TheoreticalInvestigationonStructure-PropertyRelationshipof AsymmetricClusters(CH FBN … · 2020. 6. 30. · E b(n) nE CH 3 FBN 3 −E CH 3 FBN 3 n, E b−c(n) nE CH 3 FBN 3 +0.96∗nZPE

Research ArticleTheoretical Investigation on Structure-Property Relationship ofAsymmetric Clusters (CH3FBN3)n (n= 1ndash 6)

Deng-Xue Ma1 Yao-Yao Wei2 Yun-Zhi Li2 Guo-Kui Liu 2 and Qi-Ying Xia 2

1School of Materials Science and Engineering Linyi University Linyi 276005 China2School of Chemistry and Chemical Engineering Linyi University Linyi 276005 China

Correspondence should be addressed to Guo-Kui Liu liuguokuihappy163com and Qi-Ying Xia xiaqiying163com

Received 2 April 2020 Revised 15 May 2020 Accepted 11 June 2020 Published 30 June 2020

Academic Editor Franck Rabilloud

Copyright copy 2020 Deng-XueMa et al1is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

1e structural relative stability electronic IR vibrational and thermodynamic properties of asymmetric clusters (CH3FBN3)n(n 1ndash6) are systematically investigated using density functional theory (DFT) method Results show that clusters (CH3FBN3)n(n 2ndash6) form a cyclic structure with a B atom and a Nα atom binding together Five main characteristic regions are observed andassigned for the calculated IR spectra 1e size-dependent second-order energy difference shows that clusters (CH3FBN3)3 and(CH3FBN3)5 have relatively higher stability and enhanced chemical inertness compared with the neighboring clusters 1ese twoclusters may serve as the cluster-assembled materials 1e variations of thermodynamic properties with temperature T or clustersize n are analyzed respectively Based on enthalpies in the range of 200ndash800K the formations of the most stable clusters(CH3FBN3)n (n 2ndash6) from monomer are thermodynamically favorable 1ese data are helpful to design and synthesize otherasymmetric boron azides

1 Introduction

1e extensive studies on boron azides are developed as thesemolecules have been shown to be good precursors for boronnitride (BN) film deposition [1] 1e chemistry of boronazides commenced in 1954 with the synthesis of borontriazide B(N3)3 [2] since then it developed slowly In 1963Paetzold produced trimeric (Cl2BN3)3 from the reaction ofLiN3 and BCl3 in CH2Cl2 solution [3] 1e molecularstructure of dichloroboron azide containing six-memberedboron nitrogen heterocycle with diazo groups bounded tonitrogen atoms was determined byMuller in 1971 [4] Borondihalide azides (BX2N3)3 (X F Cl or Br) from the reactionof BCl3 with trimethylsilyl azide in CH2Cl2 solution werealso recorded byWiberg et al in 1972 [5] Dehnicke reportedthe infrared spectra of the monoazide products I2MN3(MB Al Ga) and observed the formation of oligomers ofthese species in 1978 [6] Several alkyl and arylboron azideshave been synthesized using similar methods Oligomeri-zation for Me2BN3 was established by 11B NMR spectros-copy in 1966 [7] 1e chemistry of alkylboron azides was

further investigated and the development of this field hasbeen reviewed by Paetzold Fraenk and coworkers [8ndash16]

Although the chemistry of boron azides in the con-densed phase has been extensively discussed in the literatureresearch studies of these species in the gas phase are ratherlimited With the goal to use boron azides as the single-source precursors (SSP) knowledge of their gas phase sta-bility and thermodynamic properties becomes essential 1estructure of monomers Cl2BN3 and (CH3)2BN3 has beenexplored using ab initio calculation and the thermodynamicstabilities of X2BN3 with respect to its dimerization andtrimerization have been gained and discussed [17ndash20] fromthe theoretical view Previous theoretical studies of theboron azides mostly focused on the symmetric boron azides

1e effect for the break of the symmetry of substitutedboron azides is hardly considered Here in accordance withprevious theoretical studies on the asymmetric clusters ofinorganic boron azides [21 22] and experimental studies onthe asymmetric clusters of organic gallane azides and alu-minum azides (RRrsquoMN3)n (MAl Ga RCH3 RrsquoH ClBr n 3minus4) [23 24] the structure stability IR spectra and

HindawiJournal of ChemistryVolume 2020 Article ID 4106562 11 pageshttpsdoiorg10115520204106562

thermodynamic characteristics of the asymmetric clusters oforganic boron azides (CH3FBN3)n (n 1 ndash 6) were theo-retically discussed in detail 1ese discussions will providefundamental data and references for experimentalist todesign and synthesize the novel boron azides in the future

2 Computational Methods

As is well known it is important to choose an appropriatebasis set to give the accurate description of clustersrsquo structuresand energies Usually a substantial size of basis set is requiredHowever the size of clusters studied in this work excluded theuse of a very large basis set and hence all calculations wereperformed using the DFT-B3LYP method with the 6-31Glowastbasis set [25 26] via the Gaussian 09 program package withthe default convergence thresholds [27] To ensure the ade-quacy of this basis set we also optimized the clusters with the6-311+Glowast basis set As shown later on results obtained fromthese two basis sets were similar except for slightly numericaldifferences 1e energies of all clusters were also evaluatedusing the 6-311 +Glowast basis set 1e initial configurations aresearched by two ways (1) by considering the numbers ofknown clusters (HClBN3)n (n 1ndash6) in previous works [21]and (2) by placing -CH3 groups and F atoms at varioussubstitutional sites (H or Cl) on the basis of optimized(HClBN3) geometries No symmetry constraints were appliedLots of rationally initial one- two- and three-dimensionalconfigurations were built to seek the most stable structures Inthis way a large number of optimized isomers for theasymmetric clusters (CH3FBN3)n (n 1ndash6) were obtainedFrequencies as well as their respective IR intensities were thencalculated and the lack of imaginary frequencies confirmedthat the true minimum was obtained in each case Accordingto the previous study the calculated frequencies were scaleduniformly by 096 to approximately correct the systematicoverestimation [28]

3 Results and Discussion

31 Structures and Charge Distribution A number of iso-mers are calculated at each size Here structures of clusters(CH3FBN3)n (n 1minus 6) having the lowest energy were fo-cused because all properties of clusters (CH3FBN3)n(n 1ndash6) were calculated based on the lowest energy Twostable structures of the monomer CH3FBN3 were obtained(connectivity CH3FBminusNαminusNβminusNc) with a slight differencein geometrical parameters 1e clusters (CH3FBN3)n(n 2 ndash 6) are produced by the head-to-tail oligomerizationof the CH3FBN3 monomers which is a starting point for theoligomerizations Two dimers seventeen trimers sixty-fourtetramers two hundred and fifty-six pentamers and fivehundred and thirty-six hexamers are obtained in thismanner Judged by the total energies themost stable isomersat each size are labeled as 1 2 3 4 5 and 6 and shown inFigure 1 Obviously B and Nα atoms easily bond togetherand BndashB and NαndashNα bonds are not formed in the clusters(CH3FBN3)n (n 2minus 6) In other words the clusters(CH3FBN3)n (n 2minus 6) contain cyclic (BNα)2n structureswith alternating boron and α-nitrogen atoms

1e corresponding geometrical parameters are collectedin Table 1 and the data in parentheses are calculated resultsfrom the 6-311 +Glowast basis set 1e results obtained fromdifferent basis sets are generally consistent In detail bondlengths (except for BminusF bonds) from the 6-311 +Glowast basis setare slightly shorter than those from the 6-31Glowast basis set1iswhole agreement shows that it is appropriate to choose the6-31Glowast basis set to compute the titled systems 1erefore inthis work we only report the geometrical parameters ob-tained with the 6-31Glowast basis set For n 1 the azide group inthe monomer CH3FBN3 is slightly bent with a NαndashNβndashNc

angle of 1731deg 1e calculated BndashN bond length of 1447 A isbetween BndashN single (158 A) and double bonds (137 A) 1eNβminusNc bond length at 1135 A is shorter than the NαminusNβbond length at 1240 A 1e NβminusNc bond length is betweenNndashN double (125 A) and NndashN triple bonds (110 A) Forn 2 ndash 6 the computed BndashN bond length of 1601ndash1638 Apossesses typical character of BndashN single bond which issimilar to the BndashN length of other covalent boron azidespreviously determined such as (F2BN3)3 (1616 A) [19] and(C6F5B(N3)2)3 (160 A) [12] 1e BminusC and BminusF bond lengthsare in the range of 1585ndash1596 A and 1363ndash1381 A re-spectively 1e computed structural parameters of the azideunits in the clusters (CH3FBN3)n (n 2 ndash 6) are1240ndash1255 A for NαminusNβ bonds 1128ndash1133 A for NβminusNc

bonds and 1771ndash1794deg for NαminusNβminusNc bond angle It isobvious that the azide group is nearly linear 1ese resultsare perfectly consistent with those found in (Cl2BN3)3(125 A 109 A 178deg) [4] (F2BN3)3 (1249 A 1129 A 1798deg)[19] and (C6F5B(N3)2)3 (127 A 111 A 179deg) [12]1ereforethe calculation method in this work is reliable and it givescredence to our computed structural parameters of clusters(CH3FBN3)n (n 2 ndash 6)

1rough the above discussions it is obvious that NβminusNc

bond is shorter than NαminusNβ bond in the clusters(CH3FBN3)n (n 1 ndash 6) 1is can be interpreted as a higherbond order for the terminal NminusN bond showing a pre-formation of the N2 molecule Moreover the cluster size nhas an important effect on the geometries An obvious in-crease is shown for the length of B-Nα bond with cluster sizen increasing from 1 to 2sim6 owing to the tension of the ringHowever BminusNα bond length shows little change with clustersize in the range of 2sim6 which fluctuates in the range of1601ndash1638 A 1e NαminusNβ bond lengths increase as thecluster size n increases from 1 to 5 and show little changefrom n 5 to n 6 Similarly when cluster size n increasesfrom 1 to 3 the BminusC and BminusF bond lengths increaseHowever the change of BminusC and BminusF bond lengths is notobvious from n 4 to n 61eNβminusNc bond length shortensfrom 1135 A in cluster size with 1 to 1129 A in cluster sizewith 6 and tends to be constant around 1130 A withn 3 ndash 6 Compared with monomer 1 the increasing bondlengths of NαminusNβ BminusC and BminusF bonds that are outside ofrings show that N2 (NβminusNc) -CH3 and F- groups can beeasily removed to yield BN material

To give a deeper understanding on these structures wecalculate the charge distribution of the clusters (CH3FBN3)n(n 1 ndash 6) as shown in Table 2 It can be seen that the chargedistribution of CH3FBN3 molecule exhibits zwitterionic

2 Journal of Chemistry

characteristics with the charge centers of N and B atomsrespectively As for (CH3FBN3)n (n 2 ndash 6) charge distri-butions are similar to those of CH3FBN3 However becauseB atoms in these molecules all reach the high coordinationthe characteristic of zwitterionic ion for these clusters is aproblem needing more studies

32 Relative Stabilities All energies are displayed in Table 3and the data in parentheses are from the 6-311 +Glowast basis setObviously the energies obtained at the B3LYP6-31Glowast levelsare similar to those obtained with the 6-311 +Glowast basis set1e use of larger basis sets has no significant influence on thebinding energies which again shows that the 6-31Glowast basis

Denotes B atom

Denotes N atomDenotes F atom

Denotes H atom

Denotes C atom

1 2

3 4

5 6

Figure 1 Structures of the asymmetric clusters (CH3FBN3)n (n 1ndash6)

Journal of Chemistry 3

set is suitable for the clusters studied here 1us in this workwe only report the relative stability of the clusters (CH3FBN3)nwith the 6-31Glowast basis set 1e uncorrected binding energies

(Eb) corrected binding energies (Eb-c) average correctedbinding energy (Eb-c-ave) and the second-order energy dif-ference (Δ2E) are calculated using the following equations

Table 2 Atomic charge (e) of the most stable structure (CH3FBN3)n (n 1 ndash 6)

1 2 3 4 5 6Nα minus05840 minus05922 minus05847 minus05885 minus05854 minus05918Nβ 02447 02761 02760 02753 02704 02686Nc minus00175 00299 00512 00602 00608 00673B 11319 10869 10721 10745 10773 10809F minus04760 minus04973 minus05100 minus05174 minus05171 minus05227C minus10830 minus10571 minus10545 minus10551 minus10568 minus10561H 02627 02512 02499 02504 02503 02503

Table 3 Total energies (E) zero point energy (ZPE) uncorrected binding energies (Eb) corrected binding energies (Eb-c) average correctedbinding energy (Eb-c-ave) and second-order energy difference (Δ2E) (unit kJ middotmolminus1)a

Clusters E Eb ZPE Eb-c Eb-c-ave Δ2E

1 minus86354411 15049(minus86379661) (14936)

2 minus172709845 1023 30695 450 225 minus2927(minus172760268) (945) (30409) (430) (215) (minus2767)

3 minus259068489 5256 46636 3827 1276 1876(minus259143962) (4978) (46216) (3626) (1209) (1697)


5 minus431781967 9912 78067 7203 1441 397(minus431907866) (9559) (77293) (7051) (1410) (501)

6 minus518138441 11975 93724 8682 1447(minus518289497) (11528) (92798) (8474) (1412)

a1e data in parentheses are from 6-311 +Glowast basis set

Table 1 Ranges of the bond lengths (A) and bond angles (deg) for the most stable structures of the asymmetric clusters (CH3FBN3) (n)(n 1 ndash 6) optimized at the DFT-B3LYP levela

1 2 3 4 5 6

NβndashNc1135 1133 1128ndash1133 1133 1128ndash1133 1129(1126) (1125) (1120ndash1125) (1121) (1119ndash1124) (1120)

NαminusNβ1240 1240 1243ndash1246 1248 1246ndash1255 1251(1236) (1235) (1240ndash1249) (1246) (1243ndash1253) (1250)

NαminusB1447 1633 1614ndash1638 1601ndash1602 1608ndash1637 1606(1442) (1641ndash1643) (1613ndash1632) (1598ndash1600) (1603ndash1627) (1601ndash1604)

BminusC 1563 1585 1589ndash1593 1591 1591ndash1596 1592(1555) (1579) (1584ndash1588) (1587) (1587ndash1591) (1588)

BminusF 1341 1363 1376ndash1381 1385 1380ndash1386 1387ndash1388(1349) (1374) (1388ndash1393) (1397) (1387ndash1398) (1398ndash1399)

CminusH 1093ndash1098 1096ndash1098 1094ndash1098 1096ndash1098 1093ndash1098 1094ndash1098(1091ndash1096) (1094ndash1096) (1092ndash1096) (1094ndash1096) (1091ndash1096) (1093ndash1096)

BminusNαminusB941 1247ndash1252 1267ndash1269 1263ndash1282 1252ndash1253(952) (1239ndash1250) (1271) (1256ndash1312) (1260ndash1261)

NαminusBminusNα859 1002ndash1007 1029ndash1031 1050ndash1078 1062ndash1062(848) (993ndash1007) (1033) (1041ndash1064) (1066ndash1067)

NαminusNβminusB1213 12331ndash1246 1176ndash1196 1149ndash1184 1155ndash1187 1182ndash1184(1214) (1256ndash1258) (1156ndash1194) (1180ndash1186) (1133ndash1180) (1174ndash1175)

NαminusNβminusNc

1731 1771 1778ndash1789 1783ndash1784 1782ndash1794 1776ndash1778(1733) (1775) (1781ndash1791) (1783ndash1784) (1783ndash1794) (1776ndash1779)



Eb(n) nE CH3FBN3( 1113857 minus E CH3FBN3( 1113857n

Ebminusc(n) nE CH3FBN3( 1113857 + 096lowast nZPE CH3FBN3( 1113857 minus E CH3FBN3( 1113857n minus 096lowastZPE CH3FBN3( 1113857n

Ebminuscminusave(n) Ebminusc(n)

n

Δ2E(n) E CH3FBN3( 1113857n+1 + 096lowastZPE CH3FBN3( 1113857n+1 + E CH3FBN3( 1113857nminus1

+ 096lowastZPE CH3FBN3( 1113857nminus1 minus 2E CH3FBN3( 1113857n minus 2lowast 096lowast ZPE CH3FBN3( 1113857n

(1)

where E (CH3FBN3)n and E (CH3FBN3) are the total en-ergies of the clusters (CH3FBN3)n (n 2 ndash 6) and CH3FBN3respectively ZPE (CH3FBN3)n and ZPE (CH3FBN3) repre-sent the zero point energies of the most stable clusters(CH3FBN3)n (n 2 ndash 6) and CH3FBN3 respectively and the096 is a scaling factor [28]

From Table 3 the ratios of ZPE corrections to theirbinding energies Eb are large for the clusters (CH3FBN3)n(n 2minus 6) 1us it is necessary to carry out the ZPE cor-rections for the binding energies For intuitive presentationthe calculated energy is also plotted as a function of clustersize n as shown in Figure 2 1e curves of Eb (Figure 2(a))and Eb-c (Figure 2(b)) are seen to increase monotonicallywith the augment of cluster size n which means that clusterscan continue to gain energy during the clustersrsquo growthprocess 1e Eb-c-ave values increase sharply with the clusterssize n from 2 to 3 then it approaches to be stable around13ndash14 kJmiddotmolminus1 when cluster size nge 3 1erefore the geo-metrical structures of clusters (CH3FBN3)n (n 1minus 6) tendto be stable when cluster size nge 3

1e relative stability of clusters can be also estimatedthrough the Δ2E (n) According to the definition clusterswith positive Δ2E are more stable than those with negativeΔ2E A clear odd-even oscillation behavior is presented inFigure 2(d) 1e clusters (CH3FBN3)n (n 1minus 6) at n 3 5correspond to local maximal on the curve of Δ2E indicatingthat they are relatively more stable than other clusters 1istrend is in excellent agreement with that of the asymmetricclusters of the inorganic boron azides (HClBN3)n (n 1 ndash 6)[21] In particular the trimer (CH3FBN3)3 possesses thehighest stability among all clusters in terms of the largestvalue of Δ2E 1e stable structure of six-member ring oftrimer plays a vital role

33 IR Spectrum 1e IR spectrum is not only the basicproperty of compounds and effective method to analyze oridentify substances but also has a direct relationship withthermodynamic properties However there are no experi-mental data for the title compounds 1us it is necessary touse the theoretical method to calculate and predict IR spectrafor both theoretical and practical reasons Figure 3 providesthe calculated IR spectra of the clusters (CH3FBN3)n(n 1minus 6) at the B3LYP6-31Glowast level Due to intrinsiccomplexity it is difficult to assign all vibrational modes1us we only analyze and discuss some typical vibrationalmodes

1ere are five main characteristic regions for clusters(CH3FBN3)n (n 1 ndash 6) that correspond to the ndashN3 asym-metric and symmetric stretching ndashCH3 stretching and in-plane bending vibrations and the fingerprint region As formonomer CH3FBN3 the ndashN3 asymmetric and symmetricstretching vibrations with intense peak lie at 2215 and1360 cmminus1 respectively 1e modes in the range of2923ndash3022 cmminus1 are classified to the characteristic ndashCH3stretching vibrations 1e peak around 1440 cmminus1 corre-sponds to the ndashCH3 in-plane bending vibrations1e peaks atless than 1210 cmminus1 belong to the fingerprint region whichare mainly composed of wagging and scissoring of ndashCH3 andthe stretching of BminusF and BminusC bonds As can be seen fromFigure 3 similar vibrational modes are observed in clusters(CH3FBN3)n (n 2 ndash 6) 1e regions of 2917ndash30192202ndash2243 1331ndash1458 1217ndash1308 and 0ndash1204 cmminus1 areindividually assigned to -CH3 stretching vibrations -N3asymmetric stretching vibrations ndashCH3 in-plane bendingvibrations -N3 symmetric stretching vibrations and finger-print region In previous studies the NndashN asymmetricalstretching vibration for Cl2BN3 Br2BN3 Me2BN3(C6F5)2BN3 polymer and NaN3 crystal were individuallylocated at 2210ndash2219 [15] 2200ndash2215 [15] 2128 [7 14]2135ndash2209 cmminus1 [11 12] and 2128ndash2151 cmminus1 [29] fromexperiments Our calculated results are in accordance withthose in crystal which shows that the structures of N3 groupsin clusters and in crystal are identical Moreover the obtainedresult is similar to that found in the clusters (HClBN3)n(n 1 ndash 6) (2217ndash2250 cmminus1) of DFT calculations [21]

Furthermore compared with monomer the N3 asym-metric stretching vibration presents the blue-shifted phe-nomenon for clusters with n 2minus 6 However the N3symmetric stretching vibration and the ndashCH3 stretchingvibration show red-shifted trend Meanwhile in threecharacteristic regions of N3 asymmetric N3 symmetric andndashCH3 stretching vibration the number of vibration modeequals to that of azido groups and CndashH bonds respectivelyFor example the monomer 1 has three bands at 2923 2972and 3022 cmminus1 with CndashH stretching vibration and the tri-mer 3 has three bands at 2213 2225 and 2240 cmminus1 with N3asymmetric stretching vibration and the hexamer 6 has sixbands at 1237 1237 1245 1245 1247 and 1255 cmminus1 withN3 symmetric stretching vibration

34 0ermodynamic Properties 1ermodynamic functionsare important parameters for clusters to predict reactive


property in a chemical reaction According to vibrationalanalysis and statistical thermodynamic method thestandard molar heat capacity (Cθ

pm) standard molarthermal entropy (Sθm) and standard molar thermal en-thalpy (Hθ

m) of the asymmetric clusters (CH3FBN3)n(n 1 ndash 6) in the range of 200ndash800 K are evaluated andtabulated in Table 4 It is obvious that the calculatedthermodynamic functions increase with the temperatureT raising For more clear intuitive taking monomer 1 asan example the temperature-dependent relationships forCθ

pm Sθm and Hθm are expressed in formulas (2)ndash(4) and all

are plotted in Figure 4(a) 1ese correlations approximateto linear equations due to the small coefficients of T2namely the Cθ

pm Sθm and Hθm increase linearly with the

increase of temperature T 1is can be understood fromthe fact that these three thermodynamic functions aredominated by the weak translational and rotationalmotions of the clusters at lower temperature whereas thevibrational motion is intensified and makes more con-tributions to Cθ

pm Sθm and Hθm at higher temperature 1e

same linear relationships are found for clusters(CH3FBN3)n with n 2 ndash 6

Cθpm 334650 + 02460T minus 11698 times 10minus 4

T2

R2

09999

SD 03318

(2)

Sθm 2310291 + 04049T minus 14317 times 10minus 4

T2

R2

09998

SD 09034

(3)

Hθm minus36904 + 00606T + 6401 times 10minus 5

T2

R2

09999

SD 02784

(4)

where R2 represents the square of correlation coefficient andSD represents standard deviation

Moreover the cluster size-dependent relationships forCθ


are shown in Figure 4(b) All thermodynamic functionsincrease monotonically with the enlarged cluster size n inother words when one more CH3FBN3 is bound the Cθ

pmSθm and Hθ

m increase with the average of 108 Jmiddotmolminus1 Kminus1133 Jmiddotmolminus1 Kminus1 and 18 kJmiddotmolminus1 separately 1is meansthat the contribution of monomer CH3FBN3 to the ther-modynamic properties of cluster matches the clusteradditivity

Cθpm minus120847 + 1084637 n

R2

10000

SD 10282

(5)

Sθm 2110987 + 1332237 n

R2

09996

SD 80272

(6)

Hθm 10620 + 183966 n

R2

09999

SD 05260

(7)

d

E bndashc

ndashave

a

c

(kJ middot molndash1)



E b E

bndashc b

0306090

120

0369

1215

ndash30ndash15

015

Δ 2E

3 4 5 62Cluster size n



Figure 21e uncorrected binding energies Eb (a) corrected binding energies Eb-c (b) average corrected binding energy Eb-c-ave (c) and thesecond-order energy difference Δ2E (d) of the asymmetric clusters (CH3FBN3)n (n 1minus 6) versus the cluster size n


In addition the theoretical enthalpies (ΔH) and Gibbsfree energies (ΔG) of various oligomerizations frommonomer CH3FBN3 in the range of 200ndash800K are compiledin Table 5 1e values of ΔH in the processes are negative

except for the process 1⟶ 2 beyond 700K indicating thatthese oligomerization processes are exothermic 1e ΔG at agiven temperature is evaluated by the equationΔGΔHminusTΔS 1e values of ΔG are all positive which

0

100

200

300

400

500

600

2500 2000 1500 1000Frequency (cmndash1)

500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0


500 0 2500 2000 1500 1000Frequency (cmndash1)

1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity

Figure 3 IR spectra of the asymmetric clusters (CH3FBN3)n (n 1minus 6) with full width at half maxima of 20 cmminus1


reveals the oligomerizations cannot occur spontaneously inthe range of 200ndash800K 1ere are no experimentally ther-modynamic data available for the asymmetric clusters(CH3FBN3)n (n 1minus 6) so the calculated thermodynamicfunctions and the obtained relationships of them with thetemperature and cluster size n may help the experiment tofurther study the physical chemical and energetic prop-erties of the asymmetric clusters (CH3FBN3)n (n 1minus 6) orother asymmetric boron azides

35 Aromatic Properties Here the aromaticity of thestudied systems will be discussed Because our systems arenonplanar it is not suitable to use the criterion of nucleus-independent chemical shift (NICS) [30] In order to find outwhether a large π bond exists in our studied system we usethe newly proposed localized orbital locator (LOL)-πmethod [31] that can be used for studying nonplanar systemto study the π bonds of our systems 1e LOL-π is analyzedand visualized with the Multiwfn [32] From Figure 5 there

Table 4 1ermodynamic properties for the most stable clusters (CH3FBN3)n (n 1minus 6) at different temperaturesa

T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ

pm (Jmiddotmolminus1middotKminus1) Sθm (Jmiddotmolminus1 Kminus1) and Hθm (kJmiddotmolminus1)

Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

2 3 4 5 61Cluster size n

ndash200ndash100

0100200300400500600700800900

10001100

(b)

Figure 4 Variations of the thermodynamic functions (Cθpm S

θm and Hθ

m) with the temperature (T) (a) for the monomer CH3FBN3 and thecluster size n (b) and for the asymmetric clusters (CH3FBN3)n (n 1ndash6)


1 2

3 4

5 6

Figure 5 LOL-π isosurface of different systems with the isovalue of 04

Table 5 Enthalpy change and Gibbs free energy change of oligomerization at different temperaturesa

T 200 2982 400 500 600 700 800

2(1)⟶ (2) ΔH minus722 minus624 minus472 minus305 minus128 051 228ΔG 3294 5245 7230 9135 11006 12848 14664

3(1)⟶ (3) ΔH minus4370 minus4207 minus3937 minus3632 minus3303 minus2967 minus2630ΔG 3757 7711 11748 15631 19454 23221 26937




aUnits T (K) ΔH (kJmiddotmolminus1) and ΔG (kJmiddotmolminus1)


is π bond of NNNB in 1 and similar π bonds in 2-6However the π conjugation of 2ndash6 is not as good as that of 1Meanwhile Figure 5 also shows no large π bonds in allsystems

4 Conclusions

We have systematically studied the structure relativestability IR and thermodynamic properties of theasymmetric clusters (CH3FBN3)n (n 1 ndash 6) at the DFT-B3LYP6-31Glowast 1e B and Nα atoms tend to bond togetherin clusters (CH3FBN3)n (n 2 minus 6) 1e variation trend ofgeometrical parameters shows N2 (NβminusNc) -CH3 and F-

groups are easily eliminated and BN material is yielded1e calculated Δ2E of the asymmetric clusters (CH3FBN3)n (n 1 minus 6) exhibits a pronounced odd-even alternationphenomenon with cluster size n increasing indicatingthat the cluster at n 3 is more stable than other clustersFrom monomer (n 1) to clusters (n 2 ndash 6) the N3asymmetric stretching vibration presents blue-shiftedtrend while the N3 symmetric stretching vibration andndashCH3 stretching vibration are red-shifted 1e thermo-dynamic functions (Cθ

pm Sθm and Hθm) of clusters

(CH3FBN3)n (n 1 ndash 6) show linear increase with theaugment of both temperature T and cluster size n ofclusters Judged by the enthalpies in the range of2982ndash600 K the calculated thermodynamic propertiesdemonstrate that the formation of clusters (CH3FBN3)n(n 2 minus 6) from the monomer is thermodynamically fa-vorable however the formation cannot occurspontaneously

Data Availability

1e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

1e authors declare that there are no conflicts of interestregarding the publication of this paper

Authorsrsquo Contributions

Qi-Ying Xia conceptualized the study and was responsiblefor project administration Deng-Xue Ma Yao-Yao Weiand Yun-Zhi Li were involved in data curation Guo-Kui Liuwas involved in resource management Deng-Xue Ma andYao-Yao Wei wrote the original draft and Qi-Ying Xia andGuo-Kui Liu wrote and edited the manuscript Deng-XueMa and Yao-Yao Wei contributed equally to the work

Acknowledgments

1is work was supported by the Natural Science Foundationof Shandong Province (grant no ZR2017LB011) and theUndergraduate Education Reform Project of ShandongProvince (grant no Z2018S006)

References

[1] R L Mulinax G S Okin and R D Coombe ldquoGas phasesynthesis structure and dissociation of boron triaziderdquo 0eJournal of Physical Chemistry vol 99 no 17 pp 6294ndash63001995

[2] E Wiberg and H Michaud ldquoNotizen zur kenntnis einesmethylaluminiumdiazids CH3Al(N3)2rdquo Zeitschrift furNaturforschung B vol 9 no 7 p 497 1954

[3] P I Paetzold ldquoBeitrage zur chemie der bor-azide i zurkenntnis von dichlorborazidrdquo Zeitschrift fur Anorganischeund Allgemeine Chemie vol 326 no 1-2 pp 47ndash52 1963

[4] U Muller ldquoDie kristall-und molekularstruktur von bordi-chloridazid (BCl2N3)3rdquo Zeitschrift fur Anorganische undAllgemeine Chemie vol 382 no 2 pp 110ndash122 1971

[5] N Wiberg W-Ch Joo and K H Schmid ldquoUber einige azidedes berylliums magnesiums bors und aluminiums (zurreaktion von silylaziden mit elementhalogeniden)rdquo Zeitschriftfur Anorganische und Allgemeine Chemie vol 394 no 1-2pp 197ndash208 1972

[6] K Dehnicke and N Kruger ldquoDijodo- und dibromometalla-zide X2MN3 von aluminium und galliumrdquo Zeitschrift furanorganische und allgemeine Chemie vol 444 no 1 pp 71ndash76 1978

[7] P I Paetzold and H-J Hansen ldquoBeitrage zur chemie der bor-azide VI zur kenntnis von dimethylborazid und seinenaminatenrdquo Zeitschrift fur Anorganische und AllgemeineChemie vol 345 no 1-2 pp 79ndash86 1966

[8] J Muller P Paetzold and R Boese ldquo1e reaction of deca-borane with hydrazoic acid a novel access to azaboranesrdquoHeteroatom Chemistry vol 1 no 6 pp 461ndash465 1990

[9] P I Paetzold P P Habereder and R Mullbauer ldquoBeitragezur chemie der borazide VII darstellung und eigenschaftenvon diorganylborazidenrdquo Journal of Organometallic Chem-istry vol 7 no 1 pp 45ndash50 1967

[10] P I Paetzold P P Habereder and R Mullbauer ldquoBeitragezur chemie der borazide VIII 1ermischer zerfall von dio-rganylborazidenrdquo Journal of Organometallic Chemistry vol 7no 1 pp 51ndash60 1967

[11] W Fraenk T M Klapotke B Krumm and P MayerldquoBis(pentafluorophenyl)boron azide synthesis and structuralcharacterization of the first dimeric boron aziderdquo ChemicalCommunications vol 8 no 8 pp 667-668 2000

[12] W Fraenk TM Klapotke B Krumm H Noth M Suter andM Warchhold ldquoOligomeric pentafluorophenylboron azidesrdquoJournal of the Chemical Society Dalton Transactions no 24pp 4635ndash4638 2000

[13] W Fraenk T Habereder A Hammerl et al ldquoHighly ener-getic tetraazidoborate anion and boron triazide adductsdaggerrdquoInorganic Chemistry vol 40 no 6 pp 1334ndash1340 2001

[14] P I Paetzold ldquoDarstellung eigenschaften und zerfall vonborazidenrdquo in Anorganische Chemie Fortschritte der Chem-ischen Forschung vol 83 pp 437ndash469 Springer BerlinGermany 2006

[15] P I Paetzold M Gayoso and K Dehnicke ldquoDarstellungEigenschaften und Schwingungsspektren der trimeren Bor-dihalogenidazide (BCl2N3)3 und (BBr2N3)3rdquo ChemischeBerichte vol 98 no 4 pp 1173ndash1180 1965

[16] M J Travers and J V Gilbert ldquoUV absorption spectra ofintermediates generated via photolysis of B(N3)3 BCl(N3)2and BCl2(N3) in low-temperature argon matricesrdquo 0eJournal of Physical Chemistry A vol 104 no 16 pp 3780ndash3785 2000


[17] R Hausser-Wallis H Oberhammer W Einholz andP O Paetzold ldquoGas-phase structures of dimethylboron azideand dimethylboron isocyanate Electron diffraction and abinitio studyrdquo Inorganic Chemistry vol 29 no 17pp 3286ndash3289 1990

[18] L A Johnson S A Sturgis I A Al-Jihad B Liu andJ V Gilbert ldquoLow-temperature matrix isolation and pho-tolysis of BCl2N3 spectroscopic identification of the pho-tolysis product ClBNClrdquo0e Journal of Physical Chemistry Avol 103 no 6 pp 686ndash690 1999

[19] W Fraenk and T M Klapotke ldquo1eoretical studies on thethermodynamic stability and trimerization of BF2N3rdquo Journalof Fluorine Chemistry vol 111 no 1 pp 45ndash47 2001

[20] D X Ma Q Y Xia and C Zhang ldquo1eoretical studies onstructural feature and thermodynamic stability of F2BN3oligomersrdquo Journal of Atomic and Molecular Physics vol 26no 2 pp 361ndash367 2009

[21] A Wang Z Chen D Ma and Q Xia ldquoSearch for thestructures stabilities IR spectra and thermodynamic prop-erties of the asymmetric clusters (HClBN3) n (n 1minus 6)rdquoRussian Journal of Physical Chemistry A vol 90 no 13pp 2541ndash2549 2016

[22] Q Y Xia D X Ma D J Li B H Li X Q Wang and G F Jildquo1e molecular designs and properties of asymmetric het-erocycles (HBrBN3) n (n 1minus 4)rdquo Journal of StructuralChemistry vol 56 no 8 pp 1468ndash1473 2015

[23] J Kouvetakis J McMurran C Steffek T L Groy andJ L Hubbard ldquoSynthesis and structures of heterocyclic azi-dogallanes [(CH3)ClGaN3]4 and [(CH3)BrGaN3]3 en route to[(CH3)HGaN3]x an inorganic precursor to GaNrdquo InorganicChemistry vol 39 pp 3805ndash3809 2000

[24] J Kouvetakis J McMurran C Steffek T L GroyJ L Hubbard and L Torrison ldquoSynthesis of new azidoalaneswith heterocyclic molecular structurerdquo Main Group MetalChemistry vol 24 no 2 pp 77ndash84 2001

[25] A D Becke ldquoDensity-functional thermochemistry III 1erole of exact exchangerdquo 0e Journal of Chemical Physicsvol 98 no 7 pp 5648ndash5652 1993

[26] C Lee W Yang and R G Parr ldquoDevelopment of the Colle-Salvetti correlation-energy formula into a functional of theelectron densityrdquo Physical Review B vol 37 no 2 pp 785ndash789 1988

[27] M J Frisch G W Trucks H B Schlegel et al Gaussian 09Revision A02 Gaussian Inc Pittsburgh PA USA 2009

[28] A P Scott and L Radom ldquoHarmonic vibrational frequenciesan evaluation of HartreeminusFock MoslashllerminusPlesset quadraticconfiguration interaction density functional theory andsemiempirical scale factorsrdquo 0e Journal of Physical Chem-istry vol 100 no 41 pp 16502ndash16513 1996

[29] E Lieber D R Levering and L Patterson ldquoInfrared ab-sorption spectra of compounds of high nitrogen contentrdquoAnalytical Chemistry vol 23 no 11 pp 1594ndash1604 1951

[30] G V Baryshnikov B F Minaev N N Karaush andV A Minaeva ldquoDesign of nanoscaled materials based ontetraoxa[8]circulenerdquo Physical Chemistry Chemical Physicsvol 16 no 14 pp 6555ndash6559 2014

[31] T Lu and Q Chen ldquoA simple method of identifying π orbitalsfor non-planar systems and a protocol of studying π electronicstructurerdquo 0eoretical Chemistry Accounts vol 139 no 2p 25 2020

[32] T Lu and F Chen ldquoMultiwfn a multifunctional wavefunctionanalyzerrdquo Journal of Computational Chemistry vol 33 no 5pp 580ndash592 2012


thermodynamic characteristics of the asymmetric clusters oforganic boron azides (CH3FBN3)n (n 1 ndash 6) were theo-retically discussed in detail 1ese discussions will providefundamental data and references for experimentalist todesign and synthesize the novel boron azides in the future

2 Computational Methods

As is well known it is important to choose an appropriatebasis set to give the accurate description of clustersrsquo structuresand energies Usually a substantial size of basis set is requiredHowever the size of clusters studied in this work excluded theuse of a very large basis set and hence all calculations wereperformed using the DFT-B3LYP method with the 6-31Glowastbasis set [25 26] via the Gaussian 09 program package withthe default convergence thresholds [27] To ensure the ade-quacy of this basis set we also optimized the clusters with the6-311+Glowast basis set As shown later on results obtained fromthese two basis sets were similar except for slightly numericaldifferences 1e energies of all clusters were also evaluatedusing the 6-311 +Glowast basis set 1e initial configurations aresearched by two ways (1) by considering the numbers ofknown clusters (HClBN3)n (n 1ndash6) in previous works [21]and (2) by placing -CH3 groups and F atoms at varioussubstitutional sites (H or Cl) on the basis of optimized(HClBN3) geometries No symmetry constraints were appliedLots of rationally initial one- two- and three-dimensionalconfigurations were built to seek the most stable structures Inthis way a large number of optimized isomers for theasymmetric clusters (CH3FBN3)n (n 1ndash6) were obtainedFrequencies as well as their respective IR intensities were thencalculated and the lack of imaginary frequencies confirmedthat the true minimum was obtained in each case Accordingto the previous study the calculated frequencies were scaleduniformly by 096 to approximately correct the systematicoverestimation [28]

3 Results and Discussion

31 Structures and Charge Distribution A number of iso-mers are calculated at each size Here structures of clusters(CH3FBN3)n (n 1minus 6) having the lowest energy were fo-cused because all properties of clusters (CH3FBN3)n(n 1ndash6) were calculated based on the lowest energy Twostable structures of the monomer CH3FBN3 were obtained(connectivity CH3FBminusNαminusNβminusNc) with a slight differencein geometrical parameters 1e clusters (CH3FBN3)n(n 2 ndash 6) are produced by the head-to-tail oligomerizationof the CH3FBN3 monomers which is a starting point for theoligomerizations Two dimers seventeen trimers sixty-fourtetramers two hundred and fifty-six pentamers and fivehundred and thirty-six hexamers are obtained in thismanner Judged by the total energies themost stable isomersat each size are labeled as 1 2 3 4 5 and 6 and shown inFigure 1 Obviously B and Nα atoms easily bond togetherand BndashB and NαndashNα bonds are not formed in the clusters(CH3FBN3)n (n 2minus 6) In other words the clusters(CH3FBN3)n (n 2minus 6) contain cyclic (BNα)2n structureswith alternating boron and α-nitrogen atoms

1e corresponding geometrical parameters are collectedin Table 1 and the data in parentheses are calculated resultsfrom the 6-311 +Glowast basis set 1e results obtained fromdifferent basis sets are generally consistent In detail bondlengths (except for BminusF bonds) from the 6-311 +Glowast basis setare slightly shorter than those from the 6-31Glowast basis set1iswhole agreement shows that it is appropriate to choose the6-31Glowast basis set to compute the titled systems 1erefore inthis work we only report the geometrical parameters ob-tained with the 6-31Glowast basis set For n 1 the azide group inthe monomer CH3FBN3 is slightly bent with a NαndashNβndashNc

angle of 1731deg 1e calculated BndashN bond length of 1447 A isbetween BndashN single (158 A) and double bonds (137 A) 1eNβminusNc bond length at 1135 A is shorter than the NαminusNβbond length at 1240 A 1e NβminusNc bond length is betweenNndashN double (125 A) and NndashN triple bonds (110 A) Forn 2 ndash 6 the computed BndashN bond length of 1601ndash1638 Apossesses typical character of BndashN single bond which issimilar to the BndashN length of other covalent boron azidespreviously determined such as (F2BN3)3 (1616 A) [19] and(C6F5B(N3)2)3 (160 A) [12] 1e BminusC and BminusF bond lengthsare in the range of 1585ndash1596 A and 1363ndash1381 A re-spectively 1e computed structural parameters of the azideunits in the clusters (CH3FBN3)n (n 2 ndash 6) are1240ndash1255 A for NαminusNβ bonds 1128ndash1133 A for NβminusNc

bonds and 1771ndash1794deg for NαminusNβminusNc bond angle It isobvious that the azide group is nearly linear 1ese resultsare perfectly consistent with those found in (Cl2BN3)3(125 A 109 A 178deg) [4] (F2BN3)3 (1249 A 1129 A 1798deg)[19] and (C6F5B(N3)2)3 (127 A 111 A 179deg) [12]1ereforethe calculation method in this work is reliable and it givescredence to our computed structural parameters of clusters(CH3FBN3)n (n 2 ndash 6)

1rough the above discussions it is obvious that NβminusNc

bond is shorter than NαminusNβ bond in the clusters(CH3FBN3)n (n 1 ndash 6) 1is can be interpreted as a higherbond order for the terminal NminusN bond showing a pre-formation of the N2 molecule Moreover the cluster size nhas an important effect on the geometries An obvious in-crease is shown for the length of B-Nα bond with cluster sizen increasing from 1 to 2sim6 owing to the tension of the ringHowever BminusNα bond length shows little change with clustersize in the range of 2sim6 which fluctuates in the range of1601ndash1638 A 1e NαminusNβ bond lengths increase as thecluster size n increases from 1 to 5 and show little changefrom n 5 to n 6 Similarly when cluster size n increasesfrom 1 to 3 the BminusC and BminusF bond lengths increaseHowever the change of BminusC and BminusF bond lengths is notobvious from n 4 to n 61eNβminusNc bond length shortensfrom 1135 A in cluster size with 1 to 1129 A in cluster sizewith 6 and tends to be constant around 1130 A withn 3 ndash 6 Compared with monomer 1 the increasing bondlengths of NαminusNβ BminusC and BminusF bonds that are outside ofrings show that N2 (NβminusNc) -CH3 and F- groups can beeasily removed to yield BN material

To give a deeper understanding on these structures wecalculate the charge distribution of the clusters (CH3FBN3)n(n 1 ndash 6) as shown in Table 2 It can be seen that the chargedistribution of CH3FBN3 molecule exhibits zwitterionic




Denotes B atom


Denotes H atom

Denotes C atom

1 2

3 4

5 6









1 minus86354411 15049(minus86379661) (14936)


3 minus259068489 5256 46636 3827 1276 1876(minus259143962) (4978) (46216) (3626) (1209) (1697)


5 minus431781967 9912 78067 7203 1441 397(minus431907866) (9559) (77293) (7051) (1410) (501)

6 minus518138441 11975 93724 8682 1447(minus518289497) (11528) (92798) (8474) (1412)



1 2 3 4 5 6










NαminusNβminusNc







n



(1)



















T2

R2

09999

SD 03318

(2)


T2

R2

09998

SD 09034

(3)


T2

R2

09999

SD 02784

(4)





pmSθm and Hθ


Cθpm minus120847 + 1084637 n

R2

10000

SD 10282

(5)

Sθm 2110987 + 1332237 n

R2

09996

SD 80272

(6)

Hθm 10620 + 183966 n

R2

09999

SD 05260

(7)

d

E bndashc

ndashave

a

c




E b E

bndashc b

0306090

120

0369

1215

ndash30ndash15

015

Δ 2E








0

100

200

300

400

500

600


500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0



1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity






T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References





































Denotes B atom


Denotes H atom

Denotes C atom

1 2

3 4

5 6









1 minus86354411 15049(minus86379661) (14936)


3 minus259068489 5256 46636 3827 1276 1876(minus259143962) (4978) (46216) (3626) (1209) (1697)


5 minus431781967 9912 78067 7203 1441 397(minus431907866) (9559) (77293) (7051) (1410) (501)

6 minus518138441 11975 93724 8682 1447(minus518289497) (11528) (92798) (8474) (1412)



1 2 3 4 5 6










NαminusNβminusNc







n



(1)



















T2

R2

09999

SD 03318

(2)


T2

R2

09998

SD 09034

(3)


T2

R2

09999

SD 02784

(4)





pmSθm and Hθ


Cθpm minus120847 + 1084637 n

R2

10000

SD 10282

(5)

Sθm 2110987 + 1332237 n

R2

09996

SD 80272

(6)

Hθm 10620 + 183966 n

R2

09999

SD 05260

(7)

d

E bndashc

ndashave

a

c




E b E

bndashc b

0306090

120

0369

1215

ndash30ndash15

015

Δ 2E








0

100

200

300

400

500

600


500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0



1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity






T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References









































1 minus86354411 15049(minus86379661) (14936)


3 minus259068489 5256 46636 3827 1276 1876(minus259143962) (4978) (46216) (3626) (1209) (1697)


5 minus431781967 9912 78067 7203 1441 397(minus431907866) (9559) (77293) (7051) (1410) (501)

6 minus518138441 11975 93724 8682 1447(minus518289497) (11528) (92798) (8474) (1412)



1 2 3 4 5 6










NαminusNβminusNc







n



(1)



















T2

R2

09999

SD 03318

(2)


T2

R2

09998

SD 09034

(3)


T2

R2

09999

SD 02784

(4)





pmSθm and Hθ


Cθpm minus120847 + 1084637 n

R2

10000

SD 10282

(5)

Sθm 2110987 + 1332237 n

R2

09996

SD 80272

(6)

Hθm 10620 + 183966 n

R2

09999

SD 05260

(7)

d

E bndashc

ndashave

a

c




E b E

bndashc b

0306090

120

0369

1215

ndash30ndash15

015

Δ 2E








0

100

200

300

400

500

600


500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0



1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity






T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References






































n



(1)



















T2

R2

09999

SD 03318

(2)


T2

R2

09998

SD 09034

(3)


T2

R2

09999

SD 02784

(4)





pmSθm and Hθ


Cθpm minus120847 + 1084637 n

R2

10000

SD 10282

(5)

Sθm 2110987 + 1332237 n

R2

09996

SD 80272

(6)

Hθm 10620 + 183966 n

R2

09999

SD 05260

(7)

d

E bndashc

ndashave

a

c




E b E

bndashc b

0306090

120

0369

1215

ndash30ndash15

015

Δ 2E








0

100

200

300

400

500

600


500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0



1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity






T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References













































T2

R2

09999

SD 03318

(2)


T2

R2

09998

SD 09034

(3)


T2

R2

09999

SD 02784

(4)





pmSθm and Hθ


Cθpm minus120847 + 1084637 n

R2

10000

SD 10282

(5)

Sθm 2110987 + 1332237 n

R2

09996

SD 80272

(6)

Hθm 10620 + 183966 n

R2

09999

SD 05260

(7)

d

E bndashc

ndashave

a

c




E b E

bndashc b

0306090

120

0369

1215

ndash30ndash15

015

Δ 2E








0

100

200

300

400

500

600


500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0



1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity






T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References





































0

100

200

300

400

500

600


500 0

IR ac

tivity

0

200

400

600

800

1000


500 0

IR ac

tivity

0

200

400

800

600


500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400


500 0



1 2

3 4

5 6

500 0

IR ac

tivity

0

200

400

600

800

1000

1200

1400

IR ac

tivity

0

250

500

750

1000

1250

1500

1750

IR ac

tivity






T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References






































T 200 2982 400 500 600 700 800

1Cθ

pm 7773 9648 11347 12730 13862 14795 15571Sθm 30518 33977 37057 39742 42166 44375 46403Hθ

m 1130 1987 3058 4265 5596 7030 8550

2Cθ

pm 16134 20604 24312 27197 29500 31371 32919Sθm 40957 48265 54858 60605 65775 70468 74761Hθ

m 1988 3800 6094 8675 11514 14561 17778

3Cθ

pm 24225 31213 36954 41390 44912 47762 50112Sθm 50921 61950 71958 80700 88570 95714 102250Hθ

m 2847 5581 9064 12990 17312 21950 26847

4Cθ

pm 32644 42082 49789 55725 60430 64235 67370Sθm 58495 73364 86853 98627 109219 118830 127618Hθ

m 3713 7400 12094 17382 23198 29438 36023

5Cθ

pm 41159 53037 62705 70133 76011 80759 84671Sθm 68662 87408 104402 119226 132552 144638 155685Hθ

m 4656 9303 15218 21874 29193 37039 45317

6Cθ

pm 49646 63939 75559 84478 91534 97233 101926Sθm 78860 101465 121948 139806 155856 170409 183708Hθ

m 5596 11199 18327 26347 35161 44609 54574aUnits T (K) Cθ


Sθm

CθPm

Hθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)

300 400 500 600 700 800200T (K)

ndash100ndash50

050

100150200250300350400450500

(a)

Hθm

CθPm

Sθm

Cθ pm

(Jm

olK

) Sθ m

(Jm

olK

) H

θ m (k

Jmol

)


ndash200ndash100

0100200300400500600700800900

10001100

(b)


θm and Hθ



1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References



































1 2

3 4

5 6



T 200 2982 400 500 600 700 800









4 Conclusions





Data Availability






Acknowledgments


References




































4 Conclusions





Data Availability






Acknowledgments


References




















































Documents

TheoreticalInvestigationonStructure-PropertyRelationshipof AsymmetricClusters(CH FBN … · 2020. 6. 30. · E b(n) nE CH 3 FBN 3 −E CH 3 FBN 3 n, E b−c(n) nE CH 3 FBN 3 +0.96∗nZPE