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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 bond energies (De). Changes in the equilibrium bond distance (Re) and vibrational frequency (ωe), on the other hand, are influenced by the 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(a4Σ−) state, these changes are much smaller than in the CH(X2Π) state, but in the CF(a4Σ−) state, they are larger, reflecting a significant difference in the shapes of EDEC(R) curves. At large R, the shape of EDEC(R) curves for covalent and recoupled pair bonds is 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. [ABSTRACT FROM AUTHOR]

Dynamical electron correlation has a major impact on the computed values of molecular properties and the energetics of molecular processes. This study focused on the effect of dynamical electron correlation on the spectroscopic constants (Re, ωe, De), and potential energy curves, ΔE(R), of the covalently bound AH and AF molecules, A = B–F. The changes in the spectroscopic constants (ΔRe, Δωe, ΔDe) caused by dynamical correlation are erratic and, at times, even surprising. These changes can 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., ΔEDEC(R). At large R, the magnitude of ΔEDEC(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 ΔEDEC(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 ΔEDEC(R) for the most polar molecules. The variations in ΔEDEC(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 spin-coupled generalized valence bond wave function. The results reported here indicate that we have much to learn about the nature of dynamical electron correlation and its effect on chemical bonds and molecular properties and processes. [ABSTRACT FROM AUTHOR]

In the full optimized reaction space and valence-complete active space self-consistent field (vCAS) methods, a set of active orbitals is defined as the union of the valence orbitals on the atoms, all possible configurations involving the active orbitals are generated, and the orbitals and configuration coefficients are self-consistently optimized. Such wave functions have tremendous flexibility, which makes these methods incredibly powerful but can also lead to inconsistencies in the description of the electronic structure of molecules. In this paper, the problems that can arise in vCAS calculations are illustrated by calculations on the BH and BF molecules. BH is well described by the full vCAS wave function, which accounts for molecular dissociation and 2s–2p near-degeneracy in the boron atom. The same is not true for the full vCAS wave function for BF. There is mixing of core and active orbitals at short internuclear distances and swapping of core and active orbitals at large internuclear distances. In addition, the virtual 2π orbitals, which were included in the active space to account for the 2s–2p near degeneracy effect, are used instead to describe radial correlation of the electrons in the F2pπ-like pairs. Although the above changes lead to lower vCAS energies, they lead to higher vCAS+1+2 energies as well as irregularities and/or discontinuities in the potential energy curves. All of the above problems can be addressed by using the spin-coupled generalized valence bond-inspired vCAS wave function for BF, which includes only a subset of the atomic valence orbitals in the active space. [ABSTRACT FROM AUTHOR]

In the spin-coupled generalized valence bond (SCGVB) description of Be2, there is a pair of electrons in highly overlapping "inner" orbitals corresponding to a traditional σ bond, but this bond is compromised by Pauli repulsion arising from its overlap with a second "outer" pair. The presence of this outer pair of electrons leads to a repulsive potential energy curve at long range and a bound, but metastable molecule at short range. To obtain further insights into the nature of the bond in Be2, we determined the non-dynamical and dynamical correlation contributions to the potential energy curve of Be2 using four different choices for the zero-order wave function: Restricted Hartree–Fock (RHF), SCGVB, valence-CASSCF(4,4), and valence-CASSCF(4,8). The SCGVB and valence-CASSCF(4,4) wave functions yield similar breakdowns of the total correlation energy, with non-dynamical correlation being the more important contribution. For the RHF and valence-CASSCF(4,8) wave functions, dynamical correlation is critical, without which the potential energy curve is purely repulsive. High accuracy calculations on the HBen−1Be–BeBen−1H molecule as a function of n (n = 1–6) suggest that the intrinsic strength of a Be–Be σ bond uncompromised by Pauli repulsion is on the order of 62–63 kcal/mol, and its length is 2.13–2.14 Å, ∼60 kcal/mol stronger and ∼0.35 Å shorter than in Be2. [ABSTRACT FROM AUTHOR]

The number of singly occupied orbitals in the ground-state atomic configuration of an element defines its nominal valence. For carbon and sulfur, with two singly occupied orbitals in their ³P ground states, the nominal valence is two. However, in both cases, it is possible to form more bonds than indicated by the nominal valenceâ€"up to four bonds for carbon and six bonds for sulfur. In carbon, the electrons in the 2s lone pair can participate in bonding, and in sulfur the electrons in both the 3p and 3s lone pairs can participate. Carbon 2s and sulfur 3p recoupled pair bonds are the basis for the tetravalence of carbon and sulfur, and 3s recoupled pair bonds enable sulfur to be hexavalent. In this paper, we report generalized valence bond as well as more accurate calculations on the a4Σ- states of CF and SF, which are archetypal examples of molecules that possess recoupled pair bonds. These calculations provide insights into the fundamental nature of recoupled pair bonds and illustrate the key differences between recoupled pair bonds formed with the 2s lone pair of carbon, as a representative of the early p-block elements, and recoupled pair bonds formed with the 3p lone pair of sulfur, as a representative of the late p-block elements. [ABSTRACT FROM AUTHOR]

Formation of a bond between a second ligand and a molecule with a recoupled pair bond results in a recoupled pair bond dyad. We examine the recoupled pair bond dyads in the a³B1 states of CF2 and SF2, which are formed by the addition of a fluorine atom to the a4Σ- states of CF and SF, both of which possess recoupled pair bonds. The two dyads are very different. In SF2, the second FS-F bond is very strong (De = 106.3 kcal/mol), the bond length is much shorter than that in the SF(a4Σ-) state (1.666 Å versus 1.882 Å), and the three atoms are nearly collinear (θe = 162.7°) with only a small barrier to linearity (0.4 kcal/mol). In CF2, the second FC-F bond is also very strong (De = 149.5 kcal/mol), but the bond is only slightly shorter than that in the CF(a4Σ-) state (1.314 Å versus 1.327 Å), and the molecule is strongly bent (θe = 119.0°) with an 80.5 kcal/mol barrier to linearity. The a³B1 states of CF2 and SF2 illustrate the fundamental differences between recoupled pair bond dyads formed from 2s and 3p lone pairs. [ABSTRACT FROM AUTHOR]

The inertness of molecular nitrogen and the reactivity of acetylene suggest there are significant variations in the nature of triple bonds. To understand these differences, we performed generalized valence bond as well as more accurate electronic structure calculations on three molecules with putative triple bonds: N2, HCN, and HC2H. The calculations predict that the triple bond in HC2H is quite different from the triple bond in N2, with HCN being an intermediate case but closer to N2 than HC2H. The triple bond in N2 is a traditional triple bond with the spins of the electrons in the bonding orbital pairs predominantly singlet coupled in the GVB wave function (92%). In HC2H, however, there is a substantial amount of residual CH(a4∑-) fragment coupling in the triple bond at its equilibrium geometry with the contribution of the perfect pairing spin function dropping to 82% (77% in a full valence GVB calculation). This difference in the nature of the triple bond in N2 and HC2H may well be responsible for the differences in the reactivities of N2 and HC2H. [ABSTRACT FROM AUTHOR]

The current study of the small lithium molecules Li 2 +,0,- and Li 3 +,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 Li 2,3 +,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 Li 3 + and Li 2 + ions being the most strongly bound, followed by Li 3 - , Li 2 , Li 2 - and Li 3 . The minimum energy structures of Li 3 +,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 Li 2 . The interstitial orbitals found in the Li 3 +,0 molecules likely give rise to the non-nuclear attractors/maxima observed in these molecules., (© 2023 Wiley Periodicals LLC.)

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 a 4 Σ - states of the CH and CF molecules. Dynamical correlation is energetically less important in the a 4 Σ - states than in the corresponding X 2 Π states for both molecules, which is reflected in smaller changes in bond energies (D e ). Changes in the equilibrium bond distance (R e ) and vibrational frequency (ω e ), on the other hand, are influenced by the changes in the slope and curvature of the dynamical electron correlation energy as a function of the internuclear distance R, E DEC (R). In the CH(a 4 Σ - ) state, these changes are much smaller than in the CH(X 2 Π) state, but in the CF(a 4 Σ - ) state, they are larger, reflecting a significant difference in the shapes of E DEC (R) curves. At large R, the shape of E DEC (R) curves for covalent and recoupled pair bonds is similar although different in magnitude. For the CH(a 4 Σ - ) state, E DEC (R) has a minimum at R = R e + 0.72 Å as the orbitals associated with the formation of the recoupled pair bond switch places. E DEC (R) for the CF(a 4 Σ - ) 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.

It has long been known that there is a fundamental difference in the electronic structures of CH 5 - and SiH 5 - , two isoelectronic molecules. The former is a saddle point for the S N 2 exchange reaction H - + CH 4 → [CH 5 - ] ‡ → CH 4 + H - , while the latter is a stable molecule that is bound relative to SiH 4 + 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 SiH 5 - , the axial pairs represent two stable bonds-a weak recoupled pair bond dyad. In CH 5 - , 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 CH 5 - are highly overlapping, giving rise to strong Pauli repulsion and a high barrier for the S N 2 exchange reaction.

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 C 2 , Be 2 and SF 4 /SF 6 . 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.

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 XH 4 indicates that they are closer to sp hybrids than sp 3 hybrids, which implies that the underlying cause of the tetrahedral structure of the XH 4 molecules is not a direct result of the hybridization of the X atom orbitals.

Diatomic carbon, C2, has been variously described as having a double, triple, or quadruple bond. In this article, we report full generalized valence bond (GVB) calculations on C2. The GVB wave function-more accurate than the Hartree-Fock wave function and easier to interpret than traditional multiconfiguration wave functions-is well-suited for characterizing the bonding in C2. The GVB calculations show that the electronic wave function of C2 is not well described by a product of singlet-coupled, shared electron pairs (perfect pairing), which is the theoretical basis for covalent chemical bonds. Rather, C2 is best described as having a traditional covalent σ bond with the electrons in the remaining orbitals of the two carbon atoms antiferromagnetically coupled. However, even this description is incomplete as the perfect pairing spin function also makes a significant contribution to the full GVB wave function. The complicated structure of the wave function of C2 is the source of the uncertainty about the nature of the bonding in this molecule.