FROM CURRENT LITERATURE

ON THE PARTICIPATION OF THE 3$d$ ORBITALS OF THE CARBON ATOM IN THE FORMATION OF INTERATOMIC BONDS

Recently, Jilinski[^1] considered the question of the possible participation of the 3$d$ orbitals of the carbon atom in the formation of chemical bonds in molecules. Before setting forth the content of this work, it is useful to recall the following.

As is known, when a molecule is formed from atoms, the configuration of their electron shells changes to a greater or lesser degree under the influence of interatomic interaction. This change in electronic configuration, called the transition of the atom to the valence state, determines, in particular, the geometry of the molecule. The new configuration depends first of all on the properties of the electron shell of each individual atom, as well as on the character of their interaction. Theoretically, as a first approximation one may confine oneself to considering which valence states of each of the atoms taken separately are most probable. By further consideration of the entire molecule as a whole, the configuration that is closest to the actual one must be selected. This is done for the most part by comparison with experimental data. In the next approximation, corrections must be introduced that additionally take account of the mutual influence of the atoms.

In such a calculation of a molecule, usually already in the first approximation the wave function of the system is constructed so as to reproduce correctly the geometrical configuration of the molecule. In this case the atomic one-electron wave functions have the form of linear combinations of various orbitals ($s$-, $p$-, $d$- and $f$-states) of the isolated atom. Such a mathematical procedure for constructing the first approximation of the molecular wave function has been called hybridization. In the calculation, naturally, account is taken of the difference between the energy of the isolated atom in the ground state and its energy computed with the aid of hybridized atomic functions; this difference has been called the energy of the valence state of the atom. The energy of the valence state in which excited orbitals participate is the greater, the greater the excitation energy. If the latter is large in comparison with the energy of the bond being formed, then the corresponding excited atomic orbital plays no noticeable role in the resulting wave function and, therefore, the formation of this excited state of the atom has no noticeable effect on the properties of the molecule.

This method of calculation is in principle equivalent to the usual variational method, in which in the first approximation the undeformed wave functions of the isolated atoms in the ground state are taken, while the change in the configuration of the electron shells under the influence of the interaction is taken into account in the calculation in the second and subsequent approximations. In this case the perturbed wave function is constructed from one-electron atomic wave functions, which are written in the form of linear combinations of various orbitals ($s$, $p$, $d$, $f$).

The difference between the indicated methods is in practice reduced to a difference in the way the constant coefficients in the linear combinations are determined: in the “valence states” method they are determined by drawing on experimental data on the geometry of the molecule, whereas in the variational method they are determined by finding the energy minimum.

Making use of the equivalence of the indicated methods, one can arrive at an important conclusion. The calculation of the energy of the ground state of the molecular ion $\mathrm{H}_2^+$, carried out by the variational method$^{2,3}$, showed that the $2p$ state of the H atom plays an essential role in the stability of this molecule; although the latter lies at a comparatively large distance from the ground, $1s$ state, equal to $\sim 10$ eV, nevertheless the wave function of the bonding electron has the hybridized form $a(1s)+b(2p)$, and the $2p$ orbital enters it with a considerable weight. At the same time, it is known from analogous calculations that, in the formation of the bond in the neutral molecule $\mathrm{H}_2$, the $2p$ orbital plays a comparatively small role.

Such examples show that hybridization may occur not only with small, but also with large differences in the energies of the corresponding states, if only one of the bonded atoms is a cation or, more generally, has a strong positive field. Consequently, a similar effect may be expected in the formation of the so-called donor-acceptor bond*), and also in the formation of a bond in which one of the atoms has a considerably greater electronegativity than the other.

Proceeding from this conclusion, Gillespie$^1$ took advantage of it in order to show the possibility of participation in certain bonds of the $3d$ orbital of the C atom. It is known that bringing the carbon atom into the tetrahedral tetravalent state $sp^3$ requires an energy expenditure of about 7 eV. This value cannot be considered high, since compounds of tetravalent carbon, as is well known, are very stable. In order to answer the question of interest to the author, it would be necessary to determine the energy of bringing a negative carbon ion into the pentavalent state $(2s)(2p)^3(3d)$. However, in the absence of the necessary spectroscopic data, the author is forced to confine himself to an indirect estimate of this quantity and finds for it approximately 13 eV. Taking into account the considerations set forth above, it is therefore possible to conclude that the attraction of the $3d$ orbital in the C atom does not require so much energy as to make it impossible for them to participate in the formation of certain bonds, such as, for example, donor-acceptor bonds. On the contrary, a number of facts indicate that the $3d$ orbital must often exert a substantial influence on the properties of a bonded carbon atom.

One of the possible valence states with the participation of a $d$ orbital is a state in which three orbitals are arranged in approximately the same way as in tetrahedral $sp^3$ hybridization, while the fourth and fifth orbitals are $spd$ hybrids and form an angle of $71^\circ$ with one another. Fig. 1 schematically shows

Fig. 1.

*) That is, a bond formed with the aid of two electrons which, before the particles combine into a molecule, originally belong to one of them (the “donor”), for example, $\mathrm{He}+\mathrm{H}^+ \to (\mathrm{He}:\mathrm{H})^+$, $\mathrm{H}_3\mathrm{N}:+\mathrm{BCl}_3 \to \mathrm{H}_3\mathrm{N}:\mathrm{BCl}_3$, etc. The dots denote electrons. In the first example the “acceptor” of electrons is the proton, in the second—the $\mathrm{BCl}_3$ molecule.

a compound \( \mathrm{CRR'R''XY} \), formed with the aid of five such orbitals. Fig. 2 shows the shape of an \(spd\)-orbital. It is very probable that such a state of the carbon atom is found in some organometallic compounds existing as dimers or polymers. Thus, for example, trimethylaluminum forms stable dimers \( \mathrm{Al_2(CH_3)_6} \) in the gas phase, while dimethylberyllium exists in the form of long polymeric chains \( [\mathrm{Be(CH_3)_2}]_n \). The most probable structure of these compounds is one in which the metal atoms of two neighboring molecules are held close to each other by two methyl groups, which play the role of connecting bridges, just as chlorine atoms form bridges joining two molecules of aluminum chloride in \( \mathrm{Al_2Cl_6} \) (see, for example, 4). Schematically, the structure of the indicated compounds may be represented as follows:

Fig. 2.

\[ \varphi=\frac{1}{2\sqrt{2}}s+\frac{1}{2\sqrt{2}}p_x+\frac{1}{2\sqrt{2}}d_{xy} \]

Fig. 3.

Usually it is assumed that the bond of the methyl group simultaneously with two aluminum atoms is effected by means of a two-electron bond arising as the result of the overlap of the carbon \(sp^3\)-orbital simultaneously with two orbitals of two aluminum atoms, as is shown in Fig. 3. In this it is assumed that the four orbitals of each of the aluminum atoms have a tetrahedral configuration, one of them being free and capable of forming a donor-acceptor bond with another molecule. However, it is not difficult to see that such a picture is not entirely satisfactory, since the mutual overlap of orbitals so oriented is small and can lead to the formation of only comparatively weak bonds. Considerably stronger bonds will be formed if the carbon atoms of the methyl groups can use orbitals directed directly toward the aluminum atoms. The \(spd\)-orbitals indicated above are precisely such. If \(\angle \mathrm{CAlC}\) is tetrahedral, i.e. equal to \(109^\circ\), and the ring of four atoms \(\mathrm{Al \cdot C \cdot Al \cdot C}\) lies in one plane, then \(\angle \mathrm{Al,C,Al}\)

must be equal to \(71^\circ\), as is indeed obtained in the case of \(spd\)-hybridization. The considerable overlap of the \(spd\)-orbitals of the carbon atom and the tetrahedral \(sp^3\)-orbitals of the aluminum atom thus ensures the formation of strong bonds, represented schematically in Fig. 4. It is possible that some additional strengthening of the Al—C bonds is due to a partial withdrawal of electrons from the C—H bonds of the methyl group, which play the role of a bridge (so-called \(\sigma\)-conjugation). The electronic structure of the linear polymer \([\mathrm{Be}(\mathrm{CH}_3)_2]_n\) can be represented by an analogous image (Fig. 5).

Experimental data\(^{4,5}\) are in general agreement with the ideas indicated. In particular, the electron-diffraction data\(^{5}\), although they lead to the conclusion of an extremely small Al—Al distance, nevertheless, in accordance with what has been said, imply that \(\angle \mathrm{C}, \mathrm{Al}, \mathrm{C}\) is considerably larger than \(\angle \mathrm{Al}, \mathrm{C}, \mathrm{Al}\).

X-ray studies of the structure of the dimethylberyllium polymer\(^{6}\) have shown that it is a long chain which actually has the structure indicated above, with \(\angle \mathrm{Be}, \mathrm{C}, \mathrm{Be} = 66^\circ\) and \(\angle \mathrm{C}, \mathrm{Be}, \mathrm{C} = 114^\circ\), which is in good agreement with the prediction.

Fig. 4.

Fig. 5.

The involvement of \(3d\)-orbitals also makes it possible to explain in a more natural way than previously the structure of tetramethylplatinum\(^{7}\), in which one may expect that some of the carbon atoms use two \(3d\)-orbitals each; as a result each of them can, in addition to three H atoms, bind rather strongly three Pt atoms with the aid of three \(spd\)-orbitals directed toward one another at an angle of \(\sim 80^\circ\) (Fig. 6), which is in fact observed.

Fig. 6.

From the point of view set forth, one may take a new approach to the interpretation of the mechanism of certain elementary steps of chemical reactions. It is known, for example, that in the so-called carbonium ions, for example \((\mathrm{H}_3\mathrm{C}—\mathrm{H}_2\mathrm{C}—\mathrm{CH}_2)^+\), migration of a methyl group from one carbon atom to a neighboring one

occurs according to the scheme:

\[ \mathrm{ R{-}C(CH_3)(R'){-}CH_2^+ \;\longrightarrow\; R{-}C^{\delta+}(R')\cdots CH_3 \cdots C^{\delta+}(H){-}H \;\longrightarrow\; R{-}C^+(R'){-}C(CH_3)(H){-}H } \]

where this migration takes place very easily. It is usually assumed that, in the intermediate state, the C atom of the migrating methyl group uses only one \(sp^3\)-orbital to interact with two other C atoms, whose orbitals may be regarded as \(p\)-orbitals. However, it is not difficult to see that in this case the overlap of the orbitals is very small (Fig. 7), and, consequently, such a mechanism must be associated with a considerable activation energy. More natural is the assumption that, in the transition state, under the influence of the positive charge of the two C atoms, instead of the indicated \(sp^3\)-orbital there are formed two \(spd\)-orbitals, each of which overlaps strongly with the corresponding \(p\)-orbital, as shown in Fig. 8. Thus, in this intermediate state there is, as it were, formed a three-electron bond with the aid of four orbitals. It is possible that it is additionally strengthened owing to \(\sigma\)-conjugation with the three \(C{-}H\) bonds of the migrating methyl group.

Fig. 7.

Fig. 8.

Fig. 9.

It also appears probable that the \(3d\)-orbital takes part in the formation of the transition state in the reactions of bimolecular substitution in methane derivatives (Walden inversion), proceeding according to the scheme

\[ \mathrm{ RR'R''CX + Y \;\to\; X\ldots C\ldots Y \;\to\; X + RR'R''CY } \]

\[ \begin{array}{c} \ \ R\quad R'\\[-2mm] \diagdown\ \diagup\\[-1mm] \ \ C\\[-1mm] \ |\\[-1mm] R'' \end{array} \]

Here, however, the most probable is \(pd\)-hybridization, in which two equivalent orbitals are situated along one straight line but directed in opposite directions, while the other three orbitals, forming an \(sp^2\)-configuration, are located in one plane (Figs. 9 and 10). The difference from the usual views consists only in the fact that in the transition state the C atom interacts with the groups X and Y not by means of one \(p\)-orbital, but by means of two equivalent \(pd\)-orbitals. One may think that a similar configuration is possessed by the molecular ion \(\mathrm{CH_5^+}\), recently discovered by V. L. Tal’roze and A. K. Lyubimova in a mass spectrograph. It is possible that in this

three C—H bonds are situated in one plane at an angle of \(120^\circ\) to one another (\(sp^2\)-hybridization), while the two other bonds are perpendicular to this plane and are formed by two electrons with the aid of two identical \(pd\)-orbitals of the C atom, directed in opposite directions.

Among the elements of the first row of the periodic table, the involvement of the \(3d\)-orbital in bond formation can apparently occur not only in carbon, but also in nitrogen. However, the energy for transferring the N atom from the trivalent state \((2s)^2(2p)^3\) to the state \((2s)(2p)^3(3d)\) is considerably greater than the corresponding energy in the case of the C atom and is, probably, about \(23\ \mathrm{eV}\) (for other atoms of the first row this energy is still greater).

Fig. 10.

In Gillespie’s opinion it is most probable that the \(3d\)-orbitals of the N atom may participate in compounds with oxygen, as, for example, in nitric acid, where with the aid of two equivalent \(pd\)-orbitals two \(\pi\)-bonds may be formed:

\[ \mathrm{HO—N\!\left(=O\right)=O}. \]

N. S.

CITED LITERATURE

1. R. J. Gillspie, J. Chem. Soc., 1002 (1952).
2. H. O. Pritchard, H. A. Skinner, J. Chem. Soc., 945 (1951).
3. B. N. Dickinson, J. Chem. Phys. 1, 317 (1933).
4. K. W. Kohlrausch, J. Wagner, Zeits. phys. Chem. B52, 185 (1942).
5. L. O. Brockway, N. R. Davidson, J. Am. Chem. Soc. 63, 3287 (1948).
6. K. J. Snow, R. E. Rundle, Acta Cryst. 4, 348 (1951).
7. R. E. Rundle, J. H. Sturdivant, J. Am. Chem. Soc. 69, 1561 (1947).
8. V. L. Tal’roze, A. K. Lyubimova, DAN 86, 909 (1952).