An Alternative Procedure
Karl lmkampe Technische Universitat Hannover Hannover, West Germany
Writing Lewis Structures
No present day textbook of organic chemistry disregards the resonance structures. They are taken from the valence hond method and are relatively easy, involving little mathematics. The structures are applied to a-electron systems and their purpose is to determine the charge distribution and centers of reactivity and also the energetically favored isomers. Beginners often find it difficult to write down all the structures (I) and to apply correctly the concept that the actual state (resonance hybrid) is a mixture of all contributing resonance structures (canonical forms) with different influence. Handling bigger molecules involves much expenditure of time for those without much experience. Under these circumstances it is useful to consider the method using simple MO pictures. In this article the method will he explained using simple examples. It is relatively well known, is mentioned in many monographs (Z), is applied almost only to carhon compounds (3), and is hardly mentioned in the elementary textbooks although its simplicity and efficiency would justify it. The method utilizes the results of the Huckel calculation. The simpleness of the method comes from the fact that some results can he obtained without the solution of the secular determinant. It is necessary to know the basic geometry of the molecule. This cannot be ohtained from the valence hond nor the molecular orbital method. The atomic models of Gillespie are applied here (4). Before one goes deeper into the methods, several remarks concerning resonance structures are, mentioned. (1) Molecules exist whose atoms carry p a r t ~ a lcharges, although all the atoms are equal and possess the same electronegativity. An explanation is ohtained by drawing reso. name structures, e.g., ozone
This effect is denoted in the following as a charge separation due to delocalization possible with r-electrons. (2) There are molecules in which the charge separation of aelectmns results only because the atoms have different electronegativities, e.g., acrolein c==c--C==o (1)
8
c=C--F-g (11)
8
-*-a
0
g
im,
The determining factor here for the charge separation is that structures (11) and (Ill), for example, have different energies. This is a result of the different electmnegativities of the atoms. If this were not the case, the structures would have equal influences and a charge separation would not occur. For small molecules the charge separation mentioned here does not play a part, in contrast to the charge due to delocalization. It can be denoted as a second approximation. It may be added that the inductive effect which has an influence in the charge separation in a-bonds has nothing to do with this. It must be considered in addition.
H
H
Figure 1. Five canonical forms of pyrrole.
Pyrrole is an example in which the charge separation through delocalization of r-electrons and a difference in electronegativity of an atom play a part. To get a general idea one can regard five structures which have equal influence. (See Fig. 1). Bv countine the resonance structures one obtains a picture of charge relationship: In four of the five struct&es nitrogen carries a positive chawe: therefore the charge is 41~.1none of the five cases the carbon atom carries a negative charge; the charge on a carbon atom is therefore -%. The sum of the charges is zero. On considering the different electronegativities, it is noticed that structure (11) is more favorable than structure (m).The charge on the carhon atom which is adjacent to the nitrogen atom is negligibly more negative. From the MO picture the following may be concluded: One visualizes a ring having five equivalent centers and containing six a-electrons (See Fig. 2). Since there is a closed shell, ~ ~ i i - ~ ~ ~ c ~ nthere ~ ~ r is ~ ~ no ~ , ~distinction n o ~ ~ he. .,..,,,,. w o r n , . , tween the atoms, every center N H having a share of 6:5 = 1.2 Figure 2. Representation of the T-electrons. As the carhon *-electron System of Pyrrole. atoms (group 4) still possess three o-electrons an excess of negative charge to the value of 0.2 remains. In the nitrogen atom there are three oelectrons to consider. The nitrogen atom, which belongs to group 5 has in this case 4.2 electrons, so that a positive charge of 0.8 results. The outcome here is the same as that ohtained with the resonance structures. In order to ascertain the differences between the charges of the carhon atoms in the MO theory, one can utilize, e.g., the polarizabilities with the aid of a table of results. Examples now follow. Only two a-electron systems are considered here: the ally1 system and the methylenepropenylsystem. I t is important to know that the Huckel calculation yields in all systems the zero charge for each atom in a neutral molecule. This means that each atom has a share of one a-electron. An exception is molecules which possess odd numbered rings. In the examples given in this article only the charge separation due to delocalization is considered. The effect due to different electronegativities may be ignored. The basic principle of the investigation is the NBMO, the nonbonding molecular orbital. The determination of the NBMO results easily by the method of Longuet-Higgins (5) without the solution of the Huckel determinant. The
0
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existence of the NBMO can be explained by connection with the sine wave, in order to obtain a better understanding. The Allyl System
In a linear molecule the electrons have a similar possibility of movement as in a one dimensional hox where the wave functions are sine waves. Also the wave functions for a linear molecule (the LCAO's) have a connection with the sine wave. If the ends of the wave are extended one bond length over the ends of the molecule, the exact Huckel solutions are obtained (6). From these wave pictures the probability distribution may be obtained (see Fig. 3).
Ozone
If one considers all oxygen atoms as sp2 hybridized, one nelectron system with four electrons results (see Fig. 4). How many a and n-electrons belong to each atom is easy to see. As has just been stated, in an allyl system with four r-electrons 1% electrons are accommodated a t each end and one electron on the middle atom. The following calculation is given for the end atom: 4n + l a 1 % =~ 6% (in a group number of 6 this gives a charge of -U). For the middle atom 2n 2a la = 5 (in a group number of 6 this gives a charge of +1)
+
+
+
The same relationships are valid for NOz. I t has the same hybridized state as ozone, except that in the a-electron system there are merely three electrons. A charge due to delocalization does not occur. The unpaired electron has an equal chance of existing on each of the two oxygen atoms
A charge separation occurs due to differing electronegativities. This can he seen from the resonance structures shown below. Structure (VII) is energetically more favorable than structure (VIII)
Figure 3. The MO scheme of the allyl system. The fractions refer to the probability. In double occupied orbitals these numbers are to be multiplied by two.
The electron in the orhital +Z does not have a probability of existence in the center atom. The prohahility of electrons is equally shared on both the end atoms and carries a value of 'k. In the center atom only the two electrons of orbital +I are present, each with the prohability of 5, since the total probability on each atom has to be one. In the orbital ILI there remains for the outer atoms the probability of Y4 for each of the two electrons. It is obvious that changes in the charge density occur only a t the ends of the molecule, when an electron is removed or added to the molecule, because only changes in the occupancy of the orbital $2 occur. On forming the allyl anion the added electron is shared between the two outer atoms .~ ' .!
6 4 4 If an electron is removed, so likewise only the outer atoms have their charge density changed +:
c-c-c
+;
Three-center systems appear frequently. Calculations for some of these are shown.
Figure 4. The hybridization of a nonlinear three center system. The orbitals are simply represented as lines.
430 / Journal of C h e m i c a l E d ~ ~ ~ t b n
NOz+ is differently hybridized. The arrangement is linear. Therefore the atoms are sp hybridized (See Fig. 5). There are now two r-electron systems, which are perpendicular to each other.
The charge distribution is shown in the following calculation: nitrogen, 2a 2 . 1 ~= 4 (because of the group numher 5 a charge of +1 results); oxygen, 2 n + l a + 2.1 %a= 6 (no charge). Even the azide anion has two a-electron systems perpendicular to each other, each with four electrons
+
-
i!
I#-N-N~ .
I
..
+
For the end nitrogen atom: 2n + l a 2.1 5s = 6 (the charge carries -1 because of the group number 5). The middle nitrogen atom: 20 + 2 r = 4 (the charge carries +I). As a last example of this type the cyanate ion NCO- is considered. Because of its linear geometry it is in an sp hyhridized state and therefore two a-elec$ron systems perpendicular to each other with 16 valence electrons exist
+
+
N: (2n + 1c 2.1 % a ) = 6 (charge -1); C: (2a 2n) = 4 2.1 %a) = 6 (no charge). A (no charge); 0 : (271 l a proton can he bonded to the nitrogen atom or the oxygen atom. If it is bonded to the nitrogen, the molecule is energetically more favorable because a molecule without a
+
+
Figure 5 . The hybridization state of a linear three center system
charge separation results. In fact the equilibrium between the two tautomers lies on this side -I
H-I(~++
IN+Q-H 96%
t!
4%
Also other three-center systems can he handled by this scheme, for instance CHzNz, R-COOH, R-CONHz and so on. Only in rare cases is it necessary to draw hybrid orbitals; it is almost sufficient to write down the formulas with the corresponding valence electrons. The Melhylenepropenyl System
Also for the methylenepropenyl-diradical the Huckel molecular orbitals may be recognized through simple considerations without the application of mathematics. First of all, the simplest waveforms of a circular membrane are renroduced (wave with no or one node) (see Fie. 6). ~ & ~ i c t u r e s are of help in the understanding of molec". lar orbitals. On application to the methylenepropenyldiradical four molecul-a; orbitals are expectedkee ~ i g : ? ) . ~ On the middle atom there are only the two electrons of the lowest orbital, each with the probability of %, as only these two electrons are present there and no other occupied orbital has a probability distribution. (The prohability for the electron has to be one for each atom in a neutral molecule!) These electrons with equal probability spend the remaining time on the periphery of the molecule, thus with a probability of %:3 = M. The electron existing in orbital-& is found in two centen and has a probability of % a t each of these centers. From these results the values of 2 , and M, respectively, are obtained for the outer atoms in the orbital 6 3 , if one takes note of the neutrality of the atoms. The probability for the two electrons of the NBMO's together is therefore y3 on each outer atom. If the dianion is formed, the charge on the middle atom is zero and on the outer atoms
-+ A -; These considerations are sufficient, in order to understand the charge distribution in molecules with these a-electron systems. COs2- has such a n-electron system. Twentyfour valency electrons are present (see Fig. 8).
After filling of the n- and a-orbitals, six electrons remain for the r-electron system that corresponds to a dianion, so that 1%s-electrons for the outer centers and 1 relectron for the middle atom have to he taken into account
A simple calculation gives the charge on the oxygen atom 4n l a + 15s = 62h, which because of the group number 6 corresponds to a charge of -%. On the other hand the C-atom in the middle, 3a + I s = 4, has no charge. As the hybridization is quite obvious in a system of this kind, the charges on these molecules may easily he counted by only writing down the molecule with its electrons. The number of valence electrons is easy to work out and also the distribution of the n, a, and a orbitals presents no difficulties, so that after the formula
+
only the charges have to be worked out, where g represents the group number and q the charges
+
+
- (4n l a 1 % ~ =) +I3; B: 3 - (30 + 1s) = -1. A further example is HN03. The number of valence electrons is 24. F: 7
H
&' yi~ E*!$N -
+
+
\.
01 -
+
N: 5 - (3a 1 s ) = +1; OH: 6 - (2n 20 1%) = 0: 6 - (4n + l a lZha)= -%. The following molecules may be also handled in this matter; CH2N02-, urea, carbamic acid, guanidine, and so on. This method can he applied everywhere where NBMO's exist. The application to bigger molecules is simple, as long as one applies the method of LonguetHiggins; e.g., paranitroaniline has 2 NBMO's
+
After calculating the charges in the NBMO's, the extent of the charge separation for each atom is as follows
Figure 8. A circular membrane showing nodes of the waves with the lawert energy.
Figure 7. The MO scheme of the methylenepropenyl system
One would expect the same qualitative results as in the resonance theow, but with different values for the charge densities. To summarize: (1) Write down the molecule with its o-bonds and nonbonding electrons
Figure 8. The representation of the orbitals of the rnethylenepropenyldianion.
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(4) Calculate according to the formula, q = g - ( n H.C-
"\oR
H
Z
-
O 'R
(2) Draw the r-electron system and designate the r-electrons as dots as shown below
T ) ,the
Acknowledgment
The article was translated by Peter Cooper. Literalure Cited Lever, A.B.P.. J.CHEM.EDUC.. 49.819(19721. (2) Dewar. M . J. S.. "The Molecular Orbital Theory of O q m i e Chemistry" MeCrsw-Hill Book Co.. New York, 1968; Fluny, R. L.. Jr.. "Molecular Orbital Theones of Bondins in Organic Moleculen." MarcelLDekker, New York. 196% Heilhmnner, E.. Bock. H.. "Das HMO~Moddlund mfnp Anuendunp," Veda# Chemie. Weinheim, 1968; Hemdon, W. C., J. CHEM. EDUC.. 51. lO(19741; Robe*. J. 0.. "Moleeular Orbital Calculations." W. A. Benjamin, h e , New York. 1961: Streifwiesor. A . Jr.. "Molecular Orbits1 Theory for O g a n i c Chemists.'' dohn Wiley & Sons. New York. 1961. G I Platt, J. R., in "Hondbuch do7 Phyaik" XXXVII/Z. Springer;Verla#. E d i n . 1961, pus. (41 c i ~ ~ e r ~R.J.. ie, J C H E M~~~c..an.~95(19631. (5) Longuet-Higgins. H. C.. J. Chem. Pkrs., l8.265(1950). (61 Coulson. C.A.. Pmr. Roy. Sor.. Ser. A, 164.383i19381. (1)
(3) Determine with the aid of the NBMO the number of *-electrons present on each center
432 / Journal of ChemicalEducatbn
+o+
charges ( q charge, g group number).
