Internet Electronic Journal of Molecular Design 2002,1, 428–442ISSN 1538–6414
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September 2002, Volume 1, Number 9, Pages 428–442
Editor: Ovidiu Ivanciuc Special issue dedicated to Professor Haruo Hosoya on the occasion of the 65th birthday
Part 1
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Guest Editor: Jun–ichi Aihara
The Topological Index Z Before and After 1971
Haruo Hosoya
Ochanomizu University, Bunkyo–ku, Tokyo 112–8610, Japan
Received: September 10, 2002; Accepted: September 12, 2002; Published: September 30, 2002
Citation of the article:
H. Hosoya, The Topological Index Z Before and After 1971, Internet Electron. J. Mol. Des.2002,1, 428–442,
H. Hosoya
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The Topological Index Z Before and After 1971 Haruo Hosoya #,*Ochanomizu University, Bunkyo–ku, Tokyo 112–8610, Japan
Received: September 10, 2002; Accepted: September 12, 2002; Published: September 30, 2002
Abstract
The author’s first paper on the topological index Z was published in Bull .Chem .Soc .Jpn . in 1971, where good correlation was found between the boiling points of alkane isomers and their Z values. This idea is bad on the author’s unpublished work performed in 1957, when the boiling points of octane isomers were predicted by scrutinizing the structural dependency of boiling points of alkanes up to heptane. Behind stories inside and outside of the country before and after the birth of Z index are introduced. Several academic encounters of the author and reactions of the contemporary chemists to the new idea are also described. In the end some aspects of QSAR problems for octane isomers are introduced.
Keywords. Graph theory; topological index; characteristic polynomial; alkane isomer; boiling point; mathematical chemistry.
1 INTRODUCTION
The first paper on my topological index Z was published in September of 1971 in the Bulletin of the Chemical Society of Japan (BCSJ) [1]. Since then nearly four hundred papers have cited it during three decades. Even when every detail of my memory on my favorite paper and its relevant events and rumors are beginning to fade out, I enjoy the obrvation that currently twenty to thirty papers per year are still citing my original work. Some of the authors [2] claim that the term “topological index” was first coined by mylf followed by more than two hundred different topological indices propod by the group of mathematical chemists scattered worldwide, and therefore the topological index has become the general name for the gigantically enlarged family of molecular graph descriptors.
Now I recall the birth pain which I experienced at each publication in the ries of the Z –papers and also my awkward analysis of the structural dependency of the boiling point of alkane isomers, which was performed already in 1957. At that time I was an undergraduate third–year student.
# Emeritus professor at the Ochanomizu University.
* Correspondence author; fax: +81–48–267–9432; E–mail: ha.ac.jp.
The Topological Index Z Before and After 1971
Internet Electronic Journal of Molecular Design 2002, 1, 428–442
In this short paper I would like to introduce how the idea of the Z index has evolved and also how conrvative professors tried to repel new and strange ideas and intruders from their lf–perceived clod territory. In the end an interesting byproduct on the QSAR study of octane isomers will be introduced, which was found out while I was writing this manuscript.
2 BIRTH OF Z INDEX
In April first, 1969, at the age of 32 I became associate professor of chemistry of Ochanomizu University in Tokyo, after returning from one year of postdoctoral experience in John Platt’s laboratory, Ann Arbor, Michigan, where I was a biophysicist struggling with the eye balls of rats to measure electrical respon to photochemical reactions in retina. Before visiting the U.S., I had obtained my PhD at Saburo Nagakura’s laboratory, Institute for Solid State Physics, University of Tokyo with the title “Study on the Structure of Reactive Intermediates and Reaction Mechanism” mainly by measuring and calculating the electronic spectra of organic molecules with conjugated S electronic systems. At that time only lected postdoctoral fellows could try to perform ab initio calcul
ations in the Mulliken–Roothaan group, in Chicago. However, Nagakura’s laboratory was one of the largest groups in the world performing mi–empirical calculations, such as PPP and “molecules in molecules.”
Figure 1. My note (June 2, 1957) describing the prediction of the boiling point of octane
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isomers. One can read the ntence at the right bottom as “Agreement is good.”
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I was thinking and thinking what can be done for a lonely wolf in a poor university with only lady undergraduate and master cour students. I did not either want to sharpen my awkward biophysical technique, nor to construct a laboratory of physical chemistry like a miniature of that of my former boss. Before long I recalled and found an old bundle of memos and diagrams, which were worked out by mylf twelve years earlier (Figure 1).
2.1 My First QSAR Study
When I was a third–year student of chemistry in University of Tokyo, I happened to come across a table of the boiling points of alkanes up to heptanes and was fascinated by veral interesting relations between the structure and boiling point (bp ) of the hydrocarbon molecules. The bp values of a given ries increa with the number of carbon atoms, while branching always lowers bp . Although the decrement depends on the size of molecules, one can trace its smooth variation with the size. The effect of lowering by 2,2–dimethyl substitution is much more larger than the double of 2–methyl substitution, and so on. Then by drawing a cross–diagram of bp values as in Figure 2 o
ne can estimate all the decrements of bp of venteen isomers relative to n
–octane.
一寸丹心图报国Figure 2. Cross–diagram showing the change of bp values of alkanes (not the original but reproduced later).
Many of the octane isomers have a few different ancestors. For example, 3–methylheptane may be deemed either as the next higher member of 3–methylhexane by tail elongation, 2–methylhexane by head elongation, or n –heptane by 3–methyl substitution. All the increments in bp from heptane to octane for the ries were estimated from the cross–diagram of all the alkane isomers up to heptanes. Then the bp values obtained from different ries were averaged to give the most plausible bp value of the isomer concerned.
After finishing up this study I found a table of the obrved bp data in the Iwanami Dictionary of
The Topological Index Z Before and After 1971
Internet Electronic Journal of Molecular Design 2002, 1, 428–442
Physics and Chemistry [3], who page is copied in Figure 3, where melting point, liquid density, and refractive index are also tabulated. I was excited at the good agreement between the obrved and estimated values (e Figure 4).
Figure 3. Copy of Iwanami Dictionary of Physics and Chemistry [3], “octane” and “octane number”. There are three misprints. 1) bp of 2,2,3–trimethylpentane should be 110.3˚C. 2) mp of 2,2,3,3–tetramethylbutane should be + 101˚C instead of –101˚C. 3) liquid density of 4–methylheptane (0.7163) may be mistype of 0.7063.
Most of the estimated bp’s were lying within ±4˚C range of the obrved ones. This is a rather good correlation for the whole group of octane isomers who bp’s are scattered in the range of 20˚C, and the U v alue was 0.942. This was my first achievement in QSAR study, although I had no
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idea about QSAR nor graph theory at that time, when even in the community of chemistry rearchers QSAR and QSPR had not yet gained their current identity. It was in the midsummer of 1957, and my 21st birthday was approaching and as a mere student of chemistry I did not know wha
t I should do next. Naturally I never thought of its publication in a chemistry journal but wrote a brief note with diagrams for mylf and aled it at a corner of my bookshelf as my personal and precious cret.
Very recently I learned that Harry Wiener found his W index at the age of 20 and wrote the pioneering paper in JACS in 1947 [4,5]. Moreover, he developed and strengthened his theory by applying it to many other thermodynamic properties, such as liquid density and refractive index, by combining with another index p, the polarity number. Now I am filled with special feelings and emotio
ns by supposing what may have happened if I had continued to play with the other physico–chemical data in Figure 3, which actually contains three big misprints but they give big hints for further study. The story will be continued in this paper.
2.2 The Z Index and the Characteristic Polynomial
Twelve years have pasd since my first discovery in QSAR study, and I had grown up as a kind of number crunching chemist trained by a huge pile of mi–empirical MO calculations. Then after finding out my own old memo on the alkane boiling points, my first trial was to apply the Hückel method to all the isomers of alkanes but not in an ordinary way. Namely, instead of solving the solution of the characteristic polynomial (CP) of the molecular graph reprenting the topological structure of the carbon atom skeleton of the alkane isomers, I become interested in the coefficients of the characteristic polynomial.
Namely, there emed to be some hidden regularities between the t of the coefficients, {a k}, of
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