Valences shells

There are complicating issues in defmmg pseudopotentials, e.g. the pseudopotential in equation Al.3.78 is state dependent, orbitally dependent and the energy and spatial separations between valence and core electrons are sometimes not transparent. These are not insunnoimtable issues. The state dependence is usually weak and can be ignored. The orbital dependence requires different potentials for different angular momentum components. This can be incorporated via non-local operators. The distinction between valence and core states can be addressed by incorporating the core level in question as part of the valence shell. For... 

There are also very reliable approximate methods for treating the outer core states without explicitly incorporating them in the valence shell. 

It also forms compounds known as carbonyls with many metals. The best known is nickel tetracarbonyl, Ni(CO)4, a volatile liquid, clearly covalent. Here, donation of two electrons by each carbon atom brings the nickel valency shell up to that of krypton (28 -E 4 x 2) the structure may be written Ni( <- 0=0)4. (The actual structure is more accurately represented as a resonance hybrid of Ni( <- 0=0)4 and Ni(=C=0)4 with the valency shell of nickel further expanded.) Nickel tetracarbonyl has a tetrahedral configuration,... 

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

In the 6-3IG basis, the inner shell of carbon is represented by 6 primitives and the 4 valence shell orbitals are represented by 2 contracted orbitals each consisting of 4 primitives, 3 contracted and 1 uncontracted (hence the designation 6-31). That gives... 

Because carbon is a first-row element unable to extend its valence shell, hypervalence cannot exist in carbon compounds, only hypercoordination. 

Another family of basis sets, commonly referred to as the Pople basis sets, are indicated by the notation 6—31G. This notation means that each core orbital is described by a single contraction of six GTO primitives and each valence shell orbital is described by two contractions, one with three primitives and the other with one primitive. These basis sets are very popular, particularly for organic molecules. Other Pople basis sets in this set are 3—21G, 4—31G, 4—22G, 6-21G, 6-31IG, and 7-41G. 

If IS offen convenienf to speak of the valence electrons of an atom These are the outermost electrons the ones most likely to be involved m chemical bonding and reac tions For second row elements these are the 2s and 2p electrons Because four orbitals (2s 2p 2py 2pf) are involved the maximum number of electrons m the valence shell of any second row element is 8 Neon with all its 2s and 2p orbitals doubly occupied has eight valence electrons and completes the second row of the periodic table... 

Covalent bonding in F2 gives each fluonne eight electrons in its valence shell and a stable electron configuration equivalent to that of the noble gas neon... 

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... 

The structure shown is the best (most stable) Lewis structure for methyl nitrite All atoms except hydro gen have eight electrons (shared + unshared) in their valence shell... 

When writing a Lewis structure we restrict a molecule s electrons to certain well defined locations either linking two atoms by a covalent bond or as unshared electrons on a sm gle atom Sometimes more than one Lewis structure can be written for a molecule espe cially those that contain multiple bonds An example often cited m introductory chem istry courses is ozone (O3) Ozone occurs naturally m large quantities m the upper atmosphere where it screens the surface of the earth from much of the sun s ultraviolet rays Were it not for this ozone layer most forms of surface life on earth would be dam aged or even destroyed by the rays of the sun The following Lewis structure for ozone satisfies fhe ocfef rule all fhree oxygens have eighf elecfrons m fheir valence shell... 

The tetrahedral geometry of methane is often explained with the valence shell electron pair repulsion (VSEPR) model The VSEPR model rests on the idea that an electron pair either a bonded pair or an unshared pair associated with a particular atom will be as far away from the atom s other electron pairs as possible Thus a tetrahedral geomehy permits the four bonds of methane to be maximally separated and is charac terized by H—C—H angles of 109 5° a value referred to as the tetrahedral angle... 

Boron trifluoride is a trigonal planar molecule There are six electrons two for each B—F bond associated with the valence shell of boron These three bonded pairs are farthest apart when they are coplanar with F—B—F bond angles of 120°... 

Section 1 3 The most common kind of bonding involving carbon is covalent bond ing A covalent bond is the sharing of a pair of electrons between two atoms Lewis structures are written on the basis of the octet rule, which limits second row elements to no more than eight electrons m their valence shells In most of its compounds carbon has four bonds... 

Section 1 10 The shapes of molecules can often be predicted on the basis of valence shell electron pair repulsions A tetrahedral arrangement gives the max imum separation of four electron pairs (left) a trigonal planar arrange ment is best for three electron pairs (center) and a linear arrangement for two electron pairs (right)... 

There is ample evidence from a variety of sources that carbocations are mterme diates m some chemical reactions but they are almost always too unstable to isolate The simplest reason for the instability of carbocations is that the positively charged car bon has only six electrons m its valence shell—the octet rule is not satisfied for the pos itively charged carbon... 

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... 

Free radical (Section 4 16) Neutral species in which one of the electrons in the valence shell of carbon is unpaired An ex ample is methyl radical CH3... 

Valence shell electron pair repulsion (VSEPR) model (Section 110) Method for predicting the shape of a molecule based on the notion that electron pairs surrounding a central atom repel one another Four electron pairs will arrange them selves in a tetrahedral geometry three will assume a trigo nal planar geometry and two electron pairs will adopt a linear arrangement... 

Since the basis set is obtained from atomic calculations, it is still desirable to scale exponents for the molecular environment. This is accomplished by defining an inner valence scale factor and an outer valence scale factor ( double zeta ) and multiplying the corresponding inner and outer a s by the square of these factors. Only the valence shells are scaled. 

On the assumption that the pairs of electrons in the valency shell of a bonded atom in a molecule are arranged in a definite way which depends on the number of electron pairs (coordination number), the geometrical arrangement or shape of molecules may be predicted. A multiple bond is regarded as equivalent to a single bond as far as molecular shape is concerned. 

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