A Novel Method of Estimating Motor Octane Number (MON) - A Structure. Property-Relationship Approach. Shalini Singh"'. Shobha Joshib Anjali Shrivastavab ...
Journal of Scie ntific & Industrial Research Vol. 6 1, November 2002 . pp 96 1-965
A Novel Method of Estimating Motor Octane Number (MON) Property-Relationship Approach
A Structure
Shalini Singh"' . Shobha Jos hi b Anj ali Shrivas tava b and Padmakar Kh adikara * ""' Research Divisio n. Lax mi Fumi gation and Pest Contro l Pvt Ltd. 3. Kh ati pura Indore 452 007 h
Depart ment o f Chemistry. Governmen t Auto nomous and Model Holkar College. Indore 452 00 I. Ind ia Rece ived: 25 August 200 I; Rev ised rece ived: 04 Jul y 2002
A Novel method is proposed for the esti mati on or Motor Octane Number (MON ) using Pad makar- Ivan (PI) index. The regression analys is of the data shows that MONs can he estimated successfull y using PI index and that correlation o r MO I wi th PI is fami lial.
Introduction
Graph-Theoreti ca l approac hes have found applicati on in di verse areas of chemi ca l, indu stri al, environmental, pharmacoc hemi ca L and medi ca l resa rch I. The authors have used graph-theoreti ca l invari ants ca lled topolog ica l indices in their app roac h. Topologica l index is a numeri ca l representation of molec ul ar structure!' ". During the last two decades, several papers have been publi shed on the applicati ons of graph in va ri ants in predi ctin g phys ico-c hemi ca l. bi omedi cinal and tox icologica l properti es of di ffe rent graphs of molec ules}-5. For thi s purpose the bonding topology of chemi ca l species is converted, either into a sing le rea l number, or a set of real numbers l -5. Thi s single rea l number quantitatin g the topo logy of achemi chal spec ies is ca ll ed topological index 3-5
------
A pl atheora of topologica l indi ces are reported in the literature. The Wiener number (Wiener lndex/' is the first, o ldest- and widely used topological index in developing quantitati ve structure-property (QSPR ) and structure acti vity (QSA R) relati onships. Even today it is used ex tensive ly. Thi s index , symboli zed as W, suffers from th e defec t that it is used ex tensive ly . . Thi s index sy mboli zed as W, suffe rs from the defec t that it is applicable onl y in the case of *Corresponding au thor: Padmaka r V Khadikar. Tel : 9 1-73 1-53 1906; e-mail : anjalce_Shrivastava @redifTmail.com
acyc li c molec ul es (trees) . Recentl y, Gutman and coworkers7-9 have introduced a new index whi ch is ca lled Szeged index and abbreviated as Sz. Thi s index (Sz) is considered as modificati on of W to cyc lic graphs or cycle containing graphs with tree-like side . S10 . H owever, .In the cse of acyc lic graphs Szc IlalIl index coincides with W-index . Consequent to the coincidence of Sz and W in acyclic graph s recentl y, Khadikar et a [ 1l have introduced a new index whi ch is named Pad makarIva n index and abbreviated as PI. Very little is known about the applica bility of PI in QS PR/QSA R . . of our present stu d ·les 11-15 . T h'IS was prtmary aIm in vesti gati on. Therefore, in the prese nt stud y we have attempted estimati on of ' Motor Octane Number' (MON)16 using PI index . Use of graph invari ant In structure-property re lati onships (S PR), foll ows from the structureproperty-simil_a rity principle-the central paradigm of SPR studi es l -) . Accordingly. attempt has been made to predi ct MON fo r a di ve rse set of alkanes using PI index. Thi s uses co rrelati on analys is empl oy ing the method of least squares I 7-20 . The res ults are di sc ussed subsequentl y. At thi s stage, it is worth mentioning that Motor Octane Numbers (MON s) are related to ability of alkanes to form radi ca ls by crack ing at hi gher temperature and press ures. These free radi ca ls and thu s MONs are responsible for environmental pollution, parti cul arl y due to motor fu els. In thi s
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J SC II ND RES VO L 6 1 NOVEM BE R 2002
l6
stud y we have co ll ected MON s fro m the literature T he alkanes, their MONs and PI indi ces are recorded In Ta bl e 1. As stated the alln of thi s work IS to establi sh QS PR mode l(s). These are di sc ussed In subsequent sec ti ons. Tabl e I SL No.
Material and Methods Calculation of Pllfldex The recentl y introduced PI ind ex ll . ls can be ca lculated using the fo ll ow ing express ion:
Alka nes. the ir PI indices. mo tor octane numher (MO ) (obse rved as we ll as es timated) and residue (difference between o bserved and est imated) MON PI
Name
MON Ohs
Estd
Res idue
4
6
90. I
90 .45
O. 35
2
2M3
6
97 . 6
90.45
7. 15
3
2M4
12
90. 3
85. 83
4. 47
4
2M5
42
73. 5
78 10
-4.60
5
24MM6
20
69 . 9
70.72
-0. 82
6
33MM6
30
86. 6
90. 23
-3.63
7
5
12
6 1. 9
66.36
-4.60
8
23MM4
20
94. 4
94. 54
-0. 14
9
33MM6
42
83.4
78. 10
5. 30
10
22MM5
30
95.6
90. 23
5. 37
II
22MM6
42
77. 4
78 . 10
-0.70
12
4M7
42
39.0
47 . 88
-8.88
13
3M7
42
35. 0
29. 18
5 82
14
3M6
30
55 .0
5 1. 84
3. 16
15
24MM5
30
83. 5
73. 33
10. 17
16
23MM5
30
88. 5
90 23
- I . 73
17.
3ES
30
65 . 5
73. 33
-7.83
18
2M6
30
46. 6
5 1. 84
-5.24
19
3 M5
20
74.3
70. 72
3. 58
20
23MES
42
88. I
21
223MMM5
42
99. 9
22
224MMM5
42
95. 9
2 .)',
2M7
42
23. 9
29. 8
-5 .28
24
224MMM5
42
100 . 0
25
233MMM5
42
99 . 4
26
22MM4
20
93.4
94. 54
- I. 14
27
6
20
26. 0
34. 23
8. 23
28
25MM6
42
55.
7
47. 88
7. 82
29
7
30
O. 0
-5. 92
592
30
22 MM 3
12
80. 2
85. 83
-5.63
No te: 4 - buta ne ; 5- penta ne ; 6 - hexane:
Ill-
met hyl: e- et hyl
SI GH
el
PI = PI(G) =
L
963
al. NOVEL METHOD OF ESTIM ATI NG MON
I I nell (e iG) + I\:v (eiG)I,
.. . ( I )
e
where nell is the number of edges nearer to the vertex u, whi ch is one of the end of the edge e = uv. The meaning of nev is analogo us. The edges equidi stant from u and v both , are not co nsidered. The PI indices so calcu lated are prese nted in Table I. Mo lar Octon e NU II/ber (MON)
As stated earli er Motor Octane Number (MON) fo r the set of alkanes used (Table 2) are taken from the literature l(,. Slaslical Analys is
The main obj ective of the prese nt inves ti gation was to develop a predicti ve mode l (equation ) of estimatin g MON of alkanes usin g PI index. For this , we have used reg ress ion analysis. in that. we have exa mined Wilks-Shepino test for normality and Cook's D stasti stic for outli ers l7.20 Results and Discussion A perusal of Table I shows that no degeneracy is found in MONs of th e alkanes under present st ud y. However, degeneracy is observed in PI indices. This is obvious as the PI index belongs to first-generation . I In ' dex-' "I"' --. Accor d'Ing to B a lb a an-' l, the topo Ioglca first-generati on topologica l indices, inspite of their observed dege neracy, are quite successful in developing QSPR/QSAR mode ls. This found to be the case here also.
For the entire set of 30 alkanes the correlation of MON s with PI index is found to be stast ica ll y worsened . The correlation is fami li al , i.e. depends upon particular type (famil y) of alkanes. Such a fami Iial behaviour was also observed earl ier by Ba laban el a/ 23 . 2-1. The correlati on fall s into five different fa milies. The aforementi oned five fam ilies of alkanes con sisted of the fo ll owing alkanes (Table I): I: I. 2, 7, 27. 29 ; II: 3, 5, 13. 14, 18, 19,23. 30; III: 8, 12, 15 , 17, 26. 28; IV : 4.6. 9, 10. 11 , 16: and V: 20.2 1, 22.24.25. In case of fami lies I to IV, we observed that with increase in the va lues of PI index , motor oc tane number decreases. Thi s means that dec reasing co mpactness is favourabl e for mode lling MON s. The alkanes belonging to fami ly V indi cates their MONs are independent of PI index, and thu s the co mpac tn ess of the alkanes used. The data under categories (fa mili es) J to IV are subj ec ted to regression analysi s usi ng the meth od of Ieast squares 17· -'0 . TIle regress 'Ion parameters an d qua lity of correlations are presented in Table 2. In eac h case th e di stribution of res idual s was normal (Wilks-Shaj no, P = O. 644) and no outli ers were . d C00 k' s D th roug h stastl.cs 18·"0 -. determll1e Furthermore, all the four mode ls for the catego ri es (fami li es) I to IV were fo und to be stati sti ca ll y significant. The correlation coeffic ient ranged betwee n - 0.8365 to - 0.9874. Based on the data presented in Table 2 the fo ll owing approximation can be made:
Tabl e 2- Reg ress ion paramete rs and quality of correlations lor modelling MON by PI index. SL No. Correlati on Correlation for co mplele seri es as alka nes
Catego ry
Aj
Bj
S,
Sy
R
All alkanes
-0. 2545
85. 127 1
22.899 1
26. 5550
O. 2794
-4. 01 59
11 4.5549
10.2567
41. 7142
-0. 9874
II
- I. 8883
108.4956
12.0000
23. 1718
-0. 9779
22 . 3108
-0.9365 -0. 8365
MON vs PI 2
Correlatio n of MOil vs PI
III
-2. 1207
136.9527
9. 8522
IV
- 1.0111
120.5667
6. 5277
7. 9445
V
-5. 0747
0. 0000
O. 0000
5. 0747
(Independent of PI index) Regression expression MON = AjPI + Bj Ajand Bjare th e regression coefficients for I = I. II. III. IV and V category (family) to which alkane belong respectively; R-correlation coefficient ; Sx- standard devi ation in X (=1'1 index); Sy - Standard de viation in Y (= MON )
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J SC II ND RES VO L 61 NOVEMBER 2002
... (2)
The va lues of coefficients Ai and Bi. i = 1,2, 3,4 respectively, are fo r the ca tego ri es (famili es) I, II , III and [V. as determin ed by reg ress ion analysis. As seen from Table 2, by means of Eq. (2) it si poss ible to quite accu rately estimate the va lues of MON of va ri ous alkanes prese nted in Table I using PI index . Thus, using the di stan ce-based PI index it is poss ible to infer about the formation of radi cal s by crack ing of alkanes at hi gher press ures and temperatures and thus monitorin g envi ronmental pollution due to motor fuel s. Us ing Eq. (2) and the regress ion parameters given in Table 2, MONs of the alkanes und er prese nt stud y have bee n ca lculated (Tabl e 2). The compari so n of the ca lculated va lues of MON with the observed (ex perimental) ones shows that under the splitted correlation the est imated MONs are fairly close to th e ex perimental MON s; and thu s it is es tab li shed that PI index is an appropriate topological index for mode lling MON. However. it remains a long-term goa l to obtain correlati on(s) which would place the differen t alkanes under present stud y on a single curve. We are thus led to the conclusion that linea rity in our correlation ex ists only for the members of given alkane family (series), and that such members must have closely rel ated topologies and geometrics. 25 Rouvray and El-Basi 1 have emphasized the importance of graph recognition in studies of this type, and pointed out that chemical graph s can belong to families in the same way that plants belong to genera. It is worth menti oning here that due to hi gh dege neracy for PI index in so me cases there is a comparatively large differences between the observed and estimated MON. Howeve r, such differences are well within the stati stical limits. Also, that our method, unlike other analytical methods, is applicable only to the estimation of MON of pure compounds and not to gaso line sa mples. The obvious reason be ing the gaso line sa mpl es are mixture of several hydrocarbon compounds, it will be very difficult to kn ow the PI index of gaso line sa mple for the estimati on of MON by the proposed method. ConclUision
The above res ults and disc uss ion have led us to conclude th at Motor Octane Number (MON) can be estimated and modelled excellentl y usin g PI index. The correlati on of MONs wi th PI indices ex hibits
familial re lati onship ve ry mLlch simil ar to plant belonging to particul ar ge nera . Acknowledgement
Authors are thankful to Prof. Ivan Gutman fo r introducing them to th e fascin atin g field of Chem ica l Graph Theory and Topology. and [ 0 Prof. Istvan Lukovits for prov iding softwares. Ret'rences I 2 :l
Dev ill ers J. COlllparili ve QSI\R (Ta) lor and Frances. Philadcphi a) 1998. Ki cr L B & Hall L H. M oll'c llla r strllc ture des('I'iptioll (Acadelllic Press. New York ) 1999 . T()polog ica l ill di ces alld rl'l(I{e(/ descripto rs ill QSAR all d QSPI? edi led by Balahan A T und Devill er J (Gordon and
Breach Sciencc Puhli she rs. Alllslerdam). 1999. Trinajsli c N. ('/wlllical g raph theo n '. Vol. 1 and 2 (e Re. Boca Ralon Florida) 1983. .5 Basak S e. Niemi G J & Vcilh G D. In COIII/Jllta ti(Jllal chelllical g raph th eory, ediled by Rouva ry D H (Nova Science Publi shers. New York) 1988, 23
