theoretical study of the n10 clusters without double bonds

Theoretical Study of the N10 ClustersWithout Double Bonds

YI REN,1 XIN WANG,1 NING-BEW WONG,2 AN-MIN TIAN,1

FU-JIANG DING,3 LIANGFU ZHANG3

1Department of Chemistry, Sichuan University, Chengdu, 610064, People’s Republic of China2Department of Biology and Chemistry, City University of Hong Kong, Kowloon, Hong Kong3Chengdu Institute of Organic Chemistry, Chinese Academy of Science, Chengdu, 610041,People’s Republic of China

Received 17 July 2000; revised 13 November 2000; accepted 21 November 2000

ABSTRACT: Quantum chemical ab initio methods have been used to examine nine N10clusters without double bonds. In additional to the three N10 isomers previously studiedin the literature, six new N10 structures were investigated. Fully geometry optimization,harmonic vibrational frequency, and thermodynamics calculation of nine different N10molecules were performed at the RHF/6-31G∗, B3LYP/6-31G∗, and MP2/6-31G∗ levels.All of the nine structures were found to be local minima on the energy hypersurface at theRHF/6-31G∗ level, whereas eight structures are stable at the B3LYP/6-31G∗ level. At theMP2/6-31G∗ level, seven local minima were found. They would be potential high-energydensity material (HEDM). According to the results presented herein, the structureN10[V(C2v)] is the most stable molecule of all the N10 clusters without double bonds.c© 2001 John Wiley & Sons, Inc. Int J Quantum Chem 82: 34–43, 2001

Key words: N10 clusters; ab initio; high-energy density material (HEDM)

Introduction

T he intense scientific and popular interest in theC60 molecule has naturally raised the ques-

tion whether other important cluster species havebeen systematically overlooked. Nn clusters arereasonable candidates for the following two rea-

Correspondence to: A.-M. Tian; e-mail: [email protected].

Contract grant sponsor: National Science Foundation ofChina.

Contract grant number: 298730029.

sons: First, a number of (CH)n clusters have beensynthesized that are isoelectronic with Nn. It ispossible that these nitrogen structures will showanalogous stability. Second, Nn clusters would behigh-energy density materials (HEDM). Since thethermochemical N≡N triple bond energy at 298 K(946 kJ/mol [1]) is much more than three times thesingle-bond energy (3× 160 = 480 kJ/mol), this ar-gument suggests that the N2n clusters with N—Nsingle bonds will release significant amounts of en-ergy when they dissociate into N2 molecules.

For example, there are 3n N—N single bonds inN2n (n ≥ 2) clusters. It can be estimated that the N2n

International Journal of Quantum Chemistry, Vol. 82, 34–43 (2001)c© 2001 John Wiley & Sons, Inc.

N10 CLUSTERS WITHOUT DOUBLE BONDS

clusters will release energy: 946 × n − 3n × 160 =466n kJ/mol when they decompose into nN2 mole-cules. For the simplest cagelike nitrogen cluster,tetra-azatetrahedrane N4, it will release (466 × 2 =932 kJ/mol). In other words, N2n is stable in rela-tion to the 2nN atom. It is a high-energy compoundcompared with nN2 molecules.

Synthesis of these molecules would offer a po-tential route toward the storage of large amounts ofenergy, which could be used for efficient rocket fueland high-energy explosives.

Because of the implicit application background ofnitrogen clusters, there has been considerable inter-est in this field of theoretical chemistry. More andmore studies on nitrogen clusters have been pub-lished in recent years [2 – 42], and the possibility forthe existence of Nn clusters has been examined the-oretically.

Chen et al. [42] and Li et al. [30] have studiedthree N10 clusters without double bonds. Are thereother new metastable N10 isomers without doublebonds? How about the structures and stabilities ofthe new N10 isomers with only N—N single bonds?We want to address these questions in this work.

According to graph theory [43], there are ninepossible isomers with only N—N single bondsfor N10. In this investigation, we make a systematicstudy of all of the nine isomers for N10 by ab initioand density functional theory (DFT) methods, six ofwhich have not been reported before.

The geometric structures of the nine N10 clustersare shown in Figure 1 and named as Roman numer-als I, II, III, IV, V, VI, VII, VIII, and IX, respectively(see Fig. 1).

Calculation Methods

Hartree–Fock self-consistent field (HF-SCF), DFTmethods, and second-order Møller–Plesset pertur-bation theory (MP2) have been applied to optimizethe structures of nine N10 clusters. The harmonicvibrational frequencies have been predicted onthese optimized structures. The calculation meth-ods include restricted HF (RHF), hybrid Hartree–Fock/DFT method with Becke’s three parameterexchange functional along with the Lee–Yang–Parrnonlocal correlation functional (B3LYP) [44, 45], andMP2. The basis set 6-31G∗ is chosen in all calcu-lations. The convergence criterion is 10−8. All cal-culations were carried out using the Gaussian 98program [46].

We may evaluate their relative stability of nineN10 isomers using their total energies Etotal, ener-gies relative to 5N2 [1E(N10)], standard molar Gibbsfree energy of formation 1f G◦m, standard molar en-thalpy of formation 1f H◦m, standard molar enthalpyof atomization 1aH◦m at 101.325 kPa, 293.15 K, andaverage bond energy BEN—N:

1E(N10) = [E(N10)− 5E(N2)]/

10, (1)

1f G◦m[N10(g)

] = G◦m[N10(g)

]− 5G◦m[N2(g)

], (2)

1f H◦m[N10(g)

] = H◦m[N10(g)

]− 5H◦m[N2(g)

], (3)

1aH◦m[N10(g)

] = 5BE[N2(g)

]−1f H◦m[N10(g)

], (4)

where BE [N2(g)] is the bond energy of N2(g),946 kJ/mol [1]:

BEN—N = 1aH◦m[N10]/NN, (5)

where denominator NN is the number of NN bondsin N10 molecule.

Results and Discussion

The optimized N—N bond lengths at all levelsare shown in Table I. The results show that the av-erage N—N bond lengths by the DFT method arelonger than those by RHF with the same basis sets,and the calculated lengths by the MP2 method arelonger than those by the DFT method. The previousstudies draw the same conclusion [27].

The N—N bonds of the studied nine N10 isomersare all single bonds at RHF/6-31G∗ level. Averagebond lengths are between 0.1413 and 0.1455 nm(N—N bond length of NH2—NH2 of gauche C2structure is 0.1413 nm).

At the B3LYP/6-31G∗ and MP2/6-31G∗ levels,three double bonds are formed between nitrogenatoms 5 and 8, 6 and 9, 7 and 10 in the structure VIII.The bond lengths are about 0.12 nm, which equalsto the N=N bond length of NH=NH. This result in-dicates that an electronic correlation effect may havegreat influences on the structures of the N10 clusters.In order to differentiate two structures of VIII, wenamed the N10 isomer VIII without double bonds asVIII(1), and N10 isomer VIII with three double bondsas VIII(2), respectively.

The framework of nitrogen cluster II(C2v) at theRHF/6-31G∗ and B3LYP/6-31G∗ levels is destroyedat the MP2/6-31G∗ level, and three fragments areformed, including one N2 molecule and two smallN4 clusters.

For structure VI(C3v), all of the bonds are N—Nsingle bonds at the RHF/6-31G∗ and B3LYP/6-31G∗

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 35

REN ET AL.

FIG

UR

E1.

Str

uctu

res

ofni

neN

10is

omer

s.

36 VOL. 82, NO. 1


TABLE IOptimized bond lengths (nm) of nine N10 isomers.

HF/ B3LYP/ MP2/Mol. RN—N 6-31G∗ 6-31G∗ 6-31G∗

I(C2v) R1,2 0.1394 0.1417 0.1456R1,5 0.1400 0.1460 0.1494R3,4 0.1486 0.1567 0.1675R3,9 0.1447 0.1499 0.1542R7,8 0.1427 0.1460 0.1454R7,9 0.1467 0.1530 0.1527

II(C2v) R1,3 0.1406 0.1489 0.1882R1,5 0.1397 0.1458 0.1272R3,4 0.1432 0.1390 0.1268R5,7 0.1379 0.1403 0.1353R7,8 0.1493 0.1641 0.2200R7,9 0.1458 0.1519 0.1651

III(D5h) R1,2 0.1450 0.1499 0.1506R1,6 0.1464 0.1520 0.1533

IV(C2) R1,2 0.1431 0.1481 0.1486R1,3 0.1446 0.1517 0.1522R1,6 0.1336 0.1364 0.1388R2,4 0.1442 0.1500 0.1522R2,5 0.1427 0.1487 0.1508R3,4 0.1445 0.1506 0.1534R3,5 0.1423 0.1476 0.1494R4,5 0.1383 0.1437 0.1467

V(C2v) R1,3 0.1422 0.1493 0.1512R1,4 0.1415 0.1470 0.1484R1,5 0.1405 0.1429 0.1435R3,4 0.1412 0.1464 0.1495R5,6 0.1427 0.1496 0.1514

VI(C3v) R1,2 0.1460 0.1524 0.1530R2,5 0.1449 0.1500 0.1543R5,8 0.1405 0.1409 0.1260R8,9 0.1442 0.1542 0.2311

(Continued)

levels. After optimizing by MP2/6-31G∗, the bondsbetween 8 and 9, 9 and 10, 8 and 10 are broken, andthree N=N double bonds are formed between 5 and8, 7 and 10, 6 and 9.

To identify whether the nine N10 isomers are localminima, calculations of harmonic vibrational fre-quencies and infrared (IR) intensities for the N10 iso-mers at different levels are performed. The theoret-ical vibrational spectrum data at the RHF/6-31G∗,B3LYP/6-31G∗, and MP2/6-31G∗ levels are listed inTables II–IV, respectively. Among the nine N10 iso-mers, there are no imaginary frequencies for struc-tures I, III–V, and VII–IX at the three levels. Thissuggests that the seven structures will be reasonable

TABLE I(Continued)

HF/ B3LYP/ MP2/Mol. RN—N 6-31G∗ 6-31G∗ 6-31G∗

VII(Cs) R1,3 0.1421 0.1491 0.1514R1,4 0.1420 0.1499 0.1523R1,5 0.1414 0.1438 0.1443R3,4 0.1414 0.1449 0.1475R5,7 0.1412 0.1444 0.1435R5,10 0.1425 0.1470 0.1474R7,8 0.1449 0.1536 0.1569R7,9 0.1429 0.1485 0.1515R9,10 0.1489 0.1565 0.1601

VIII(C3v) R1,2 0.1442 0.1468 0.1459R2,5 0.1423 0.1462 0.1471R5,6 0.1424 0.2336 0.2311R5,8 0.1395 0.1229 0.1247

IX(C2) R1,2 0.1437 0.1494 0.1493R1,6 0.1404 0.1429 0.1435R1,9 0.1444 0.1509 0.1525R2,3 0.1423 0.1488 0.1501R2,7 0.1448 0.1509 0.1555R3,7 0.1407 0.1444 0.1434R7,9 0.1464 0.1542 0.1596R9,10 0.1407 0.1412 0.1460

local minima on the N10 potential energy hypersur-faces. As for structure II, all frequencies calculatedat the RHF/6-31G∗ level are positive, but thereis one imaginary frequency at the B3LYP/6-31G∗level (72 cm−1). After optimizing at the MP2/6-31G∗level, the framework of N10(II) is broken. N10(VI) isstable at the RHF/6-31G∗ and B3LYP/6-31G∗ levels,but it is a second transition state with two imaginaryfrequencies at the MP2/6-31G∗ level. The smallestvalue of the lowest vibrational frequency of nineN10 isomers at RHF/6-31G∗ occurs in isomer II, only74 cm−1, which indicates comparatively weakerN—N bonds, less thermochemical stability of iso-mer II. It is consistent with the conclusion from thefollowing energy analysis. Because there are threedouble bonds in isomer VIII(2) at B3LYP/6-31G∗and MP2/6-31G∗ levels, it has a high IR peak at1655 cm−1 (24 km/mol).

The calculated total energies of the nine N10 iso-mers and the energies relative to 5N2 are shown inTables V–VII. The lower relative energy indicatesthe isomer is more stable. The energy of structureII(C2v) relative to 5N2 is the highest at the RHFand DFT level. At the RHF level, the relative en-


REN ET AL.

TABLE IITheoretical vibrational frequencies (cm−1) and infrared intensities (km/mol, in parentheses) for nine N10isomers [RHF/6-31G∗].

N10(I) N10(II) N10(III) N10(IV) N10(V)

A2 386(0) A2 74(0) E2 645(0) A 96(0) A2 222(0)B1 435(7) B1 268(11) A1 803(0) A 184(0) A1 274(3)B2 607(0) B2 412(7) E2 827(0) B 205(1) B1 474(0)A1 630(2) A1 485(0) E1 882(0) B 442(6) B2 624(8)B2 753(0) B2 644(15) A2 920(6) A 457(0) A1 657(0)A2 756(0) A2 646(0) A1 1006(0) A 566(0) A2 785(0)A1 787(9) B1 677(8) E2 1034(0) B 838(1) B1 860(1)B1 822(0) A1 709(1) E1 1085(2) A 839(1) A2 864(0)A2 889(0) B1 797(1) E2 1094(0) B 875(8) B2 869(1)B1 933(17) A1 855(1) E1 1118(0) A 883(0) A1 930(1)A1 934(3) A2 919(0) E1 1174(0) A 918(12) B2 953(1)A2 994(0) B2 927(1) A1 1219(0) B 921(13) A1 981(7)A1 1035(4) B1 941(0) E2 1227(0) B 996(1) B1 1033(6)B1 1041(1) A1 958(1) E2 1231(0) A 1020(0) A1 1043(1)B2 1074(0) B2 974(17) B 1118(8) A1 1060(1)A2 1110(0) A2 1007(0) A 1163(3) B2 1099(0)B1 1116(1) A1 1063(2) B 1167(2) A2 1104(0)B2 1121(2) A1 1119(3) A 1218(0) B1 1164(0)A1 1166(10) B1 1122(7) B 1237(1) B1 1214(10)A2 1209(0) A2 1126(0) A 1286(0) B2 1241(4)B2 1215(1) B2 1265(3) B 1308(3) A1 1309(0)A1 1259(1) A1 1425(3) A 1386(0) A2 1334(0)B2 1343(2) B2 1564(10) B 1474(0) B2 1457(0)A1 1466(6) A1 1572(10) A 1478(1) A1 1461(1)

N10(VI) N10(VII) N10(VIII) N10(IX)

E 655(1) A′ 332(8) A2 725(0) A 506(2)E 823(2) A′′ 525(0) A1 726(11) B 659(1)E 865(0) A′ 599(2) E 747(3) A 758(0)A1 890(0) A′ 708(3) A2 828(0) B 810(6)A1 970(2) A′′ 759(0) E 843(0) A 823(4)E 978(1) A′ 832(2) E 901(2) B 852(0)E 1055(1) A′′ 852(2) E 925(1) A 877(1)A1 1108(1) A′ 864(0) A1 937(1) A 898(0)E 1132(0) A′ 915(1) A1 980(4) B 950(9)E 1168(0) A′′ 940(13) A1 1109(10) B 981(8)A1 1189(2) A′ 983(4) A2 1120(0) A 1017(1)A2 1195(0) A′′ 989(4) E 1156(1) B 1022(4)E 1227(5) A′ 1024(7) E 1201(3) B 1053(1)A1 1237(0) A′′ 1113(1) A1 1332(3) A 1063(0)A1 1298(2) A′ 1156(4) E 1372(3) A 1114(0)

A′′ 1183(0) B 1169(3)A′ 1198(5) A 1178(4)A′ 1217(0) B 1212(5)A′′ 1240(2) A 1232(1)A′ 1282(1) B 1232(2)A′′ 1295(4) A 1258(4)A′ 1339(1) B 1353(6)A′ 1501(1) A 1381(1)

38 VOL. 82, NO. 1


TABLE IIITheoretical vibrational frequencies (cm−1) and infrared intensities (km/mol, in parentheses) for nine N10isomers [B3LYP/6-31G∗].

N10(I) N10(II) N10(III) N10(IV) N10(V)

A2 269(0) A2 72i(0) E′′2 465(0) A 96(0) A2 191(0)B1 317(0) B1 27(0) A′′1 640(0) A 152(0) A1 234(2)A1 409(27) B2 226(35) E′2 660(0) B 174(1) B1 372(1)B1 416(13) B1 326(10) E′′1 708(0) B 366(7) A2 493(0)B2 520(0) A1 396(0) E′′2 711(0) A 393(0) B2 532(5)B2 531(1) A2 451(0) A′′2 713(10) A 483(0) A1 537(0)A1 604(4) B2 475(9) E′2 771(0) A 641(0) B1 588(0)A2 606(0) A1 506(1) A′1 831(0) B 646(2) B2 682(2)B1 624(1) A1 561(2) E′1 847(2) A 678(0) A1 707(1)A1 659(4) A2 587(0) E′′1 873(0) B 693(6) A2 715(0)A2 726(0) A1 597(0) E′2 953(0) B 746(9) A1 749(2)A2 750(0) B2 608(2) E′1 964(1) A 752(9) B2 785(4)A1 757(0) B1 613(0) A′1 1018(0) A 798(0) A2 800(0)B2 800(0) B1 717(0) E′′2 1038(0) B 821(0) A1 837(0)A2 807(0) B2 790(24) B 866(15) B1 847(2)B1 810(1) A2 811(0) A 907(3) A1 880(4)A1 859(2) A1 834(0) B 929(0) B1 891(12)B1 872(0) B1 929(0) A 942(0) B2 896(1)B2 909(0) A2 942(0) B 998(3) B2 1005(3)B2 983(1) A1 955(0) A 1041(0) B1 1018(1)A2 1037(0) B2 955(4) B 1091(3) A2 1046(0)A1 1042(1) A1 1178(0) A 1158(1) A1 1066(0)B2 1067(1) A1 1287(5) B 1220(1) B2 1198(0)A1 1117(3) B2 1308(11) A 1224(0) A1 1203(1)


E 377(0) A′′ 171(1) E 199(3) A 298(0)A2 477(0) A′ 279(4) A1 372(4) A 411(0)E 605(0) A′′ 441(0) E 462(36) B 493(4)E 657(6) A′ 493(2) A2 487(0) B 503(7)A1 693(5) A′ 529(3) E 540(18) A 608(6)A1 743(4) A′′ 543(0) A2 541(0) B 619(13)E 786(0) A′ 592(4) A1 665(6) A 622(0)A1 799(1) A′ 621(0) E 703(14) A 707(3)E 863(0) A′′ 648(0) E 779(0) B 718(0)E 875(1) A′ 713(0) A1 824(1) B 732(7)A1 880(0) A′′ 722(0) E 895(10) A 734(0)A2 894(0) A′ 742(12) A2 969(0) A 775(1)E 929(3) A′′ 754(19) A1 993(0) B 782(1)A1 973(1) A′′ 781(0) E 1063(5) A 783(0)E 1005(3) A′ 813(4) E 1613(22) A 854(0)A1 1110(1) A′′ 913(1) A1 1636(22) B 862(2)

A′ 930(5) B 882(2)A′′ 967(0) B 935(5)A′ 972(7) A 945(9)A′′ 996(0) A 973(1)A′ 998(0) A 990(0)A′ 1078(1) B 1056(0)A′ 1084(0) A 1077(1)A′ 1218(0) B 1097(5)


REN ET AL.

TABLE IVTheoretical vibrational frequencies (cm−1) and infrared intensities (km/mol, in parentheses) for nine N10isomers [MP2/6-31G∗].

N10(I) N10(III) N10(IV) N10(V)

A1 199(41) E′′2 419(0) A 90(0) A2 176(0)B1 201(0) A′′1 585(0) A 173(0) A1 238(1)A2 207(0) E′2 592(0) B 182(0) B1 342(1)B1 343(11) E′′2 625(0) B 345(6) A2 428(0)B2 402(4) A′′2 669(11) A 395(0) A1 499(0)A1 494(11) E′′1 673(0) A 474(0) B2 513(4)B2 498(0) E′2 737(0) A 572(0) B1 524(0)A2 512(0) A′1 798(0) B 577(1) B2 623(1)A2 609(0) E′1 798(4) A 611(1) A1 633(0)A1 609(1) E′′1 809(0) B 624(3) A2 689(0)B1 620(0) E′2 899(0) B 699(8) A1 693(0)B2 637(0) E′1 925(2) A 714(4) A2 718(0)A2 725(0) A′1 974(0) A 746(0) B2 744(4)A1 730(0) E′′2 991(0) B 765(0) A1 798(0)B1 752(1) B 824(6) B1 815(9)A1 785(9) A 860(0) B1 852(0)B1 829(8) B 883(2) A1 863(4)A2 854(0) A 894(3) B2 864(2)B2 859(1) B 961(2) B2 959(4)B2 935(2) A 1000(0) B1 999(1)A2 1006(0) B 1032(3) A2 1010(0)A1 1013(1) A 1081(1) A1 1018(0)B2 1043(5) B 1098(3) B2 1095(2)A1 1054(4) A 1107(0) A1 1100(1)


E 363i(46) A′′ 148(0) E 182(2) A 174(0)A1 234(2) A′ 270(4) A1 369(4) B 340(22)E 345(9) A′ 399(2) E 442(28) A 380(0)A2 493(0) A′′ 412(1) A2 477(0) B 386(3)E 511(6) A′′ 451(0) E 499(22) A 514(6)A1 633(19) A′ 499(4) A2 549(0) A 537(0)E 640(3) A′ 529(0) A1 612(18) B 538(7)E 700(5) A′ 568(4) E 639(7) A 653(0)A1 751(21) A′′ 598(0) E 766(0) B 656(5)E 777(9) A′ 627(3) A1 804(0) A 678(3)A1 794(2) A′′ 639(1) E 857(10) B 693(0)A2 942(0) A′′ 668(6) A2 954(0) A 728(0)A1 954(1) A′ 678(11) A1 974(0) A 736(3)E 979(99) A′′ 734(8) E 1030(1) B 737(0)A1 1478(8) A′ 782(3) E 1465(12) A 793(0)E 2559(4955) A′ 872(4) A1 1482(17) B 827(1)

A′′ 877(0) B 839(3)A′ 930(10) B 888(3)A′′ 947(1) A 903(12)A′ 948(1) A 931(0)A′′ 977(0) A 977(0)A′ 997(0) B 997(4)A′ 1034(1) A 1012(1)A′ 1130(1) B 1063(7)

40 VOL. 82, NO. 1


TABLE VEnergy analysis and thermochemical data for nine N10 isomers Etotal (a.u.), 1E, 1fG◦m, 1fH◦m, 1aH◦m,BEN—N (kJ/mol) [RHF/6-31G∗].

Lable Etotal 1E 1fG◦m 1fH◦m 1aH◦m BEN—N

I(C2v) −543.74453 251.5 2838.0 2642.5 2085.4 139.0II(C2v) −543.70606 266.1 2916.6 2728.1 1999.8 133.3III(D5h) −543.76763 250.0 2800.5 2598.1 2129.8 142.0IV(C2) −543.78332 245.9 2718.8 2532.5 2195.4 146.4V(C2v) −543.86335 224.8 2523.8 2330.9 2397.0 159.8VI(C3v) −543.82656 234.5 2640.3 2440.5 2287.4 152.5VII(Cs) −543.78726 244.8 2723.5 2531.4 2196.5 146.4VIII(C3v) −543.82273 235.5 2633.2 2435.9 2292.0 152.7IX(C2) −543.83159 233.2 2619.0 2422.2 2305.7 153.7

ergy of II(C2v) is 266.1 kJ/mol. The relative energiesare fairly sensitive to the theoretical method. Theeffect of electron correlation obviously decreasesthe relative energy. The relative energy of II(C2v) is204.4 kJ/mol at the B3LYP/6-31G∗ level. The otherisomers have lower energies than II, but their en-ergies relative to 5N2 are still quite high. For theV(C2v) structure, which is the most stable N10 iso-mer with no N=N bonds, the energy relative to 5N2

molecules is 224.8 kJ/mol at the RHF/6-31G∗ level,173.0 kJ/mol at the B3LYP/6-31G∗ level. Based onthe total energy and relative energy, the followingseries at the B3LYP/6-31G∗ level is represented forthe N10 isomer without N=N double bonds:

V(C2v) > IX(C2) > VI(C3v) > VII(Cs) > IV(C2)> III(D5h) > I(C2v) > II(C2v).

Considering the zero-point energy, enthalpy andentropy correction, the statistical thermodynamicscalculation at 298.15 K are evaluated on the ba-

sis of the calculated vibrational frequencies at thesame level as the optimization. Using Eqs. (2)–(5),the thermochemical data of various N10 isomerand N2, including standard molar Gibbs free en-ergy of formation 1f G◦m, standard molar enthalpyof formation 1f H◦m, standard molar enthalpy of at-omization 1aH◦m, and average bond energy BEN—N,are calculated in which the bond energy of N2(g)BE[N2(g)] = 946 kJ/mol is selected. All ofthe calculated thermochemical data are listed inTables V–VII. It can be noted that the V(C2v), whose1f G◦m value is the smallest and the BEN—N value isthe largest in N10 isomers without N=N bonds at allof the levels, is the most thermodynamically stable.The thermodynamic stability series of N10 isomersis:

VIII(2)(C3v) > V(C2v) > IX(C2) > VI(C3v) > VII(Cs)

∼ IV(C2) > III(D5h) > I(C2v) > II(C2v)

TABLE VIEnergy analysis and thermochemical data for nine N10 isomers Etotal (a.u.), 1E, 1fG◦m, 1fH◦m, 1aH◦m,BEN—N (kJ/mol) [B3LYP/6-31G∗].




REN ET AL.

TABLE VIIEnergy analysis and thermochemical data for nine N10 isomers Etotal (a.u.), 1E, 1fG◦m, 1fH◦m, 1aH◦m,BEN—N (kJ/mol) [MP2/6-31G∗].



at the B3LYP/6-31G∗ level, which is close to the en-ergy series.

Published work [27] suggested the stability or-der is interrelated with the symmetry order of N8

clusters. Li et al. [30] also gave a similar conclusion.Our study shows that there is no relation betweenenergy series and symmetry order for N10 clusterswithout double bonds. The energy with higher sym-metry may be the higher or lower than the N10

isomer with lower symmetry. The isomers with thesame symmetries have quite different energies, e.g.,the energy of V(C2v) is lower than I(C2v) and II(C2v),respectively.

Koopmans’ theorem is applied to evaluate theionization potential (Ip) in our study. Meanwhile,the energy gap 1ε[E(LUMO)− E(HOMO)] is calcu-lated. The comparative results of Ip and 1ε valuesat three different levels are listed in Table VIII. Itcan be found that the Ip and 1ε values of stable iso-

mers are generally greater than the transition stateand second-order transition state, and the isomerwith the greater Ip and 1ε values is more stable,which is consistent with the result of Chen et al. [42].It indicates that the stability of the most stableV(C2v) structure is not only contributed to the low-est optimized energy but also to the perspective ofthe ionization process and charge transfer proce-dure.

Conclusion

Based on graph theory, all nine structures of N10

clusters without double bonds have been obtained.Except N10(II) and N10(VI), seven isomers couldbe stable at our calculation levels, in which sixstructures are newly calculated. There is no directrelation between energy series of isomers and theiraverage bond lengths, as well as their symmetries.

TABLE VIIIIonization potentials [Ip = −E(HOMO)] and energy gaps [1ε = E(LUMO)− E(HOMO)] of N10 isomers (in eV).

RHF/6-31G∗ B3LYP/6-31G∗ MP2/6-31G∗

Lable Ip 1ε Ip 1ε Ip 1ε

I(C2v) 12.94 15.12 8.80 5.85 12.90 13.56II(C2v) 12.44 14.22 8.30 5.10 10.61 9.52III(D5h) 13.02 14.81 8.69 5.26 12.99 14.12IV(C2) 12.40 17.07 8.49 7.24 12.66 16.12V(C2v) 13.34 16.49 9.11 7.00 13.27 15.33VI(C3v) 12.67 15.84 8.71 5.96 9.90 6.96VII(Cs) 12.65 15.32 8.59 5.90 12.73 14.34VIII(C3v) 12.87 15.55 8.65 8.42 12.68 13.80IX(C2) 12.37 15.65 8.50 6.47 12.63 14.96

42 VOL. 82, NO. 1


There are three N=N double bonds in the stableN10(VIII) structure named VIII(2). The V(C2v) struc-ture is the most stable isomer in all of the isomerswithout N=N double bonds. Energy analysis indi-cates the total energies of N10 clusters are all muchlarger than that of five N2 molecules. If synthesized,N10 clusters, like other N clusters, would be poten-tial high-energy density materials.

ACKNOWLEDGMENTS

This research is supported by the National Sci-ence Foundation of China (298730029).

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theoretical study of the n10 clusters without double bonds

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