Methane electron density

Methane has four pairs of valence electrons, each shared in a chemical bond between the carbon atom and one of the hydrogen atoms. The electron density in each C—H bond is concentrated between the two nuclei. At the same time, methane s four pairs of bonding electrons repel one another. Electron-electron repulsion in methane is minimized by keeping the four C—bonds as far apart as possible. 

Figure 6.13 Relief map of the electron density for methanal (formaldehyde) in the molecular plane. There is a bond critical point between the carbon and the oxygen nuclei, as well as between the carbon nucleus and each hydrogen nucleus. No gradient path or bond critical point can be seen between the two hydrogen nuclei because there is no point at which the gradient of the electron density vanishes. There is no bond between the hydrogen atoms consistent with the conventional picture of the bonding in this molecule.

Sander applied DFT (B3LYP) theory to carbenic philicity, computing the electron affinities (EA) and ionization potentials (IP) of the carbenes." " The EA tracks the carbene s electrophilicity (its ability to accept electron density), whereas the IP represents the carbene s nucleophilicity (its ability to donate electron density). This approach parallels the differential orbital energy treatment. Both EA and IP can be calculated for any carbene, so Sander was able to analyze the reactivity of super electrophilic carbenes such as difluorovinylidene (9)" which is sufficiently electrophilic to insert into the C—H bond of methane. It even reacts with the H—H bond of dihydrogen at temperamres as low as 40 K, Scheme 7.2) ... 

Very recently, various DHB complexes were analyzed [39].12 The complexes of ammonia and hydronium ions were included in this analysis, in addition to the complexes with acetylene and methane, and their derivatives. Generally, in such complexes, lithium hydride and berylium hydride (and its fluorine derivative) act as the Lewis bases (proton acceptors) while hydronium ion, ammonia ion, methane, acetylene, and their simple derivatives act as the proton donors. Therefore, it was possible to investigate the wide spectrum of DHB interactions, starting from those that possess the covalent character and extending to the systems that are difficult to classify as DHBs (since they rather possess the characteristics of the van der Waals interactions). Figure 12.8 displays the relationship between H—H distance and the electron density at H—H BCP.13 One can observe the H—H distances close to 1 A, (as for the covalent bond lengths) and also the distances of about 2.2—2.5 A, typical for the van der Waals contacts. This also holds for the pc-values - of the order of 0.1 a.u. as for the covalent bonds and much smaller values as for the HBs and weaker interactions. 

The examples presented in this work by no means cover the subject of the C-H bond activation on a spectrum of catalytic media. Interaction of methane with the small clusters discussed here obviously cannot pretend to fully mimic catalytic centers in reality. Nevertheless, they seem to justify drawing generalized conclusions regarding the mechanism of catalytic activation in terms of electron withdrawal or donation to the interacting hydrocarbon molecule. A variety of properties contribute consequently to the emerging scheme (electronic density redistribution, geometry evolution in critical points, energetical factors, vibrational analyses) which substantially increases credibility of the conclusions. 

In the tetrahedral methane molecule (its parameters then correspond to subscript 0 in eqs. (3.132), (3.133)), we notice that the 57X57XE matrix further simplifies as s nm = 1 and, therefore, simple analytical expressions become possible. Also, we notice that the FA approximation is adequate here as, for example, even very large elongation of one C-H bond by 0.1 A leads to changes of the bond geminal amplitudes u, v, and w not exceeding 0.003. The same applies to the expectation values of the pseudospin (f) operators representing the one- and two-electron density matrix elements. 

To better understand the reactivity, the transition states for the series of reactions were studied using DFT methods. As illustrated in Fig. 21, the results show that each transition state can be characterized by a single imaginary frequency that involves simultaneous dissociation of the C-Cl bond and formation of the Re -Cl bond. The structural variation along the series of chlorinated methanes suggests that the transition state becomes more product-like as the number of hydrogen n in CH Cl4 increases. For example, the Re... Cl distance in (CO)s Re... Cl... CH Cl3 M decreases monotonically from 2.95 A (n = 0) to 2.84 A (n = 1) to 2.76 A (n = 2), and finally to 2.52 A for the product (CO)5Re-Cl. The calculated electron density distribution also displays a similar trend as displayed in Table 1. 

Electron withdrawal in these molecules is the result of a bond polarization from an inductive effect (Chapter 5). The electrons in a o bond between carbon and a more electronegative element such as N, O, or F will be unevenly distributed with a greater electron density towards the more electronegative atom. This polarization is passed on more and more weakly throughout the carbon skeleton. The three fluorine atoms in CF3H reduce the p K"a to 26 from the 48 of methane, while the nine fluorines in (CFa CH reduce the pKTa still further to 10. 

The electron density was studied for the ground state of three groups of molecules (1) methane-methanol-carbon dioxide, (2) water-hydrogen peroxide, and (3) ferrous oxide-ferric oxide. 

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