Molecular Distance-Edge Vec tor ( ) and Chro mato graphic Retention In dex of Alkanes

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1 Jour na of the Chi nese Chem i So ci ety Moecuar Distance-Edge Vec tor ( ) and Chro mato graphic Retention In dex of Akanes Shushen Liu ab ( ) Haiing Liu b ( ) Zhining Xia c ( ) Chenzhong Cao d ( )and Zhiiang S. Li ac * ( ) a Co ege of Bio en gi neer ing Chongqing Uni ver sity Chongqing China b De part ment of Ap pied Chem is try Guiin In sti tute of Tech no ogy Guiin China c Co ege of En vi ron men ta and Chem i En gi neering Chongqing Uni ver sity Chongqing China d De part ment of Chem is try Xiangtan Teacher Co ege Xiangtan 400 China A new method of quan ti ta tive struc ture-retention re a tion ship (QSRR) is pro posed for es ti mat ing and pre - dict ing gas chro mato graphic re ten tion in di ces of a kanes by us ing a nove mo ec u ar dis tance-edge vec tor ed vec tor con tain ing 0 e e ments. The QSRR mode (M) be tween the vec tor and chro mato graphic re - ten tion in di ces of 64 a kanes was de ve oped by us ing mu ti pe in ear re gres sion (MLR) with the cor re a tion co - ef fi cient be ing R = and the root mean square (RMS) er ror be tween the es ti mated and mea sured re ten tion in di ces be ing RMS = In or der to ex pain the equa tion sta bi ity and pre dic tion abi i ties of the M mode it is es sen tia to per form a cross-vaidation (CV) pro ce dure. Sat is fac tory CV re suts have been ob tained by us ing one ex ter na pre dicted sam pe ev ery time with the av er age cor re a tion co ef fi cient bei ng R = and av er age RMS = 7.8. If com pounds about one third drawn from a 64 a kanes con struct an ex ter na pre dic tion set and the 4 re main ing con struct an in ter na i bra tion set the sec ond QSRR mode (M) can be cre ated by us - ing i bra tion set data with sta tis tics be ing R = and RMS = The chro mato graphic re ten tion in di - ces of com pounds in the ex ter na test ing set can be pre dicted by the M mode and good pre dic tion re suts are ob tained with R = and RMS = IN TRO DUC TION Es ti ma tion and pre dic tion of var i ous physico-chemi prop er ties such as chro mato graphic re ten tion in dex of or - ganic mo e cues based on their struc tures have be come ma jor in ter ests of many chem ists and sci en tists in re cent years. It is nec es sary to de scribe the struc ture of the ex am ined com pound as a sca ar such as a top o og i in dex or as a vec tor con sist ing of sev era struc tura pa ram e ters in de ve op ing a quan ti ta tive struc ture-property re a tion ship (QSPR) mode. More than one hun dred top o og i in dexes in cud ing Wiener in dex Hosoya in dex Randic in di ces etc. were de ve oped and these struc - tura descriptors have been ap pied in QSPR stud ies widey. -6 How ever the struc ture of a com pound be ing de scribed by ony us ing one num ber seems to be not so rea son abe. The mo - ec u ar dis tance-edge vec tor con tain ing ten e e ments was first pro posed to de scribe the struc ture of a kanes (see our pre - vi ous pa per for de tais and good re suts were ob tained). 78 In eva u at ing the va ues of e e ments in the vec tor a geo met ric dis tance be tween the two types of at oms must be cu ated and the e e ment wi be equa to zero if there ex ists very arge va ues in a dis tances. So it is nec es sary to mod ify the vec tor and then a nove vec tor ed the vec tor has been pro posed and is re ated to gas chro mato graphic re ten tion in di - ces of a kanes in our pres ent pa per. The main pur pose of any chro mato graphic sys tem is to re sove mix tures of e e ments or com pounds into ess com pex mix tures or u ti matey into pure com po nents. One im por tant func tion of the chro mato graphic sys tem is that it can pro vide re ten tion data which can serve as com pe men tary in for ma tion for the pos i tive iden ti fi ca tion of re soved com po nents. For ex - am pe know edge con cern ing struc ture vs. re ten tion among iso mers can greaty hep in the cor rect struc tura as sign ment of an un known com pound when there is an ac cu rate choice be - tween sev era pos si be iso mers. In this pa per the newy de ve - oped mo ec u ar dis tance-edge vec tor ( ) was used to uti ize mo ec u ar mod e ing of quan ti ta tive struc ture-retention in dex re a tion ship (QSRR) and to pre dict some un known chro mato - graphic re ten tion in di ces. THE O RET I CAL Ca cu a tion of Mo ec u ar Dis tance-edge Vec tor ( vec - tor) Taking -trimethypentane (Fig. ) as an ex am pe the cu a tion of a new mo ec u ar dis tance-edge vec tor ed the vec tor in the pres ent pa per wi be i us trated as fo ows by us ing the mo ec u ar graph. As pointed out in the ref er ence 7-8 the car bon at oms in any akane mo e cue ex am ined can be cas si fied as four ba sic types ac cord ing to the con nect ing C-C bond num ber be tween

2 456 J. Chin. Chem. Soc. Vo. 47 No. 000 Liu et a. Tabe. Distances and q Vaues of -Trimethypentane m q k j d( Ck C j ) ( k m j ) q (C -C 6 )(C -C 7 )(C -C 8 )4(C -C 5 )(C 6 -C 7 ).89 (C 6 -C 8 )4(C 6 -C 5 )(C 7 -C 8 )4(C 7 -C 5 )(C 8 -C 5 ) (C -C 4 )(C 6 -C 4 )(C 7 -C 4 )(C 8 -C 4 )(C 5 -C 4 ).58 (C -C )(C 6 -C )(C 7 -C )(C 8 -C )(C 5 -C ) (C -C 4 )(C 6 -C 4 )(C 7 -C 4 )(C 8 -C 4 )(C 5 -C 4 ) (C 4 -C ) (C 4 -C 4 ) (C -C 4 ) at oms. Type and 4 for pri mary (CH -) sec ond ary (CH <) ter nary (-CH<) and qua ter nary (>C<) car bons be ing sym bo ized in C C C and C 4 in Fig. rep re sent the car bon at oms con nect ing one two three and four C-C bonds re spec - i tivey. Let d k j ex press the dis tance which is ac tu ay the C-C bond num ber be tween C i k and C j where the ith car bon atom be - ongs to type C k whie the th car bon atom be ongs to type C j. For -trimethypentane the ex am pe com pound a va - i ues of d k j are isted in Ta be (co umn 4) where rep re - sents no dis tance or no ink ing be tween the two at oms (i and ). If n kj stands for the path way num ber from the kth atom(k) through the jth atom(j) i.e. item num ber of mu ti pi - ca tion in the right side the vec tor is de fined as fo ows: kj nkj k m j = = d( C C ) k b b m j q ( k 4; j k; q 0) ( ) The va ues of ten e e ments in equa tion () can be ob - tained by ap py ing in for ma tion given in Ta be. For ex am pe the va ues of and in the vec tor for com pound -trimethypentane are cu ated as fo ows: Fig.. The car bon ske e ton graph of - trimethy - pentane. g g 4 Modeing Re a tion ship be tween the Vec tor and Chro - mato graphic Retention In di ces of Akanes A mu ti pe in ear re gres sion (MLR) method was used to de veop a mode for the quan ti ta tive re a tion ship be tween chro mato graphic re ten tion in di ces of a kanes and their ten descriptor e e ments of the vec tor or MDE vec tor. The mod - e ing equa tion was given in the fo ow ing form: RI b b q q 0 where b 0 is the in ter cept term of the re gres sion equa tion; and b q is the re gres sion co ef fi cient for the cor re spond ing qth descriptor q which is the con tri bu tion vaue of the qth e e - ment q to the RI vaue of the com pound. RE SULTS AND DIS CUS SION 0 q Data set The ex per i men tay mea sured gas chro mato graphic re - ten tion in di ces (RI) of 64 a kanes com pounds are taken from a ref er ence. 9 The range of the ex per i men ta RI va ues was o - cated from 00 to 000 and the num ber of car bon at oms per akane spanned from one through ten. The 64 com pounds com posed a work ing data set. Of these 64 aiphatic a kanes com pounds were ran domy cho sen as an ex ter na test ing data or pre dic tion set and the re main ing 4 com pounds com prised an in ter na train ing data or i bra tion set. The ex ter na pre ( )

3 Mo ec u ar Dis tance-edge Vec tor J. Chin. Chem. Soc. Vo. 47 No Tabe. The Vector and Chromatographic Retention Index for 64 Akanes No Compounds RI RI M RI # RI M RI CV Propane Butane methypropane * Pentane methybutane Hexane * methypentane methypentane dimethybutane * dimethybutane Heptane methyhexane * methyhexane dimethypentane dimethypentane * dimethypentane dimethypentane ethypentane * trimethybutane octane methyheptane * methyheptane methyheptane dimethyhexane * dimethyhexane dimethyhexane dimethyhexane * dimethyhexane dimethyhexane ethyhexane * trimethypentane trimethypentane methy--ethypentane * nonane methyoctane methyoctane * methyoctane dimethyheptane dimethyheptane * dimethyheptane dimethyheptane dimethyheptane * dimethyheptane dimethyheptane dimethyheptane * ethyheptane trimethyhexane trimethyhexane * trimethyhexane trimethyhexane trimethyhexane * trimethyhexane trimethyhexane trimethyhexane * methy--ethyhexane methy-4-ethyhexane methy-4-ethyhexane * decane methynonane methynonane * methynonane methynonane trimethyheptane * trimethyheptane *: The retention indices predicted by mode M. #: RI=RI M -RI

4 458 J. Chin. Chem. Soc. Vo. 47 No. 000 Liu et a. Tabe. The Regression Coefficients and Statistics for Various Modes Stat. M Mode M* Mode M Mode M* Mode CV Mode b o b b b b b b b b b n R RMS dic tion set was never used un ti af ter a mode had been de ve - oped ony by us ing the train ing set. A ex per i men ta gas chro - mato graphic re ten tion in di ces of 64 a kanes are aso isted in Ta be (see RI item in co umn for de tais). Descriptors The mo ec u ar dis tance-edge vec tor a vec tor with ten descriptor e e ments has a good dis crim i nat ing abi ity for ev - ery iso mer of a a kanes with car bon at oms from one to ten. For the ex am ined 64 a kanes the va ues of e e ments in the vec tor are a dif fer ent from each other (see the first to th co umn in Ta be ). On the other hand this nove MDE vec tor or vec tor has a good cor re a tion with physico-chemi prop er ties such as boi ing points heat ca pac ity mo ar vo - ume mo ar re frac tion and so on of the com pounds as we which wi be re ported in the near fu ture. Be cause a their va ues of 0 are equa to zero among 64 a kanes the first 9 e e ments of the vec tor for the ex am - ined com pounds are ony isted in Ta be and the tenth e e - ment 0 can be omit ted. Re gres sion ana y sis A mu ti pe in ear re gres sion (MLR) tech nique was used to de veop in ear mod es that ink the gas chro mato graphic re - ten tion in dex to the vec tor of the ex am ined com pounds. This re gres sion equa tion is given by the equa tion () as men tioned above. By ap py ing MLR the best mode con tain ing 9 vari - abes for 64 a kanes in the work ing data set is de ve oped with a root mean square er ror of RMS = 5.98 and a cor re a tion co - ef fi cient of R = which is quite sat is fac tory and better than those re ported in the re cent it er a ture. 0 Ten re gres sion co ef fi cients and con fi dence imit (95% eve) and sev era ba - sic sta tis tics such as num ber of sam pes (n) root mean square er ror (RMS) cor re a tion co ef fi cient (R) and so on for the above in ear mode noted mode M are cu ated by the MLR tech nique (sec ond co umn in Ta be ). Mean whie the stan dard re gres sion co ef fi cients (sec ond co umn in Ta be ) are aso ob tained to eva u ate ef fects of var i ous e e ments in the vec tor on re ten tion in di ces. Ob vi ousy the con tri bu tion of and in the vec tor to gas chro mato graphic re ten tion in - dex (RI) are the great est and this is be cause the num ber of at - oms be ong ing to type and type for 64 a kanes is the arg - est whie the 4 and 9 have ess ef fect on RI be cause the num ber of car bon atom be ong ing to type 4 is sma. The ob served gas chro mato graphic re ten tion in di ces RI EXP and cu ated gas chro mato graphic re ten tion in di ces RI M from mode M are a isted in Ta be. In a sim i ar way the RI M data are pot ted against RI EXP which is given in Fig.. From Ta be and Fig. it shows that there are no ob serv - abe pat terns or de vi a tions from nor ma be hav ior. These re - suts in di cate that the mode M has high in ter na sta bi ity. The ex ter na sta bi ity of the quan ti ta tive structureretention re a tion ship (QSRR) mode In or der to fur ther va i date the ex ter na sta bi ity of the above M mode a new mode the noted M mode was ob - Fig.. Pot of a 64 es ti mated RI by mode M vs ex - per i men ta RI.

5 Mo ec u ar Dis tance-edge Vec tor J. Chin. Chem. Soc. Vo. 47 No tained by us ing 4 com pounds in the train ing set ar bi trariy drawn from a 64 com pounds. This M mode was used to pre dict the gas chro mato graphic re ten tion in dex (RI) of com pounds in the ex ter na pre dic tion set. The re gres sion co ef - fi cients and re a tive sta tis tics of this new mode M are given in Ta be (see the fourth and fifth co umns). The re suts showed that the M mode with R = and RMS = has the same sta bi ity as the M mode. The cor re a tion co ef fi - cients and root mean square er ror be tween ex per i men ta RI va ues and pre dicted RI va ues by the M mode are R = and RMS = re spec tivey. The es ti mated gas chro mato graphic re ten tion in di ces RI M for 4 com pounds in the in ter na train ing set and the pre dicted gas chro mato - graphic re ten tion in di ces RI M* for com pounds in the ex ter - na pre dic tion set by the M mode are isted to gether in Ta be (see co umn M). The 4 es ti mated RI M va ues are pot ted against the re spond ing 4 mea sured RI EXP va ues given in Fig.. The pre dicted RI M* va ues are pot ted against the re spond ing mea sured RI EXP va ues given in Fig. 4. These re suts in di cate that the M mode has not ony high in ter na sta bi ity but aso good pre dic tion abi ity for the ex ter na data. Fig.. Pot of 4 es ti mated RI by mode M vs ex per i - men ta RI. Fur ther more the eave-one out method ed a crossvaidation tech nique CV was used to va i date the above QSRR mode. The pre dicted RI va ues of 64 a kanes were ob - tained by em poy ing 64 eave-one out pro ce dures in which a i bra tion set con tain ing 6 a kanes was used to mode the re - a tion ship be tween the vec tor and gas chro mato graphic re - ten tion in dex (RI) and this re a tion ship was used to pre dict the RI of the re main ing com pound each time. The 64 pre dicted RI were aso isted in Ta be (see ing item CV). The 64 pre dicted RI pot ted against the 64 ex per i men ta RI EXP are given in Fig. 5. The av er age re gres sion co ef fi cients and av er - age sta tis tics are isted in Ta be. Those re suts have shown that the QSRR mode has both high in ter na and good ex ter na sta bi ity. The pre dic tion abi ity of the QSRR mode In or der to ex pain the pre dic tion abi ity of the QSRR mode for ex ter na data fur ther 6 com pounds which a con - tain car bon at oms be ing dif fer ent from the above 64 com - pounds in the work ing set in mod e ing the QSRR re a tion ship were se ected to serve as an ex ter na pre dic tion set. The M mode is used to pre dict the va ues of these 6 a kanes and the re suts are isted in Ta be 4. Pri mary con cu sion A new set of mo ec u ar dis tance-edge in ter ac tion pa - ram e ters con sti tut ing the vec tor were first de ve oped in our ab o ra to ries and ex ce enty uti ized to ex press the chem i struc ture of a kanes. The nove vec tor is we re ated not ony to the cap i ary co umn gas chro mato graphic re ten tion in dex but aso to many phys i prop er ties and ther mo dy namic func tions for a kanes. The char ac ter iza tion of mo ec u ar di - ver sity and de ve op ment of func tiona di ver sity by us ing the mo ec u ar dis tance-edge in ter ac tion vec tor are in prog ress and wi ap pear in the near fu ture. Fig. 4. Pot of pre dicted RI by mode M vs ex per i - men ta RI. Fig. 5. Pot of 64 pre dicted RI by cross-vaidation method vs ex per i men ta RI.

6 460 J. Chin. Chem. Soc. Vo. 47 No. 000 Liu et a. Tabe 4. The Vector and Retention Index for 6 Externa Prediction Akanes No Compounds RI RI M p undecane p -methydecane p -methydecane p4 4-methydecane p5 5-methydecane p6 dodecane AP PEN DIX Def i ni tion of R RMS EV(%) and F R ( y y ) ( y y ) RMS ( y y ) n Key Words Mo ec u ar dis tance-edge vec tor; Vec tor; Chro - mato graphic re ten tion in dex; Akanes; Quan ti ta tive struc ture-retention re a tion ship; Mo ec u ar mod e - ing; Chemometrics; Chemoimformatics. EV F AC KNOWL EDG MENT ( y y ) / ( n q ) ( y y ) / ( n ) ( y y ) / q ( y y ) / ( n q ) The au thors thank the Fok Yin-Tung Fund (FYTF) Min - is try of Me chan i In dus tries Fund (MMIF) Chongqing University Sci ence Fund (CQUF) and Guiin In sti tute of Tech no ogy Fund (GITF) for fi nan cia sup port. Re ceived Sep tem ber 999. REF ER ENCES. Wiener H. J. Am. Chem. Soc Hosoya H. Bu. Chem. Soc. Ja pan Randic M. J. Am. Chem. Soc Baaban A. T. Pure App. Chem Randic M. J. Math. Chem Nikoic S.; Trinajstic N.; Mihaic Z. J. Math. Chem. 99 (-4) Liu S.; Cao C.; Li Z. J. Chem. Inf. Comput. Sci Liu S.; Cao C.; Li Z. Chem. in Hong Kong (in Eng ish) Wu J.; Lu W. Chin. Ana. Chem. (in Chi nese) 984 (7) Yin C.; Pon Z.; Yi Z.; Li Z.; Zhang M. Chi nese J. Chem. (in Eng ish) 999 7()