Atomic properties and the reactivity of carbenes

Atomic properties and the reactivity of carbenes PRESTON J.

MACDOUGALL' AND

RICHARD F. W. BADER

Department of Chemistry, McMaster University, Hamilton, Ont., Canada U S 4Ml

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Received November 26, 1985

PRESTON J. MACDOUGALL and RICHARD F. W. BADER. Can. J. Chem. 64, 1496 (1986). The properties of the atoms in a number of substituted carbenes and silylene provide an understanding of the relative stabilities of their lowest lying singlet and triplet states and of their differing chemical reactivities. The theory of atoms in molecules defines all of an atom's properties, including its energy. In this research one finds that the methylenic carbon or silicon atom is energetically most stable in the triplet state of each system, while the ligands are most stable in the corresponding singlet state. It is also found that the average electron populations of the carbon and silicon atoms are largest in the triplet states. In systems where the carbon or silicon atom bears a net positive charge, as found in CHNH2, CF2, and SiH2, the excess in the transfer of charge to the more electronegative ligands in the singlet states stabilizes the ligands more than it destabilizes the central atom. These systems have singlet ground states. The relative susceptibility of singlet and triplet carbenes to electrophilic and nucleophilic attack is determined by the properties of the Laplacian of the charge distribution. This quantity assimilates the model of localized electrons in terms of local concentrations of electronic charge. It also determines regions from which electronic charge is locally depleted. These regions are found to coincide with those where the lowest-lying vacant orbital is concentrated.

PRESTON J. MACDOUGALL et &CHARD F. W. BADER. Can. J. Chem. 64, 1496 (1986). Les propriCtCs des atomes dans un certain nombre de carbknes et de silylknes substituCs fournissent une base pour la comprkhension des stabilitks relatives de leurs Ctats singulet et triplet de plus basses energies ainsi que de leurs diverses rCactivitCs chimiques. La thCorie I'atome dans les molCcules dCfinit toutes les propriCtCs des atomes, y compris leur Cnergie. Dans cette recherche, on trouve que les atomes de carbone ou de silicium mtthylCniques sont, d'un point de vue CnergCtique, plus stable dans I'Ctat triplet de chaque systkme alors que les ligands sont plus stables dans 1'Ctat singulet correspondant. On a aussi trouvt que les populations Clectroniques moyennes des atomes de carbone et de silicium sont plus ClevCes dans les ttats triplets. Dans les systkmes les atomes de carbone ou de silicium portent une charge positive nette, comme dans ou CHNH2, CF2 et SiH2, l'excks dans le transfert de charge vers les ligands plus ClectronCgatifs des Ctats singulets a comme effet de plus stabiliser les ligands que de dCstabiliser l'atome central. Les Ctats fondamentaux de ces systkmes sont singulets. En se basant sur les propriCtCs de la distribution de charge de Laplace, on a dCterminC les susceptibilitCs relatives des carbknes singulet et triplet aux rCactions d'attaque Clectrophile et nucleophile. Cette fonction assimile le modkle des Clectrons 1ocalisCs en fonction de concentrations locales de la charge Clectronique. On dCtermine aussi les rCgions i partir desquelles la charge Clectronique est localement CpuisCe. On a trouvC que ces r6gions coi'ncident avec celles dont l'orbitale basse vacante est concentrke. [Traduit par la revue]

Introduction This paper relates the chemistry of carbenes and related compounds to the properties of their constituent atoms and the bonds which link them. The atoms and bonds are in turn defined in terms of salient properties of the charge distribution, properties that are determined by the forces acting within the system. Thus the concepts of atoms and bonds serve to both summarize the physics of a system and provide for its translation into the language of chemistry. The chemistry of a carbene is dependent upon its spin multiplicity (1). On the basis of chemical evidence methylene has been shown to have a triplet ground state (2a). This was in accord with Herzberg's earlier spectroscopic findings (2b). Difluoromethylene and silylene, SiH2, on the other hand, possess singlet ground states (3). This paper relates the relative stabilities of the singlet and triplet states to the properties of the central carbon or silicon atom and to the behaviour of the nonbonded charge concentrations in the valence shells of these atoms. These charge concentrations; two in a triplet and one in a singlet, are described not within an orbital model but rather in terms of a property of the total charge density, its Laplacian. The total charge density exhibits local maxima only at the positions of nuclei and its topology, while providing the basis for the definition of atoms and molecular structure (4), gives no indication of concentrations of charge as anticipated in terms of the Lewis electron pair model or localized orbital models of electronic structure. On the other hand, the Laplacian of a scalar 'TO whom all correspondence should be addressed.

function such as p, the quantity VZp, magnifies any local variations in the function. Just as energy changes of chemical interest are found to be only small fractions of the total energy of a molecular system, so chemically important properties are found to correspond to relatively small local variations in the charge density. These local variations in the otherwise smooth topology of p are translated by its Laplacian into the familiar model of localized bonded and nonbonded "electron pairs", i.e. local concentrations of electronic charge (5). When the Laplacian of p is negative at a given point in space (V2p < O),.it means that the value of p at that point is greater than the average of its values at all neighbouring points. A local maximum in -VZp thus means that electronic charge is concentrated or compressed in the region of the maximum. Correspondingly, a local minimum in - V2 p means that charge is locally depleted, or that the charge density is expanded in the region of theminimum. It must be borne in mind that stationary points in the Laplacian of p do not determine maxima or minima in p itself but rather the points where ele'ctronic charge is locally compressed (V2 < 0) or expanded (V2 > 0). Singlet carbenes are known to exhibit ambiphilic characteristics. It has been shown that the local charge concentrations and depletions, the lumps and holes in a charge distribution as defined by the Laplacian of p, determine the sites of electrophilic and nucleophilic attack, respectively (5). The sizes and shapes of these lumps and holes in the charge distributions of a variety of carbenes, silylenes, and vinylidenes are used to rationalize the predominance of either electrophilic or nucleophilic behaviour in these molecules.

MACDOUGALL AND BADER

TABLE1. Geometries and energies

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System

Geometrical parameters (deg, A)

E(HF) (hartrees)

C-Li = 1.924, 0 = 111.93 C-H = 1.072, 0 = 131.14 C-H = 1.099, 0 = 102.82 C-F = 1.304, 0 = 118.70 C-F = 1.283, 0 = 104.48 Si-H = 1.472, 0 = 118.15 Si-H = 1.510, 0 = 93.45 C-H1 = 1.078, C-N = 1.384, N-H2 = 0.999, LC(H1CN) = 125.43, &(CNH2) = 144.38, LC(HlCNH2) = 128.61 C-H1 = 1.098, C-N = 1.308, N-H2 = 0.997, N-H3 = 1.000, i$(HlCN) = 106.38, 4(HlCNH2(3)) = 119.35(125.80) C1-H1 = 1.073, C1-C2 = 1.385, C2-C3 = 1.390, LC(HlClC2) = 132.98, &(ClC2C3) = 124.81, C2-H2 = 1.079, C3-H4 = 1.074, C3-H5 = 1.076, LC(ClC2H2) = 117.15, i$(C2C3H4(5)) = 121.01(121.36) C1-H1 = 1.072, C1-C2 = 1.524, C2-0 = 1.233, C2-H2 = 1.090, LC(HlClC2) = 131.96, LC(ClC2H2) = 117.43, LC(ClC2O) = 122.88 C1-HI = 1.091, C1-C2 = 1.443, C2-0 = 1.192, C2-H2 = 1.108, &(HlClC2) = 110.96, &(ClC20) = 129.03, LC(ClC2H2) = 108.21, &(HlClC20) = -95.2, LC(HlClC2H2) = 88.9 C1-C2 = 1.495, C2-C3 = 1.478, C2-H1 = 1.078, LC(ClC2C3) = 59.26, g(ClC2Hl) = 116.05, LC(C3ClC2Hl) = 111.1

Calculations The results for the singlet states were obtained from single determinantal calculations using the 6-3 1G** basis set. Calculation of the triplet state functions used the same basis but employed the unrestricted SCF procedure (the 6-21G** basis was used for singlet and triplet SiH2). All geometries were optimized at either of these two levels of theory and the results are given in Table 1 . The bonds in CLi2 are ionic with little directional character and the bending force constant for this molecule is very small. The predicted geometries of such triatomic molecules are very dependent upon the adequacy of the basis set used to describe the negatively charged central atom.' With the addition of an extra set of diffuse s, p, and d functions on the C atom the CLi2 molecule in its triplet state is 2Grev and Schaefer (6) have found that two sets of d orbitals are necessary to properly describe the ground state of CSi2, which is bent. We have since calculated that the net charge on C in this molecule is -2.69 e. We employed their expanded basis set for C in our geometry optimization of triplet CLi2.

predicted to be bent with a bond angle of 1 1 1.9".The molecule is still a floppy one and the energy difference between the linear and equilibrium geometries is only 1.4 kcal/mol. Convergence difficulties were encountered in the calculation of the singlet state of this molecule, but it has been previously shown that the ground state of CLi2 is a triplet (7). The singlet state of formylmethylene is calculated to have a nonplanar geometry at the 6-31G** basis set as previously reported by Bouma et al. (8). We find a slightly lower energy for this state than that found by Bouma et al. ,-who state that with correlation, formylmethylene isomerizes to ketene. In the linear geometry of a carbene the 2p, and 2p, orbitals on carbon (the 3al and l b l orbitals, respectively, of the bent molecule) are degenerate and of n symmetry. With an increasing departure from linearity the 3al orbital becomes increasingly more stable than the 1bl orbital. Thus for linear or near linear geometries Hund's rule applies to yield a 3 E , or 3 ~ ground state from the configurations ... n 2 or ...3a11 bl . For a strongly bent geometry the ground state will be a singlet, ...3a2,

1

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CAN. J. CHEM. VOL. 64, 1986

'A,. Thus there is a close connection between the geometry and spin multiplicity of a carbene and one notes in Table 1 that the calculated bond angles of the triplet states are always larger than those of the singlets. A 'A' state is also obtained by double occupation of the l b l orbital and the ground state of a singlet carbene is better described in terms of a linear combination of these two lowest 'Al detenninantal state functions. A two-state CI calculation (at the single-state geometries) was carried out for CH2, CF2, and SiH2 to determine its effect on the properties of the electronic charge distribution. The contribution of the upper state to the total charge distribution was only a few percent in each case. While the effect on the singlet-triplet energy separation was significant, the quantitative changes in p amounted to only a few percent and qualitatively the charge distributions were left unaltered. These results are summarized in the Appendix. Our two configuration CI calculations impose the frozen orbital approximation. Two configuration SCF calculations which do not invoke this approximation give smaller singlet-triplet splitting energies, 22.0 and 12.8 kcal/mol for methylene (9, 10). The latter was obtained using a basis of quality similar to ours. A recent review emphasizes the sensitivity of the singlettriplet splitting to the level of theory used (1 1). Atomic properties and ground state multiplicities As has been demonstrated (12) and recently reviewed for the chemical reader (13), the atomic boundaries and the network of bonds are determined by the gradient vector field of the charge density (see Fig. 1). The atomic boundaries exhibit a zero flux in the gradient vectors of p and they thus satisfy the quantum condition for the definition of a subsystem with well-defined properties. Five atomic properties will be used in the present investigation: (a) atomic charge of atom R , q(R) is obtained by integration of p over the basin of atom R to obtain its average electron population N(R) followed by the subtraction of this average electron population from the nuclear charge, Zn , [I] q(R) = Za - Jnpd7 = Zn - N(R) (b) Atomic dipole p ( R ) is obtained by weighting the integration of p with the position vector r with origin at the nucleus of a , [21 ~ ( a =) Snrpd7 (c) Spin population S(R), is obtained by integrating the spin density u(r) = pa(r) - pP(r), the difference between the a-and P-spin densities, over the basin of R to give the average number of excess a electrons (if S(R) > 0)on atom R(14) (d) The degree of localization of the electrons on atom R and denoted by 1(R) is obtained by integrating the Fermi hole over the basin of the atom, F(R,R), and comparing it with the average number of electrons in the atom (15a) [41 F ( a 7 R ) = -Zi,i[Sn+i+jd712 Conceptually this is equivalent to averaging, over all reference coordinates within atom a , the extent to which the "exchange charge density" (15b) is contained within that atom. The limiting value of the integrated Fermi hole, F ( R , R ) , is -N(R). At this limit the N ( a ) electrons are completely localized on atom a , there is no exchange of these electrons-with

other electrons in the system and the fluctuation in the average population N(R) is zero. Thus the ratio IF(R,R)/N(R)I determines the fraction of the maximum possible localization and when multiplied by 100 determines the percent localization of the electrons on atom R , / ( a ) . (e) The energy of atom R , E(R), is most simply obtained by integrating the kinetic energy density over the atom to obtain its average kinetic energy, T(R). Since the atom is a quantum subsystem, the virial theorem applies and E ( R ) = - T(R) . 3 For equilibrium geometries, as is true here, the sum of the atomic energies equals the total energy of the molecule, We begin with a discussion of the atomic properties of the systems listed in Table 2. The ground states of CH2 and the systems listed above it are triplets, while those of the remaining systems are singlets. The charge distributions of CH2 and SiH2 shown in Fig. 1 serve to illustrate the definition of atomic boundaries and how the resulting atomic properties reflect the principal features of a charge distribution. There is an almost equal sharing of bonding density between C and H in saturated hydrocarbons, q(H) = -0.06 e in CH4. This remains true for the two states of methylene where the charges on H are of even smaller magnitude. In SiH2 there is a substantial transfer of charge from Si to H as is evident in the display of p; the distribution on H is expanded and more diffuse compared to that for CH2, and p is separately localized in each atomic basin to a greater extent in SiH2 than it is in CH2. This difference in the degree of localization of charge is quantified by the values of 1(R) (Table 2) which show that the electrons on the H atoms in SiH2 are 76% localized compared to a value of only 48% in CH2. The properties of p at the bond saddle point serve to characterize the nature of the bond (Table 3). The value of p at the bond saddle point, the quantity pb, tends to smaller values as the bonding tends towards the ionic limit. Thus pb is greater for CH2 than it is for SiH2 which in turn possesses a value greater than that for CLi2, for which the bonding is ionic. One notes that the remaining core density on each Li atom is highly localized (Table 2). Negative values of V2pb, the value of the Laplacian of p at the bond saddle point, indicate that the negative curvatures of p (those perpendicular to the bond) dominate the interaction. This behaviour is typical of a shared interaction such as is found in CH2 - charge is accumulated along the bond path as a result of the perpendicular contractions of p (5, 16). In SiH2, V2pb > 0 indicating that the Si-H interactions are dominated by the contractions of p away from the interatomic surface towards each of the nuclei. This behaviour is typical of bonds with substantial charge transfer and localized atomic distributions. The reader is again referred to Fig. 1 to appreciate the differing behaviours associated with a large pb and negative VZpbvalue and a low pb and positive V2pb value. There is considerable charge transfer from carbon to fluorine and nitrogen (Table 2) and the V2pb values for the C-F and

..

3~ecause the a~~roximate state functions used here do not satisfy the Hellmann-Feynman theorem, there are small net forces calculated for the nuclei at the equilibrium geometry. Thus the ratio IE/TI differs slightly from unity, The values of T ( a ) were multiplied by the 1~7~1 ,tio in order that the sum of the atomic energies would equal E.

These are small corrections, the ratios for the triplet and singlet states, respectively, are 1.om1 and 0.9991 for CH2, 1.0002 and 1 for SiH2.

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TABLE2. Atomic properties of carbenes YXY' LiCLi (T) HC(C1H=CH2) (T)

4(x)

q(y)

dy')

s(x)

s(y)

S(y')

+0.912 +0.075 (C'H, +0.074) (CH2, +0.002) +0.018 (C'H, 1.109) ( 0 , -1.091)

+ 1.984

+ 1.675

+0.008 +0.023

+1.754

+0.014

+0.008 (C'H, -0.442) (CH,, +0.746) (C', -0.314) ( 0 , +0.511) (H, +0.035)

+

-0.044 (C'H, + 1.287) ( 0 , -1.332) +0.028

(TI HCH

E(T)-E(S)t

(TI HC(NH2) (S) (TI

-0.044 -0.520 (N, - 1.330) (H, +0.405) -0.598 (N, - 1.448) (H, +0.425) -0.720

FCF (S) (TI HSiH (S)

AE(Yr)

p,(X)*

1(Y)

- 1.98

98% (Li)

0.33

0.90 -31

(S)

AE(X) AE(Y)

+ 13

+ 32

-75 -130

-116

+22 +29

+74

-0.776 -0.738 +4 -0.754

*Atomic dipoles in atomic units. I au = 2.542 D. A positive value for means the negative end of dipole is directed away from ligands. tAll energy differences are in kcal mol-' and all refer to E(trip1et state) - E(sing1et state). $The individual atomic contributions to AE from the formyl group are: AE(C1) = -59, AE(0) = +74, and AE(H) = -2 all in kcal mol-'.

-20

+12

+22

44% (H)

o

1.03 1.02

48% (H)

1.67

49%(H)

+ 12

$ 4u

+I14

+74

5

8c

0.30

$ 2

$5

1.90 3.13 2.48

95%(F)

2.56

76% (H)

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CAN. J. CHEM. VOL. 64, 1986

FIG. 1. Contour maps and corresponding relief maps of the singlet charge distributions in the plane of the nuclei for CH2 and SiH2. The same vertical scaling is used in the relief maps. The maxima in p at the positions of the C and Si nuclei are not shown. The black dots on the contour map denote the positions of the bond saddle points. Also shown are the bond paths and the atomic boundaries defined by the interatomic surfaces. AS illustrated in the relief maps, the value of p at a bond saddle point pb, is the minimum value attained by p along the bond path and the maximum value attained in the interatomic surface. A bond path and its associated surface are defined respectively by the gradient vectors of p which originate and terminate at the bond saddle point. The contour values in au are 0.002,0.004, and 0.008 increasing by powers of 10 to a maximum value of 20 au.

C-N bonds indicate that these interactions are dominated by a contraction of charge towards each of the nuclei. These interactions are, however, not ionic but very polar shared interactions as indicated by the relatively large values of p,. Essentially all of the unpaired spin density is localized on the carbon atom in the triplet states of CLi2 and CH2. There is a small excess in the transfer of P-spin density compared to a-spin density to the carbon atom in these systems with the result that the ligands have small net a spin populations. In CHNH, , CF2, and SiH2 there is a significant delocalization of the spin density

onto the ligands as a result of the transfer of charge to the ligands from the carbon and silicon atoms in these molecules. There is also a significant delocalization of the spin density in fomylmethylene and vinylmethylene into the CH=O and CH=CHz fragments. Since there is no net transfer of charge from the methylenic carbon in these two molecules, the spin delocalization is accomplished through a spin polarization rather than by a transfer of charge. From the data given in Table 2 it is seen that the spin populations of the methylenic carbons are reduced from the value of two. Negative spin populations, approximately

:

MACDOUGALL AND BADER

TABLE 3. Bond properties and reactivity sites

System CLiz (T) HCC1H=C"H2 (T) HCCrH=O (T)

Bond

pb

au

VZpb au

C-Li C-H C-C' C'-C" C-H C-C'

~t

Nonbonded maxima VZp au

Hole in VSCC Width* au

VZp au

No hole No hole No hole

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c1=o

HCNH2 (S) (cis) (trans) CFz (TI

(9

SiHz (T) (S)

C'-H C-H C-C' Cf=0 C' -H C-H C-H H-C C-N N-H H-C C-N N-H N-H C-F C-F Si-H Si-H

1.3

No hole 1.4 1.2 1.3

1.6 1.8 4.1 3.2 -

tl indicates major axis is perpendicular to the plane of the Y-X-Y' nuclei. In singlet formylrnethylene the major axis of the C'=O bond is perpendicular to the plane of the formyl group. All other bonds have their major axis in the Y-X-Y' plane. *There are two such holes in the singlet states of all systems, while only one in the triplet states.

equal to the reduction in S(C), are present on the adjacent carbon atoms. The terminal oxygen and carbon atoms again have positive spin populations. The presence of alternating net spin populations on neighbouring atoms as a mechanism for spin delocalization has been previously noted (14). This mechanism is different from that operative in the amino- and difluoromolecules where there is a simple transfer of charge and all the atoms exhibit spin populations of the same sign. The final property listed in Table 3 is the bond ellipticity E defined as E = (A1/A2 - 1) where A, and h2 are the magnitudes of the two negative curvatures of p at the bond saddle point with XI > h2 (17). When these two curvatures are not equal, the charge density in the interatomic surface falls off from its maximum value at the saddle point more slowly in the plane containing the smallest of the two curvatures, indicating that charge density is preferentially accumulated in this particular plane. The C=C bond in ethylene, for example, has E > 0 and the axis of the smaller curvature lies in the plane perpendicular to the plane of the nuclei - charge density is preferentially accumulated in the plane of the "T"orbital. The data in Table 3 indicate that the charge of the methylenic bonds is preferentially accumulated in the plane of the nuclei in the singlet molecules and in the plane perpendicular to this for all of the triplet molecules. A carbon-carbon bond order n can be defined in terms of the value of pb (17), giving n = 1, 2, 3, respectively for ethane, ethylene, and acetylene. In terms of the bond order and bond ellipticity parameters, one can show that in addition to the spin polarization present in the formyl- and vinylmethylenes, there is

an essentially complete delocalization of the n density in these systems. The two C-C bonds in vinylmethylene have equal bond orders of 1.6 and similar ellipticities with their major axes in the 7~ plane.'The C-C bond order in the triplet state of formylmethylene is 1.5 again indicating a delocalization of the 7~ density. The spin populations, bond orders, and bond ellipticities indicate that vinylmethylene is best described as a vinyl radical with an extra unpaired and localized a electron resulting from the loss of a terminal hydrogen atom. Hutton et a1. (18) have arrived at the same description of this molecule on the basis of its esr sDectrum. The perturbation of the nonbonded charge density on carbon is minimal in the methylene systems because of the essentially equal sharing of the bonding charge density between the C and H atoms. his is reflected in the near zero atomic charges on carbon in these systems and in their small atomic dipoles. Hence the triplet state is of lower energy than the singlet state for methylene because of Hund's rule, as it is for the carbon atom itself. Indeed the singlet-triplet energy gaps are of the same order of magnitude for the two systems. The relative singlettriplet stabilities in the remaining systems will be discussed by comparing the properties of their charge distributions with those for the two corresponding states of CH2. The single most distinguishing feature of the examples listed in Table 2 relative to methylene is the extent and direction of charge transfer. A transfer of charge from the ligands to the carbon as in CLi2 leaves the triplet as the ground state. When charge is transferred to the ligands as in CHNH2, CF2, and SiH2, the singlet state is more stable than the triplet. In the two

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CAN. 1. CHEM.VOL. 64, 1986

remaining systems where the methylenic carbon is bonded to another carbon atom, the net charges on C are similar to those found in CH2 itself and the triplet states are again the ground states. One notes as well that the central carbon and silicon atoms of the triplet states are more electronegative than they are in the corresponding singlets; q(C) is more negative for the triplet than for the singlet state in every system listed in Table 2. The energies listed in Table 2, A E ( a ) , are the differences in the atomic energies between the triplet and singlet states for each molecular system. We first discuss the systems with a charge transfer from carbon or silicon to the ligands. In each of these systems the central atom is most stable in the triplet state and its energy change is the largest of the atoms in the molecule. The ligands, on the other hand, are most stable in the singlet states. These relative atomic stabilities parallel the differences in the average atomic populations between the triplet and singlet states. The populations for C and Si are largest in the triplet states while those for H, N, and F are largest in the singlet states. In the CHNH2, CF2, and SiH2systems the excess in the transfer of charge to the more electronegative ligands in the singlet states stabilizes the ligands more than it destabilizes the less electronegative central atom and the singlet states are most stable. Given the differing populations in these systems, the favoured state is the singlet as the largest amount of negative charge is placed on the most electronegative atoms in this state. The singlet-triplet atomic charge and energy differences for formylmethylene follow the same patterns as those already discussed if the formyl group is considered as a single entity. Within this group there is a significant charge transfer from the carbon to the oxygen atom. The oxygen atom has its largest electron population and lowest energy in the singlet state and behaves as do the ligands discussed above. The formyl carbon, however, possesses a larger population and its lowest energy in the triplet state, both differences being greater than for the methylenic carbon. As discussed above there is a polarization of the spin density and a delocalization of the a density in this molecule and in the related vinylmethylene. This delocalization of the charge density and the accompanying alternation of the spin population leads to a greater stabilization of the two neighbouring carbon atoms in the triplet states of these unsaturated carbenes than it does to the terminal carbon and oxygen atoms in the corresponding singlet states, and the ground states are triplets. The methylenic carbon always possesses a larger electron population and lower energy in the triplet than in the singlet state of a carbene. From the examples studied here it is found that the triplet is the ground state when carbon bears a net negative charge. Thus this extra stabilization of the methylenic carbon in the triplet state dominates the total singlet-triplet energy difference when the net charge on carbon is negative. When there is a substantial transfer of charge to the ligands and carbon bears a net positive charge, the ground state is a singlet. Previous workers have attributed a triplet ground state in vinylmethylene to a delocalization of a density and a singlet ground state in systems with ligands possessing unshared pairs of electrons as in CFz to a back-donation of the a density (19-21). This latter argument does not account for the existence of a singlet ground state in SiH2. Harrison et al. (22) have proposed that electronegative substituents differentially stabilize singlet carbenes, while electropositive substituents stabilize triplet carbenes. It has also been argued that a donors stabilize the singlet more than the triplet, while a acceptors have the opposite effect (23).

The orbital model of a back-donation wherein an electronegative atom such as fluorine or nitrogen donates electronic charge to a less electronegative atom such as carbon is not apparent as such in the properties of a total charge distribution. For example, a back-donation is predicted to occur in the singlet states of CF2 and CHNH2 and yet the methylenic carbon has a larger electron population in the triplet than in the singlet states of these two systems. Also, as noted in Table 3, the ellipticities of the C-F and C-N bonds in the singlet molecules have their major axes in the plane of the nuclei, opposite to what is found for bonds with partial a character. It is a general observation that in a bond X-Y with significant charge transfer from X to Y there is a polarization of both atomic charge distributions in the direction counter to the direction of the charge transfer (24). What one observes is that the magnitude of the atomic back-polarization on Y parallels the anticipated consequences of the a back-donation model. Thus, the magnitude of p(Y) is largest when there is an orbital vacancy on X; in CH3F, p(F) = 0.32 au while in singlet CF2, p(F) = 0.52 au. Also, within the carbene series, p(F) and p(N) are larger in the singlet states than in the triplets (Table 4). The a-donation model is invoked to account for unusually short X-Y bond lengths and the data in Table 4 show that the state, singlet or triplet, with the shortest X-Y bond also has the largest value for p(Y). In CF2 or CHNHz this is the anticipated singlet state while in SiH2, where the ligand has no unshared electrons, it is the triplet. However, the polarization of H is of the same magnitude as the others despite this difference. The triplet ground states of formyl and vinylmethylene have been accounted for in terms of the a-acceptor model (23). As already noted, the present theory provides a quantitative assessment of both spin and charge delocalization through the assignment of corresponding atomic populations, bond orders, and bond ellipticities. As demonstrated below, the properties of the Laplacian of p provide the mechanism underlying the atomic back-polarizations and charge delocalizations. Valence charge concentrations and ground state multiplicities The Laplacian of p for a free atom reflects the quantum shell structure by exhibiting a corresponding number of alternating pairs of regions of charge concentration (V2p < O), and charge depletion (VZp> 0) beginning with a spike-like concentration at the nucleus. Upon bonding, local maxima and minima are formed in the valence shell of charge concentration (VSCC) and the number of resulting bonded and nonbonded maxima thus formed are in general agreement with localized models of electronic structure. The local concentrations of charge in the valence shell of an atom as determined by the Laplacian of p mimic not only the model of localized bonded and nonbonded pairs, they also reflect the presence of local concentrations of unpaired electrons. In Fig. 2 the Laplacian distribution for triplet CF2exhibits two distinct maxima on the carbon atom in the symmetry plane perpendicular to the plane of the nuclei. The singlet state of the same molecule exhibits a single nonbonded maximum on carbon. The magnitude of this single maximum (corresponding to the model of a localized electron pair) is larger than the two identical maxima present in the triplet state, each of which models a single unpaired electron. The values of the nonbonded maxima in the Laplacian of p are given in Table 3. Similar observations apply to the other pairs of molecules listed in Table 3 (Fig. 3) with the exceptions of CHCH=O and CHCH=CH2. In these molecules the triplet states exhibit a single nonbonded

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FIG. 2. Displays of the Laplacians of the charge distributions for the triplet and singlet states of CF2. The lower diagrams are for the plane of the nuclei, the upper ones for the perpendicular symmetry plane containing the C nucleus. The function plotted is -V2p, a maximum in this function denoting a maximum in the concentration of charge. The core or first quantum shell of each atom exhibits a spike-like charge concentration at the nucleus surrounded by a deep region of charge depletion. This is followed by the valence shell of charge concentration (VSCC) and the outer or valence region of charge depletion. The VSCC of carbon in the triplet state shows two bonded maxima and two nonbonded maxima in the perpendicular plane. The p i n t labelled a in the lower diagram is not a maximum. It is another view of the saddle point a between the nonbonded maxima. The VSCC of carbon in the singlet state also shows two bonded maxima but only a single, larger, nonbonded maximum. The point labelled h and its mirror p i n t are positions where the VSCC on carbon has been broken. There is no radial maximum or lip defining a shell at these pints. The maxima present in the VSCC's of the F atoms are not shown as they are larger by a factor of ten than those on the carbons.

0

w

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CAN. 1. CHEM. VOL. 64, 1986

u A-A FIG. 4. Contour plot of the Laplacian of p for the triplet state of vinylmethylene; in the plane of the nuclei (upper diagram) and the cross-section, A-A, through the divalent carbon. The dots denote the bonded and the single nonbonded maximum in charge concentration. FIG. 3. Contour plots of VZpin symmetry planes perpendicular to the planeof the nuclei containing the C or Si nucleus. For the triplets (a) CLi2,( b )CH2, ( c )CF2, and (d) SiH2and for the singlets (e) CH2, (f) CF2, and (g) SiH2. The right-hand side of each figure corresponds to the nonbonded side of the C or Si atom. Dashed lines denote negative values - regions where charge is concentrated. Solid lines denote positive values - regions of charge depletion. Each dot denotes a maximum in -V2p, a maximum in charge concentration. Each triplet state exhibits two and each singlet one such maxima in this plane. Figures ( c ) and (f) are the contour maps corresponding to the top two relief diagrams of Fig. 2. Contour values in au are k0.002, k0.004, 20.008 increasing in powers of 10 up to k8.0. maximum (Fig. 4) as a result of the delocalization of the n density into the CH=CH2 and CH=O fragments. We begin with some general observations. The nonbonded maxima in the singlet states are considerably larger than those in the tiplet states. In those molecules which have a triplet ground state there are no regions of charge depletion (or holes as we shall refer to them) in the VSCC and the nonbonded maxima are not p r o n ~ u n c e d This . ~ behaviour is typified by the methylenic carbon in vinylmethylene as illustrated in Fig. 4. The delocalization of the valence charge concentration is most pronounced in the triplet state of CLi2 where the C atom bears a large net 4The magnitude of V2p at the intervening saddle points is only a few percent less than its value at the maxima, and the extrema are not pronounced.

negative charge (Fig. 3a). The VSCC is also polarized towards the ligands in this molecule to the extent that what correspond to nonbonded maxima in the other examples are now maxima on the bonded side of the molecule. The nonbonded charge in the singlet states of these molecules on the other hand is very localized (Fig. 3e) with the result that regions of charge depletion or holes are also present in the VSCC of the methylenic carbon in the singlet state, in accord with their ambiphilic nature. For the molecules which have singlet ground states, the nonbonded maxima are large and very pronounced in both the singlet and triplet states of each system as illustrated for CF2 in Fig. 2. In these systems the ligands bear substantial negative charges and the methylenic carbon atom is strongly polarized into its nonbonded region, more so in the singlet than in the triplet states (see p(C) values in Table 2). Correspondingly the single nonbonded maximum in the singlet is approximately twice the magnitude of either maximum in the triplet. Thus as a consequence of the charge transfer to the ligands, the nonbonded charge concentrations on carbon are localized and holes are present in the VSCC's in both the singlet and triplet states of these molecules. In summary, in carbenes where the methylenic carbon is neutral or negatively charged, there is a delocalization of the nonbonded charge concentration in the triplet state while the nonbonded charge concentration is localized in the singlet state. In these systems the ground state is the delocalized triplet. In carbenes where there is a substantial charge transfer to the

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ligands the VSCC of the methylenic carbon is very localized into bonded and nonbonded charge concentrations in both the triplet and singlet states. The localization is greatest in the singlet states and these are the ground states in such systems. Substituent effects on chemical reactivity The extent of atomic back-polarization of Y in an X-Y bond can be rationalized in terms of the properties of the Laplacian of p. Of interest is the case where Y has unshared pairs of electrons, such as fluorine. In an axially symmetric system such as H-F, fluorine exhibits a uniform nonbonded torus of charge concentration subtending an angle at the nucleus of 101.2'. The manner and extent to which this torus of nonbonded charge is polarized in a system without axial symmetry is determined by the properties of the VSCC of the bonded neighbour, X. If X does not possess an orbital vacancy then its VSCC does not exhibit any pronounced regions of charge depletion. In this case the polarization of the nonbonded torus of charge concentration of F is very slight and the small maxima induced in the torus are staggered with respect to the bonded maxima on X.* In ClF5 for example, the axial F exhibits four nonbonded maxima which are staggered with respect to the four bonded maxima on the C1 atom. In CH3F, fluorine has three nonbonded maxima which are staggered with respect to the three bonded maxima on carbon. The maxima induced in the nonbonded torus by these polarizations exceed in value the resulting minima in V2p by less than 1.O% and correspondingly, the atomic back-polarization of F is relatively small. In the case where X possesses an orbital vacancy the polarization of the nonbonded torus on F and the resulting back-polarization of its density are very pronounced. In the singlet state of CF2, the VSCC on carbon exhibits two pronounced holes so positioned as to mimic a vacant p n orbital, Fig. 3c. The VSCC of carbon in a carbocation exhibits the same pattern of charge depletion. In singlet CF2 the density on F, including the nonbonded torus of charge concentration, undergoes significant polarization towards the regions of charge depletion on carbon. The result is the formation of two minima and two maxima in the nonbonded torus. Since the minima result from the polarization of the nonbonded charge towards the holes on carbon, the nonbonded maxima on fluorine now eclipse the maxima on carbon. These are large effects; the resulting nonbonded maxima on fluorine exceed the minima in the nonbonded torus of charge concentration by 25% and the atomic dipole is large (Table 4). This situation parallels the model of n back-donation, but as previously noted there is only a polarization of the atomic charge on Y, not a transfer back to the vacancy on X. The VSCC of carbon in triplet CF2 has regions of charge depletion in the plane of the nuclei (Figs. 2 and 3 c ) . The nonbonded torus on F undergoes a similar to that in the singlet state, but to a lesser extent. The resulting nonbonded charge maxima exceed the minima by 8% and they again eclipse the nonbonded maxima on carbon which are above and below the plane of the nuclei in this case. The atomic polarization on F is also less than in the singlet state. In the orbital model of a triplet carbon every orbital on carbon is at least singly occupied and hence no n back-donation is expected. The Laplacian of p, by indicating the presence of regions of charge depletion on carbon, does correctly anticipate atomic back-polarization in

'~remer and Kraka (25) have proposed that the staggered conformation results from maximum avoidance of vicinal bonded charge concentrations.

TABLE 4. Bond distances and atomic dipoles YXY' cF2 (s) CF2 (TI HCNH2 (S) HCNH2 (T) SiH2 (S) SiH2(T)

R(X-Y') 1.283 1.304 1.308 1.384 1.510 1.472

A

CL(Y')au 0.524 0.414 0.518 0.230 0.418 0.452

RG.5 . Contour diagrams of V2p with bond paths and interatomic surfaces overlayed. These are planes perpendicular to the planes of the nuclei, containing one of the bond axes. For (a)singlet CF2,( b )singlet SiH2, and ( c ) singlet CHNH2. The arrows indicate the effect of back-polarization on the interatomic surfaces. In the absence of strong back-polarization, as in CH3For CH3NH2,the surfaces are not pushed in the direction indicated by the arrows. the triplet case. Since the holes on carbon are less pronounced in the triplet than in the singlet state, the extent of polarization is less. These same mechanisms are operative in the CHNH2 system. In the singlet state of this molecule the -NH2 group is planar so as to align the nonbonded charge concentration on nitrogen with

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CAN. J . CHEM.VOL. 64, 1986

TABLE 5. Structural and atomic properties of cyclic carbenes

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System

Bond

V2pb au

E

t

Nonbonded maximum n

q(a)

p(C1) *au

V2p au

Hole in VSCC Width au

V2p au

*I au = 2.542 D, a positive p value means that the negative end of the dipole is directed away from the ligands. t l indicates that the major axis is perpendicular to the plane of the ring. All other bonds have their major axis in the plane of the ring.

the n-like region of charge depletion on carbon. The nitrogen is polarized towards carbon to such an extent that it no longer possesses a nonbonded charge concentration and its atomic dipole is large, Table 4. In triplet CHNH2 the nitrogen atom is pyramidal and possesses a nonbonded charge concentration as does N in NH3 (5). The VSCC of carbon in the triplet state has a nuclei region of charge depletion in the plane of the H-C-N and the nonbonded charge concentration on N is aligned with it. As with CF2, the polarization of the ligand is less pronounced in the triplet than in the singlet. The shape of the interatomic surface illustrates the effect that such back-polarization has on an X-Y bond (Fig. 5). It is observed that the bulging in these interatomic surfaces is not axially symmetric, but that in the singlet states it is more pronounced above and below the plane of the nuclei. It is also observed that the extent of bulging increases as p(Y) increases. In ref. 5 it was proposed that nonbonded maxima in -V2p(r) are sites of electrophilic attack and points of maximum charge depletion in the VSCC are sites of nucleophilic attack. It is generally found that VSCC 's of atoms with incomplete valence shells, such as C in carbenes, do not completely envelope the nucleus. In Fig. 2 any radial line from the C nucleus in triplet CF2 passes through a maximum as it crosses the VSCC, but in the case of the C atom in singlet CF2 there exist radial paths which do not pass over such a "lip". As a result a critical point corresponding to a point of maximum charge depletion in the VSCC does not exist. To characterize the susceptibility of such atoms to nucleophilic attack we report (Tables 3 and 5) the width of the hole in the VSCC. This measurement is illustrated in Fig. 3e. We also report the value of V2p at the hole center. To characterize the susceptibility of the divalent atoms to electrophilicattack, the values of V2p at the nonbonded maxima are reported in Tables 3 and 4. The triplet states of CH2 and CLi2 do not exhibit regions of charge depletion in the VSCC's of the methylenic carbon atoms. Hence the triplet states of these molecules are not susceptible to attack by nucleophiles. They are, however, very susceptible to attack by electrophiles. The delocalized nature of the nonbonded charge concentration in these molecules indicates that it is easily polarized, thereby accounting for their reactive nature

towards electrophiles. As pointed out earlier, singlet carbenes have both lumps and holes in their VSCC's, making them susceptible to both electrophilic and nucleophilic attack (Fig. 3). The singlet states of carbenes in which charge is transferred to the ligands are found to be less susceptible to nucleophilic attack than singlet CH2 (26). The arrow in Fig. 3f indicates that the direction of approach of a nucleophile to the VSCC of the C atom in singlet CF2 is at an acute angle to the C-F bond axes. The resulting electron-electron repulsion between the approaching nucleophile and the negatively charged F atoms creates a barrier to nucleophilic attack. This same argument applies to singlet SiH2 and singlet CHNH2. Sosa and Schlegel have calculated that indeed the singlet states of CF2 and SiH2 have high insertion barriers relative to that of singlet CH2, and that the angle of approach is as described above for both CF2 and SiH2 (27). The small hole width and completion of the VSCC of the C atom in singlet CHNH2 indicate it is less susceptible to nucleophilic attack than singlet CH2, even before ligandnucleophile repulsions are considered. The delocalization of spin and charge density in a,@-unsaturated methylenes was previously discussed. As mentioned, these systems are best described as biradicals with one of the unshared electrons delocalized into the .rr system. Thus, the reactivity of these systems will be free radical-like. As a result of the presence of a single nonbonded charge concentration (Fig. 4), they are predicted to be less reactive than alkylmethylenes which have two such maxima. Singlet formylmethylene has been predicted to rearrange easily to ketene via an intramolecular aC-H insertion (8). This rearrangement is foreshadowed by the alignment of the aC-H bond with the hole in the VSCC of the divalent C atom and the unusually small angle this bond makes with the C-C bond axis, 108.2" compared to 117.4' in the triplet state. This is an example of a singlet carbene with a ligand which possesses no unshared electrons. In the absence of an unshared pair the density of the C-H bond is polarized towards the hole in the VSCC of the methylenic carbon, as indicated by its low p, value (Table 5). This behaviour is analogous to hyperconjugation in carbocations (17). The reactivity of the singlet states of two cyclic carbenes and a vinylidene (Table 5) are considered next. Others have shown

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MACDOUGALL AND BADER

I

FIG.6. Contour plots of V2p. Local maxima in -V2p are denoted by solid circles. (a) The symmetry plane bisecting the ring in cyclopropylidene. Note the delocalization of charge into the center of the ring. ( b )A similar plane in cyclopropenylidene. The triangle indicates a critical point in the VSCC of the methylenic carbon atom corresponding to a site of nucleophilic attack. There is a mirror site as well. ( c )The plane containing the ring nuclei in cyclopropylidenecarbene. The sites of nucleophilic attack on the methylenic carbon are also in this plane. (d)The plane containing the T bond in cyclopropylidenecarbene.

that they possess singlet ground states (20,28). Considering the small bond angle in three-membered ring carbenes (59.3" in cyclopropylidene and 55.4" in cyclopropenylidene), one can account for the singlet ground states of these systems by recalling that the 3a, orbital becomes increasingly more stable relative to the 1bl orbital as B(RCR) decreases. Note that in the latter two examples in Table 5 there is significantcharge transfer from the methylenic C atom to its neighbouring atom(s). Hence the singlet ground states of these systems agree with the charge transfer argument as well. In cyclopropylidenethe two types of C-C bonds differ only slightly from the C-C bond in cyclopropane for which n = 0.99 and E = 0.49. On the basis of the data in Tables 3 and 5, the reactivity of the methylenic carbon in cyclopropylidene is predicted to be similar to that of singlet CH2; susceptible to both nucleophilic and electrophilic attack. A comparison of Figs. 3e and 6a illustrates this similarity. Cyclopropenylidene has been predicted to be unreactive towards nucleophiles (29). The bond orders given in Table 5 indicate that there is some delocalization of charge in this system. The effect of this on the VSCC of the methylenic C atom is illustrated in Fig. 6b. In this case there is a point of maximum charge depletion in the VSCC of the methylenic C atom, that is, a critical point in VZp.Because of this delocalization, charge is much less depleted at this point than in other carbenes. Thus one would predict cyclopropenylidene to be even less susceptible to nucleophilic attack than singlet CHNH2, for example. Even though the data in Table 5 predict the nonbonded charge concentration on cyclopropylidene to be similar in reactivity to that of cyclopropenylidene, nucleophilic

behaviour will be dominant in the latter because of its greater selectivity as an electrophile (26). The final example is cyclopropylidenecarbene. This vinylidene has an unusually short C2=C1: bond (1.275 A) and a correspondingly high bond order (n = 2.60). The partial triple-bond character of the Cl-C2 bond arises from conjugation with the three-membered ring (17). This is suggested by the reduction in the bond order of the adjacent C-C bonds, n(C2-C3) = 0.932. The extent of charge concentration in the .rr plane (Fig. 6d) illustrates the highly nucleophilic nature of this C=C: fragment (30). Figure 6c shows the plane containing the hole in the VSCC of the methylenic carbon atom, VZpat the hole center = + 0.4, roughly that for singlet CH2. However, the hole width is extremely small resulting from the extent that the bonded and nonbonded charge concentrations cover the VSCC, reducing the size of the region a nucleophile can attack.

Conclusions 1. We find the energy of the central atom to be lower in the triplet state while the energy of the ligand is lower in the singlet state. It is also found that the average electron population of the central atom is largest in the triplet state. As a result, transfer of charge to the ligands preferentially stabilizes the singlet state while transfer of charge to the central atom stabilizes the triplet state. We expect these observations to remain valid at higher levels of theory. The trend is supported by performing a twostate CI calculation on singlet methylene, for which AE(C) = -68 kcal/mol and AE(H) = 2 1 kcal/mol (cf. Table 2). These observations allow one to rationalize, non-empirically, the

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CHEM. VOL. 64, 1986

ground state multiplicities of simple carbenes in terms of welldefined atomic properties. 2. The orbital model of IT back-donation is found t o b e inconsistent with the observed properties of the charge density. Instead, back-polarization of negatively charged ligands is found to b e the operative mechanism that accounts for the trends in X-Y bond lengths (Table 4). 3. In unsaturated carbenes it is found that spin polarization, and not charge transfer, stabilizes the triplet states. 4. Finally, the properties of the Laplacian distribution allow one to discuss carbene reactivity in terms of an observable property directly related t o the energetics of the system. A previous model based on electronegativity (22) was deemed "unnecessary in understanding substituent effects on S T (singlet-triplet) gaps" in the publication of a more recent model. The latter model was based on empirical IT-acceptor and IT-donor indices derived from Mulliken population analyses (23). O n the basis of conclusions 1, 2 , and 3 above, the latter model is unnecessary also.

Acknowledgements Acknowledgement is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. One of us (P.J.M.) wishes to thank the Xerox Research Centre of Canada for the award of a Graduate Research Fellowship. 1 . P. S. SKELLand R. C. WOODSWORTH. J. Am. Chem. Soc. 7 8 , 4496 (1956);7 8 , 6427 (1956);81, 3383 (1959). 2. ( a ) F. A. L. ANET, R. F. W. BADER,and A.-M. VAN DER AUWERA.J. Am. Chem. Soc. 82,3217 (1960);R. F. W. BADER and J. I. GENEROSA. Can. J. Chem. 43, 1631 (1965); ( b ) G. HERZBERG. Proc. R. SOC.London, Ser. A, 262, 291 (1961). 3. C. W. BAUSCHLICHER, H. F. SCHAEFER, I n , and P. S. BAGUS. J. Am. Chem. Soc. 99,7106 (1977);M. E. COLVIN,R. S. GREV, H. F. SCHAEFER, HI, and J. BICERANO.Chem. Phys. Lett. 99, 399 (1983). and A. J. DUKE.J. Am. 4 . R. F. W. BADER,S. G. ANDERSON, Chem. Soc. 101, 1389 (1979);R. F. W. BADER,T. T. NGUYENDANG,and Y. TAL.J. Chem. Phys. 7 0 , 4316 (1979). and C. D. H. LAU.J. Am. 5 . R. F. W. BADER,P. J. MACDOUGALL, Chem. Soc. 106, 1594 (1984). HI. J. Chem. Phys. 82,4126 6 . R. S. GREVand H. F. SCHAEWR, (1985). and J. F. HARRISON. J. Am. Chem. Soc. 104,3827 7 . A. MAVIUDIS (1982). 8. W. J . BOUMA,R. H. NOBES,L. RADOM,and C. E. WOODWARD. J. Org. Chem. 47, 1869 (1982). 9 . J . H. MEADOWS and H. F. SCHAEFER, In. J. Am. Chem. Soc. 98, 4383 (1976). and I SHAVITT. J. Am. Chem. Soc. 100, 10. C. W. BAUSCHLICHER 739 (1978). 1 1 . I. SHAVITT.Tetrahedron, 41, 1531 (1985). 12. R. F. W. BADER,T. T. NGUYEN-DANG, and Y. TAL.Rep. h o g . Phys. 44,893 (1981);R. F. W. BADERandT. T. NGUYEN-DANG. Adv. Quantum Chem. 14, 63 (1981).

13. R. F. W. BADER.ACC.Chem. Res. 18, 9 (1985). 14. R. F . W. BADERand R. A. GANGI.J. Am. Chem. Soc. 93, 1831 (1971);R. F. W. BADER,M. E. STEPHENS,and R. A. GANGI. Can. J. Chem. 55, 2755 (1977). 15. ( a ) R. F. W. BADERand M. E. STEPHENS. J. Am. Chem. Soc. 97, 7391 (1975);( b ) J . C. SLATER.Quantum theory of atomic structure. Vol. 11. McGraw-Hill, New York. 1960. 16. R. F. W. BADERand H. ESSBN.J. Chem. Phys. 80, 1943 (1984). 17. R. F. W. BADER,T. S. SLEE,D. CREMER, andE. KRAKA.J. Am. Chem. Soc. 105, 5061 (1983). 18. R. S. HUTTON, M. L. MANION,H. D. ROTH, and E. J. WASSERMAN. J. Am. Chem. Soc. 96,4681 (1974). 19. R. GLEITERand R. HOFFMANN. J. Am. Chem. Soc. 90, 5457 (1974). 20. N. C. BAIRDand K. F. TAYLOR.J. Am. Chem. Soc. 100, 1333 (1978). J . Chem. Soc. Chem. Cornrnun. 688 (1980). 21. L. PAULING. R. C. LIEDTKE,and J. F. LIEBMAN.J. Am. 22. J . F. HARRISON, Chem. Soc. 101, 7162 (1979). 23. P. H . MUELLER,N. G. RONDAN,K. N. HOUK,J. F. HARRISON, D. HOOPER,B. H. WILLEN,and J. F. LIEBMAN.J. Am. Chem. SOC.103, 5049 (1981). 24. R. F. W. BADERand W. H. HENNEKER. J. Am. Chem. Soc. 87, 3063 (1965);R. F. W. BADER,P. M. BEDDALL, and P. E. CADE. J. Am. Chem. Soc. 93, 3095 (1971). andE. KRAKA.J. Am. Chem. Soc. 107,381 1 (1985). 25. D. CREMER 26. R. A. Moss. Acc. Chem. Res. 13, 58 (1980). J. Am. Chem. Soc. 106, 5847 27. C. SOSAand H. B. SCHLEGEL. (1984). 28. J . W. KENNEY,I n , J. SIMONS,G. D. PURVIS,and R. J. BARTLETT. J. Am. Chem. Soc. 100, 6930 (1978). 29. T. J . LEE, A. BUNGE,andH. F. SCHAEFER, III. J. Am. Chem. SOC.107, 137 (1985). 30. P. J . STANG.Chem. Rev. 7 8 , 383 (1978).

Appendix Effect of two state CI on properties of singlet CH2

Value property

One configuration

Two configurations

E('T) - E(OS) E(Os) 9(H) C-H bond

-30.86 kcal/mol* -38.8763 au -0.0473 e

-26.72 kcal/mol -38.8829 au -0.0438 e

Pb V 2 ~ b

E

- 1.1225 au

0.2905 au 0.1746

0.2899 au -1.1182 au 0.1628

- 1.5537 au

- 1.4696 au

Nonbonded charge concentration v2p(r)

*This value reduces to -27.7 kcal/mol when E('T) is obtained from a restricted open-shell calculation rather than from UHF. This value compares favourably with thevalue -26.2 kcal/mol obtained in ref. 10 whichused a basis set of similar size, but with different exponents for the d functions in the singlet and triplet states.