Structure and Stability of X4Y4H4(XY = CC, BN)

PING YIN,1 XIAN-YANG CHEN,2 CHONG-DE LI,1 XIN-QUAN XIN1

1State Key Laboratory of Coordination Chemistry, Department of Chemistry, Nanjing University,Nanjing 210093, People’s Republic of China2Department of Chemistry, Shanghai Jiaotong University, Shanghai 200240, People’s Republic of China

Received 12 July 2000; revised 22 December 2000; accepted 30 January 2001

ABSTRACT: Ab initio calculations have been carried out to study the structures andrelative stabilities of the planar eight-membered ring B4N4H4 and its isoelectronic speciesC8H4 at the HF/6-31G∗, MP2/6-31G∗ , MP2/6-311G∗∗, and MP4SDQ/6-31G∗ levels. Theanalyses of Milliken population, vibration frequencies, π-molecular orbital components,and orbital energy levels were used to evaluate the relative stabilities of these two similarsystems. The homodesmotic reactions were also taken to be a useful index of relativestability for X4Y4H4 (XY = CC, BN) and gave the resonance energies withMP4SDQ/6-31G∗ of C8H4 (−37.2 kcal/mol) < B4N4H4 (−29.2 kcal/mol). Furthermore,we calculated the thermodynamic functions of these reactions to discuss the influence oftemperature. It is concluded that B4N4H4 may exist in theory and could be a little morestable than C8H4. c© 2001 John Wiley & Sons, Inc. Int J Quantum Chem 82: 293–298, 2001

Key words: X4Y4H4 (XY = CC, BN); planar eight-membered ring; stability;homodesmotic reaction; resonance energies

Introduction

T he introduction of two acetylenic into cyclooc-tatetaene could reduce the angular strain in-

herent and out-of-plane distortion caused by thepseudo John-Teller effect and would give a pla-nar eight-membered carbocycle 1,5-diene-3, 7-dinyeC8H4 [1]. Then the synthesis and theoretical stud-ies of C8H4 and its derivatives have been an active

Correspondence to: P. Yin; e-mail: yinping426@263.net.Contract grant sponsors: Doctorial Foundation of the State

Education Commission of China; National Science Foundationof China.

subject due to their special structures and proper-ties. Ab initio molecular orbital (MO) calculationson C8H4 showed that it may have aromatic charac-ter and stability by using vibration spectra analysis,isodemic reaction, and nature bond orbital analyses[2, 3].

On the other hand, increasing attention has beenpaid to III–V group compound chemistry espe-cially since the discovery of borazine [4]. Poweret al. [5 – 7] have synthesized planar six-memberedbenzene analogs B3P3H6 and Al3N3H6, planar four-membered [Me2AlNHDipp]2, and cubic structure[MeAlNMes]4 · 3C7H8. These benzene analogs havedrawed attention to the issue of aromaticity. Fink

International Journal of Quantum Chemistry, Vol. 82, 293–298 (2001)c© 2001 John Wiley & Sons, Inc.

YIN ET AL.

et al. [8] used electronic energies of homodesmoticreaction to calculate the resonance energies of(HXYH)3 (X = B, Al; Y = N, P). Matsunaga et al. [9]investigated the bond energies and stabilities of iso-mers. But until now the synthesis and theoreticalinvestigation of B4N4H4, the isoelectronic species ofC8H4, have not been reported to our knowledge,and it is not clear if B4N4H4 has structure and char-acters similar to that of C8H4.

It is our aim to report the planar structure andrelative stability of B4N4H4 through theoretical cal-culations in comparision to its counterpart C8H4,which can help to unravel the intrinsic nature ofthe rings themselves and will be useful in futureconsiderations of the influence of substituents. Theanalyses of Milliken population, vibration frequen-cies, π-molecular orbital components, and orbitalenergy levels are based on ab initio calculationsat HF/6-31G∗ and MP2/6-31G∗ levels. Moreover,we used homodesmotic reactions as an indicatorto judge their relative stabilities and also discussedthe effect of temperature on these reactions at theMP4SDQ/6-31G∗ level.

Computational Methodology

All computational studies in this work were per-formed on 211 workstations of Nanjing Universityusing the Gaussian-94 [10] series of computer pack-

ages with ab initio method. Geometries have beenoptimized at the HF/6-31G∗, MP2/6-31G∗, andMP2/6-311G∗∗ levels. Milliken population, vibra-tion frequencies, π-molecular orbital components,and orbital energy levels have been examined tocharacterize the nature of X4Y4H4 (XY = CC, BN)at the HF/6-31G∗ level. Single-point calculations atthe MP4SDQ/6-31G∗ on the HF/6-31G∗-optimizedgeometries were also carried out to better investi-gate resonance energies.

Homodesmotic reaction is usually characterizedas a measure of aromaticity. Sax et al. [11] extendedit into inorganic compouds in their study of reso-nance energy in Si6H6. Here we use the followinghomodesmotic reactions (reaction A and reaction B)to calculate the resonance energies for C8H4 andB4N4H4 by electronic structure energies:

C8H4 + 4H2C=CH2 → 2H2C=CHCH=CH2

+ 2HC≡CHC=CH2 (A)

B4N4H4 + 4H2B=NH2→ 2H2B=NHBH=NH2

+ 2HB≡NHB=NH2 (B)

Both H2X=YHXH=YH2 and HX≡YHX=YH2

(XY = CC, BN) are planar transoid conformers. Fur-thermore, to investigate the effect of temperatureon these homodesmotic reactions, the general sta-tistical thermodynamics was used to evaluate thethermodynamics functions. The selected tempera-ture range is from 100 to 1100 K, in step of 200 K.

TABLE IStucture parameters of planar eight-membered ring X4Y4H4 (XY = CC, BN) at HF/6-31G∗, MP2/6-31G∗, andMP2/6-311G∗∗ levels.a,b

C8H4 B4N4H4Bond distance/angle HF/6-31G∗ MP2/6-31G∗ MP2/6-311G∗∗ HF/6-31G∗ MP2/6-31G∗ MP2/6-311G∗∗

r(X1–Y2) 1.3367 1.3640 1.3659 1.4737 1.4694 1.4674r(Y2–X3) 1.4554 1.4432 1.4441 1.3842 1.3977 1.3979r(X3–Y4) 1.1924 1.2372 1.2345 1.2669 1.2856 1.2848r(Y4–X5) 1.4554 1.4432 1.4441 1.4035 1.4153 1.4174r(H9–Y6) 1.1924 1.0861 1.0849 0.9961 1.0122 1.0090r(H12–X5) 1.1924 1.0861 1.0849 1.1898 1.1943 1.1925

6 (X1Y2X3) 116.1 115.7 115.5 113.7 112.9 113.06 (Y2X3Y4) 153.9 154.3 154.5 168.6 170.1 171.36 (X3Y4X5) 153.9 154.3 154.5 140.1 140.2 139.16 (Y4X5Y6) 116.1 115.7 115.5 117.6 116.7 116.66 (X5Y6H9) 121.9 121.5 121.7 121.7 122.0 122.46 (X6Y5H12) 121.9 121.5 121.7 117.3 118.4 118.3

a Bond distances in Å, and bond angles in degrees.b The subscripts of X, Y, and H atoms are consistent with that in Figure 1.

294 VOL. 82, NO. 6

STRUCTURE AND STABILITY OF X4Y4H4

The geometrical parameters and frequencies usedare obtained at the HF/6-31G∗ level, and the en-ergies at MP4SDQ/6-31G∗ level are used as theelectronic contributions. The computations of thethermodynamic quantities were accomplished witha home-made program.

Results and Discussion

Table I gives the optimum geometric parame-ters of C8H4 and B4N4H4, which are consideredin Figure 1, which is a perspective drawing ofthe geometry of the planar X4Y4H4 (XY = CC,BN). The B—N optimized bond lengths in the pla-nar eight-membered ring B4N4H4 are successively1.4694/1.3977/1.2856/1.4153 Å at the MP2/6-31G∗level, which are shorter than the single-bond length(1.645 Å) and longer than the triple-bond length(1.246 Å) according to Ref. [12]. They are differ-ent from the bond lengths of C8H4 because strongbond alternations do not exist in the B4N4H4 system,but they are not equivalent to a certain value justlike (HAlNH)4 [13]. So the change of bond lengthsin B4N4H4 is between these two above-mentionedcases. Table II shows Milliken population of the twospecies. The total Milliken population of B4N4H4,especially the π-electron Milliken population, alsodoes not change alternatively like that of C8H4,which is consistent with the change of bond lengthsin B4N4H4. These facts indicate that B4N4H4 com-pound may be a weak conjugated system, and therecould be a certain delocalization of the lone pairfrom N atoms into empty p orbitals of the adjacentB atoms.

These opinions are verified by the harmonic vi-bration frequencies of C8H4 and B4N4H4 at HF/6-31G∗ level presented in Table III. Both B4N4H4 andC8H4 exhibit real vibration frequencies at the planargeometries, which means that they could be estab-

FIGURE 1. View of the geometry of planar X4Y4H4(XY = CC, BN). The corresponding structure parametersare listed in Table I.

lished as true local minina on the potential energysurface and exist in theory in spite of no reported ex-perimental frequencies for comparison. For B4N4H4,the frequencies 129.0 cm−1 (A′) and 197.0 cm−1 (A′)belong to an out-of-plane distorted vibration model,which consists of all four B atoms and four N atoms.These two relative smaller frequencies display thatthe planar BN eight-membered ring is not easy todistort and is a little more stable than C8H4.

Table IV lists the π-molecular orbital componentsand orbital energy levels of two above molecules.The contributions of 2pz and 3pz in C, B, and Natoms are mainly considered in the orbital coeffi-cients, and the listed values are the square root ofsquare sum of the orbital coefficients of 2pz and 3pz.B4N4H4, similar to C8H4, could form four bondingπ-molecular orbitals. However, the multiple bondsare polarized due to the electronegativity differ-ence between B and N atoms; thus the electronsare more or less localized on the N atoms. Thiscan also be seen from the MO pattern, which dis-plays smaller coefficients on the boron pz orbitalscompared to the nitrogen pz orbitals in HOMO (thehighest occupied molecular orbital). In addition,LUMO (the lowest unoccupied molecular orbital)–HOMO energy gap indices for C8H4 and B4N4H4

TABLE IIMilliken population of X4Y4H4 (XY = CC, BN) at HF/6-31G∗ level.a

C8H4 B4N4H4

π σ Total π σ Total

X1–Y2 0.248 0.429 0.677 0.058 0.293 0.351Y2–X3 −0.001 0.369 0.368 0.069 0.376 0.445X3–Y4 0.270 0.808 1.078 0.146 0.590 0.736Y4–X5 −0.001 0.369 0.368 0.086 0.433 0.519

a The subscripts of X and Y atoms are consistent with that in Figure 1.

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 295

YIN ET AL.

TABLE IIIHarmonic vibration frequencies (cm−1) for X4Y4H4(XY = CC, BN) at HF/6-31G∗ level.

Molecule Sym. Freq.

C8H4 Ag 478.6 841.9 1280.9 1770.0 2504.23415.5

B1g 606.4 1088.6B2g 412.1 789.9B3g 296.6 788.9 1215.1 1508.0 3393.8B1u 522.6 1145.1 1305.5 1743.3 3414.5B2u 708.7 962.5 1508.7 2480.5 3395.3B3u 250.3 848.4

B4N4H4 A′ 272.9 407.7 435.3 671.7 761.8 824.7909.2 990.9 1023.3 1203.0 1238.41300.1 1402.3 1426.1 1493.2 1974.22102.9 2755.0 2760.2 3865.23865.9

A′′ 129.0 197.0 264.8 539.7 550.8 551.5616.5 974.6 977.0

are 0.342 (a.u.) and 0.489 (a.u.), respectively. That is,Eg (C8H4) < Eg(B4N4H4), and it is well known thatthe larger value of Eg a species has, the more stableit usually is. So this argument also explains the sta-bility of B4N4H4 over C8H4. As to the energy gapindex between HOMO and second HOMOs, theyare E′g(C8H4) (0.125 a.u.) > E′g(B4N4H4) (0.059 a.u.),which indicates that the cyclic hydrocarbons moreeasily form conjugated second HOMOs.

Table V displays the results of 1Erxn for ho-modesmotic reactions. The homodesmotic reactionkeeps greater similarity of bond types because thereare equal numbers of the same kinds of hydrids,so it is more sharply focused on the difference indelocation between adjacent multiple bonds. Bothreaction A and reaction B establish the same rela-tive order for the degree of aromaticity in B4N4H4and C8H4 at all four levels, namely B4N4H4 > C8H4.The negative values of 1Erxn put two species on theantiaromatic side of the scale except that B4N4H4

has positive 1Erxn at the MP2/6-311G∗∗ level. Theabove-mentioned ab initio calculations discussedthe relative stabilities of C8H4 and B4N4H4 using thehomodesmotic reactions. To obtain a better under-standing of the stabilities of these two molecules,further calculations of the thermodynamic proper-ties of the homodesmotic reactions with differentenvironmental temperatures have been introducedin this work. As can be seen from Table VI, for each

TABLE IVThe π -molecular orbital components and orbitalenergy levels for C8H4 and B4N4H4 atHF/6-31G∗ level.

EnergyMolecule (a.u.) Orbital components

C8H4 0.0553(LUMO)

0.384C1− 0.384C2 −0.250C3+ 0.250C4+ 0.384C5 − 0.384C6− 0.250C7+ 0.250C8

−0.2871(HOMO)

0.293C1 + 0.293C2 − 0.266C3− 0.266C4 + 0.293C5 + 0.293C6− 0.266C7 − 0.266C8

−0.4118 − 0.079C1 + 0.079C2 + 0.331C3+ 0.331C4 + 0.079C5 − 0.079C6− 0.331C7 − 0.331C8

−0.4302 0.329C1 + 0.329C2 + 0.069C3− 0.069C4 − 0.329C5 − 0.329C6− 0.069C7 + 0.069C8

−0.5163 0.212C1 + 0.212C2 + 0.225C3+ 0.225C4 + 0.212C5 + 0.212C6+ 0.225C7 + 0.225C8

B4N4H4 0.1200(LUMO)

0.518B1 − 0.020N2 − 0.398B3+ 0.018N4 + 0.519B5 − 0.022N6− 0.397B7 + 0.018N8

−0.3690(HOMO)

0.032B1 − 0.400N2 + 0.070B3+ 0.395N4 + 0.031B5 − 0.400N6+ 0.071B7 + 0.396N8

−0.4278 − 0.136B1 − 0.082N2 + 0.147B3+ 0.446N4 + 0.136B5 + 0.080N6− 0.148B7 − 0.446N8

−0.4800 0.077B1 + 0.486N2 + 0.141B3+ 0.060N4 − 0.077B5 − 0.486N6− 0.140B7 − 0.060N8

−0.5305 0.115B1 + 0.346N2 + 0.168B3+ 0.235N4 + 0.116B5 + 0.346N6+ 0.168B7 + 0.234N8

of the homodestic reactions, the enthalpy changes1H◦ are negative in the temperature range 100–1100 K. So both reactions A and B are exothermic. Asto the Gibbs free energy changes 1G◦, they remainnegative and rise slowly in reaction A, which meansthis reaction is spontaneous, while they increasesharply from negative value (−102.75 kJ/mol) topositive value (10.63 kJ/mol) in reaction B. The en-tropy changes 1S◦ are negative for reaction B andchange from negative value (−41.84 J/mol · K) tosmall positive value (10.31 J/mol ·K) for reaction A,which suggests that in reaction B the entropy de-creases, while in reaction A the entropy decreasesat first and increases later. The resonance ener-

296 VOL. 82, NO. 6

STRUCTURE AND STABILITY OF X4Y4H4

TABLE VResults of homodesmotic reaction energies (kcal/mol) for X4Y4H4 + 4H2X=YH2 → 2H2X=YHXH=YH2 +2HX≡YHX=YH2 (XY = CC, BN).

MP4SDQ/6-31G∗HF/6-31G∗ MP2/6-31G∗ MP2/6-311G∗∗ //HF/6-31G∗

1Erxn (C8H4) −45.5 −32.4 −32.9 −37.21Erxn (B4N4H4) −27.2 −29.2 134.5 −29.2

gies 1U◦ are all negative during the temperaturerange, and reaction B obtains negative smaller value(−92.27 kJ/mol) at high temperature. Therefore,B4N4H4 has stability preference at high temperaturecompared to C8H4.

Up to now, it is difficult to measure the structuresand stabilities of B4N4H4 and C8H4 in direct exper-iments, so the calculated results based on quantumchemistry and statistical thermodynamics will pro-vide useful information for experimental research.

Conclusion

Ab initio electronic structure calculations sys-tematically investigating two isoelectronic speciesB4N4H4 and C8H4 have been applied to assist inunderstanding the chemistry of the III–V groupanalogs of organic molecules. The major conclu-sions that can be drawn from this work are asfollowing:

1. We have obtained planar eight-memberedring B4N4H4 just like C8H4. We did not findthe alternate B—N bond lengths in B4N4H4, tobe the same as those in C8H4, and they are alsodifferent from the equal Al—N bond length in(HAlNH)4.

2. Although the planar B4N4H4 has not been syn-thesized, the frequencies calculated suggestthis compound could be stable and exist intheory.

3. The π-molecular orbital analysis shows thatB4N4H4 has four bonding π orbitals like C8H4,but its HOMO is mainly composed by pz or-bitals of N atoms due to the electronegativitydifference between the boron atom and the ni-trogen atom.

4. All discussion in this work is consistent withthe conclusion that the order of the relativearomaticity and relative stability for two mole-cules is B4N4H4 > C8H4.

TABLE VIThermodynamic functions of reaction A and reaction B in the temperature range of 100–1100 K.

1U◦ (kJ/mol) 1H◦ (kJ/mol) 1G◦ (kJ/mol) 1S◦ (J/K ·mol)

Reaction A100 K −187.28 −188.11 −183.92 −41.84300 K −183.83 −185.50 −176.41 −30.29500 K −175.37 −179.53 −171.92 −15.22700 K −167.07 −172.89 −170.06 −4.05900 K −158.90 −166.38 −170.10 4.14

1100 K −151.09 −160.24 −171.58 10.31

Reaction B100 K −114.50 −115.33 −102.75 −125.80300 K −111.77 −114.27 −77.44 −122.77500 K −106.88 −111.04 −53.75 −114.57700 K −101.93 −107.75 −31.43 −109.03900 K −97.07 −104.56 −10.04 −105.01

1100 K −92.27 −101.42 10.63 −101.87

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 297

YIN ET AL.

ACKNOWLEDGMENTS

This work was supported by the Doctorial Foun-dation of the State Education Commission of Chinaand the National Science Foundation of China, andit also benefitted from the valuable comments ofProfessor Guan-Zhi Ju.

References1. Huang, N.; Mak, T. C. W.; Li, W. Tetrahedron Lett 1981, 22,

3765–3768.2. Chan, T.; Huang, N. Tetrahedron 1983, 39, 427–432.3. Wang, F.; Wang, X.; Jin, F.; Zhou, G.; Tian, A. Acta Chim

Sinica 2000, 58, 347–350.4. Stock, A.; Pohland, E. Ber Dtsch Chem Ges 1926, 59, 2215–

2223.5. Power, P. P. Angew Chem Int Ed Engl 1990, 29, 449–460.

6. Waggoner, K. M.; Hope, H.; Power, P. P. Angew Chem Int EdEngl 1988, 27, 1699–1700.

7. Waggoner, K. M.; Power, P. P. J Am Chem Soc 1991, 113,3385–3393.

8. Fink, W. H.; Richards, J. C. J Am Chem Soc 1991, 113, 3393–3398.

9. Matsunaga, N.; Gordon, M. S. J Am Chem Soc 1994, 116,11407–11419.

10. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.;Johnson, B. G.; Robb, M. A.; Cheeseman, G. R.; Keith, T.;Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.;Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.;Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Bink-ley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; Head-Gordon,M.; Gonzalez, C.; Pople, J. A. Gaussian-94; Gaussian: Pitts-burgh, 1995.

11. Sax, A. F.; Janoschek, R. Phosphorus Sulfur 1986, 28, 151–166.

12. Mckee, M. L. J Phys Chem 1992, 96, 5380–5385.

13. Chen, X.; Li, C.; Wu, T.; Yao, T.; Ju, G. Theor Chem Acc 1998,99, 272–276.

298 VOL. 82, NO. 6