest new factors affecting the reactivity of compounds similar to cyclophosphamide; as their reactivity mainly relies on the frontier molecular orbitals, the factors causing changes in the frontier molecular orbitals, alter the reactivity of these compounds too.

A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction

A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.