Experimental organic chemistry Balaban investigated the synthesis and properties of
pyrylium salts. He discovered a new synthesis of pyrylium salts by diacylation of
alkenes, the Balaban-Nenitzescu-Praill reaction. Nowadays, Balaban is recognized as a world authority in this field. He wrote the only book in this area. Balaban also developed new synthesis of oxazoles by
AlCl3 catalyzed substitution of aromatic compounds with
azlactones, followed by dehydration. In addition, he had been exploring new syntheses of
indolizines and of
naphthalene derivatives. In order to explain the extraordinary stability of hydrazyls such as
2,2-diphenyl-1-picryl-hydrazyl, Balaban and his co-workers prepared related hydrazyls with lower
steric shielding and accordingly lower stability. Then the first push-pull diarylaminyls were synthesized and shown to have stabilities depending both on electronic and
steric effects. Another experimental research direction involves the synthesis of
chelate compounds having
boron as the central atom.
Theoretical chemistry Balaban had a permanent interest in
theoretical chemistry. He is considered as one of pioneers of
chemical graph theory. The first book about this interdisciplinary field was edited by Balaban and appeared in 1976:
Chemical Applications of Graph Theory. One area in which cubic (or trivalent) graphs play a dominant role is the enumeration of [
n]annulene valence isomers (CH)
n where
n is an even number. With two coauthors, Balaban published in 1986 on this topic a 3-volume monograph (
Annulenes, Benzo-, Hetero-, Homo-Derivatives and Their Valence Isomers). Some of these valence isomers undergo thermal or pohotochemical automerizations. More recently, Balaban edited in 1997 a book titled
From Chemical Topology to Three-Dimensional Geometry in which various two- and three-dimensional nets were discussed. On using an approach similar to that imagined by
Randić for his connectivity index χ, but replacing the
adjacency matrix by the
distance matrix, and compensating graph-size-increase, a new
topological index (TI)
J was proposed under the name "average distance-based connectivity index"; it is now known as the "Balaban index". Not only is it much less degenerate than all previous TIs, but it allows a simple encoding for the presence of
multiple bonds or
heteroatoms. Other new TIs were studied: several TIs based on informational descriptors, and triplet-based indices that result from converting
matrices into systems of
linear equations. The
Lewis acid-catalyzed syntheses of diamondoid hydrocarbons discovered by Schleyer proceed via multiple
1,2-rearrangements. The graph-theoretical analysis of the simplest such reaction involves an ethyl cation with five substituents which undergoes an automerization. This process is characterized by a 20-vertex or a 10-vertex graph depending whether one carbon atom of ethane is or is not labeled. These graphs constitute the first
reaction graphs, in which vertices symbolize reaction intermediates and edges symbolize elementary reaction steeps.
Graph theory Starting from the 10-vertex graph known as the 5-cage or the
Petersen graph, Balaban observed relations among the known cages. Having discovered how a cage with smaller
girth g was hidden in a cage with girth
g + 1, Balaban published a paper on what was later proved to be the first 10-cage, known as the
Balaban 10-cage. In 1973, he found the unique 11-cage, known as the
Balaban 11-cage, as was proved by mathematicians using a lengthy computer search. Proposals made by Balaban about new possibilities for evaluating the performance of researchers, improving the way citations are used for this purpose (e. g., via the
Hirsch index) included the use of author indexes of widely circulated treatises, or modifying the way one considers the impact factors of journals. Honoring invitations to contribute to special issues of journals dedicated to the philosophy of chemistry, Balaban published in
Hyle an essay on how the "Sherlock Holmes principle" (if one eliminates the impossible, then whatever remains, no matter how improbable, must contain the truth) can be implemented by
chemical graph theory which allows for instance to find all
chemical isomers for a given formula. == Scientific publications ==