Monovalent atom

The element before carbon in Period 2, boron, has one electron less than carbon, and forms many covalent compounds of type BX3 where X is a monovalent atom or group. In these, the boron uses three sp hybrid orbitals to form three trigonal planar bonds, like carbon in ethene, but the unhybridised 2p orbital is vacant, i.e. it contains no electrons. In the nitrogen atom (one more electron than carbon) one orbital must contain two electrons—the lone pair hence sp hybridisation will give four tetrahedral orbitals, one containing this lone pair. Oxygen similarly hybridised will have two orbitals occupied by lone pairs, and fluorine, three. Hence the hydrides of the elements from carbon to fluorine have the structures... 

Consider a methane molecule CH, and suppose that some or all of its hydrogen atoms are replaced by some other monovalent atom. If the atoms attached to the carbon are all different, that is, the carbon atom is asymmetric, the resulting molecule is chiral and exists in two so-called enantiomorphic forms mirror images of each other. (For further information on chirality see the interesting expository paper [PreV76]). 

For example, atoms of both the alkaline-earth family (ZAval = 2) and the chalcogen family (ZAval = 6) correspond to FAemp = 2, and their stoichiometric proportionality (or coordination number) to monovalent atoms is therefore commonly two (AH2, ALi2, AF2, etc.). It is a remarkable and characteristic feature of chemical periodicity that the empirical valency FAemp applies both to covalent and to ionic limits of bonding, so that, e.g., the monovalency of lithium (Vuemp = 1) correctly predicts the stoichiometry and coordination number of covalent (e.g., Li2), polar covalent (e.g., LiH), and extreme ionic (e.g., LiF) molecules. Following Musher,132 we can therefore describe hypervalency as referring to cases in which the apparent valency FA exceeds the normal empirical valency (3.184),... 

For a general closed-shell AX , species, the Lewis-type assumption of a shared A X electron-pair bond for each coordinated monovalent atom X nominally requires m orbitals on A to accommodate the 2m bonding electrons, plus additional orbitals for any nonbonded pairs. Thus, for m bonds and t lone pairs, apparent octet-rule violations occur whenever... 

The polyhedral boranes and carboranes discussed above may be regarded as boron clusters in which the single external orbital of each vertex atom helps to bind an external hydrogen or other monovalent atom or group. Post-transition main group elements are known to form clusters without external ligands bound to the vertex atoms. Such species are called bare metal clusters for convenience. Anionic bare metal clusters were first observed by Zintl and co-workers in the 1930s [2-5], The first evidence for anionic clusters of post-transition metals such as tin, lead, antimony, and bismuth was obtained by potentiometric titrations with alkali metals in liquid ammonia. Consequently, such anionic post-transition metal clusters are often called Zintl phases. 

Tab. 3.6-3. Overview of cage compounds of the type [M Om(REH)x(RE)y] of the monovalent atoms M (alkali metals and copper) and the pnictogen atoms E (P, As).

This problem is fully analogous to the well-known problem of Slater 17) t who discussed the case of three monovalent atoms A, B, C lying on a straight line and investigated the substitution reaction ... 

The electron transitions depicted in Fig. 10 correspond to transitions of the system between states characterized by different adsorption curves. Such adsorption curves which represent the energy of the system E as function of the distance r between the particle C and the adsorbent surface for the case when particle C is a monovalent atom are schematically depicted in Fig. 11 (3, 4)- The curve I represents adsorption on an unexcited crystal, i.e., on a crystal that does not contain free electrons and holes. Curve I represents curve I shifted a distance u upwards parallel to itseff that is, it corresponds to adsorption on an excited crystal containing a free electron (in the conduction band) and a free hole (in the valence band). Curves p and n represent the adsorption curves for, respectively, strong donor, and strong acceptor chemisorption (curve n can lie either below or above curve p). The minima of curves I, n, p, I correspond to the states OL, CbL d- pL, CpL eL, CL cL -1- pL. 

Chromium has a maximum co-ordination number of six the chromium atom, therefore, may combine with, at most, six monovalent atoms or groups, over and above its ordinary valency value, with formation of a complex radicle. Hence chromic chloride is capable of associating with, or adding on, six molecules of ammonia with formation of the derivative, [Cr(NH3)8]Cl3. Ammonia may be replaced by a substituted ammonia group or some other basic group, such as alkyl amine, pyridine, or ethylenediamine. 

The sphere radius, R, and edge-length, L, may be written in terms of the radius of the sphere containing one electron, r and the number of monovalent atoms in the cluster AT, as... 

We expect the sphere to be more stable than the cube, since it has a 20% smaller surface area and hence less surface energy. This is indeed the case. The average kinetic energy of a sphere containing monovalent atoms can be written from eqs (5.6) and (5.2) as... 

Similarly, the average kinetic energy of a cube containing Jf monovalent atoms can be written from eqs (5.7) and (5.2) as... 

Fig. 6.2 The ratio of the kinetic energy of an Jf monovalent atom cluster to that of the infinite bulk as a function of J/ for cubic (solid curve) and spherical (dashed curve) boundary conditions.

With this question as a guide it became apparent that delocalization in systems such as benzene and allyl must be examined within a broader family of isoelectronic species. This was done in 1984 by Shaik and Bar102 and by Epiotis,105 and in 1985 it was demonstrated by computational means by Shaik and Hiberty.106 Thus, one can, for example, assemble the isoelectronic A clusters of monovalent atoms with different electron counts, e.g., 3 and 4 in Scheme 7. 

VB model, though successful for the interactions between monovalent atoms, breaks down when 71 bonds are considered. The aim of this chapter is to bring a quantitative answer to a question which can be so summarized What is the nature of the driving force which makes benzene more stable in a D6h geometry than in an alternated Dih geometry of Kekule type Exactly the same type of question applies to the allyl radical which will also be investigated and will allow the study of the effects of configuration interaction (Cl) and basis set extension. 

The classical choice of the starting orbitals is based on the following idea. Suppose that we deal with a chemical bond formed between two monovalent atoms A and B by the pairing of their valence electrons, one on A, the other on B. It is natural to assume that when one electron in the molecule is close to nucleus A, its molecular orbital will resemble the atomic orbital that it would occupy in A, and a similar situation would occur in the vicinity of B. This leads to the idea that the molecular orbital may be approximated by a linear combination... 

The VBSCD serves also as a model for understanding the status of electronic delocalization in isoelectronic series. Consider, for example, the following exchange process between monovalent atoms, which exchange a bond while passing through an X3 cluster in which three electrons are delocalized over three centers. 

Following Pauling, we have admitted extra orbitals on monovalent atoms involved in molecular systems with some metallic character or very delocalized bonds. In conjunction with a spin-free valence bond formalism, these extra orbitals have allowed us to devise new kinds of VB structures, the Pauling s structures, as we call them. These structures permit the monovalent atoms to form two covalent bonds simultaneously, as a consequence of electron transfer from neighbors and, thus, give information about delocalization of charge in the system, that is not directly inferred from the usual Kekule or ionic structures. Therefore, the Pauling s structures complement the VB description of molecular systems. 

Mikheikin et al. (11) have formulated an alternative approach where terminal valencies are saturated by monovalent atoms whose quantum-chemical parameters (the shape of AO, electronegativity, etc.) are specially adjusted for the better reproduction of given characteristics of the electron structure of the solid (the stoichiometry of the charge distribution, the band gap, the valence band structure, some experimental properties of the surface groups, etc.). Such atoms were termed pseudo-atoms and the procedure itself was called the method of a cluster with terminal pseudo-atoms (CTP). The corresponding scheme of quantum-chemical calculations was realized within the frames of CNDO/BW (77), MINDO/3 (13), and CNDO/2 (30) as well as within the scope of the nonempirical approach (16). 

For an organic compound the first step is usually to find the molecular formula, probably from the mass spectrum, and to calculate the number of double bond equivalents (DBEs). An acyclic saturated hydrocarbon has the formula where M = 2N+2. Each double bond or ring in the molecule reduces the value of M by two. So if M = 2N the molecule has one DBE we cannot tell from the formula whether it is in the form of a ring or unsaturation. A benzene ring corresponds to 4 DBEs three double bonds and a ring. The presence of oxygen or other divalent elements does not affect the value of M. Each monovalent atom such as chlorine can be treated as a proton for the purpose of calculation, while one proton has to be subtracted for each trivalent atom such as nitrogen. 

Maximum covalency. The maximum number of monovalent atoms or groups with which an element will enter into covalent combination in the theory of maximum covalency proposed by Sidgwick, a maximum number of possible covalent linkages governed by the position of the element in the periodic system, being two for hydrogen, four for the elements in the first short period, six for the elements in the second short period, and eight or more for the heavier elements. 

The electronic bands of an infinite crystal can cross as a function of some parameter (pressure, concentration etc.). If one treats the e /r,2 term of the electron repulsion correctly, one sees that the crossing transition of the two bands is a first-order phase transition, between the metallic and insulating states. This transition was predicted by Mott in 1946 and has carried his name ever since. In fact, the original Mott criterion does not predict such a transition for Hg, but the criterion was derived for monovalent atoms. For divalent mercury it should not be applicable. Also the semiempirical Herzfeld criterion, which was very successful in predicting the insulator to metal transition in compressed xenon, predicts bulk Hg to be non-metallic. All this seems to imply that Hg is a rather special case. 

The relationships between these different series have been definitely established by means of reactions which enable us to pass from one series to another. Such reactions bring out a very important fact that the hydrocarbons of the unsaturated series differ from those of the saturated series in a very definite way, viz., in the formation of addition products. These addition products, most readily formed with the halogens or halogen-hydro acids, are always the result of the addition of twOj fourj or six monovalent atoms to each unsaturated molecule, with the conversion of the unsaturated compound into a saturated one. 

Although acetylene adds four monovalent atoms while ethylene adds only two, it does not follow that the greater unsaturation is accompanied by a more rapid rate of addition. As a rule, the activity of the triple bond, measured by the rate of addition, is lower than the activity of the double bond. Acetylene forms explosive mixtures with air, and care should be exercised by the student to keep the generator away from all flames. 

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