A Notation for Orbitals Robert A. Stairs Trent University, Peterborough. ON K9J 7B8. Canada A concise notation to describe the annroximate svmmetrv .. n, e1c.J and ihe atomic orbitals involvea in the consrruction of \,alence bonds or molecular orbitals. whether bonding or not, would clearly he useful. This is apparent from the several attempts that have been made. For instance, Douglas, McDaniel, and Alexander' write for the postulated second bond between sulfur and oxygen in S042-, "d-p-T". Cotton, Wilkinson, and Gans2 would write this as "da-pr". Huheey3is unable to settle on asingle form and writes in one d a c e "d--0-" and in another "T,.,". This is ;;suggest that a clearand logical notation can be madeun of two distinct elements. whichare (1) a descrintion of the atomic orbitals on each at'om, hybridif this is approoriate. and ( 2 ) the a~nronriatesvmmetw svmbol placed 'between the atom symmbols.~~his avkds the.redundan; repetition of the Greek letter and places the bond svmbol hetween the symbols for the interacting atoms, in-a visually appropriate way. Some examples are shown in the table. The first few need no explanation. The last two cases show the power of the notation to describe more complicated interactions, such as multicenter molecular orbitals. Minor modifications of the notation were necessary in the last case: the dashes in the nonbonding p-m-p orbital indicate a "long bond" (similar to that in "Dewar benzene") between nonadjacent atoms. ro,
' Douglas, 6. E.; McDaniel, D.
H.: Alexander, J. J. Concepts and Models of InorganicChemistry.2nd ed.: Wiley: New York. 1983: p 61. Cotton, F. A,; Wilkinson, G.: Gaus, P. L. Basic Inorganic Chemis try, 2nd ed.; Wiley: New York, 1987: p 332. Huheey. J. E. Inorganic Chemistry, 3rd ed.: Harper & Row: New
York, 1983.
980
Journal of Chemical Education
In the bonding and antibonding orbitals i t is necessary, if the g, u notation is used, to place the subscript outside parentheses. The notation, being essentially a linear one, fails to describe "closed" three-center, two-electron bonds of the sort encountered in BlaHla and Alz(CH3)s. There seem to be no limitations on its ability to describe interactions in linear or pseudolinear (chain, cyclic) groups of atoms.
Examples of Notation for Orbital Interactions Atomic System
Orbital Notation svQs
H2
SO..S
CHI
(sp3)0s
CO
PZ~PZ PU'P PwXPw
0 2
P "u P
-M -
CEO
Ci-
W Ci
SOF
(dZsp3)(r (SP) dxyirPX *' PX (PXTdm T P& Pr)-iru-Px (p, r' d, X' pd,
d * ~
Comments Bonding. Antibonding. Parentheses enclose a singie atomic orbital. The interaction is along the common z axis. The subscripts may be amitled if not needed for clarity. Center of inversion present. The s i g m bond and the "back bond" in an octahedral complex. Bonding, nonbanding,and antibonding orbitals in an octahedral complex where two CI- iigands are in competition for an empty d orbital on the metal. The "second bond".
