Bonding orbitals, symbols

The electron density in both molecular orbitals is symmetrical about the axis between the two nuclei. This means that both of these are sigma orbitals. In MO notation, the Is bonding orbital is designated as eru. The antibonding orbital is given the symbol An asterisk designates an antibonding orbital... 

The valence atomic orbitals which are available to form the orbitals of a CC single bond, directed along the x axis, are the 2s and 2px atomic orbitals on each carbon atom. Their admixture—in proportions which depend on the number of neighbors at each carbon and on the subsequent hybridization—creates two (s, p ) hybrids on each atom. One of these hybrids points away from the other atom and can be used for bonding to additional atoms. The pair of hybrids which point at each other overlap and interact in the conventional fashion [we symbolize the non-interacting orbitals by an interruption of the bond axis (Fig. 1)]. The two bond orbitals which are formed in this manner both have [Pg.3]

If the pair of carbon atoms shown above each have only two neighbors so that they are doubly-bonded in the conventional sense, there is an extra p orbital available on each atom. These p orbitals point along the (z) direction, perpendicular to the plane of the molecular fragment. The interaction of these two atomic orbitals via overlap creates a new pair of bond orbitals with local tt symmetry (Fig. 2, where again we have symbolized the non-interacting or-... 

The symbol ( S—]+ represents tercovalent argononic sulfur. Like Si, it is argononic in that, counting shared as well as unshared electron pairs, it has four pairs in its outer shell, giving it the electron number of argon. A tercovalent argononic sulfur atom resembles a normal (neutral) tercovalent phosphorus atom. The bond orbitals of S + are similar to those of S. ... 

The symbol u>, when used to denote a 3c/4e triad (e.g., cuAbc). bond orbital (e.g., u>Ab c) or ligand label (e.g., F ), is unlikely to be confused with other common usages such as angular frequency. Its shape has three points and two connecting arcs to suggest three-center character with two connecting electron pairs. 

For singlet systems the bonding patterns for Rumer diagrams are conventionally obtained by writing the symbols for the orbitals in a ring (shown here for six), and drawing all diagrams where all pairs of orbital symbols are connected by a line and no lines cross[2, 13]. 

Vi corresponds to a bonding orbital that essentially involves Are interaction of the C atom with the first H atom its charge density i/zf is concentrated in the region between these two atoms. Tlrls matches the idea of a localized C-H bond Tire electron pair of this orbital is assigned to a bond between these two atoms and symbolized by a dash in the valence bond formula. 

Here 1, 2, represent the electrons. P is the operation of permuting the electrons among the spin-orbit functions, for example, interchanging 1 and 2 between afi and ba. There are (2n) of these operations in the permutation group 2n is the number of electrons for n bonds. The symbol (—l)p is 1 if P involves an even number of interchanges of pairs of electrons and — 1 if it involves an odd number. The function in the brackets satisfies the Pauli exclusion principle. R represents the 2 operations of interchanging the spin functions a and 0 for orbitals (such as a and 6) that are bonded together. 

Protonated alkanes (C H2 , 3 ) also play a significant role in alkane reactions. Saturated hydrocarbons can be protonated to alkonium ions, of which the methonium ion CH5+, 422 [Eq. (3.119)] is the parent, and formation of these pentacoordinate carbocations involves two-electron three-center (2e—ic) bonds. The dotted lines in the structure symbolize the bonding orbitals of the three-center bonds [Eq. (3.119)] their point of junction does not represent an additional atom. 

So (2pyA + 2p>,B) is a bonding orbital, to which we give the symbol 7tu. What would the antibonding orbital formed from 2p> orbitals be ... 

These MOs do not have cylindrical symmetry—in fact you have to rotate them 180° about the axis between the nuclei before you get back something looking like what you started with but with opposite phase—and as a result the symmetry of these orbitals is given the symbol It the bonding orbital is a jc orbital and the antibondlng orbital is a jc orbital. Bonds which are formed by filling jc orbitals are called it bonds, and you ll notice that because of the it symmetry the electron density in these bonds does not lie directly between the two nuclei but rather to either side of the line joining them. 

Figure 1.14. Symbolic representations of the SCF-MO bonding orbitals for beryllium hydride (BeH2) (a) Be 2s and positive Is H contribution, (b) Be 2p and negative Is contributions, (c) beryllium hydride (BeH2) halves shown as two sp orbitals from Be and two Is orbitals...

Figure 1.15. Symbolic representations for boron tribydride (monomeric borane), BH3 of the SCF-MO bonding orbitals (a) B 2s and positive Is H contributions (b) B 2p and one of two degenerate contributions from hydrogen (H) (c) B 2p and the other degenerate contribution from hydrogen (H) (d) boron trihydride (monomeric borane), BH3 where the s-type orbitals on the hydrogens (H) have been omitted for clarity. The boron is in the plane defined by the three hydrogens (H).

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

For the given orbital oeeupations (eonfigurations) of the following systems, determine all possible states (all possible allowed eombinations of spin and spaee states). There is no need to form the determinental wavefunetions simply label eaeh state with its proper term symbol. One method eommonly used is Harry Grays "box method" found in Eleetrons and Chemical Bonding. 

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