Research Article Nanoquantitative Structure-Property

Research ArticleNanoquantitative Structure-Property Relationship Modeling onC42 Fullerene Isomers

Sorana D Bolboacs1 and Lorentz Jaumlntschi23

1Department of Medical Informatics and Biostatistics Iuliu Hatieganu University of Medicine and Pharmacy6 Louis Pasteur Street 400349 Cluj-Napoca Romania2Department of Physics and Chemistry Technical University of Cluj-Napoca 103-105 Muncii Bulevardul400641 Cluj-Napoca Romania3Doctoral Studies-Chemistry Babes-Bolyai University 11 Arany Janos Street 400028 Cluj-Napoca Romania

Correspondence should be addressed to Lorentz Jantschi lorentzjantschigmailcom

Received 5 October 2015 Revised 1 January 2016 Accepted 4 January 2016

Academic Editor Teik-Cheng Lim

Copyright copy 2016 S D Bolboaca and L Jantschi This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

The interest of scientists in nanostructures has been increased in the last years and proper methods for their assessment areneeded In silicomethods found their usefulness in the replacement of experimental evaluation and are successfully used as efficientalternatives for estimation and prediction of compoundrsquos properties or activities In this paper it is shown that a QuantitativeStructure-Property Relationship method is proper to be applied also on nanostructures Based on computational experimentseveral models to describe the total strain energy of C

42fullerene isomers were obtained and their characteristics are presented

Furthermore the best performing model obtained on C42fullerene isomers was validated on C

40fullerene isomers

This paper is dedicated to Professor Mircea V Diudea on the occasion of his 65th birthday

1 Introduction

Since their discovery in 1985 [1] fullerenes attracted inter-est in different fields of science including medical field(eg for potential use as antibiotics [2ndash4] as inhibitors oferythroid cellsmdashfullerenol [5] as drug delivery system [6]or as inhibitors of inflammatory mediators [7]) Fullerenemolecules are constructed from carbon atoms and take theshape of sphere (also known as buckyballs) ellipsoid ortube [8] First spherical fullerene C

60 was discovered in

1985 [1] Fullerenes have different properties and showeddifferent number of associated isomers (Table 1) [9] Thesmallest fullerene (C

28) was stabilized bymetal encapsulation

(with Ti Zr and U) by Dunk et al [10] Chen et al showedthat C

32fullerene has stronger aromaticity compared with

C30

and C34 respectively [11] Fifteen distinct isomers with

different energies were reported by Manna and Ghanty whoencapsulate U into various C

36cages [12] Muhammad et al

showed that C20

is a closed-shell fullerene and fullerenesC26

and C30

are pure open-shell compounds whereasC36 C40 and C

42are intermediate open-shell compounds

[13]The C

42fullerenes are small not necessary spherical

cages The C42

cages enclosed high pentagonhexagon ratio[14] Fullerene C

42along with C

60showed highest values of

the main peak on Matrix-Assisted Laser Desorption Ioniza-tion Time-of-Flight (MALDI-TOF) on mass spectrometricmeasurement [15]

Some activities of fullerenes have been modeledusing quantitative structure-activity relationship (QSAR)approaches (such as anti-HIV protease inhibition activity[16] antiviral activity [17] and drug delivery system[18]) However C

60received the main attention while

other fullerenes were neglected in regard of QSARQSPR(Quantitative Structure-Property Relationship) modelingThe aim of our research was to model the total strain

Hindawi Publishing CorporationJournal of ChemistryVolume 2016 Article ID 1791756 8 pageshttpdxdoiorg10115520161791756

2 Journal of Chemistry

Table 1 Several small fullerenes and their number of isomers

Number Fullerene Number of isomers1 C

282

2 C30

33 C

326

4 C34

65 C

3615

6 C38

177 C

4040

8 C42

459 C

4489

10 C46

116Source httpwwwnanotubemsuedufullerenefullerene-isomershtml[accessed June 7 2015]

Spartan Babel

HyperChem

charges

httplacademicdirectorgChemistrySARsSMPI

(i) 1512 (ii) 242 filtered total strain energy

Nano-QSPR C42 fullerene models

SSr = sum of squares of residualsSSr from vertical offsets = min

lowast hin with partial

lowast hinlowast mollowast xyz file1 2

3

4

5

SMPI descriptors (xi)TSE (yi)

Scheme 1 Flowchart of the applied methods The pool of filteredSMPI (Szeged Matrix Property Indices) descriptors contains thosedescriptors with absolute values between 10minus7 and 107

energy of the isomers of C42

fullerene using the structuralinformation

2 Materials and Methods

All C42

fullerene isomers were included in the analysisData related to continuum elasticity expressed as total strainenergy (TSE in eV) and the structures as lowastxyz files of C

42

fullerene isomers were taken from [19] (Table 2)The analysis was conducted on the downloaded file of

the C42

isomers without any modification on the availablegeometry According to [19] the fullerene geometries werebased on the geometry of the structures in Yoshidarsquos FullereneLibrary (UNIX files) and reoptimized using Dreiding-likeforce-field [20] Here the obtained geometry is used

The steps applied in the analysis are depicted in Scheme 1In the first step of the analysis the downloaded files

were translated into lowastmol file with Spartan software(httpswwwwavefuncomproductsspartanhtml) In thesecond step the lowastmol file is transformed as lowasthin file using

Table 2 C42fullerene isomers identification number (IsoID) and

total strain energy (TSE)

IsoID TSE (eV)01 3106002 3053703 2979104 2980505 3061806 2985007 3060808 2978209 2852710 2939311 2947512 2834013 2815714 2714715 2995516 2817517 2827618 2947419 2740820 2817521 2728322 2914023 2876524 2774325 2748726 2835327 2801428 2905129 2748930 2897231 2748432 2665733 2663934 2737135 2655436 2797337 2976438 3110139 2663940 2750141 2667242 2866543 2828444 2673745 25661

Babel software (httpopenbabelorg) The partial chargeswere calculated in the third step using HyperChem software(httpwwwhypercom) by applying PM3 (ParameterizedModel number 3 [21]) single point (energy) semiempirical

Journal of Chemistry 3

Table 3 Characteristics of nano-QSPR models obtained on C42isomers

Equation 119877

2119877

2

adj se119865(119901) |119905min|(119901) PredErr 119876

2 seloo 119865loo(119901loo)

(1) 08883 08857 04577 342(438 times 10minus22)

1805(109 times 10minus21) 4677 08656 05039 275

(156 times 10minus20)

(2) 09612 09593 02729 520(232 times 10minus30)

669(410 times 10minus8) 3192 09545 02960 439


(3) 09836 09824 01796 820(130 times 10minus36)

437(840 times 10minus5) 1976 09809 01939 701


(4) 09898 09888 01431 974(287 times 10minus39)

355(101 times 10minus3) 1595 09768 02171 418

(228 times 10minus34)1198772 determination coefficient 1198772adj adjusted determination coefficient se standard error of estimate 119865(119901) Fisherrsquos statistic (119901-value) |119905min| the minimum of

absolute 119905-statistic associated with the intercept and coefficients of the model PredErr percentage prediction error 1198762 determination coefficient in leave-one-out analysis loo leave-one-out analysis

calculations The structural features of the investigated nan-oclass of compounds were extracted using unsymmetricalSzeged set an extension of corresponding Szeged Matrix[22] (forth step) The calculated values of the structuraldescriptors and the collected values of total strain energywere included in nano-QSPR modeling in the fifth step ofthe analysis and models with the highest goodness-of-fit(defined as highest correlation coefficients) were analyzedand validated in leave-one-out and leave-many-out analyses[23 24]

Leave-one-out analysis retrieves valid models if determi-nation coefficient (1198762) takes values higher than 05 Leave-many-out analysis was conducted for themodels with highestabilities in estimation expressed as the highest value ofthe correlation coefficient The set was split using a simplerandom technique [25] in training and test with 23 ofcompounds in training set The models obtained in trainingsets were used to predict the TSE in the test sets The leave-many-out analysis was run five times for equations identifiedas being with highest estimation and internal predictionabilities in order to assess their prediction abilities

The assessment of the prediction ability was done on anexternal dataset represented by C

40isomers considering the

same propertyThe TSE values and the structures for externalvalidation were taken from the same source as C

42isomers

httpnanotubemsuedufullerenefullerenephpC=40 (ac-cessed December 20 2015) Several metrics were used toassess the prediction ability of the model [23 24] determina-tion coefficient on the external set (1198772ext) predictive squarecorrelation coefficient on external set (1198762

1198652 [26]) external

prediction ability (11987621198653) root mean square error of predic-

tion (RMSEP) mean absolute error of prediction (MAEP)percentage predictive error (PredErr) and concordancecorrelation coefficient (CCC [27])

3 Results and Discussion

Structural information of the investigated C42

isomers wasobtained by calculation of the pool of descriptors givenby Szeged Matrix Property Indices (SMPI) method [28]Performing models in regard of goodness-of-fit (highestcorrelation coefficient) with 1 2 3 and 4 SMPI descriptorswas obtained and is given in (1)ndash(4)

119884TSE(1) = minus117625 + IJUGE times 196 (1)

119884TSE(2) = minus54287 minus IIUGF times 193 times 10minus3+ IJUGE

times 181

(2)

119884TSE(3) = 83880 minus IFEGE times 141 minus IIUGF times 366

times 10

minus3+ IJUGE times 216

(3)

119884TSE(4) = minus19961 minus IFETB times 2163 + IFUGB times 4090

minus IIUGF times 262 times 10minus3 + IJUGE times 156(4)

where 119884TSE is total strain energy estimated by the modelIJUGE IIUGF IFEGE IFETB and IFUGB are SMPI descrip-tors Two descriptors (IFETB and IFUGB) account for theatomic number as atomic property the other two descriptorsaccount for electronegativity (IJUGE and IFEGE) whileone accounts for the first ionization energy (IIUGF) Theinvestigated property is related to the geometry of com-pounds (fourth letter ldquoGrdquo in the name of descriptors) withone exception when it is related to topology (fourth letterldquoTrdquo in the IFETB descriptor) The other letters reflect thelinearization operator (first letter) matrix operation (secondletter) and interaction descriptor (third letter)

As expected the determination coefficient increases asthe number of descriptors in the models increases while thestandard error of the estimate decreases (Table 3)

The distance between determination coefficient of themodel and determination coefficient obtained in leave-one-out analysis varied from 00027 to 00227 the smallestdistance being obtained by (3) (Table 3) On the other handthe smallest difference between standard errors (estimationmodel and leave-one-out model) is obtained by the samemodel (3)

The analysis of the results presented in Table 3 showedthat the model with four descriptors is the one with smallestpercentage of prediction error Furthermore the data onthe scatter closest to the straight line is observed for themodel given by (4) (Figure 1) Figure 1 shows the absence ofthe differences between models from (3) and (4) with thedispersion of the point in the scatter closest to the line formodel given by (4)

The main characteristics of the models given by (3) and(4) obtained in leave-many-out analysis (training versus test


Table 4 Characteristics of nano-QSPR models in leave-many-out analysis C42isomers

Id Model Training TestEquation (3) Intercept IFEGE IIUGF times 10minus3 IJUGE 119877

2119865-stat 119877

2119865-stat

1 74437 minus127 minus357 209 09797 360 09877 2642 6824 minus121 minus346 207 09788 369 09935 3613 90268 minus148 minus379 220 09794 376 09894 3584 67839 minus122 minus353 212 09853 534 09851 1715 85405 minus149 minus351 217 09828 458 09835 219Equation (4) Intercept IFETB IFUGB IIUGF times 10minus3 IJUGE 119877

2119865-stat 119877

2119865-stat

6 minus12059 minus1988 3719 minus287 155 09901 568 09637 727 minus27784 minus2087 4014 minus230 154 09819 310 09814 1548 minus9146 minus2086 3901 minus300 156 09878 459 09636 649 minus22597 minus2169 4202 minus235 148 09830 331 09794 13910 minus22328 minus1871 3637 minus235 147 09887 497 09701 85

Table 5 Prediction power of nano-QSPR given by (3) and (4) on C40isomers

Equation 119877

2

ext 119876

2

1198652119876

2

1198653RMSEP MAEP |119905

(119884minus119884pred)|(119901) PredErr

(3) 06183 09501 NR 160 5128 324 (837 times 10minus69) 6319(4) 08462 05144 NR 160 527 52 (496 times 10minus38) 6491198772

ext determination coefficient on the external set 11987621198652 predictive square correlation coefficient on external set 11987621198653 external prediction ability RMSEProot mean square error of prediction MAEP mean absolute error of predictionPredErr percentage predictive error NR not reliable value

analysis 23 of compounds in training set run 5 times) arepresented in Table 4

The results presented in Table 4 showed the stabilityof the models with internal prediction power (defined asdetermination coefficient in test sets) closed to the estima-tion power (determination coefficient in training set) fromboth investigated models Therefore the results obtained intraining sets closely follow the results on the whole samplefor (3) with 1198772 in the same range when two decimals are ofinterestThe1198772 obtained in test set in all five runs of the leave-many-out analysis was equal to 099 so slightly higher thanthe 1198772 obtained in training sets (098) In three cases out offive the 1198772 in training sets for (4) was in the same range fortwo decimals with the 1198772 value given in Table 3 Howeverwithout any exception the 1198772 in test sets was smaller thanthe 1198772 in training sets for (4) with values that varied from00005 (id 7 in Table 4) to 00264 (id 6 in Table 4) Theseresults showed that (3) performs slightly better in terms ofdetermination coefficients in leave-many-out analysis

The plots of the models obtained in the fourth run for (3)and fifth run for (4) as examples are given in Figure 2

The equations identified with estimation power andinternal prediction abilities namely (3) and (4) were furtherapplied onC

40isomers to test the external prediction abilities

The prediction power of (4) proved to be better comparedwith prediction power of (3) (see Figure 3 and Table 5)

Despite the fact that the predictive square correlationcoefficient on external set is higher for (3) compared with thevalue obtained with (4) all other calculated metrics sustainthat the model given by (4) has better prediction abilities(highest determination coefficient on external set lowestmean absolute error of prediction and lowest percentage ofpredictive error see Table 5) Furthermore the analysis of the

overall spread of the points in the scatter-plot leads to theconclusion that (4) had better prediction abilities comparedwith (3) Nevertheless the mean of residuals proved to besignificantly different than the expected value (zero) It couldbe concluded that the model given by (4) better fit the dataon which it was constructed compared with all other modelsNevertheless are the structural features extracted by SMPIdescriptors on C42 isomers able to predict the TSE on C40isomers

SMPI descriptors used by (3) and respectively (4) wereused to predict the TSE on C

40isomers One out the three

descriptors from (3) proved to have the slope not significantlydifferent by zero andwas not included in further analysisTheidentified models obtained on C

40isomers are given in


times 170

119877

2= 08483

119877

2

adj = 08401

se = 065

119865 (119901) = 103 (707 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 288 (00066)

119899 = 40

119876

2

1198653= 07834

RMSEP = 160

MAEP = 052


R2 = 08883

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

33Es

timat

ed T

SE b

y (1

)

(a)

R2 = 09612

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(2)

(b)

R2 = 09836

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(3)

(c)

R2 = 09898

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(4)

(d)

Figure 1 Observed versus estimated TSE by (1)ndash(4)

TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(3)

(a)

TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(4)

(b)

Figure 2 Internal prediction versus estimation power in training and test analysis for (3) and (4)


76

77

78

79

80

81

82

83Pr

edic

ted

TSE

by (3

)

27 29 31 3325Observed TSE(a)

20

21

22

23

24

25

26

27

Pred

icte

d TS

E by

(4)

27 29 31 3325Observed TSE(b)

Figure 3 Analysis of (3) and (4) on external dataset represented by C40isomers

PredErr = 064

CCC = 09179(5)

119884TSE(6) = minusIFETB times 1505 + IFUGB times 3149

minus IIUGF times 264 times 10minus3 + IJUGE

times 121

119877

2= 08853

119877

2

adj = 08479

se = 057

119865 (119901) = 69 (376 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 310 (00038)

119899 = 40

119876

2

1198653= 08362

RMSEP = 160

MAEP = 043

PredErr = 052

CCC = 09390

(6)

where 119884TSE is total strain energy estimated by the modelIJUGE IIUGF IFETB and IFUGB are SMPI descriptorsTwo descriptors (IFETB and IFUGB) account for the atomicnumber as atomic property one descriptor accounts forelectronegativity (IJUGE) and one accounts for the firstionization energy (IIUGF) The investigated property isrelated to the geometry of compounds (fourth letter ldquoGrdquo in

the name of descriptors) with one exception that is relatedwith compounds topology (IFETB descriptor) The otherletters reflect the linearization operator (first letter) matrixoperation (second letter) and interaction descriptor (thirdletter) Note that both models have the mean of residual notsignificantly different by zero (119901 gt 049)

The analysis of the metrics associated with (5) and (6)leads to the conclusion that model given by (6) performbetter than the model given by (5) The same conclusion isobtained by analyzing the plots of observed versus predictedTSE (Figure 4)

The results of our study showed that the identified nano-QSPR models fit the data based on which the model wasidentified (C

42isomers) but could be used for selection of

those structural descriptors with fair abilities in predictionon external dataset (C

40isomers) To sum up equations

relating electronegativities ionization potential and energyhave been identified on C

42isomers and proved to work also

on C40

isomers Note that electronegativities and ionizationpotential are atomic properties and since the investigated setcontains just C and H atoms the identified relation betweenthe three properties could be assigned also to the topologyand geometry of the investigated compounds

To the best of our knowledge structure-property rela-tionship approaches were not applied on C

42or C40fullerene

isomers The small-diameter fullerenes (C20 C34 C42 and

C60) were mainly investigated in regard of properties (such as

adsorption [29] distribution ofCCdistance [14] and Schlegeldiagrams of molecular structures [30]) Therefore this is thefirst report of a quantitative relationship between structureand property of C

42fullerene Undoubtedly the advancement

from theoretical to experimental studies is desired

4 Conclusions

The C42fullerene isomers were successfully modeled and the

total strain energy was characterized as function of informa-tion extracted from structure of the compounds The models


27 29 31 3325Observed TSE

25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)

27 29 31 3325Observed TSE (b)


with goodness-of-fit in leave-one-out (1198762 = 09768) andleave-many-out analyses proved also that prediction poweris the one with four descriptors The total strain reactionproved a function of electronegativity and first ionizationenergy in relation to geometry of compoundsThe structuraldescriptors able to fairly explain the total strain energy onC

42

isomers proved also able to explain the same property on C40

fullerene isomers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] H W Kroto J R Heath S C OrsquoBrien R F Curl and R ESmalley ldquoC

60 BuckminsterfullerenerdquoNature vol 318 no 6042

pp 162ndash163 1985[2] R Dinesh M Anandaraj V Srinivasan and S Hamza ldquoEngi-

neered nanoparticles in the soil and their potential implicationsto microbial activityrdquo Geoderma vol 173-174 pp 19ndash27 2012

[3] A J Huh and Y J Kwon ldquoNanoantibiotics a new paradigmfor treating infectious diseases using nanomaterials in theantibiotics resistant erardquo Journal of Controlled Release vol 156no 2 pp 128ndash145 2011

[4] Y S Zhang T H Dai M Wang D Vecchio L Y Chiang andM R Hamblin ldquoPotentiation of antimicrobial photodynamicinactivation mediated by a cationic fullerene by added iodidein vitro and in vivo studiesrdquo Nanomedicine vol 10 no 4 pp603ndash614 2015

[5] N V Tishevskaya Yu M Zakharov E V Golubotovskii etal ldquoEffects of fullerenol C

60(OH)

24on erythropoiesis in vitrordquo

Bulletin of Experimental Biology andMedicine vol 157 no 1 pp49ndash51 2014

[6] S Pacor A Grillo L ETHorđevic et al ldquoEffects of two fullerenederivatives on monocytes and macrophagesrdquo BioMed ResearchInternational vol 2015 Article ID 915130 13 pages 2015

[7] A L Dellinger Z Zhou and C L Kepley ldquoA steroid-mimickingnanomaterial that mediates inhibition of human lung mastcell responsesrdquo Nanomedicine Nanotechnology Biology andMedicine vol 10 no 6 pp 1185ndash1193 2014

[8] A Hirsch and M Brettreich Fullerenes Chemistry and Reac-tions John Wiley amp Sons New York NY USA 2005

[9] D Tomanek Guide Through the Nanocarbon Jungle Morgan ampClaypool San Rafael Calif USA 2014

[10] P W Dunk N K Kaiser M Mulet-Gas et al ldquoThe smalleststable fullerene MC

28(M=Ti Zr U) stabilization and

growth from carbon vaporrdquo Journal of the American ChemicalSociety vol 134 no 22 pp 9380ndash9389 2012

[11] Y-M Chen J Shi L Rui and Q-X Guo ldquoTheoretical study onC32fullerenes and their endohedral complexes with noble gas

atomsrdquo Journal of Molecular Structure THEOCHEM vol 907no 1ndash3 pp 104ndash108 2009

[12] D Manna and T K Ghanty ldquoEnhancement in the stability of36-atom fullerene through encapsulation of a uranium atomrdquoJournal of Physical Chemistry C vol 117 no 34 pp 17859ndash178692013

[13] S Muhammad K Fukuda T Minami R Kishi Y Shigetaand M Nakano ldquoInterplay between the diradical character andthird-order nonlinear optical properties in fullerene systemsrdquoChemistrymdashA European Journal vol 19 no 5 pp 1677ndash16852013

[14] E Małolepsza Y-P Lee H A Witek S Irle C-F Lin andH-M Hsieh ldquoComparison of geometric electronic and vibra-tional properties for all pentagonhexagon-bearing isomers offullerenes C

38 C40 and C

42rdquo International Journal of Quantum

Chemistry vol 109 no 9 pp 1999ndash2011 2009[15] E I Kauppine ldquoCarbon Nanotubes and NanoBudsmdashSynthesis

Structure Functionalisation and Dry Deposition for TCE andTFTApplicationsrdquo July 2015 httpwwwjstgojpsicpws2009finlandabstractwg2 02kaupdf

[16] M Ibrahim N A Saleh W M Elshemey and A A ElsayedldquoFullerene derivative as anti-HIV protease inhibitor molecularmodeling and QSAR approachesrdquo Mini-Reviews in MedicinalChemistry vol 12 no 6 pp 447ndash451 2012


[17] L Ahmed B Rasulev M Turabekova D Leszczynska andJ Leszczynski ldquoReceptor- and ligand-based study of fullereneanalogues comprehensive computational approach includingquantum-chemical QSAR andmolecular docking simulationsrdquoOrganic amp Biomolecular Chemistry vol 11 no 35 pp 5798ndash5808 2013

[18] A Trpkovic B Todorovic-Markovic andV Trajkovic ldquoToxicityof pristine versus functionalized fullerenes mechanisms of celldamage and the role of oxidative stressrdquo Archives of Toxicologyvol 86 no 12 pp 1809ndash1827 2012

[19] D Tomanek C42 Isomers In Guide through the NanocarbonJungle Buckyballs Nanotubes Graphene and Beyond 2015httpwwwnanotubemsuedufullerenefullerenephpC=42

[20] S L Mayo B D Olafson and W A Goddard ldquoDREIDING ageneric force field formolecular simulationsrdquo Journal of PhysicalChemistry vol 94 no 26 pp 8897ndash8909 1990

[21] J J P Stewart ldquoPM3rdquo in Encyclopedia of Computational Chem-istry P von and R Schleyer Eds JohnWiley amp Sons NewYorkNY USA 1998

[22] M V Diudea O M Minailiuc G Katona and I GutmanldquoSzeged matrices and related numbersrdquo MATCH Communica-tions in Mathematical and in Computer Chemistry vol 35 pp129ndash143 1997

[23] S D Bolboaca and L Jantschi ldquoQuantitative structure-activityrelationships linear regressionmodelling and validation strate-gies by examplerdquo BIOMATH vol 2 no 1 Article ID 1309089 11pages 2013

[24] S D Bolboaca L Jantschi andMVDiudea ldquoMolecular designand QSARsQSPRs with molecular descriptors familyrdquo CurrentComputer-Aided Drug Design vol 9 no 2 pp 195ndash205 2013

[25] S D Bolboaca ldquoAssessment of random assignment in trainingand test sets using generalized cluster analysis techniquerdquoApplied Medical Informatics vol 28 no 2 pp 9ndash14 2010

[26] N Chirico and P Gramatica ldquoReal external predictivity ofQSAR models Part 2 New intercomparable thresholds fordifferent validation criteria and the need for scatter plot inspec-tionrdquo Journal of Chemical Information andModeling vol 52 no8 pp 2044ndash2058 2012

[27] Linrsquos Concordance December 2015 httpservicesniwaconzservicesstatisticalconcordance

[28] L Jantschi ldquoSzeged Matrix Property Indicesrdquo 2014 httplacademicdirectorgChemistrySARsSMPI

[29] X Liu Y Wen Z Chen et al ldquoModulation of Dirac points andband-gaps in graphene via periodic fullerene adsorptionrdquo AIPAdvances vol 3 no 5 Article ID 052126 2013

[30] Y-N Chiu J Xiao C D Merritt et al ldquoSpecial geminalsand Schlegel diagrams of molecular structures of fullerenesand metallofullerenesrdquo Journal of Molecular StructureTHEOCHEM vol 530 no 1-2 pp 67ndash83 2000

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Volume 2014

Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


Journal of


Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


Table 1 Several small fullerenes and their number of isomers

Number Fullerene Number of isomers1 C

282

2 C30

33 C

326

4 C34

65 C

3615

6 C38

177 C

4040

8 C42

459 C

4489

10 C46

116Source httpwwwnanotubemsuedufullerenefullerene-isomershtml[accessed June 7 2015]

Spartan Babel

HyperChem

charges

httplacademicdirectorgChemistrySARsSMPI

(i) 1512 (ii) 242 filtered total strain energy

Nano-QSPR C42 fullerene models

SSr = sum of squares of residualsSSr from vertical offsets = min

lowast hin with partial

lowast hinlowast mollowast xyz file1 2

3

4

5

SMPI descriptors (xi)TSE (yi)

Scheme 1 Flowchart of the applied methods The pool of filteredSMPI (Szeged Matrix Property Indices) descriptors contains thosedescriptors with absolute values between 10minus7 and 107

energy of the isomers of C42

fullerene using the structuralinformation

2 Materials and Methods

All C42

fullerene isomers were included in the analysisData related to continuum elasticity expressed as total strainenergy (TSE in eV) and the structures as lowastxyz files of C

42

fullerene isomers were taken from [19] (Table 2)The analysis was conducted on the downloaded file of

the C42

isomers without any modification on the availablegeometry According to [19] the fullerene geometries werebased on the geometry of the structures in Yoshidarsquos FullereneLibrary (UNIX files) and reoptimized using Dreiding-likeforce-field [20] Here the obtained geometry is used

The steps applied in the analysis are depicted in Scheme 1In the first step of the analysis the downloaded files

were translated into lowastmol file with Spartan software(httpswwwwavefuncomproductsspartanhtml) In thesecond step the lowastmol file is transformed as lowasthin file using

Table 2 C42fullerene isomers identification number (IsoID) and

total strain energy (TSE)

IsoID TSE (eV)01 3106002 3053703 2979104 2980505 3061806 2985007 3060808 2978209 2852710 2939311 2947512 2834013 2815714 2714715 2995516 2817517 2827618 2947419 2740820 2817521 2728322 2914023 2876524 2774325 2748726 2835327 2801428 2905129 2748930 2897231 2748432 2665733 2663934 2737135 2655436 2797337 2976438 3110139 2663940 2750141 2667242 2866543 2828444 2673745 25661

Babel software (httpopenbabelorg) The partial chargeswere calculated in the third step using HyperChem software(httpwwwhypercom) by applying PM3 (ParameterizedModel number 3 [21]) single point (energy) semiempirical



Equation 119877

2119877

2


2 seloo 119865loo(119901loo)

(1) 08883 08857 04577 342(438 times 10minus22)

1805(109 times 10minus21) 4677 08656 05039 275


(2) 09612 09593 02729 520(232 times 10minus30)

669(410 times 10minus8) 3192 09545 02960 439


(3) 09836 09824 01796 820(130 times 10minus36)

437(840 times 10minus5) 1976 09809 01939 701


(4) 09898 09888 01431 974(287 times 10minus39)

355(101 times 10minus3) 1595 09768 02171 418








42isomers


1198652 [26]) external








times 181

(2)


times 10


(3)











2119865-stat 119877

2119865-stat


2119865-stat 119877

2119865-stat



Equation 119877

2

ext 119876

2

1198652119876

2

1198653RMSEP MAEP |119905

















times 170

119877

2= 08483

119877

2

adj = 08401

se = 065

119865 (119901) = 103 (707 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 288 (00066)

119899 = 40

119876

2

1198653= 07834

RMSEP = 160

MAEP = 052


R2 = 08883

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

33Es

timat

ed T

SE b

y (1

)

(a)

R2 = 09612

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(2)

(b)

R2 = 09836

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(3)

(c)

R2 = 09898

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(4)

(d)


TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(3)

(a)

TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(4)

(b)



76

77

78

79

80

81

82

83Pr

edic

ted

TSE

by (3

)


20

21

22

23

24

25

26

27

Pred

icte

d TS

E by

(4)



PredErr = 064

CCC = 09179(5)



times 121

119877

2= 08853

119877

2

adj = 08479

se = 057

119865 (119901) = 69 (376 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 310 (00038)

119899 = 40

119876

2

1198653= 08362

RMSEP = 160

MAEP = 043

PredErr = 052

CCC = 09390

(6)










on C40



42or C40fullerene






4 Conclusions





25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)




42


fullerene isomers



References








60(OH)















38 C40 and C





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Equation 119877

2119877

2


2 seloo 119865loo(119901loo)

(1) 08883 08857 04577 342(438 times 10minus22)

1805(109 times 10minus21) 4677 08656 05039 275


(2) 09612 09593 02729 520(232 times 10minus30)

669(410 times 10minus8) 3192 09545 02960 439


(3) 09836 09824 01796 820(130 times 10minus36)

437(840 times 10minus5) 1976 09809 01939 701


(4) 09898 09888 01431 974(287 times 10minus39)

355(101 times 10minus3) 1595 09768 02171 418








42isomers


1198652 [26]) external








times 181

(2)


times 10


(3)











2119865-stat 119877

2119865-stat


2119865-stat 119877

2119865-stat



Equation 119877

2

ext 119876

2

1198652119876

2

1198653RMSEP MAEP |119905

















times 170

119877

2= 08483

119877

2

adj = 08401

se = 065

119865 (119901) = 103 (707 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 288 (00066)

119899 = 40

119876

2

1198653= 07834

RMSEP = 160

MAEP = 052


R2 = 08883

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

33Es

timat

ed T

SE b

y (1

)

(a)

R2 = 09612

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(2)

(b)

R2 = 09836

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(3)

(c)

R2 = 09898

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(4)

(d)


TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(3)

(a)

TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(4)

(b)



76

77

78

79

80

81

82

83Pr

edic

ted

TSE

by (3

)


20

21

22

23

24

25

26

27

Pred

icte

d TS

E by

(4)



PredErr = 064

CCC = 09179(5)



times 121

119877

2= 08853

119877

2

adj = 08479

se = 057

119865 (119901) = 69 (376 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 310 (00038)

119899 = 40

119876

2

1198653= 08362

RMSEP = 160

MAEP = 043

PredErr = 052

CCC = 09390

(6)










on C40



42or C40fullerene






4 Conclusions





25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)




42


fullerene isomers



References








60(OH)















38 C40 and C





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




2119865-stat 119877

2119865-stat


2119865-stat 119877

2119865-stat



Equation 119877

2

ext 119876

2

1198652119876

2

1198653RMSEP MAEP |119905

















times 170

119877

2= 08483

119877

2

adj = 08401

se = 065

119865 (119901) = 103 (707 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 288 (00066)

119899 = 40

119876

2

1198653= 07834

RMSEP = 160

MAEP = 052


R2 = 08883

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

33Es

timat

ed T

SE b

y (1

)

(a)

R2 = 09612

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(2)

(b)

R2 = 09836

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(3)

(c)

R2 = 09898

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(4)

(d)


TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(3)

(a)

TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(4)

(b)



76

77

78

79

80

81

82

83Pr

edic

ted

TSE

by (3

)


20

21

22

23

24

25

26

27

Pred

icte

d TS

E by

(4)



PredErr = 064

CCC = 09179(5)



times 121

119877

2= 08853

119877

2

adj = 08479

se = 057

119865 (119901) = 69 (376 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 310 (00038)

119899 = 40

119876

2

1198653= 08362

RMSEP = 160

MAEP = 043

PredErr = 052

CCC = 09390

(6)










on C40



42or C40fullerene






4 Conclusions





25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)




42


fullerene isomers



References








60(OH)















38 C40 and C





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


R2 = 08883

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

33Es

timat

ed T

SE b

y (1

)

(a)

R2 = 09612

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(2)

(b)

R2 = 09836

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(3)

(c)

R2 = 09898

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estim

ated

TSE

by

(4)

(d)


TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(3)

(a)

TrainingTest

26 27 28 2925 31 3230

Observed TSE

25

26

27

28

29

30

31

32

Estp

red

TSE

(4)

(b)



76

77

78

79

80

81

82

83Pr

edic

ted

TSE

by (3

)


20

21

22

23

24

25

26

27

Pred

icte

d TS

E by

(4)



PredErr = 064

CCC = 09179(5)



times 121

119877

2= 08853

119877

2

adj = 08479

se = 057

119865 (119901) = 69 (376 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 310 (00038)

119899 = 40

119876

2

1198653= 08362

RMSEP = 160

MAEP = 043

PredErr = 052

CCC = 09390

(6)










on C40



42or C40fullerene






4 Conclusions





25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)




42


fullerene isomers



References








60(OH)















38 C40 and C





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of


76

77

78

79

80

81

82

83Pr

edic

ted

TSE

by (3

)


20

21

22

23

24

25

26

27

Pred

icte

d TS

E by

(4)



PredErr = 064

CCC = 09179(5)



times 121

119877

2= 08853

119877

2

adj = 08479

se = 057

119865 (119901) = 69 (376 times 10

minus16)

1003816

1003816

1003816

1003816

119905min1003816

1003816

1003816

1003816

(119901) = 310 (00038)

119899 = 40

119876

2

1198653= 08362

RMSEP = 160

MAEP = 043

PredErr = 052

CCC = 09390

(6)










on C40



42or C40fullerene






4 Conclusions





25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)




42


fullerene isomers



References








60(OH)















38 C40 and C





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



25

26

27

28

29

30

31

32

33Pr

edic

ted

TSE

by (5

)

(a)

25

26

27

28

29

30

31

32

33

Pred

icte

d TS

E by

(6)




42


fullerene isomers



References








60(OH)















38 C40 and C





























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

























Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of










Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Documents

Research Article Nanoquantitative Structure-Property