James B. Hendrickson Brandeis University waltham, Massachusens 02154
A Logical Characterization of Organic Chemistry
For the student, organic chemistry is too often an enormous and onerous chore; for his teacher the subject is ordered, logical and basically simple. For the student, organic chemistry is too often an enormous and onerous chore because there are so many structural variations and reactions which must be memorized. For his teacher, however, the subject is ordered, logical and basically simple. This paradox arises because the order is basically there but has proved difficult to formulate in textbooks: the teacher has absorbed asystematic overview by virtue of ;longer time of contact. An attempt is made here to formulate deliberately a simple logical system,' to create a frame of theory to put all the various structures and reactions into a single perspective, and so to make learning simpler and more structured for the student. The value for learning organic chemistry comes in seeing all possihle structural elements and reaction families as combinations of a few fundamental conceptual groupings. In particular, with structural elements, students can see that many possible functionality variants are easily grouped into a few natural headings. Hence in each group iuterconversions are similar and parallel so that they need not all be learned separately as if unrelated. Furthermore, overall limits become clear on what is possible so that students can avoid their common fear that an infinite opportunity for structural variation exists. Similarly as to reactions, whole families of reactions are condensed into a few groupings so that all the reactions taught can be understood as minor variants of these main classifications. clarifvine the mass of reactions to be learned hy structuring thesudject. We start bv notine" that most reactions occur at onlv one or two carbon atoms, the others in a molecule remaining unchanged. Hence we shall focus on sinele carbons seoaratelv and ask: what can they he like, and how can this change in reaction? Thus we shall deal onlv in the net structural chance in a reaction, and that one carhbn a t a time.
a
Character of Carbon Atoms A chemical structure has two basic features. its backbone carbon skeleton, and its reactive sites, the functional groups. A descri~tionof anv sinele carbon atom in i t should then reflect its hkektal environment and i u reactive functionality. The former consists of the number of attached carbons and hydrogens; the latter consists either of attached heteroatoms (N,O,X,S,P, etc.) or of double and triple n-bonds to adjacent carbons. Thus we may denote the kinds of~attachmentsa single carbon can have as four basic categories: H for attached hydrogen; R for a-bonds (skeletal) to adjacent carbons; II for n-bonds to adjacent carbons; and Z for any bonds (a- or n-) t o heteroatoms. Functionality generally may be denoted by F, which includes hoth multiple bonds (II)and heteroatom functional groups (a). Then the number of each kind can be designated by h, a, r , z ; respectively, adding up to 4. This is summarized in Figure 1.Any of these numbers can range from 0 to 4, except for n which is limited t o 2(n = 1: =; r = 2: C=C). An unshared electron pair or a bond to a metal is simply the conjugate base of the bond t o hydrogen and is included in H (and h).
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216 1
Journal of chemical Education
any
single carbon atom:
Oxidation state
BOND
TYPE
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,"
STRUCTURE
x = z-h
NUMBER
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SKELETON + FUNCTIONALITY =0 f= 1 Primary 2 Sccondaw 3 Tertiary 4 Quaternan
--,
0 saturated hydracarbon
I R-OH,R-X,R-NH, 2 RCHO, R,CO. etc. 3 RCOOH. RCOOR, RCN, efe. 4 CO,. COCI,, H,NCONH,, ete.
Figure 1. Symbdic characterization ot swuctues.
Citrini"
Figwe 2. Sample sbuctures characterized.
This affords a simple description of any carbon. Its . single skeletal level is indicited by the value of a, the number of attached carbons, already verbally known as primary or terminal carbons (a = 1) and secondar; (a = 2), tertiary (a = 3), and quaternary (a = 4) carbons, the a = 0 carbon heing one with no attached carbons (as in CHc CH30H, HCOOCH3, COz, etc.). The functionality level of any single carbon may be designated as f = n z, the sum of both carbon-carbon n-bond functional groups and heteroatom functional groups. Since n is limited to 1or 2, the two kinds of functionality consolidated in f can be distinguished by putting one bar over the f-value for s = 1(double bond) and two bars for s = 2 (triple bonds). Any carbon may be characterized then by two digits, n and f, its skeletal and funclional levels, respertively; and cverythine" else attached is~. hvdroeen. - . determined hv a f = 4 - h . Thus any carbon in any given structure may he quickly characterized by a two-digit number, uf, and this is illustrated in Figure 2. This two-digit number (of) may be called the character (if c = 10a f ) of a single carbon atom. The fun-
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'Developed from (a) Hendrickson,J. B., J. Amer. Chem. Soc., 93, 6847 (1971)and (b) Hendrickson, J. B., J.Amer. Chem. Soe., 97,5784 (1975).
damental nature of the conce~tual-moups (H.R.U.Z) may he stressed in two important observations. First. although all electronegative heteroatoms (N,O,X,S,P) are consolidatd into Z the vaiues of z define families of ready chemical interconvertihility. For z = 1the family of substiR-CI Rtution reactions unites them all (R-OH NH2, etc.); z = 2 represents the aldone family of aldehydes and ketones and their commonly interconverted derivatives, acetals, ketals, imines, oximes, hydrazones, etc.; z = 3 is the carhoxyl family of acid chlorides, anhydrides, esters, amides, amidines, imino-ethers, nitriles, etc., all hydmlyzahle to carhoxylic acids and in turn made from them; while z = 4 is the family of carhon dioxide derivatives, with all honds from the carbon to heteroatoms. as in carbonates. urethanes, ureas. guanidines, isocynnates, etc., also interconvertihle. Second. the characterization allows immediate derivation of the oxidation state of any single carbon2 as x = z - h. These derived oxidation states mav he used directlv in determining oxidation state change a t ali carbons in oxidation and redu; tion reactions, and so in finding overall oxidation state change for balancing the stoichiometry of their equations. This will he evident in the one-carbon examples in Figure 1, and oxidation states of the several carhons are shown for the firsttwo examples in Figure 2. ~
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Nature of Oraanlc Reactions With structures so organized, we may turn t o chemical reactions. in which the character chan~es,but rarely a t more in any than one or two carbons. In general what we R, reaction at a eiven carbon atom is the loss of one group (H, II or Z) and ils replacement by another, i.e., one bond breaks and another is made. A reaction a t one carbon then may he represented by the symhol for the group added followed by that for the group lost. This gives 4 X 4 = 16 reaction types a t any given carhon, and they are summarized in Figure 3. Reactions in which H is gained andlor Z is lost are of course reAdded
Lost
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+ H Reduction + R Construction
- H Oxidation - R Fraernentation -n ~ d d i t i o n - Z Reduction
+ n Elimination
+ Z Oxidation
Mode Oxidative Reductive Isohypsic
One Carbon Only
Two Carbons Involved FragConstruc- menta- Elimition tion nation
Addi-
- - - - -tion ZH HZ ZZ
---RH
ZR
RZ
HR nR
RrI
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HH
Zn
nH nZ nR
Hn Rn
-
RR
Elimination
Figure 3. Families of reactims at single carbans.
nm
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ductions (from x = z h ) while oxidations add Z andlor lose H. Constructions are the svntheticallv imoortant family which add R (i.e., RH, RZ, ~ I I , - a n d~ ~ ) , ' t h is, a i which f L m carbon-carbon sinele (o-) honds. while the loss of R is called a fragmentation ~eaction.Similarly, the family of four reactions (IIH. . . nR.. IIIIJIZ) which add x are eliminations and the converse, which lose II(HII, RII, IIII, ZII) are addition reactions. Of course. m v reaction at a carhon is characterized both by what is lost kd-what is gained, so that two of the descriptors usually apply, as in oxidative construction (RH), reductive elimination (IIZ), addition/construction (RE), eliminationlfragmentation (IIR), etc. The 16 reaction families are tabulated in one way in Figure 3 according to whether they involve one or two carbons and are oxidative or reductive or neither (= isohypsic). When a reaction must involve two carbons, the symbol for each carbon must he shown, as in dehydration of an alcohol (IIH.n'Z)'or Grignard addition to ketone (RH.RZ); when these reactions are isohypsic overall, the change a t one carhon is oxidative, that a t the other reductive. An overall oxidation would he oxidative a t hoth. as in hromination of an olefin (ZII, Zn), whercas hydrogenation of an olefin is an overall reduction (Hn.H111.The isohv~sicHI1 and IIRappear twicein Figure 3, hoth asconstructidn~fra~mentation and as additionlelimination. The douhle-letter families may he recognized: ZZ is substitution a t a single carhon (-OH for -C1, etc.); H H is the acid-base reaction: RR, a replacement of one carhon attachment by mother, is mostly hescriptive of migrating carhons in rearrangements; and n n refer*.to double-bond shifts, viz, the central carhon of an allylic rearrangement or alleneacetylene transformation. Since there are three pairs of opposite types (oxidation1 reduction, construction/fragmentation and additionlelimination) they can he mounted for logical presentation on a three-dimensional coordinate system as shown a t the hottom of Figure 3, hut this is rather harder to perceive. Here the four double-letter families are all a t the origin, and the other 12 families lie in three perpendicular planes, such that reversed-letter pairs are all joined through the origin. The Character Triangle The central representation which combines all structural elements and reactions is a maph called the Character Trim& for a single carbon itom. There are 15 possihle characters (of) and these may he displayed graphically as points in an equilateral triangle, as shown in Figure 4, with values of a, 1, and h increasing in each of the three directions. For cornnounds with noC-C doubleor trinle honds (r = 0). f = z and the vertical axis is a scale of oxidation states ( x = z - h)... as calibrated a t the left. The horizontal axis shows increasingcarbon substitution (skeletal level, o) to the right. The maoh . mint for each of the I5 c h a r a c t ~ ais. ex~andedin Firmre . 4 to a circle containing a structural representation of the character of the carhon as well as the two-digit ( a / ) character numher below. The parallels in each of thetthree directions indicate constancv and level of o, f , and h. Thus the vertical lines are c o n s t k i n o and from left to right the columns are o = 0 (no attached carbons), o = 1(primary carbons), a = 2 (secondary), etc. Considering functionality as heteroatom functional groups only (F = Z; s = O), the top left point is f = 4 (COz, etc.) the next lower level, f = 3, is two points, HCNI HCOOR(03) and RCOOHBCN (13), while the next level a t f = 2 shows the aldones: formaldehyde (02). aldehydes (12), and ketones (23,and their derivatives. The 30 lines of the triangle all represent reactions interconverting the two joined carbon characters. AU parallel lines have the same reaction symbol, one symbol for one direction, reverse symbol for the reverse direction. Thus there are 10 vertical lines representing FH (=ZH or IIH) going up and HF going down. The vertical changes are oxidations up and re~
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ZFerguson, L. N., J. CHEM. EDUC., 23,550 (1946). Volume 55, Number 4, April 1978 / 217
Figue 4. W ' m Character Tr!agle for single mtmm. h b m character (cf) indicated under each carbon state. Conshuctlon= solid linestote right. Oxidation state scale at left refers only to cases of u = 0 ( f = 4.
ductions down, as shown on the accompanying oxidation state scale on Figure 4. It is convenient in familiarizing oneself with the graph to consider first only hetero-atom functionality, omitting cases with C-C double and triple honds, i.e., ( r = O), and then F = Z and the vertical oxidations are ZH reactions and the reductions are HZ. Being vertical on the graph these reactions all occur without any change in the carbon skeleton, i.e., a = O. Changes in the carhon skeleton are constructions (and the reverse, fragmentations) and these are lines with a horizontal comnonent. reactions to the rieht heine constructions. The set df 10 reactions aimed down To the right are RF (or RZ if r = O), reductive constructions, while the 10 lines aimed up to the right are RH, oxidative constructions. The "douhle-letter" reactions like ZZ. etc.. all occur within one point. substitutions at saturated carlion within points 11,21, $1 (primary, secondarv, tertiarv). aldehvde interconversions with oxime. acetal. etclwithin i 2 a n d similar ketone derivatization in 22, while the interconversions in the carhoxylic acid family are all consolidated in point 13. The Character Tetrahedron
The character triangle misses the distinction hetween multiple C-C honds and heteroatom functionality (F = n + 2)and t h i ~can onlv be ohtnined hv creatina a third dimension to the graph. ~ h i ~done i s by expanding F into Z and II and accordingly the character triangle into a character tetrahedron (Fig. 5), leaving the original triangle as a base with ( r = 0) and adding two more triangles parallel above it, (r= 1) with 6 points, and ( z = 2) with 3 points, the top point of (a = 3) being truncated as disallowed. The added horizontal r-planes are distinguished the heaviest lines in Figure 5 and the whole tetrahedron contains all the 24 possihle combinations for any given rarhon atom. The oxidation states of the pointsare all (including u-functions) given accurately now by the scale at the left. reoresentine v e & d nlanes of constant x throueh the tetrahkdrin. In F i g k e 5 the;epresentations of each carbon now distinguish C-C multiple honds and the character num218 1 Journal of Chemical Education
Flgue 5. The Character Tetrahedmn. Heavy lines mr a = 1 and r = 2. Shaded planes for aame skeletal level (o) as labeled above. Inset = dhBnims of reactb families. Solid lines = constructions to right IRH. RZ). Dash llnes = R r consbuctlons lo rigM. Ddted lines = refunctiokdlzations. Oxidation scale valid fw all carbon s t a s . Carbon Characters 10 C-nmlhyls 11 Primary alrohols. halMe~,etc. 12 Aldehydes and derivatives 13 Carboxylic acids and derivatlves 20 Methylenes 21 Sewndary alcohols. halides. etc. 22 Ketones and derivatlves 30 Methines 31 TeRiarY alcohols. halides. etc. 40 Quaternary centers 11 12 13 21 22 31 Olefins 21 22 31 Aromatlccarbons fl 73 Acetylenes and sllenes
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h e n below each likewise distinguish by the use of overhars for z. I t may he notedthatthe t h - e states of an aromatic carbon are thus given by 21,22, and 31. The character tetrahedron of Figure 5 has essentially the same axes aa in F i m e 3 since the oxidation-reduction axis (I = z h ) is vertick a t left and the elimination-addition, or z-axis, is perpendicular to the plane, while the third axis for construction-fragmentation, the a-axis, is left and right, as shown bv the inset in Fiaure 5. Constancv of values for a. h. and z is now seen as plan& in the tetrahedron, constant r the three horizontal planes and the three sloping planes of constant a shaded and labeled in Figure 5. Reactions which occur within any plane maintain this constancy, i.e., reactions in the constant-a planes do not alter the skeleton but are only oxidation-reduction and addition-elimination, while reactions in the horizontal planes (Ar = 0) do not affect C C multiple bonds, etc. AU reaction lines represent a meeting of two planes since any reaction involves only two noups and the oth& two are unchanged, cf., oxidation of secondary alcohol to ketone (7.H)lies in the base plane (n = 0) and the (o = 2 ) plane and accordingly has no R or I1 group in the symhol. This character tetrahedron contains all oossihle chemistrv occurring a t any one carbon atom, and successive reactions a t any carbon, as in a synthesis, can be followed as a route through the tetrahedron from point to point. Since the tetrahedron is rather dense with symbols, planes from it may he isolated (as in Figure 4 considered as r = 0) and its reaction families studied, each point or each line or family of lines a
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natural and familiar group of chemical reactions. In Figure 4 for a = 0 (F = Z) the vertical lines are all families of oxidations (up) and reductions (down) and on each may be collected the reagents that activate the transformation for different heteroatoms, Z. Thus the line 11 10 may be metal reduction of primary halides, or LiAIH4 on primary halides or tosylates, etc., while 12 13 is aldehyde oxidation (AgzO, KMu04, etc.) to acids, aldoxime dehydration to nitriles, ozonolysis of acetals t o esters, etc.
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Organic Synthesls
Since the character tetrahedron organizes all possihle organic reactions, i t is an excellent storage vehicle for the information required to design organic syntheses. I t is convenient to separate here the construction reactions from the others (the refunctionalizations) since constructions are central to synthesis. The reason is simple. Since the available starting materials for synthesis are smaller than the target molecule, construction reactions are mandatory, hut refunctionalizations are in principle not. An ideal synthesis, from the viewpoint of economy, would be one in which the starting materials available from the store are correctly functionalized to carry out all the necessary constructions in sequence without refunctionalizing in between, and after the last one arrive directly at the target, both its constructed skeleton and its functionality correctly placed. This will be the shortest, ideal synthesis and requires no refunctionalization reactions. Hence the way to start learning organic synthesis is to focus on organizing all possihle construction reactions, and they are all contained in the tetrahedron as reactions moving to the right, and shown with solid lines in the representation of Figure 5. The tetrahedron of Figure 5 may he shifted to an alternative representation, in some ways easier to grasp and to use for synthesis, by converting to a simple Cartesian coordinate system with main perpendicular axes for a and f and an axis for a perpendicular to these, up from the plane as before. This results in Figure 6, in which the three parallel shaded decks are, in rising order, for no C-C multiple hond ( a = 0;f = z), for double bonds (C=C; a = I), and for triple bonds (C=C; a = 2). The three-deck figure has been clarified by omitting all but the vertical additions-eliminations (ZIIJIIZ) between decks. This shift to altered perpendicular axes (from I ,a, a to f , a, T ) sacrifices the clarity of locating oxidation states easily hut focusses more clearly on synthetic needs. On Figure 6 reductive reactions are still oriented downward in each a-plane but the horizontal (Af = 0) reactions are oxidative. The constructions all have a rightward component, in the direction of increasing a. The construction reactions may now he located; they are of three types: RH, RZ, and RE. The first two have no a-component (Aa = O), i.e., alter no *-bonds, and so lie in the horizontal planes and are most easily recognized. The oxidative constructions, RH, are the horizontal solid lines to the right in these planes, parallel to the a-axis, while the reductive constructions, RZ, pass down and to the right, i.e., increasing in a(+R) and decreasing in f(-Z), in the horizontal Aa = 0 planes. There are ten parallel lines for ten RH reactions in the a = 0 plane, and ten more for RZ. In the a = 1plane there are three of each and one each in the r = 2 plane, for atotal of 14 lines each for RH and RZ constructions. These major construction families may be construed as construction halfreactions since any one characterizes the net structural change in construction a t one carbon atom. Since it requires two carbons to constitute a full const~ctionreaction, i.e., each end of the hond being constructed, then any construction is the combination of two half-reactions. Most common constructions take place without overall change in oxidation, i.e., they are isohypsic. Such isohypsic constructions are thus the product of an oxidative construction and a reductive construction half-reaction, as RH.RZ for the structural changes in the linking carbons.
Figure 6. The Character Tetrahedron: alternate presentation far synthesis. RH constructions labeled with letters (A-D) RZ Consbuctions labeled with numbers (1-4) R r constructions (dash lines): two representative reactiom labeled i and I.
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The RII reactions require a change at one further carbon, the other end of the double bond (as in C==C C C-C-C) undereoine addition. and so mav he oxidative or reductive depenkngon the change there ~ z I I ,oxidative and HII, reductive). These will be found to be generally electrophilic and nucleophilic additions, respectively, in mechanistic terms. The RII reactions come down from one a-nlane to the next. as well as down by Af = -1, since f includes a, and also to the right for Aa = +l.The nine possible RII reactions are shown as the heaviest lines in Figure 6. An easv wav to classifv construction reactions for svnthesis design can be-derived from this chart. Any conrtruc~onmay he seen as a combination of two independent half-reactions for two carbons linked, and each is considered separately. The half-reactions will be designated f i t as RH and RF, the latter broken down into RZ and RII. They can then he designated to show the functionality level on the substrate for construction, i.e., f = 0,1,2,3,4. The R H oxidative constructions are labeled with letters with group A being f = 0, B being f = 1, etc.. and the RF constructions distineuished hv laheline with numbers equal to f : the K% reductive constructions are to be plain numhers and the HI1 (oxidative or reductive) dintinguished hy an overhar. In the course of construction the carbon undergoing RH construction retains its starting functionality level (Af = 0) while that undergoing RF decreases its functionality level by 4= -1. The resulting eleven possihle families of construction half-reactions are summarized
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Starting Functionality
0
RH
Volume 55, Number 4, April 1978 1 219
These simple labels for the eleven families thus broadly define the starting functionality and the product functionality a t any carbon undergoing construction as well as the reaction mode (RH, RZ, Rn). The classifications may be further subdivided if required? but as they stand they correspond with broad cateeories alreadv in common use. Thus the RZ halfreaction 1;epresents aikylations, with f = 1, Af = -1, as in R-R, and RZ half-reaction 2 indicates carbonyl R-X 3 refers to addition (f = 2, Af = -1: >>C?) R->C-OH); R-CO-R and 4 conversions like R-CN or R-COOLi is carbonation with CO2 or equivalents. The R n half-reactions are additions, simple additions to double bonds (e.g., Michaeior conjugate addition) labeled 1 and those to triple bonds 2 (in which f = 2 1). The RH half-reactions are usually carbanions,
