Counting electrons

Determination of the number of total valence electrons on an organometallic complex is simplest when following the second classification system in which all ligands are considered neutral and will, therefore, be presented first. By this system, the number of total electrons can be determined by the formula  

Total valence electrons = Metal group + Electrons donated by all even-and odd-electron ligands - Overall charge on the complex 

To follow this system, simply determine ttie number of electrons on the neutral version of each ligand. 

Tlie second classification system has the advantage of revealing the oxidation state as part of the determination of the total number of electrons. The reader should realize, however, that oxidation state and total number of electrons are not linked. Both the system with charges and the system without charges lead to the same total number of electrons. 

The relationship between the charge of the complex, oxidation state, and assigned charges of ligands can be written as 

One of the first things one does when looking at an organometallic reaction is to count the number of electrons the metal has in the reactant and product. This is called the electron count for the metal. Next, the oxidation state of the metal is determined. Lastly, it is often useful to determine how many electrons are in the d orbitals of the metal, a number referred to as the d electron count. The result of these determinations gives insights into both the reactivity of the metal complexes and what has occurred during the reaction. 

Alkenes also contribute two electrons to a metal, by coordination of the it bond. To show this a line is drawn between the metal and the center of the double bond. As the -it system becomes larger, more electrons can be donated to the metal. Allyl can donate three electrons, butadiene can donate four, cyclopentadienyl (Cp) can donate five, and benzene can donate 

A similar situation arises in the cyclopentadienyl ligand. A neutral cyclopentadienyl ligand contributes five electrons. This is because a neutral ligand would be a radical that can make one cr bond, and donate two tt bonds. The resonance structures lead us to represent the ligand as a pentagon with a circle in the middle. 

Another common set of ligands are alkylidenes and alkylidynes. These are defined as carbon ligands that make double and triple bonds to metals, respectively. They can be viewed as involving the bonding of carbenes (ICR2) and methines ( CR), respectively, to metals. An alkylidene contributes two electrons to the metal count, one each from the a and TT bonds. An alkylidyne contributes three electrons to the metal count. 

A section of the periodic table showing the transition metals and the number of electrons they contribute to a complex. 

Therefore, wc will not spend lime on the issue. The correspondence suggests that there may be a general pattern for any ML complex. Tills, along with electron counting, is the topic of concern in the next section. 

FIGURE 16.2. A generalized orbital interaction diagram for a ML complex where the ligands arc arranged in a spherical manner around the transition metal. 

This brings up the mechanics of electron counting. The convention that we shall use is to treat all ligands as Lewis bases. Listed in 16.7 arc some typical two-clcctron a donor groups. In 16.8 are listed some two-electron a donors which also have one 

Polyenes are also considered as Lewis bases. They are counted such that all tt bonding and nonbonding levels are occupied. Some representative examples are given in 16.10. Listed below each structure are the number of electrons donated to 

A few simple examples will make this electron counting rule clearer. In Cr(CO)6 the CO groups donate two cr electrons each for a total of 12 electrons. The charge 

For the purpose of assigning oxidation states, organometallic ligands such as cyclopentadienyl, alkyl, and allyl are often considered to be anionic. Thus, the formal oxidation states of the metals in Ti(Cp), RjTa (R = Bu CH ), and [Ni(allyl)J are Ti, Ta, and Ni + provided the ligands are treated as Cp, R, and. With alkylidene, alkylidyne, and NHC carbenes, the assignment of the oxidation state is a little more complicated. As discussed later, it is best understood in conjunction with the electron counting scheme. 

Neutral stable molecules such as CO, PPhj, CHjCN, and tetrahydro-furan (THF) are all two-electron donors. Chelating ligands such as Dppe, BISBI, HOCH CH H, and H NCH CH NH, where two lone pairs are involved, are four-electron donors. Anions such as chloride, cyanide, and monodentate acetate are also two-electron donors. 

For organic groups such as alkyl, alkylidene, and cyclopentadienyl, we must first decide how many a- or r-electrons are available for bonding to the metal. If we treat alkyl, aryl, and ij -allyl ligands as neutral radicals, then each of these is a one-electron donor. If we treat them as anions, by taking one electron from the metal and adding it to the radical, then they would be two-electron donors. 

The number of r-electrons in neutral molecules such as ethylene, butadiene, and benzene are two, four, and six. Therefore, ethylene, if-butadiene, and if-benzene are two-, four-, and six-electron donors, respectively. Similarly, if Cp is treated as a radical then in if-, rf-, and ij -Cp complexes, five, three, and one electron, respectively, are available for bonding with the metal. 

However, if Cp is treated as an anion, again by taking one electron from the metal and adding it to Cp, then if-, if-, and i -Cp are six-, four-, and two-electron donors. We now illustrate both ways of electron counting for a few complexes that are of special relevance to homogeneous catalysis. 

---

Moving now to nitrogen we see that it has four covalent bonds (two single bonds + one double bond) and so its electron count is 5(8) = 4 A neutral nitrogen has five electrons m its valence shell The electron count for nitrogen m nitric acid is one less than that of a neutral nitrogen atom so its formal charge is +1... 

The green oxygen m Figure 1 5 owns three unshared pairs (six electrons) and shares two electrons with nitrogen to give it an electron count of seven This is one more than the number of electrons m the valence shell of an oxygen atom and so its formal charge is —1... 

FIGURE 1 5 Counting electrons in nitnc acid The electron count of each atom is equal to half the number of electrons it shares in covalent bonds plus the number of electrons in its own unshared pairs... 

Valence electrons of neutral atom Electron count Formal charge... 

The electron counts of nitrogen in ammonium ion and boron in borohydride ion are both 4 (half of eight electrons in covalent bonds) Because a neutral nitrogen has five electrons in its valence shell an electron count of 4 gives it a formal charge of +1 A neutral boron has three valence electrons so that an electron count of 4 in borohydride ion corresponds to a formal charge of -1... 

For main group elements the number of framework electrons contributed is equal to (t + a — 2) where v is the number of valence shell electrons of that element, and x is the number of electrons from ligands, eg, for Ff, x = and for Lewis bases, x = 2. Examples of 2n + 2 electron count boranes and heteroboranes, and the number of framework electrons contributed by their skeletal atoms, ate given in Table 1. 

Some metaHacarboranes present anomahes to the electron-counting formaUsms. Symmetrical sandwich... 

Because the electron-counting paradigm incorporates the 18-electron rule when appHed to transition-metal complexes, exceptions can be expected as found for classical coordination complexes. Relatively minor exceptions are found in (Tj -C H )2Fe2C2BgHg [54854-86-3] (52) and [Ni(B2QH22)2] A [11141-32-5] (53). The former Q,n electrons) is noticeably distorted from an idealized stmcture, and the latter is reminiscent of the and complexes discussed above. An extremely deficient electron count is obtained for complexes such as P7036-06-9] which have essentially undistorted... 

As the C B series of tetracarbaboranes is classified in the electron-counting formaUsm as nido, these molecules are expected to have open stmctures even though extra hydrogens are absent. Spectroscopic studies (130) have confirmed this expectation for 2,3,4,5-C4B2H3 [28323-17-3]. One isomer of (CH3)4C4BgHg has the open nonicosahedral stmcture shown in Figure 11 and another isomer, the 1,2,3,8-tetramethyl compound [54387-54-1], is apparently even more open (131). Other tetracarbaboranes include isomers of nido-Q]. and (132). 

The closo, nido, arachno classification is given on the basis of framework electron count and not stmcture. 

The first closo metaHaborane complexes prepared (159) were the nickelaboranes [< /(9j 0-( q -C H )Ni(B22H22)] and closo-l]l- r]-Q ]) -l]l-53i] pri Q [55266-88-1] (Fig. 13). These species are equivalent to closo-C ]]ri ][ i closo-Q, p5 2 by tbe electron-counting formaUsm. The mixed bimetallic anion [ /(9j (9-(Tj -C H )2CoNi(B2QH2Q)] and other related species were reported later (160). These metallaboranes display remarkable hydrolytic, oxidative, and thermal stabiUty. 

Characterization of these clusters indicate an unusual 2n framework electron count having geometries reminiscent of stricdy metallic clusters (11,164). 

For tetranuclear cluster complexes, three stmcture types are observed tetrahedral open tetrahedral (butterfly) or square planar, for typical total valence electron counts of 60, 62, and 64, respectively. The earliest tetracarbonyl cluster complexes known were Co4(CO)22, and the rhodium and iridium analogues. The... 

The emitted P particles excite the organic molecules which, in returning to normal energy levels, emit light pulses that are detected by a photomultiplier tube, amplified, and electronically counted. Liquid scintillation counting is by far the most widely used technique in tritium tracer studies and has superseded most other analytical techniques for general use (70). 

---