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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, A 2 (A = C-F). At large R the magnitude of Δ E DEC ( 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 Δ E DEC ( R ) slows, eventually leading to a minimum for C 2 -O 2 . Examination of the SCGVB wavefunction for the N 2 molecule around the minimum in Δ E DEC ( R ) did not reveal a clear cause for this puzzling behavior. As before, the changes in Δ E DEC ( R ) around R e were found to have an uneven effect on the spectroscopic constants of the A 2 molecules.

In a series of recent papers, we investigated the effect of dynamical electron correlation on the potential energy curves and spectroscopic constants of several diatomic molecules, including the simple diatomic hydrides (AH) and the more complex diatomic fluorides (AF) and homonuclear diatomic molecules (A 2 ) with A = B-F (AF) or A = C-F (A 2 ), respectively. Our goal was to understand the dependence of the dynamical electron correlation energy, E DEC , on the internuclear distance, R , and quantify how dynamical electron correlation influences the spectroscopic constants ( D e , R e , and ω e ) of these molecules. At large R , we found that the magnitude of E DEC ( R ) had a simple dependence on R, with E DEC ( R ) increasing nearly exponentially with decreasing R . However, as R continued to decrease, there were significant variations in E DEC ( R ). These variations led to differing changes in the predicted spectroscopic constants of the molecules. In many molecules, the changes in E DEC ( R ) could be correlated with changes in the underlying spin-coupled generalized valence bond wave function, either in the orbitals or the spin-coupling coefficients. In the current paper, we extend these studies to higher main group elements, comparing the effects of E DEC ( R ) on P 2 and As 2 versus N 2 , and on Cl 2 and Br 2 versus F 2 . We find that there are significant differences between the effects of dynamical electron correlation on the molecules in the first and subsequent rows of the periodic table.

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.

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 (R e , ω e , D e ), and potential energy curves, ΔE(R), of the covalently bound AH and AF molecules, A = B-F. The changes in the spectroscopic constants (ΔR e , Δω e , ΔD e ) 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., ΔE DEC (R). At large R, the magnitude of ΔE DEC (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 ΔE DEC (R) in the region around R e were as unexpected as they were surprising, e.g., distinct minima and maxima were found in the curves of ΔE DEC (R) for the most polar molecules. The variations in ΔE DEC (R) for R ≲ R e 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.

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.

The nature of the bonding in the bifluoride anion, FHF - , has long been a topic of discussion with little resolution. A recent (2021) spectroscopic-theoretical study concluded that the bonds in this molecule represent a "crossover from hydrogen to chemical bonding." Spin-coupled generalized valence bond (SCGVB) theory is an advanced orbital theory that describes a broad range of molecules and molecular processes, and its application has provided valuable insights in the electronic structure of many molecules with "unusual" bonding motifs. SCGVB calculations on the FHF - anion indicate that the bonding in this molecule cannot be attributed to a traditional hydrogen bond or a traditional covalent bond. Instead, the bonds in FHF - represent a new bonding motif-two polarized, delocalized F - anions held together by a positively charged hydrogen atom, i.e., the bonding resembles that for a proton-bound anion pair.

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.

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.

In the spin-coupled generalized valence bond (SCGVB) description of Be 2 , 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 Be 2 , we determined the non-dynamical and dynamical correlation contributions to the potential energy curve of Be 2 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 HBe n-1 Be-BeBe n-1 H 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 Be 2 .

In an earlier study of benzene, Small and Head-Gordon found that the spin-coupled generalized valence bond (SCGVB) wave function for the π system predicted a distorted (non-D 6h ) geometry, one with alternating CC bond lengths. However, the variations in the energy were very small and the predictions were made using a very small basis set (STO-3G). We re-examined this prediction using a much larger basis set (aug-cc-pVTZ) to determine the dependence of the energy of benzene on the distortion angle, Δθ CXC (Δθ CXC = 0° corresponds to the D 6h structure). We also found a distorted geometry with the optimum Δθ CXC being 0.31° with an energy 0.040 kcal mol -1 lower than that for the D 6h structure. In the optimum geometry, adjacent CC bond lengths are 1.3861 Å and 1.4004 Å. Analysis of the SCGVB wave function led us to conclude that the cause of the unusual non-D 6h geometry predicted by the SCGVB calculations seems to be a result of the interaction between the Kekulé and Dewar components of the full SCGVB wave function. The addition of doubly ionic configurations to the SCGVB wave function leads to the prediction of a D 6h geometry for benzene and a dependence on Δθ CXC essentially the same as that predicted by the complete active space self-consistent field wave function., (© 2020 Wiley Periodicals, Inc.)

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

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 sp 3 , sp 2 , 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.

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.

In a previous paper in this series, we discussed the formation of recoupled pair bonds in the a 4 Σ - states of CF and SF in which the recoupling process was essentially complete at the equilibrium geometry of the molecule. In this paper, we examine the a 4 Σ - state of oxygen monofluoride (OF), which could also have a recoupled pair bond. Unlike the other two molecules, generalized valence bond calculations predict that the recoupling in OF is woefully incomplete at R e and the resulting potential energy curve for the OF(a 4 Σ - ) state is purely repulsive; the binding energy, ≈11 kcal/mol, is entirely due to dynamical correlation. A number of factors account for these differences, but the nature of the dominant correlation effect in the oxygen 2p lone pair as well as the spatial extent of the 2p orbital are paramount.

Crabtree et al. recently reported the microwave spectrum of nitrosyl-O-hydroxide (trans-NOOH), an isomer of nitrous acid, and found that this molecule has the longest O-O bond ever observed: 1.9149 Å ± 0.0005 Å. This is in marked contrast to the structure of the valence isoelectronic trans-NSOH molecule, which has a normal NS-OH bond length and strength. Generalized valence bond calculations show that the long bond in trans-NOOH is the result of a weak through-pair interaction that singlet couples the spins of the electrons in singly occupied orbitals on the hydroxyl radical and nitrogen atom, an interaction that is enhanced by the intervening lone pair of the oxygen atom in NO. The NS-OH bond is the result of the formation of a stable recoupled pair bond dyad, which accounts for both its length and strength.

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(a(4)Σ(-)) 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.

Ozone (O3) and sulfur dioxide (SO2) are valence isoelectronic species, yet their properties and reactivities differ dramatically. In particular, O3 is highly reactive, whereas SO2 is chemically relatively stable. In this paper, we investigate serial addition of hydrogen atoms to both the terminal atoms of O3 and SO2 and to the central atom of these species. It is well-known that the terminal atoms of O3 are much more amenable to bond formation than those of SO2. We show that the differences in the electronic structure of the π systems in the parent triatomic species account for the differences in the addition of hydrogen atoms to the terminal atoms of O3 and SO2. Further, we find that the π system in SO2, which is a recoupled pair bond dyad, facilitates the addition of hydrogen atoms to the sulfur atom, resulting in stable HSO2 and H2SO2 species.

In this article we describe the unique insights into the electronic structure of molecules provided by generalized valence bond (GVB) theory. We consider selected prototypical hydrocarbons as well as a number of hypervalent molecules and a set of first- and second-row valence isoelectronic species. The GVB wave function is obtained by variationally optimizing the orbitals and spin coupling in the valence bond wave function. The GVB wave function is a generalization of the Hartree-Fock (HF) wave function, lifting the double occupancy restriction on a subset of the HF orbitals as well as the associated orthogonality and spin coupling constraints. The GVB wave function includes a major fraction (if not all) of the nondynamical correlation energy of a molecule. Because of this, GVB theory properly describes bond formation and can answer one of the most compelling questions in chemistry: How are atoms changed by molecular formation? We show that GVB theory provides a unified description of the nature of the bonding in all of the above molecular species as well as contributing new insights into the well-known, but poorly understood, first-row anomaly.

There are many well-known differences in the physical and chemical properties of ozone (O3) and sulfur dioxide (SO2). O3 has longer and weaker bonds than O2, whereas SO2 has shorter and stronger bonds than SO. The O-O2 bond is dramatically weaker than the O-SO bond, and the singlet-triplet gap in SO2 is more than double that in O3. In addition, O3 is a very reactive species, while SO2 is far less so. These disparities have been attributed to variations in the amount of diradical character in the two molecules. In this work, we use generalized valence bond (GVB) theory to characterize the electronic structure of ozone and sulfur dioxide, showing O3 does indeed possess significant diradical character, whereas SO2 is effectively a closed shell molecule. The GVB results provide critical insights into the genesis of the observed difference in these two isoelectronic species. SO2 possesses a recoupled pair bond dyad in the a"(π) system, resulting in SO double bonds. The π system of O3, on the other hand, has a lone pair on the central oxygen atom plus a pair of electrons in orbitals on the terminal oxygen atoms that give rise to a relatively weak π interaction.

The ground state, X1Σg+, of N2 is a textbook example of a molecule with a triple bond consisting of one σ and two π bonds. This assignment, which is usually rationalized using molecular orbital (MO) theory, implicitly assumes that the spins of the three pairs of electrons involved in the bonds are singlet-coupled (perfect pairing). However, for a six-electron singlet state, there are five distinct ways to couple the electron spins. The generalized valence bond (GVB) wave function lifts this restriction, including all of the five spin functions for the six electrons involved in the bond. For N2, we find that the perfect pairing spin function is indeed dominant at Re but that it becomes progressively less so from N2 to P2 and As2. Although the perfect pairing spin function is still the most important spin function in P2, the importance of a quasi-atomic spin function, which singlet couples the spins of the electrons in the σ orbitals while high spin coupling those of the electrons in the π orbitals on each center, has significantly increased relative to N2 and, in As2, the perfect pairing and quasi-atomic spin couplings are on essentially the same footing. This change in the spin coupling of the electrons in the bonding orbitals down the periodic table may contribute to the rather dramatic decrease in the strengths of the Pn2 bonds from N2 to As2 as well as in the increase in their chemical reactivity and should be taken into account in more detailed analyses of the bond energies in these species. We also compare the spin coupling in N2 with that in C2, where the quasi-atomic spin coupling dominants around Re.

The electronic structure of the ground state of NO and those of F(NO) and H(NO), that is, the XNO and NOX isomers with X = F, H, were analyzed within the framework of generalized valence bond theory. In distinct contrast to the ground state of NS, it was found that the two-center, three-electron π interaction in NO(X(2)Π) is composed of a lone pair on O and a singly occupied orbital on N. Thus, F and H addition to NO preferentially leads to FNO and HNO. Somewhat surprisingly, the NOF and NOH isomers were found to be weakly bound, although for different reasons. The NOF state has a very unusual through-pair interaction with a NO-F bond length 0.444 Å longer than its covalent counterpart in OF(X(2)Π), while NOH arises from the N((2)D) + OH(X(2)Π) separated atom limit, similar to what we found for NSH.

The electronic structures of the ground states (X(2)Π) of NS and those (X(1)A') of F(NS) and H(NS), where X(NS) collectively refers to the XNS and NSX isomers, were analyzed within the framework of generalized valence bond theory. The ground state of NS has a recoupled pair π bond, which has a profound effect on its reactivity. For example, the lowest-energy isomer of F(NS) is NSF, which has a recoupled pair bond dyad with N-SF and NS-F bonds lengths and strengths similar to their covalent counterparts in NS and SF. The ground state of NSH, on the other hand, is only weakly bound with a NS-H bond energy 40.20 kcal/mol smaller than that in SH and a N-SH bond energy 40.20 kcal/mol less than that in NS. At its equilibrium geometry, the NSH molecule is best viewed as derived from the N((2)D) + SH(X(2)Π) separated fragments, with the weak NS-H bond resulting from unfavorable interactions between the SH bond pair and the nitrogen lone pair. Addition of F/H atoms to the nitrogen atom in NS disrupts the NS recoupled pair bond, which weakens both the FN-S/HN-S and F-NS/H-NS bonds. In contrast to the formation of recoupled pair σ bonds, formation of the recoupled pair π bond in NS is expressed as a change in the spin-coupling coefficients, rather than an interchange of the orbitals.

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 a(3)B1 states of CF2 and SF2, which are formed by the addition of a fluorine atom to the a(4)Σ(-) 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(a(4)Σ(-)) 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(a(4)Σ(-)) 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 a(3)B1 states of CF2 and SF2 illustrate the fundamental differences between recoupled pair bond dyads formed from 2s and 3p lone pairs.

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 (3)P ground states, the nominal valence is two. However, in both cases, it is possible to form more bonds than indicated by the nominal valence--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 a(4)Σ(-) 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.

Sulfur and fluorine can participate in a variety of bonding motifs, lending significant diversity to their chemistry. Prior work has identified three distinct minima for disulfur tetrafluoride (S2F4) compounds: two FSSF3 isomers and one SSF4 species. We used a combination of sophisticated explicitly correlated coupled cluster calculations and generalized valence bond (GVB) theory to characterize the electronic structure of these species as well as additional stationary points on the potential energy surface with F2SSF2 connectivity. On the singlet surface, the two stationary points considered in this work with an F2SSF2 structure are first- or second-order saddle points and not minima. However, on the triplet surface, we discovered a novel C2 symmetric F2SSF2 minimum that was anticipated from the structure of an excited state ((3)B1) of SF2. Analysis using the GVB wave function in conjunction with the recoupled pair bonding model developed by our group provides a straightforward explanation of the bonding in all of the S2F4 structures considered here. In addition, the model predicted the existence of the F2SSF2((3)B) minimum.

Recoupled pair bonds (RPBs) are conditional bonds-they only form for selected central atoms and ligands. A complete theoretical description of RPBs requires an understanding of the properties of the central atom and ligands that enable such bonds to be formed. In this work, we show that ligand electronegativity is positively correlated with recoupled pair bond strength for a variety of ligands interacting with the 3p(2) pair of sulfur. We also describe substituent (X) effects on the SF(a(4)Σ(-)) state by investigating X2SF species. These effects generally mirror those observed for covalently bound analogues, but we found that recoupled pair bonding can lead to breakdowns in the expected relationships among bond length, strength, and force constant for some of these species. Finally, we compare the properties of two molecules of practical interest that are bound by recoupled pair bonds: the dimethyl sulfur fluoride and hydroxide radicals (DMS-F and DMS-OH).

It is well known that hypervalent molecules are more stable with very electronegative ligands such as fluorine. For example, while SF6 is uniquely stable and experimentally well characterized and many of the features of SF4 have been characterized, neither H4S nor H6S has been observed. Furthermore, no hypervalent sulfur species with mixed hydrogen and fluorine ligands have been experimentally characterized to date. In this work, we present detailed calculations of the electronic structure of H2S, SF2, and HSF. While all three compounds have similar bent singlet ground states, the potential energy surfaces of various low lying electronic states as a function of bond angle reveal very different behaviors, in particular for linear geometries. We use the disparate bonding motifs of the low-lying triplet states to rationalize the differences between SF4 and the hypothetical H4S molecule. We also make predictions about the effects of hydrogen substitution on the energetics and geometries of hypervalent sulfur fluoride compounds.

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.

The ground states (X(2)A″) of HSO and SOH are extremely close in energy, yet their molecular structures differ dramatically, e.g., re(SO) is 1.485 Å in HSO and 1.632 Å in SOH. The SO bond is also much stronger in HSO than in SOH: 100.3 kcal/mol versus 78.8 kcal/mol [RCCSD(T)-F12/AVTZ]. Similar differences are found in the SO2 isomers, SOO and OSO, depending on whether the second oxygen atom binds to oxygen or sulfur. We report generalized valence bond and RCCSD(T)-F12 calculations on HSO/SOH and OSO/SOO and analyze the bonding in all four species. We find that HSO has a shorter and stronger SO bond than SOH due to the presence of a recoupled pair bond in the π(a″) system of HSO. Similarly, the bonding in SOO and OSO differs greatly. SOO is like ozone and has substantial diradical character, while OSO has two recoupled pair π bonds and negligible diradical character. The ability of the sulfur atom to form recoupled pair bonds provides a natural explanation for the dramatic variation in the bonding in these and many other sulfur-oxygen compounds.

Based on detailed, high level ab initio calculations on a number of halogenated compounds of second row, late p-block elements, the SF(n), ClF(n), PFn, SCl(n), and SF(n)Cl families, we found that a new type of bond--the recoupled pair bond--accounts for the ability of these elements to form hypervalent, or hypercoordinated, compounds. Hypervalent molecules are formed when it is energetically favorable for the electrons in a lone pair orbital to be recoupled, allowing each of the electrons to form chemical bonds with ligands. In this paper, we characterize the structures and energies of the ground and low-lying excited states of the ClF(n)(+) (n = 1-6) ions, using high level ab initio methods [MRCI, CCSD(T)/RCCSD(T)] with large correlation consistent basis sets. We computed a number of quantities, including ClF(n)(+) structures, bond dissociation energies, and ClF(n) ionization energies and compared our results with the available experimental data. Both the bond dissociation energies and the ionization energies oscillate, variations that are readily explained using the recoupled pair bonding model. Comparisons are drawn between the ClF(n)(+) cations and their counterparts in the isoelectronic SF(n) series, which possess many similarities. We found two significant differences between the ClF(n)(+) and the SF(n) series: (i) the bond dissociation energies of ClF(n)(+) are much weaker than those of the corresponding SF(n) species, and (ii) there is no stable (3)A2 state in ClF2(+) corresponding to the stable state found in SF2. An examination of the Mulliken populations at the HF/AVTZ level for ClF(n)(+) and SF(n) species predicts that the F atom in the axial (recoupled pair bonding) position is more highly charged than the F atom in the equatorial (covalent bonding) position; there is also less charge transfer to the F atoms in ClF(n)(+) than in SF(n). The positive charge on Cl(+) makes it more difficult for an F atom to attract electrons from Cl(+) than from S and correspondingly less favorable to recouple the electrons in the lone pair orbitals in the ClF(n)(+) species.

The dramatic differences between the properties of molecules formed from the late p-block elements of the first row of the periodic table (N-F) and those of the corresponding elements in subsequent rows is well recognized as the first row anomaly. Certain properties of the atoms, such as the relative energies and spatial extents of the ns and np orbitals, can explain some of these differences, but not others. In this Account, we summarize the results of our recent computational studies of the halides of the late p-block elements. Our studies point to a single underlying cause for many of these differences: the ability of the late p-block elements in the second and subsequent rows of the periodic table to form recoupled pair bonds and recoupled pair bond dyads with very electronegative ligands. Recoupled pair bonds form when an electron in a singly occupied ligand orbital recouples the pair of electrons in a doubly occupied lone pair orbital on the central atom, leading to a central atom-ligand bond. Recoupled pair bond dyads occur when a second ligand forms a bond with the orbital left over from the initial recoupled pair bond. Recoupled pair bonds and recoupled pair bond dyads enable the late p-block elements to form remarkably stable hypervalent compounds such as PF(5) and SF(6) and lead to unexpected excited states in smaller halides of the late p-block elements such as SF and SF(2). Recoupled pair bonding also causes the F(n-1)X-F bond energies to oscillate dramatically once the normal valences of the central atoms have been satisfied. In addition, recoupled pair bonding provides a lower-energy pathway for inversion in heavily fluorinated compounds (PF(3) and PF(2)H, but not PH(2)F and PH(3)) and leads to unusual intermediates and products in reactions involving halogens and late p-block element compounds, such as (CH(3))(2)S + F(2). Although this Account focuses on the halides of the second row, late p-block elements, recoupled pair bonds and recoupled pair bond dyads are important in the chemistry of p-block elements beyond the second row (As, Se, and Br) and for compounds of these elements with other very electronegative ligands, such as OH and O. Knowledge of recoupled pair bonding is thus critical to understanding the properties and reactivity of molecules containing the late p-block elements beyond the first row.

Early flowtube studies showed that (CH(3))(2)S (DMS) reacted very rapidly with F(2); hydrogen sulfide (H(2)S), however, did not. Recent crossed molecular beam studies found no barrier to the reaction between DMS and F(2) to form CH(2)S(F)CH(3) + HF. At higher collision energies, a second product channel yielding (CH(3))(2)S-F + F was identified. Both reaction channels proceed through an intermediate with an unusual (CH(3))(2)S-F-F bond structure. Curiously, these experimental studies have found no evidence of direct F(2) addition to DMS, resulting in (CH(3))(2)SF(2), despite the fact that the isomer in which both fluorines occupy axial positions is the lowest energy product. We have characterized both reactions, H(2)S + F(2) and DMS + F(2), with high-level ab initio and generalized valence bond calculations. We found that recoupled pair bonding accounts for the structure and stability of the intermediates present in both reactions. Further, all sulfur products possess recoupled pair bonds with CH(2)S(F)CH(3) having an unusual recoupled pair bond dyad involving π bonding. In addition to explaining why DMS reacts readily with F(2) while H(2)S does not, we have studied the pathways for direct F(2) addition to both sulfide species and found that (for (CH(3))(2)S + F(2)) the CH(2)S(F)CH(3) + HF channel dominates the potential energy surface, effectively blocking access to F(2) addition. In the H(2)S + F(2) system, the energy of the transition state for formation of H(2)SF(2) lies very close to the H(2)SF + F asymptote, making the potential pathway a roaming atom mechanism.

In previous work, we reported that the lowest-lying excited states of SF, SCl, SF(2), SFCl, and SCl(2) have recoupled pair bonds. In this study, we examine the analogous low-spin states--the (2)Σ(-) and (2)Δ states of SF and SCl and the excited singlet states of SF(2), SCl(2), and SFCl--which also possess recoupled pair bonds. In contrast to the excited states treated previously, the states studied in the present work have the same spin multiplicities as their respective ground states and are thus potentially observable via electronic excitation. Of particular interest are the minima on the (1)A″ potential energy surface of SFCl corresponding to bond-stretch isomers analogous to those found on the (3)A″ surface. In addition, we discovered that the first two excited states ((1)A″) accessible via vertical excitations from the ground state of SFCl have the electronic structure of the bond-stretch isomers. Thus, electronic excitation spectroscopic studies of SFCl could reveal a signature of the bond-stretch isomers. We will also present limited data on the lowest singlet Rydberg states of the triatomic species. Calculations were performed at the MRCI+Q/aug-cc-pV(Q+d,5+d)Z levels of theory.

Following a previous study of bonding and isomerism in the SF(n) and singly chloro-substituted SF(n-1)Cl (n = 1-6) series, we describe bonding in the ground and low-lying excited states of the completely substituted series, SCl(n) (n = 1-6). All structures were characterized at least at the RCCSD(T)/aug-cc-pV(Q+d)Z level of theory. Both differences and similarities were observed between SCl(n) and our previous results on SF(n-1)Cl and SF(n). Several minimum structures that exist in SF(n) and SF(n-1)Cl are absent in SCl(n). For example, the optimized structure of SCl(2)((3)A(2)) is a transition state in C(s) symmetry, whereas the analogous states are minima in SF(n) and SF(n-1)Cl. Second, we found a continuation of a trend discovered in the SF(n-1)Cl series, where Cl substitution has a destabilizing effect that weakens bonds with respect to SF(n). This effect is much stronger in the SCl(n) series than it is in the SF(n-1)Cl series, which is why SCl(2) is the most stable observed species in the family and why SCl(4), SCl(5), and SCl(6) are unstable (SCl(n-2) + Cl(2) additions are endothermic for n = 4-6).

Using high-level MRCI and CCSD(T) quantum chemical calculations, we report structures, energetics, and other properties of the sulfur fluoromonochloride family (SF(n-1)Cl, n = 1-6). Our group previously studied the sulfur fluoride family (SF(n), n = 1-6) and found that several of the excited states of SF and SF(2) as well as the ground states of SF(3)-SF(6) exhibited a new type of bonding, called recoupled pair bonding. Comparing the SF(n-1)Cl and SF(n) species allows us to study isomerism, apicophilicities, and substituent effects due to the Cl substitution. The primary findings of this work are twofold. First, replacing F with Cl weakens the adjacent S-F bonds by destabilizing the molecule with respect to the pure SF(n) analog. Second, an isomer with a singly occupied S-Cl antibonding orbital is more stable than the analogous isomer with a singly occupied S-F antibonding orbital, thus explaining apicophilicities. This work has also allowed us to further refine and expand our understanding of the nature of the recoupled pair bond model. Finally, we discovered the presence of bond-stretch isomers in the first excited ((3)A'') state of SFCl.

Following our previous studies of hypervalency in SF(n) (n = 1-6) and ClF(n) (n = 1-7), we have characterized the structures and energetics of PF(n) (n = 1-5) species with RCCSD(T) coupled cluster calculations and triple- and quadruple-zeta quality correlation consistent basis sets. The prior studies demonstrated that hypervalent bonding occurs when it is energetically favorable to uncouple a pair of electrons to form new bonds, a process we describe as recoupled pair bonding. In contrast to S and Cl, ground state P((4)S) has no 3p(2) pairs that can be recoupled, but the 3s(2) pair of all three elements is susceptible to recoupled pair bonding when more energetically accessible bonding pathways have been exhausted. We found that this can first occur when F is added to PF(2)(X(2)B(1)), which yields PF(3)(X(1)A(1)) via normal covalent bonding but yields PF(3)(a(3)B(1)) via recoupled pair bonding. PF(3)(a(3)B(1)) lies 92.1 kcal/mol above PF(3)(X(1)A(1)) but is still bound by 42.0 kcal/mol with respect to PF(2)(X(2)B(1)) + F at the RCCSD(T)/aug-cc-pVQZ level. We characterized both of the isomers of PF(4): the more stable and familiar one that has two covalent equatorial bonds and two axial hypervalent bonds (that use both electrons of the recoupled 3s(2) pair) and the less-studied one that has three covalent bonds and only one hypervalent bond. The transition state between these two minima was also located. In addition to the states that can be formed from P((4)S), there is another group of low-lying excited state species that can be formed from P((2)D) via various combinations of covalent and recoupled pair bonding. Additions of the latter type include PF(B(3)Pi) formed from P((1)D) + F and PF(2)(B(2)B(2)) formed from either PF(a(1)Delta) + F or PF(B(3)Pi) + F.

Density functional theory and ab initio methods have been used to calculate the structures and energies of minima and transition states for the reactions of methane coordinated to a transition metal. The reactions studied are reversible C-H bond activation of the coordinated methane ligand to form a transition metal methyl hydride complex and dissociation of the coordinated methane ligand. The reaction sequence can be summarized as L(x)M(CH(3))H <==> L(x)M(CH(4)) <==> L(x)M + CH(4), where L(x)M is the osmium-containing fragment (C(5)H(5))Os(R(2)PCH(2)PR(2))(+) and R is H or CH(3). Three-center metal-carbon-hydrogen interactions play an important role in this system. Both basis sets and functionals have been benchmarked in this work, including new correlation consistent basis sets for a third transition series element, osmium. Double zeta quality correlation consistent basis sets yield energies close to those from calculations with quadruple-zeta basis sets, with variations that are smaller than the differences between functionals. The energies of important species on the potential energy surface, calculated by using 10 DFT functionals, are compared both to experimental values and to CCSD(T) single point calculations. Kohn-Sham natural bond orbital descriptions are used to understand the differences between functionals. Older functionals favor electrostatic interactions over weak donor-acceptor interactions and, therefore, are not particularly well suited for describing systems--such as sigma-complexes--in which the latter are dominant. Newer kinetic and dispersion-corrected functionals such as MPW1K and M05-2X provide significantly better descriptions of the bonding interactions, as judged by their ability to predict energies closer to CCSD(T) values. Kohn-Sham and natural bond orbitals are used to differentiate between bonding descriptions. Our evaluations of these basis sets and DFT functionals lead us to recommend the use of dispersion corrected functionals in conjunction with double-zeta or larger basis sets with polarization functions for calculations involving weak interactions, such as those found in sigma-complexes with transition metals.

As a result of new studies into the nature of hypervalent molecules, we identified a new type of bond called a recoupled pair bond. Hypervalency or hypercoordination was shown to arise by decoupling a pair of valence electrons, each of which becomes available to participate in a new bond. Energy must be expended to decouple an electron pair, so the first recoupled pair bond is weaker than the analogous covalent bond. However, the second bond, which involves a singly occupied antibonding orbital in the hypervalent fragment, is stronger than the analogous covalent bond. Following an initial study of SF(n) species (n = 1-6), the present work explores the ClF(n) (n = 1-7) series to further examine the explanatory usefulness of the recoupled pair bonding model. Optimized structures and energies of the ground and low-lying excited states of the ClF(n) molecules were determined by employing high level ab initio calculations [MRCI, CCSD(T)] with correlation consistent basis sets. Low-lying states that are due to recoupled pair bonding are found in ClF ((3)Pi) and ClF(2) ((2)A(1), (2)B(1), (2)A', (4)A(2)). The bond energies for F addition to form ClF(2), ClF(4), and ClF(6) were found to be much lower than those leading to ClF, ClF(3), and ClF(5). The same type of oscillation is observed in SF(n) species. The differences between ClF(n) and SF(n) reflect the fact that the 3s(2) and 3p(2) electron pairs are more strongly bound in Cl than in S. This behavior and other trends observed in the ClF(n) species demonstrate the improved predictive ability of the recoupled pair bonding model over other models for describing hypervalent bonding.

What breakthrough advances will petascale computing bring to various science and engineering fields? Experts in everything from astronomy to seismology envision the opportunities ahead and the impact they'll have on advancing our understanding of the world.

State-of-the-art ab initio quantum mechanical methods and large basis sets are employed for the study of the electronic structure of the first two states of CuC, (4)Sigma(-) and (2)Pi. A one-electron sigma bond state ((4)Sigma(-)) competes with a two-electron sigma-bond state ((2)Pi) for the ground state of the CuC system. The combined effects of core-valence correlation and relativity point to an X-state of (2)Pi symmetry with D(e)=51.9 kcal/mol and r(e)=1.772 A. The (4)Sigma(-) state is predicted to lie 2.1 kcal/mol higher at r(e)=1.787 A.

The electron affinity of NO has been measured to be 0.026 eV by laser photodetachment experiments. This low electron affinity (just 2.5 kJ/mol or 210 cm-1) presents a computational challenge that requires careful attention to several aspects of the computational procedure required to predict the electron affinity of NO from first principles. We have used augmented correlation consistent basis sets with several coupled cluster methods to calculate the molecular energies, bond dissociation energies, bond lengths, vibrational frequencies, and potential energy curves for NO and NO-. The electron affinity of NO, EA0, using the CCSD(T) method and extrapolating to the complete basis set limit, is calculated to be 0.028 eV. The calculated bond dissociation energies, D0, for NO and NO- are 622 and 487 kJ/mol, respectively, compared with experimental values of 626.8 and 487.8 kJ/mol. From the calculated potential energy curves for NO and NO- the vibrational wavefunctions were determined. The calculated vibrational wavefunctions predict Franck-Condon factor ratios in good agreement with the values determined in the photodetachment experiment.

We report electronic structure calculations on 13 states of the experimentally unknown manganese carbide (MnC) using standard multireference configuration interaction (MRCI) methods coupled with high quality basis sets. For all states considered we have constructed full potential energy curves and calculated zero point energies. The X state, correlating to ground state atoms, is of 4sigma- symmetry featuring three bonds, with a recommended dissociation energy of D0 = 70.0 kcal/mol and r(e) = 1.640 angstroms. The first and second excited states, which also correlate to ground state atoms, are of 6sigma- and 8sigma- symmetry, respectively, and lie 17.7 and 28.2 kcal/mol above the X state at the MRCI level of theory.

Computational modelling is one of the most significant developments in the practice of scientific inquiry in the 20th century. During the past decade, advances in computing technologies have increased the speed of computers by a factor of 100; an increase of a factor of 1000 can be expected in the next decade. These advances have, however, come at a price, namely, radical change(s) in computer architecture. Will computational scientists and engineers be able to harness the power offered by these high-performance computers to solve the most critical problems in science and engineering? In this paper, we discuss the challenges that must be addressed if we are to realize the benefits offered by high-performance computing. The task will not be easy; it will require revision or replacement of much of the software developed for vector supercomputers as well as advances in a number of key theoretical areas. Because of the pace of computing advances, these challenges must be met by close collaboration between computational scientists, computer scientists and applied mathematicians. The effectiveness of such a multidisciplinary approach is illustrated in a brief review of NWCHEM, a general-purpose computational chemistry code designed for parallel supercomputers.

Computational studies of basic chemical processes not only provide numbers for comparison with experiment or for use in modeling complex chemical phenomena such as combustion, but also provide insight into the fundamental factors that govern molecular structure and change which cannot be obtained from experiment alone. We summarize the results of three case studies, on HCO, OH + H(2), and O + C(2)H(2), which illustrate the range of problems that can be addressed by using modern theoretical techniques. In all cases, the potential energy surfaces were characterized by using ab initio electronic structure methods. Collisions between molecules leading to reaction or energy transer were described with quantum dynamical methods (HCO), classical trajectory techniques (HCO and OH + H(2)), and statistical methods (HCO, OH + H(2), and O + C(2)H(2)). We can anticipate dramatic increases in the scope of this work as new generations of computers are introduced and as new chemistry software is developed to exploit these computers.