covalent, ionic and resonating single bonds

Journal of Molecular Structure (Theochem), 229 (1991) 163-188 Elsevier Science Publishers B.V., Amsterdam

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COVALENT, IONIC AND RESONATING SINGLE BONDS

GJERGJI SINI, PHILIPPE MAITRE and PHILIPPE C. HIBERTY*

Laboratoire de Chimie Theorique, Bat. 490, Universitk de Paris-Sud, 91405 Orsay Cedex (France)

SASQN S. SHAIK*

Department of Chemistry, Ben-Gurion University of the Negev, Beer Sheva, 84105 (Israel)

(Received 15 March 1990)

ABSTRACT

Three bond types of electron-pair bonding emerge from multi-structure valence bond (VB) computations of 10 different single bonds. The first bond type is observed in H-H, Li-Li, C-H and Si-H. These are all covalent bond types whose major bonding comes from the covalent Heitler-London (HL) configuration, with a minor perturbation from the resonance interaction between the covalent and zwitterionic (Z) configurations. The second bond type is observed for Na-F. This is an ionic bond type in which the major bonding is provided by the electrostatic stabilization of the ionic configuration, Na+F-, with a slight perturbation from the HL-Z resonance interaction. The third bond type is observed for F-F, H-F, C-F and SGF. These are the resonating bond types in which the major bonding event is the resonance energy stabilization due to the HL-Z mixing. No special status should be attached to either the covalency or ionicity of these last bond types, even if they may appear purely “covalent”, such as F-F, or “highly ionic”, as C-F, by charge distribution criterion. The phenomenon of resonating bonding is shown to emerge from weakly bound or unbound covalent HL configurations which originate when the “preparation” for bonding of the fragments becomes energy demanding, as for fluorine.

The mechanism of HL bond weakening is through costly promotion energy and overlap repulsion of a lone pair with a bond pair of the same symmetry. The essential requirements for a fragment A to qualify as a resonating binder are therefore: (a) to possess two AOs which maintain a very large energy gap between them, and which by virtue of overlap capability can both enter into bonding; and (b) to have three electrons in these two AOs which thereby mutually antagonize each other’s bonding. The propensity for resonating bonding is discussed, in the light of these qualifications, for the main elements across the Periodic Table. It is concluded that the elements with the highest propensity for resonating bonding are F, 0 and N. Any combination A-B where either A or B or both are resonating binders is likely to lead to a resonating bond (e.g. O-O, N-F, C-F, C-O, and so on). The resonating bonds are shown to coincide with the group of “weakened” bonds in the classification of Sanderson, and with those bonds which exhibit negative or marginally positive deformation densities in electron density determinations. Negative or marginally positive deformation densities may serve as the experimental signature of the theoretical concept of resonating bonding. The Li-H bond appears to possess a special status. While the computations tend to classify this bond among the covalent types, the results also show that the HL and ionic Li+H- configurations are nearly degenerate and maintain a very weak coupling. Therefore the

*Associated with the CNRS (UA 506).

0166-1280/91/$03.50 0 1991- Elsevier Science Publishers B.V.

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Li-H bond will have a metastable character, as far as ionicity-covalency, in the presence of medium perturbations which are at least of the magnitude of the coupling between the ionic and covalent structures.

INTRODUCTION

There are probably only a handful of concepts in chemistry which are as fundamental as the concept of the electron-pair bond of the “valence bond” [ 1,2]. It is this concept that has shaped much of our intuition about the structure of molecules and their reactivity patterns. Yet many years after the con- ception of the idea by Lewis [ 1 ] and Langmuir [ 21 and its theoretical formulation by Heitler-London [ 31, Pauling [ 41, Slater [ 51 and Coulson-Fischer [ 61, we are still struggling with the qualitative understanding of the nature of the chemical bond and the origins of bonding [ 7-91. Suffice it to say that the enigma of the origins of bonding in Fz [ 10,111, the vivid debate about the covalency or ionicity of Li-C bonds [ 121, and the findings of both positive and negative deformation densities in single bonds which, for all purposes, seem to be of the same chemical nature [ 131, show that we are still groping for a better understanding of the fundamentals of bonding in the simplest of bonds -the single bond.

Early valence bond (VB ) theory provides an ingenious description of the electron-pair bond as a superposition of two extreme bonding situations which themselves carry a clear chemical connotation. Following Pauling [7], the electron-pair bond A-B is described by a blend of the spin-paired Heitler- London (HL) form, and the two possible zwitterionic situations, as expressed in eqn. (1):

Y,A_n=C1(A’-‘B)+C2(A:-B+)+C3(A+:B-) (I)

Thus, depending on the relative magnitude of the mixing coefficients, C1-C3, in the equation, a bond can be described to lie anywhere in the range spanned by pure covalency to pure ionicity; a description which is apparently consistent with chemical behaviour and wisdom [ 7,14,15]. The general validity of this picture has recently been discussed by Hiberty and Cooper [ 161 and by Mal- rieu and co-workers [ 171 and has been shown to persist irrespective of the computational method. Thus the ionic-covalent superposition scheme provides a conceptual framework for understanding the major features of both the energetics and the charge distribution of the electron-pair bond in a manner consistent with general chemical experience [ 181.

Pauling has also devised simple empirical formulae for estimating the covalent bonding contributed by the HL form to the A-B bond. The most suc- cessful formula [ 191 is the geometric mean relationship (eqn. (2) ) where

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DA-* and DB_B are the experimental bond energies of the homonuclear constituents of A-B.

DHL = ( DA-ADB-B) “’ (2)

Indeed, Sanderson [20] has shown the enormous potential of the idea and calculated the bond energies as well as the ionic-covalent blending coefficients in almost every imaginable bond. Sanderson’s scheme involves first an esti- mation of the blending coefficient of the ionic form in a given bond using the notion of electronegativity equalization, and then calculating the bond energy by simply taking a weighted average of the covalent bonding energy (eqn. (2) ) and the electrostatic stabilization ( -e2/RAB) contributed by the ionic form.

Despite the practical success of Sanderson’s scheme, or for that matter of any semiempirical approach based on eqn. (l), it is clear that such schemes necessarily conceal important quantum-mechanical information about bonding. Firstly, it is not apparent what the precise role is of the resonance energy stabilization arising from the mixing of the structures in eqn. (1). Is the resonance interaction a minor event of bonding or is it rather a key event, and if so when and in what types of bonds? Secondly, the empirical schemes neglect to consider explicitly the ionic contribution to homonuclear bonds such as H-H, F-F, as so on. Though the symmetrized zwitterionic VB structure of a homonuclear bond is, on average, nonpolar, it does contain structures with large fluctuations from the mean electronic population [ 5,211, and in this sense the ionic component of the homonuclear bond is not strictly identical to the covalent HL structure. This becomes further evident from the delocalization tails of the Coulson-Fischer atomic orbitals ( AOs) for homonuclear bonds in the spin-coupled valence bond (SCVB ) and generalized valence bond (GVB ) methods [ 181. At least in the case of F-F it is well established that a proper treatment of the ionic form is critical for reproducing the bond energy [ 221, and this situation is likely to be valid also for other weak bonds such as O-O and N-N. It is essential therefore to use a non-empirical VB method to ascertain the precise role of the resonance stabilization brought about by the mixing of the ionic and HL structures in both homonuclear and heteronuclear bonds. Such a non-empirical scheme may reveal additional fundamental features of the electron pair bonding, other than just ionicity-covalency.

The beauty of VB theory is that the qualitative concepts which are associated with the bond description in eqn. (1) can indeed be tested by quantitative means and at the state-of-the-art level. Recently, the Orsay group [22] has developed a multistructure- and correlation-consistent VB method which is especially suited for studying the bonding problem in the form of eqn. (1) . The method has been tested on several problems of structure, bonding and reactivity and has been found to be computationally reliable [ 22b; 231; hence it offers a means of probing the problem of electron-pair bonding at a rather high computational level.

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In the present study we followed the above goal by investigating 10 different single bonds: H-H, F-F, Li-Li, H-F, H&-H, H,Si-H, H&-F, H,Si-F, Li-H and Na-F. This series covers the traditional covalent-ionic range of eqn. (1)) and poses some conceptual challenges. First, some of these bonds, for example H-H, C-H and Li-Li, belong to the class of bonds which show positive deformation density in the internuclear region, as opposed to others such as F-F and C-F which show negative or negligible deformation density in the same region [ 11,131. Interestingly, these classes coincide with Sanderson’s cate- gories [ 201 of “unweakened” and “weakened” bond types, respectively. In the following sections we show that the same distinction of bond types emerges also from the non-empirical VB scheme, and that the distinction originates in the nature of the spin-paired bonding in the HL configuration in eqn. (1) .

Second, there are specific dilemmas with regard to the ionic or covalent nature of some of the selected bonds on the basis of charge distribution and other analyses. For example, is the ionic contribution to the Si-H bond so significant as implied by charge integration analysis of qn= -0.72 to -0.77 [24]? or is the bond primarily covalent as deduced from the natural population analysis of qn = - 0.22 [25]? Similar questions arise with respect to the Si-F, C-F and Li-H bonds [ 24,251. The latter bond is particularly intriguing, because, according to the empirical estimate in eqn. (2)) the Li-H bond must be covalent (see p. 133 in ref. 14); a description consistent with earlier VB computations by Yardley and Balint-Kurti [ 261, but in contrast with Bader charge analysis which indicates an almost fully ionic bond, Li+O.glH-O.gl much as for LiF [ 24b].

These are some of the focal questions posed in the present paper. As shown, most of these questions can be reasonably answered in terms of the superposition of ionic and covalent VB structures, in accord with the original ideas of VB theory. A new feature which emerges from the non-empirical computations, and is latent in the original scheme, is that, in addition to the traditional classes of covalent (or covalent-heteropolar) and ionic bonding there is a distinct class of resonating bonding. In the latter type it is the resonance interaction that is the major event of the bonding irrespective of the charge distribution in the bond, be this bond nonpolar as in F-F or very polar as in C-F. It is argued that the resonating bond types correspond to the “weakened” class in Sanderson’s scheme and to the class of single bonds which exhibit negative deformation densities in the internuclear region. An attempt is made to generalize the ideas to bonding across the Periodic Table.

THEORETICAL METHODS

The geometries of the various molecules were either optimized or taken from experiment. The various geometrical details and the basis sets are summarized

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TABLE 1

Geometrical parameter@ and basis sets for the target molecules

A-B Basis set

H-H Li-Li H&-H HaSi-H Li-H Na-F F-F H-F H&-F H,Si-F

6-31G** 6-31G 6-31G*b 6-31G*“” 6-311G**d 6-31G*” DZ+Pf DZ+Pf 6-31G* 6-31G*”

Geometric parameter@

R(H-H) =0.74 R(Li-Li)=2.76 R(C-H) = 1.094, Tdh R(Si-H) = 1.461, Tdhi R(Li-H) = 1.60 R(Na-F) = 1.926’ R(F-F) = 1.432 R(F-H) =0.935 R(C-H)=l.O&R(C-F)=1.365, 0(H,C,F)=109.05h R(Si-H) = 1.46, R(Si-F) = 1.595, B(H,Si,F) =109.3’

“Bond lengths in Ingstriim, bond angles in degrees. b6-31G** for the hydrogen involved in the X- H bond being broken. “An effective core potential with optimized 31G valence basis set is used for the silicon. See ref. 50. dA set of diffuse orbitals has been added (Tables 2 and 3, entry for Li-H) for the hydrogen atom. “A set of diffuse orbitals has been added for the fluorine atom. ‘Ref. 51. gGeometric parameters are VB optimized unless noted otherwise. hExperimental geometries for CH,, SiH4 and CH, (R (C-H) =_1.079 A, Dab) are taken from ref. 52. ‘MRD-CI optimized geometry for SiH, (R(C-H) = 1.480 A, B(H,Si,H) =lll.l”) taken from ref. 53.jRef. 54.

in Table 1. The multi-structure VB method has been described elsewhere in great detail [ 221, and what follows here is a short summary of the main features.

Technical details

The VB computations involve VB configuration interaction (CI) calculations between non-orthogonal valence-bond functions (VBFs ) .

The various orbitals of each molecule are partitioned into “active” and “inactive”. The active orbitals are those that are involved in the electron pair bond, while the “inactive” orbitals are the rest. For example, in the H&-H case only the C-H bond orbitals are treated as “active”, whereas the CH3 group orbitals are treated as “inactive”. To ensure a clear relationship between the VBFs and the corresponding types of bond (covalent or zwitterionic ) , between two fragments, the orbitals are strictly localized on either one fragment or the other. In this way a covalent VBF does not contain any implicit contribution from a zwitterionic one, and vice versa. The orbitals are determined through separate Hartree-Fock calculations on the fragments, which provide two kinds of orbitals: the virtual ones, and the occupied ones, hereafter called self-consistent-field (SCF) optimized orbitals.

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Generation of the VB functions (VBFs)

For a single bond, a set of three VBFs is constructed from the SCF-optimized orbitals of the neutral fragments. These VBFs which are called “elementary” are generated with the aim of ensuring the correlation of the active electrons (those involved in the active bond) and thus correspond to the three spin- pairing schemes of the HL and zwitterionic types in eqn. (1). Each elementary VBF is then complemented by a set of complementary VBFs, which are generated from the elementary VBFs by monoexcitations to virtual orbitals of the fragments [ 271. The complementary VBFs can be divided into three main sets, which accounts for the key aspects of the bond orbitals; the rehybridization types, the polarization types and the orbital size types [ 22b]. The final VB process corresponds then to CI among single excitations, which according to the generalized Brillouin theorem [ 281 is equivalent to an orbital optimization procedure, and in our case the optimization is concerned with the degrees of orbital hybridization, polarization and size.

The’variational linear combination of the subset of VBFs which correspond to the same spin pairing and charge types is equivalent to a single effective VB configuration having bond orbitals which are optimized for that particular VB character (i.e. HL or zwitterionic), with respect to the hybridization, polarization and size of the orbitals. The energy of such a variational wavefunction corresponds to the variational energy of a VB structure of the HL or zwitterionic types. These variational energies of the VB structures are used throughout the text in the discussions of the energies of the VB configurations in the sense of eqn. (1) . Thus, in the end, the results of the CI between the entire set of VBFs can be conceptualized in terms of a minimal set of effective VB configurations, each having its own optimized orbitals.

As the nature of the LiH bond, covalent or ionic, has been controversial, we have treated this molecule at a higher level and performed a full VB CI for each of the covalent and zwitterionic diabatic states and for the adiabatic ground state, the 1s core orbital of lithium has been kept doubly occupied.

The inactive orbitals

These orbitals are treated always as doubly occupied and allowed to relax by monoexcitations, but their electrons are not further correlated by the VB procedure. In some cases, like in the zwitterionic configurations of the F-F molecule the relaxation of the inactive orbitals for the particular charges of the fragments [ 22a,b] has a dramatic effect on the bond energy.

VB energies and coefficients

The variational procedure of the entire set of VBFs provides the energy of the molecule, and the bond energy is, in turn, given by the difference between

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TABLE 2

Coefficients of the elementary VB configurations for the target molecules

A-B A-B A’B- A-B+

H-H 0.761 0.147 0.147 Li-Li 0.792 0.075 0.075 H&-H 0.710 0.107 0.194 H&-H 0.747 0.232 0.035 Li-H 0.594 0.265 0.037 Li-H” 0.713 0.204 0.037 Na-F 0.066 0.898 0.005 F-F 0.725 0.255 0.255 H-F 0.574 0.440 0.050 H&-F 0.443 0.516 0.057 H,Si-F 0.272 0.556 0.000

“A set of diffuse orbitals was added for the hydrogen atom.

the energies of the molecule and its constituent fragments. The latter have their energies calculated at the Hartree-Fock level, in which case our CI scheme is dissociation-consistent [ 22a,b].

The configurations with the highest coefficients are the elementary configurations for each bond, these are listed in Table 2 for the 10 bonds considered in this study. It can be seen that the elementary HL VBF has the largest coefficient for H-H, Li-Li, F-F, C-H, Si-H, C-F, H-F and Li-H, while for Na-F and Si-F the largest coefficient belongs to a zwitterionic VBF. There is, therefore, no essential clue in the wavefunctions of these bonds which indicate the differences discussed in the Introduction.

The non-orthogonal CI program was written by Lefour and Flament [ 22~1 using the Prosser-Hagstrom transformation [ 29 1. The orbitals and energies of the open-shell fragments were calculated at the Hartree-Fock level with Davidson’s restricted Hartree-Fock (RHF) hamiltonian [ 301. The MON- STERGAUSS program [ 311 was used throughout this work.

RESULTS AND DISCUSSION

Bond energies

Table 3 shows the energies of the effective [32] HL and zwitterionic (Z) configurations, along with computed and experimental bond energies for the 10 molecules of the study. It can be seen that the computed bond energies are reasonably close to the experimental ones, in view of the rather simple basis sets that we used, However, the direct comparison [22b] of some of the VB calculations in Table 3 and the best MO/C1 calculations performed in the same

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we must qualify this observation because of the extreme proximity of the two configurations.

Figure 1 (b) illustrates the common ionic bond. Bonding in this case is provided mainly by the ionic configuration, due to its electrostatic stabilization, augmented by a minor perturbation due to the mixing in of the covalent HL configuration. The Na-F bond (Table 3) is a typical member of this bonding type, having RE of 0.6 kcal mol-l in comparison with the bond energy of 102.5 kcal mol-I.

Finally, Figures 1 (c) and 1 (d) show the resonating or resonance stabilized bonds. The common feature to all the class members is the very large resonance stabilization, which is also the major bonding event. In comparison with the large resonance interaction, the self-stabilization of the configurations themselves is a less significant bonding event. This class includes both polar bonds, e.g. H-F and C-F (Fig. 1 (d) ), alongside traditionally “covalent” ones, e.g. the F-F bond (Table 3 and Fig. 1 (c ) ) . The Si-F bond (Table 3 ) may be annexed to this class simply because of the very large resonance stabilization of 53.1 kcal mol-’ which is a prominent feature of the Si-F bonding.

It is interesting to compare some of the above conclusions with other notions about the various bonds. The natures of H-H, Li-Li, C-H and Na-F are as expected and are in agreement with probably any other method of looking at chemical bonding. This is not the situation however with the Si-H bond which appears to be significantly ionic in the charge integration analyses methods [ 241, but entirely covalent in our scheme which is in agreement with the natural population analysis of this bond [25]. In fact, considering the resonance stabilization energy (RE in Table 3) which is a measure of the mixing of the ionic structure into the covalent one we might say that the Si-H bond is more covalent than C-H. The case of the F-F bond is probably the most interesting because in a traditional thinking this bond is nothing else but “covalent”. However, in our scheme the entire F-F bonding energy comes from the resonance between the ionic and covalent structures.

The H-F [ 331, C-F and Si-F bonds [ 24,251 are traditionally considered to be covalent bonds with high ionicity or ionic bonds with some or high covalency. Charge distribution analyses based on integration methods [24] indicate, for example, that the C-F bond is highly ionic (or= - 0.74 to - 0.77)) and more so is the Si-F bond ( qF= - 0.92). While we do not contest the validity of the charge partition methods, our computations suggest that any deduc- tion based on charge analyses [24,25] will conceal more than reveal that the H-F and C-F bonds owe their major bonding to the resonance and not to either bond ionicity or covalency.

Even the Si-F bond which, in our scheme too, has a major ionic character cannot be conveniently termed ionic because of its large resonance energy. Consideration of this and analogous Si-X bonds (e.g. Si-0, Si-Cl, etc.) as ionic cannot account for their stability toward heterolytic cleavage in solution

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[ 341, because normally the electrostatic energy of a bond is expected to be fully compensated [ 351 by the solvation energy of the ions, and it is the covalency and the quantum-mechanical mixing that induce high barriers to heterolytic cleavages [ 361. It is reasonable to think, therefore, that the reluctance of Si- F toward heterolytic cleavage is related to the large resonance energy of this bond.

In summary of the resonating bond type, our VB analysis suggests that no special status should be attached to either the ionicity or covalency of these bond types, even if such bonds may possess apparently ionic (such as C-F and Si-F) or covalent (such as FlF) charge distributions. In addition to the nov- elty as a bond type, we note that the resonating bonds coincide with those bonds which exhibit negative deformation densities in electron density determinations [11,13] and with the group of “weakened” bonds in Sanderson’s scheme [ 201.

The Li-H bond requires a special discussion. As seen in Table 3, upon improvement of the basis set the ionic, Li+H-, and the HL covalent configurations approach one another with concomitant reduction in the RE stabilization due to their mixing. We have verified that the two configurations are close in energy and that the HL structure undergoes significant stabilization at different basis sets, as was also found in an earlier study [ 261. We can therefore say with some degree of confidence that Li-H is clearly unlike the ionic Na-F bond, but is approximately an equal mixture of the ionic and covalent structures. However, because of the small resonance interaction of the two configurations, the Li-H bond may have an ambident character, as far as ionicity- covalency, in the presence of medium perturbations which are at least of the magnitude of the coupling between the ionic and covalent structures.

All the above features form an incentive to trace the origins of the resonating bonding type, within the computational complexity of the multistructure VB method, and to base these origins on some lucid concepts of electronic structure. Our strategy follows the philosophy that the whole may be understood by reconstruction from its building-block components [ 321 and we therefore search the origins of the resonating bonding in the quantum-chemical behaviour of the VB configurations and on their mixing patterns.

The VB configurations and the weakening of HL bonding by the F atom

The energies of the configurations are given in Table 3 relative to the sum of the free fragment energies defined as the zero of the energy scale. These energies are the result of a variational treatment of the VBFs which contribute to individual configurations and correspond to energies of effective configurations [ 23,321. The effective configurations can be represented by the usual wavefunctions in a minimal basis set, as shown in eqns. (3a)- (3~)) where we use only those orbitals of A and B that participate in the electron-pair bonding.

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In turn, these orbitals correspond to single centre AOs or hybrids which opti- mize the energies in their respective configurations [ 2213,231.

Y!nL=A’-‘B=NnL{ lab] - ]ab]} (3a)

Y’,(A+B-)=A+ :B-=NA+n-{jbb]} (3b)

Y,(A-B+)=A:- B+=NA-n+{ laa]} (3c)

The spin pairing of the two electrons in the a and b AOs or hybrids endows the HL configuration with self-stabilization energy which is proportional to the monoelectronic term 2hs, where hs is the product of the resonance and overlap integrals defined over the a-b bond AOs or hybrids [37]. The spin pairing energy is therefore expected to reflect the bonding strength of the atom or fragment, unless the true strength is masked by additional effects not ex- plicit in eqn. (3a). Inspection of the E(HL) quantity in Table 3 shows that indeed most of the values are negative, revealing the spin pairing stabilization energy relative to the separated atoms or fragments. In agreement with this, the strong binders like H and CH3 indeed possess more negative E (HL) than, e.g., Li which is a weaker binder. Yet the picture is not that simple, because all the cases which involve F in the bond possess small absolute values of E (HL) in comparison with unfluorinated analogues, e.g. H-F vs. H-H. Two of the cases, F-F and Na-F, even possess unbound HL configurations with E (HL) > 0, and this despite the fact that F is a very strong binder. We note that all the bonds which possess weakened HL bonding, except for NaF, are of the resonating type. It is therefore crucial to ascertain this HL bond weakening effect and to understand its origins.

That there is a special effect mostly in the HL configuration of the A-F bonds can be elucidated by inspection of the zwitterionic configurations in Table 3. The column E(Z,,,) refers to the variational energy of the wavefunction made of the linear combination of the two zwitterionic structures (eqns. (3b) and (3~). For a homonuclear case the mixing of the two zwitterionic configurations leads to stabilization which has a monoelectronic expression identical with the HL spin pairing stabilization [ 321, as illustrated in the determinant mixing diagram (Fig. 2) which generates the HL and Z, configurations from their constituents determinants [ 321. In a heteropolar case the stabilization energy of the Z,, configuration depends on the 2hs term as well as on the energy gap between the two interacting ionic structures, while the stabilization of the HL configuration is always proportional to 2hs. In any event, the stabilization energy of the Zopt configuration can provide us with information about the expected strength of the spin pairing in the HL configuration [ 381. Inspection of the data for H-H in Table 3 shows that the stabilization energy of Zopt with respect to its constituent determinants is 83.2 kcal mol-l, close to the HL stabilization energy of 95.9 kcal mol-’ (remember that

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Z opt

(4

la61

- , ,’ ‘.

#’ ‘. a’ ‘.

,’ ‘. ,’ ‘\

,’ ‘, - :-

‘\ #’ ‘. a’

‘\ a’ ‘\ ,’

‘. .’ ‘\ ’ Y’

HL

03

l5bl

Fig. 2. Determinant mixing diagrams [31] showing the generation of Z,t and HL from their constituents determinants. (a) Z,,, for a homonuclear case: the orbitals in the determinants refer to AOs or hybrids on the two molecular centres. (b) HL for a general case, homonuclear or heteronuclear.

the identity of the two quantities is not expected in our non-empirical scheme equivalent to a computation with different orbitals for different configurations). Similar observation can be made for the Li-Li, C-H and Si-H cases in which, like the H-H case, the Zopt configuration is stabilized to roughly a similar extent as the HL configuration [ 381. This behaviour can be contrasted with the disparity between the stabilization patterns of the Zopt and HL configurations of the A-F bonds (A = F, H, CH3, SiH3 or Na) . Thus Zopt, for the F-F case, is stabilized by 93 kcal mol-l, while the corresponding HL configuration is destabilized by 35.4 kcal mol- ’ (Table 3 ) . The same observation can be made for all the other A-F bonds in Table 3; they are all typified by a large coupling of the zwitterionic configurations and a much smaller stabilization of the corresponding HL configurations [ 381. It is apparent now that the unique- ness of the resonating A-F (A = F, H, CH, or SiH3 ) bonds coincides with, and is perhaps related to, the weakening of the HL bonding, and that this weakening is the effect which masks the actual strength of the spin pairing in the HL configuration. It remains to be ascertained to what extent the HL bond weakening is an intra-fragment property, and to what extent it is due to repulsive ,fragment-fragment interactions.

This may be deduced by looking at the deviation of the HL bond energies from the mean values of the HL bond energies of their homonuclear constituents. Since there are positive as well as negative values of E(HL), it is clear that a geometric mean as in eqn. (2) cannot be used and one may consider instead the arithmetic mean formula (eqn. (4) ). The results of eqn. (4) are collected in Table 4 together with the computed values, and we note that by

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TABLE 4

VB calculated and eqn. (4) based DHL values

A-B DHL (kcal mol-‘)

VB” Eqn. (4)b

Li-H 46.0 55 H-F 50.7 30 Na-F -22.2 -15 H&-H 89.7 88 H,Si-H 81.8 83 H&-F 37.5 22 HaSi-F 67.4 18

“Dn,= -E( HL) in Table 3. ‘Using eqn. (4). Entries for Na-F to H,Si-F were obtained by as- suming that Na behaves like Li, and CH, and SiH, behave like H so that the respective HL homonuclear bond energies are smaller than the experimental bond energies by 10, 8 and 8 kcal mol-‘. Thus; DHL (Na-Na) =6 k ca mol-‘, D,,(H,C-CH,) =80 kcal mol-’ and DHL(HBSi- 1 SiH,) =70 kcal mol-‘.

reversing the sign of the E (ML ) quantity in Table 3 we obtain the computed HL bond energies DnL given in Table 4.

DHL(A-B) =0.5[DHr,(A-A) +DHL(B-B)] (4) To estimate all possible combinations of DnL (A-B ) we assumed that the

HL bond energies of the H&-CHB, H,Si-SiH, and Na-Na behave like the corresponding energy of the H-H and Li-Li bonds, respectively; namely all having Dm_ values close to the full bond energy. This assumption allows us to predict, by use of eqn. (4)) the HL bond energies for the bonds in the last five entries. The results listed in Table 4 show that the quantitative predictions of eqn. (4) are only fair, but that the qualitative picture is reasonably reproduced. Thus, in consistency with the notion of eqn. (4 ), the HL bonding ability of an atom B is roughly transferable to any A-B bond. In particular it is seen that, while H, CH, and SiHB transfer their strong HL bonding ability, the atom F transfers a weak HL bonding ability to all the A-F molecules. The intra-fragment effect seems, therefore, to be responsible for the global qualitative picture of Dun. In turn, the deviations in the Dm_ values of eqn. (4) with respect to the computed results, for example in the case of H$i-F, imply that part of the effect is due to fragment-fragment interactions.

The HL bond-weakening effect and possible origins of the propensity of fluorine for resonance bonding

All the above discussion points to one observation, i.e. that the F atom possesses a property which weakens the HL bonding and that this weakening coincides with the emergence of the resonating group of A-F bonds (A = F, H,

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CH3 or SiH3) in Table 3. What are the factors which make F different from the other atoms and fragments considered in our study? The following explanation is based on well-recognized concepts of hybridization, promotion, and overlap repulsion [ 7-9,32,39,40].

Consider the pictorial bond diagram representation [8,32] of the covalent HL configuration in the simplest example of H-F (Fig. 3). In Fig. 3 only the three AOs which are capable of interatomic overlap (the Is A0 of hydrogen and the 2s and 2p, AOs of fluorine) are shown. In Fig. 3(a) the spin paired electrons reside in the 1s and 2p, AOs, and this HL bond is, by convention, shown by the line connecting these two AOs. Because of the overlap of the ls- 2s AOs there is a three-electron repulsion between the 2s electron pair and the HL bond in the ls-2p, spin pair. The monoelectronic expression of this overlap repulsion [ 321 is similar to the HL bonding but with an opposite sign, namely - 2hs where the hs quantity is the product of the resonance and overlap integrals of the ls-2s AOs. Since in first-row elements the 2s A0 possesses both larger overlap capability and certainly larger interatomic resonance integrals than the 2p, A0 [ 8,9,41], the overlap repulsion [ 321 may well override the HL bonding in which case the configuration shown in Fig. 3 (a) will be destabilized relative to the free atoms.

Another HL configuration of the same symmetry is shown in Fig. 3 (b), where the bond pair now resides in the ls-2s AOs while the three electron repulsion is due to the 2p,-1s A0 overlaps, Owing to the strong bonding capability of the 2s A0 of F, the HL bonding interaction is now much stronger than in the case of the ls-2p, bond pair in Fig. 3 (a). However, the improved bonding is achieved at the expense of the atomic excitation 2s+2px, which in the case of fluorine is extremely costly (computed as 482 kcal mol-’ in the present study [42] ). Therefore, the HL configuration shown in Fig. 3 (b) is significantly higher in energy than the separated atoms.

The optimized HL configuration is a linear combination of the above two configurations, and this mixing of course lowers the energy so that the final HL configuration may end up being bound, relative to the free atoms, depending on the balance of the repulsion/promotion and configuration mixing effects. The linear combination of the configurations in parts (a) and (b) of Fig. 3 is equivalent to a single configuration in which F is “prepared for bonding” with hybridized orbitals [22,39,40], as shown in part (c) of the figure. The hybridization, on the one hand, reduces the overlap repulsion by virtue of the reduced overlap between the hybrid-pair of F with 1s A0 component of the HL bond, and simultaneously increases the HL bonding of the hybrid with the 1s A0 of hydrogen; but on the other hand, the hybridization is itself costly due to the enormous 2s-2p energy gap. Even if the hybridization is no more than 10% (i.e. “sp”’ ), the total payment, in both atomic excitation and residual lone pair-bond pair repulsion, will still require roughly 50 kcal mol-’ of energy. Therefore, two major factors are predicted to contribute to the weakness of the

178

2P*

2s +

F H

2Px

2s

h

h’

+

a’ a’

+ IS

t 8’ #’

,’ #’

,’ t ’

,’ .’

+

#’ ,’

F H

_e-- + IS

_s--

+

__-- _e--

(4

(W

w

F H

Fig. 3. Schematic representations of the HL-type configurations for H-F. The interatomic spin pairing is shown by a line connecting the two orbitals. (a) An HL bond pair involving the 2p,-1s AOs. (b) An HL bond pair involving the 2~1s AOs. (c) An HL bond pair in the hybrid (h) and the Is AO. The hybridized representation corresponds to an optimized linear combination of the H-L-type configurations shown in (a) and (b).

179

HL bonding: (i) the high cost of the actual hybridization; and (ii) the meagre improvement of the HL bonding interaction as well as the significant residual overlap repulsion caused by the insufficiency of the actual hybridization. These HL bond-weakening factors originate in the large 2.~2~ energy gap in combination with the better overlap capability of the 2s A0 relative to the 2p AO.

In the case of H-F this weakening effect results in a moderately bonded HL configuration (Table 3), with a bonding energy of 50.7 kcal mol-’ which is roughly half as much as the “actual” strength which is deduced from the coupling of the zwitterionic configurations [38]. If we take 50 kcal mol-l as a “ball-park” figure of the weakening effect per F atom in a HL configuration, we can qualitatively predict the behaviour of the remaining A-F bonds. In the case of Na-F, the combination of ca. 50 kcal mol-’ of “preparing” F for bonding and the poor HL bonding ability of Na results in an unbound HL configuration (Table 3). In the F-F bond, the very costly weakening effect of the two F atoms [40a], ca. 100 kcal mol-l, roughly overrides the HL bond coupling which is ca. 93 kcal mol-l as can be deduced from the coupling of the zwitterionic configurations. Adding the repulsion of the adjacent n type lone pairs leads to an unbound HL configuration (Table 3). In the CH3-F bond, the atomic “preparation for bonding” effect is joined by a moderate repulsion between the rc type lone pairs on F and the C-H bonds to produce a slightly bound HL configuration (Table 3 ) . In comparison, in the SiH3-F molecule the adjacent repulsions between the n lone pairs and Si-H bond diminish due to the Si-F longer distance, relative to CH3F, and the resulting HL configuration is accordingly more bound than in CH3-F (Table 3).

To generalize the conclusions it is important to understand the behaviour of other fragments in our study, such as CH3, SiH3 and Li. Consider the CH, fragment in a free state and in bonding. In both situations the configuration of carbon is promoted, though the hybridization in the C-H bonds is different in the free (planar) and bonded (pyramidal) fragments. Thus, there is no energy rise due to atom excitation in preparing CH, for bonding, and this is in fact expressed by the very fluxional potential of CH3 toward pyramidalization [ 431. Another important effect is the reduced overlap repulsion as shown in the HL configuration for a H&-X bond in Fig. 4. It is seen that the CH3 fragment does possess an electron pair, in a bonding a, type orbital, which is capable of undergoing three-electron repulsion with the bond pair in the HL configuration through the overlap with the orbital of X. But, unlike the case of an F fragment, in the CH3 fragment the repulsive interaction is small due to both the delocalized and sp3 hybridized nature of the a, type orbital. Taking the above effects together, the CH3 fragment is a good HL binder and it will carry its bonding capability to any HL configuration H,C’-‘X. Whenever the fragment X is of the same type as CH3, as for example H or CH, itself, then the HL bonding energy will be significant as is indeed computed for the case of H3C-H where the HL bond energy is ca. 90 kcal mol-l (Table 3). What

180

Sal

Fig. 4. Schematic representation of the HL configuration of H&-X. Only the a, type orbitals of CH, are shown.

emerges, therefore, is that the propensity of a fragment to produce a weakened HL bond depends on the presence of lone pairs having the same symmetry as the bond orbital of the fragment. This causes both net atomic excitation and overlap repulsion which raise the energy of the HL configuration. These qual- ities typify F but are absent in H, CH3 or SiH3.

A final point which requires clarification is the origin of the small resonance interaction in the covalent bonds as opposed to the very large interaction in the resonating bonds. At the outset we recall that in non-orthogonal configuration mixing the effective matrix element is H,, -ES& and hence the mixing may become very small when the overlap S,, becomes critically large [ 441. Consider now the comparison between the A-F class of bonds with CHB-H as a representative of the covalent class of bonds. The hybridization of CH, results in a large overlap between the bond orbitals in CH,--H, and&his leads also to a large S,, between the HL and zwitterionic configurations ‘[ 321. This es- sentially means a significant similarity between these configurations, so that no significant resonance energy can be expected from their mixing. A limiting situation is an overlap of unity, in which case the resonance energy would be exactly zero. It turns out that the S,, (HL-Z,,) overlap is 0.96 in CH3-H and larger than 0.95 for all the other covalent bonds in Table 3. These critically large overlaps are at the root of the small RE of these covalent bonds. In contrast, the bond orbitals of the resonating A-F bonds maintain smaller overlaps due to the compact AOs of fluorine and especially due to its hindered hybridization. This necessarily means a smaller S,, overlap between the respective HL and Zopt configurations. Indeed, the computed overlaps are 0.65-0.89 for the F-F, F-H and F-CH, bonds, in comparison with more than 0.95 for all the covalent bonds. These smaller overlaps in the resonating bonds indicate a lower degree of similarity between the HL and Z configurations and hence stronger

181

HL mixings [44] result, followed by large REs for all the A-F bonds. These facts form the basis of the distinction between the covalent and resonating bond classes (Table 3 ) .

The propensity for resonating bonding among other elements

It is interesting to consider the qualifications of other fragments, which also possess two binding AOs with three electrons, as possible resonating binders. Among the first-row elements, 0 and N are similar to F, and share with it common binding features. Thus, like F, these atoms also possess filled 2s AOs which are very low lying and have a better overlap capability [8,9,41] than the corresponding 2p orbitals. This creates high three-electron repulsion in the corresponding HL configurations, and the resulting hybridization reduces the repulsion and intensifies the bonding ability only at the expense of the high cost of the atomic excitation due to the large 2s-2p energy gap. The destabili- zation of the HL configuration and, in turn, the strong HL-Z coupling will make A-O and A-N combinations (where A is a general fragment) good can- didates for resonating bonds.

The situation is different for the third-row analogues, e.g, P, S and Cl. In these cases the 3s orbital has a poorer overlap capability than the 3p A0 [ 8,9] and, more so, the 3s-3p gaps are much smaller than the corresponding 2s-2p gaps. The reversal in the overlap capabilities of the 3s/3p AOs causes a smaller three-electron repulsion between the 3s pair and the HL bond pair (see Fig. 3 (a) ) and a reduced importance, for bonding, of the promoted 3s+3p configuration (see Fig. 3 (b) ) . This will of course be translated into a smaller degree of hybridization [8,9,45] of the second-row element. The reduced hybridization and the smaller 3s-3p energy gap will in turn mean a much smaller in- vestment in atom excitation. The reduced three-electron repulsion and atom excitation will in turn result in a bonded HL configuration which is only slightly weakened by the “preparation for bonding” effect. The resulting electron-pair bonding will tend, therefore, toward the covalent type with a reduced importance of the resonance energy due to the mixing between the HL and Z configurations.

It is therefore apparent that the importance of the resonance energy, and hence of the resonating bonding, will depend largely on two properties of the atom; the ns-np gap and the relative overlap capabilities of the two AOs. As this gap becomes larger and the overlap capability of the ns A0 increases relative to that of the np A0 the HL configuration will exhibit weaker bonding and the importance of the resonance interaction in the bonding will accordingly increase. It is known that the ns-np gap as well as the ns/np relative overlap capabilities both generally decrease from right to left and from top to bottom of the Periodic Table, in accord with discussions by Epiotis [ 8,411 and Kutzelnigg [9]. Based on this trend it is expected that the resonance energy

182

contribution due to HL-Z mixing will increase from left to right along a row and remain marginal beyond the third row. Accordingly, the chances of finding resonating bonding will probably be clustered mostly among the first-row elements, F, 0 and N. Thus, while the F-F, O-O, N-O, N-F and F-O, C-F, C-O, H-F and H-O bonds are expected to be resonating types, the corresponding higher row bonds are likely to be all of the covalent type. The mixed cases like the S-F, S-O, Si-0, Si-N, P-F, P-O, etc., bonds are particularly interesting, and might all resemble the Si-F bond by having both high degrees of ionicity and large resonance energies.

Covalent and resonating bonds and the lone pair bond weakening effect of Sander-son

The preceding analyses are related to the “lone pair bond weakening effect” described by Sanderson [ 201. Sanderson analysed the weak X-X bonds for X= F,O or N. Through the correlation that exists between the X-X bond energy and the covalent radius of X, Sanderson estimated that the N-N, O-O and F-F bonds are weakened by as much as 56-74 kcal mol-l, and the same estimates are obtained by looking at the ratio of multiple to single bond energies [ 9,201 of the various atoms. Similar bond-weakening effects are observed for H-F, O-H, N-H, C-F and other bonds in which one of the atoms possesses lone pair(s). Thus, as argued by Sanderson, “the bond weakening effect” is not due to adjacent lone pair-lone pair repulsion [ 461, but is rather an intrinsic property of atoms like F, 0 and N which appear to carry over their “bond weakening effect” to any chemical bond. The “bond weakening effect” is primarily a property of the first-row elements F, 0 and N, and becomes less pro- nounced down the Periodic Table, and is non-existent for C-C, Si-Si, C-H, etc., bonds where lone pairs are absent. Based on our conclusions, it is now possible to identify the Sanderson bond-weakening effect with our observation of the resonating bonding and to trace the origins in the weakening of the covalent HL bonding due to a presence of a lone pair of the same symmetry as the bond pair. Furthermore, the trends of bond weakening observed by Sand- erson coincide with our predicted trends in the Periodic Table and with our distinction between the resonating bonds with weakened HL bonding and covalent bonds which have high HL bonding. In summary, the highly weakened bonds in Sanderson’s scheme correspond to the resonating bond type, while the unweakened bonds correspond to the covalent bond type.

Covalent and resonating bonds and deformation density measurements

The comparison of our bond types with Sanderson’s scheme becomes all the more intriguing because approximately the same bond classes (“weakened” and “unweakened”) emerge distinct upon inspection from quite a different

183

direction. Thus, deformation density (40) measurements and computations [ 11,131 show that in the internuclear region of “unweakened” bonds such as H-H, Li-Li, C-H, C-C and Si-Si there is a positive deformation density, &> 0. Namely, in the internuclear region there is a piling up of electron density relative to the promolecule made of the spherically averaged atoms in the same molecular geometry. However, the same technique shows negative or small positive deformation densities in the internuclear region of “weakened” bonds such as F-F, O-O, C-F, C-O, N-O, N-N and C-N [ 11,131. Since positive deformation densities indicate presence of binding regions [ 471, then without going into the usual debate of what is the proper promolecule [ 40a,48], it is quite clear that we are observing some fundamental difference in the electronic reorganization which attends the bonding in these two classes. It is all the more interesting that the observations of negative or positive deformation densities as well as of the presence of absence of the “bond weakening effect” do not correlate with the traditional covalent or ionic character of the bonds because both polar and covalent bonds are present among the two groups.

A basis for a general explanation of negative deformation density can be found in a very detailed study of F2 by Kunze and Hall [40a]. These authors have shown that the negative or positive (depending on the choice of the promolecule) & of F2 is due to the hybridization of F. Since the F atom of the promolecule is unhybridized, the effect of hybridization in the actual molecule is to push one lone pair away from the midbond to the outer regions of the bond along the bond axis. The midbond region thereby acquires a negative deformation density while the outerbond regions become richer in electron density. The overlap and bonding interaction of the two singly occupied bond hybrids restore some density, but the net effect is that Ap remains small or negative in the midbond region.

This reasoning can be extended to all other resonating A-F bonds. It is apparent, therefore, that the negative or marginal Ap property of these bonds and their resonating nature share exactly the same origins; i.e. the presence of a lone pair of o symmetry that undergoes some hybridization to reduce the mu- tual antagonism with the obond. Moreover, since the essence of the resonating bonding is the weakened HL bonding, we can expect to find a correlation between the Ap property and the sign and magnitude of the HL bonding energy, D (HL). In the light of this correlation and the D (HL) data (Table 3)) we expect the C-F bond which has a weakly bound HL configuration to involve positive but almost insignificant deformation density, as was indeed found by Dunitz and collaborators [49]. If our reasoning is correct we should further expect the H-F bond to exhibit a larger Ap in comparison with the C-F bond. All other single bonds for which either negative or marginally positive Ap have been observed [11,13] (that is O-O, N-N, N-O, C-O and so on) are in harmony with our above predictions regarding the probable nature of these bonds. Our approach thus provides a means of predicting trends in the Ap property in

184

a variety of bonds by relying on the propensity of fragments in atoms to weaken or strengthen the HL bonding. It may turn out after all that the theoretical concept of resonating bonding does possess an experimental signature of negative or marginally positive deformation densities.

CONCLUDING REMARKS

Quantitative multistructure VB theory shows the existence of three classes of single bonds. The first two classes are the traditional covalent and ionic bond types which are observed for H-H, Li-Li, C-H, Si-H and Na+F-. The third bond type is the resonating bond in which the major bonding event is the resonance energy stabilization due to the HL-Z mixing, irrespective of the actual “covalency” or “ionicity” of the bond as deduced by the charge distribution criterion. Such bonds are F-F, C-F, H-F and, to a large extent, also Si- F.

The phenomenon of resonating bonding is shown to emerge from weakly bound or unbound covalent HL configurations which originate when the “preparation” for bonding of the fragments becomes energy demanding, as in the case of fluorine. The essential requirements for a fragment to qualify as a resonating binder are: (a) to possess two orbitals which maintain a very large energy gap between them, and which by virtue of overlap capability can both enter into bonding; and (b) to have three electrons which mutually antagonize, by overlap repulsion, the bonding of these two AOs. With these features the HL configuration will be raised in energy due to the promotion energy and the overlap repulsion of the lone pair with the bond pair.

The propensity for resonating bonding is discussed, in the light of these qualifications. It is concluded that the elements with the highest propensity for resonating bonding are F, 0 and N. Any combination of these atoms in a single bond is likely to generate a resonating bond (e.g. O-O, N-F, C-F, C-O, H-N and H-O ) .

The resonating bonds are shown to coincide with the group of “weakened” bonds in the classification of Sanderson, and with those bonds which exhibit negative or marginally positive deformation densities in electron-density determinations. Negative or marginally positive deformation densities may serve as the experimental signature of the theoretical concept of resonating bonding.

The exact nature of the Li-H bond appears to be more elusive. While the computations tend to classify this bond among the covalent types, the results also show that the HL and ionic Li+H- configurations are nearly degenerate and maintain a very weak resonance interaction. Therefore the Li-H bond may have an ambident character, as far as ionicity-covalency is concerned, in the presence of medium perturbations which are at least of the magnitude of the resonance mixing between the ionic and covalent structures.

185

ACKNOWLEDGEMENT

The research at BGU was supported by the Basic Research Foundation ad- ministered by the Israel Academy of Sciences and Humanities.

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37 This term is sometimes called the exchange energy in VB theory. See discussion in R. McWeeny and B.T. Sutcliffe, Methods of Molecular Quantum Mechanics, Academic Press, London, 1969, p. 151. See also the effective Heisenberg hamiltonian formulation of this term (termed g there), in P. Blaise, J.P. Malrieu, D. Maynau and B. Oujia, J. Mol. Struct. (Theochem), 169 (1988) 469.

38 The effective matrix element of the two zwitterionic configurations can be deduced from the energies of the two configurations and the stabilization energy of the Z,,, relative to the lowest of the two zwitterionic configurations. These matrix elements are given in parentheses beside their respective molecules. Hz (83.2 kcal mol-‘), Lii? (10.4 kcal mol-‘), LiH (34.5 kcal mol-’ or 27.5 kcal mol-’ when a set of diffuse orbital is added for the hydrogen atom), H&-H (105.5 kcal mol-‘), H,Si-H (82.0 kcal mol-I), Na-F (7.3 kcal mol-‘), H&-F (111.9 kcal mol-‘), F-F (92.8 kcal mol-‘), H-F (109.4 kcal mol-‘) and H,Si-F (60.8 kcal mol-‘).

39 (a) R. McWeeny and F.E. Jorge, J. Mol. Struct. (Theochem), 169 (1988) 459. (b) W. Kutzelnigg, J. Mol. Struct. (Theochem), 169 (1988) 403. (c) J.E. Carpenter and F. Weinhold, J. Mol. Struct. (Theochem), 169 (1988) 41.

40 (a) K.L. Kunze and M.B. Hall, J. Am. Chem. Sot., 108 (1986) 5122. (b) M.B. Hall, J. Am. Chem. Sot., 100 (1978), 6333. (c) M.B. Hall, Inorg. Chem., 17 (1978) 2261.

41 (a) N.D. Epiotis, J. Mol. Struct. (Theochem), 153 (1987) 1. (b) N.D. Epiotis, Topics Curr. Chem., 150 (1989) 48.

42 C.E. Moore, Atomic Energy Levels, Nat. Bur. Stand. Ref. Data. Ser., National Bureau of Standards (U.S.), Washington, DC, 1971.

43 P.C. Engelking and W.C. Lineberg, J. Am. Chem. Sot., 100 (1978) 2556. 44 The computed matrix elements, due to the 2*2 interaction of Ql = Z,,, and @z = HL, corre-

spond to the (Hlz - ES,._,), and are given in parentheses beside the respective molecules: H, (18.4 kcal mol-‘), Liz (4 kcal mol-‘), LiH (9.4 or 6 kcal mol-’ when a set of diffuse orbitals is added to the hydrogen atom), H&-H (20.3 kcal mol-I), H,Si-H (14.6 kcal mol-‘), Na- F (14.9 kcal mol-‘), H&-F (129.9 kcal mol-‘), F-F (127.3 kcal mol-‘), H-F (92 kcal mol-‘) and HaSi-F (76.7 kcal mol-‘).

45 W.A. Goddard, III, and L.B. Harding, Ann. Rev. Phys. Chem., 29 (1978) 363. 46 R.T. Sanderson, Polar Covalence, Academic Press, New York, 1983, pp. 69-89. 47 (a) R.P. Feynman, Phys. Rev., 56 (1939) 540.

(b) J.C. Slater, J. Chem. Phys., 57 (1972) 2389. 48 W.H.E. Schwarz, P. Valtazanos and K. Ruedenberg, Theor. Chim. Acta, 68 (1985) 471. 49 J.D. Dunitz, W.B. Schweizer and P. Seiler, Helv. Chim. Acta, 66 (1983) 123; 134. 50 Y. Bouteiller, C. Mijoule, M. Nizan, J.C. Barthelat, J.P. Daudey, M. Pelissier and B. Silvi,

Mol. Phys., 65 (1988) 295. 51 T.H. Dunning and P.J. Hay, Gaussian Basis Sets for Molecular Calculations, in H.F. Schae-

fer (Ed.), Electronic Structure Theory, Plenum Press, New York, 1977.

188

52

53 54

55

56

57

58 59

60 61 62 63

M.D. Harmony, V.W. Laurie, R.L. Kuczkowski, R.H. Schwendeman, D.A. Ramsay, F.J. Lo- vas, W.J. Lafferty and A.G. Maki, J. Phys. Chem. Ref. Data, 8 (1979) 619. P.R. Bunker and G. Olbrich, Chem. Phys. Lett., 109 (1984) 41. B. Rosen (Ed.), Spectroscopic Data Relative to Diatomic Molecules, Pergamon Press, Ox- ford, 1970. K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, Vol. 4, Van Nos- trand, Princeton, NJ, 1979. B. Barakat, R. Bacis, F. Carrot, S. Churassy, P. Crozet, F. Martin and J. Verges, Chem. Phys., 102 (1986) 215. R.C. Weast (Ed.), Handbook of Chemistry and Physics, 67th edn., CRC Press, Boca Raton, FL, 1986-1987. S.W. Benson, J. Phys. Chem., 85 (1981) 3375. D.R. Stoll and H. Prophet, Natl. Bur. Stand. Ref. Data Ser., No. 37, National Bureau of Standards (U.S.), Washington, DC, 1971. A.M. Doncaster and R. Walsh, Int. J. Chem. Kinet., 13 (1981) 503. D.A. Dixon, J. Phys. Chem., 92 (1988) 86. M.E. Jacox, J. Phys. Chem. Ref. Data, 13 (1984) 945. P. Ho, M.E. Coltrin, J.S. Binkley and C.F. Melius, J. Phys. Chem., 89 (1985) 4647.

covalent, ionic and resonating single bonds

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