Peroxide Linkage N O Molecule:2 4

Prediction of New ONOONO Isomers

XUEFENG WANG, QI-ZONG QINLaser Chemistry Institute, Fudan University, Shanghai 200433, China

Received 15 May 1998; revised 15 June 1999; accepted 15 June 1999

Ž .ABSTRACT: Ab initio and density functional theory DFT have been applied topredict the existence of the ONOONO molecules. Two new isomers, cis-perp-cis andcis-perp-trans ONOONO, are found to be minima on the potential energy hypersurface

Ž .calculated at MP2 level with 6-311G d basis set and Becke3P86 and Becke3LYP levelswith the cc-PVDZ basis set. Vibrational frequencies are calculated at the optimizedstructures. Calculations at both ab initio and DFT methods show that cis-perp-cis isenergetically favored in all three O—O bonded ONOONO isomers. Q 2000 John Wiley &Sons, Inc. Int J Quant Chem 76: 77]82, 2000

Key words: N O ; ab initio calculation; density function theory; ONOONO isomers;2 4peroxide linkage molecule

Introduction

initrogen tetroxides, weakly bound dimersD of NO , have been extensively investigated2w x w xin gas phase 1 , in molecular beams 2 , and in

w xcondensed phase 3]6 . The photodissociation ofN O aroused a particular interest in atmosphere2 4

w xchemistry 7, 8 and has been investigated recentlyw xin its physisorbed state 9 . The most stable form

of NO dimer is planar with D symmetry in2 2 hwhich a central N—N bond links two coplanarNO fragments, and its structure and frequencies2have been calculated previously with various theo-

w xretical methods 10]14 . The two NO groups can2

Correspondence to: Q.-Z. Qin.

also be linked by an O—N bond to form anotherisomer of N O , i.e., ONONO , which has been2 4 2

w xreported in condensed phase 3]6 and theoreticalw xstudies 11]13 . McKee presented a computational

evidence for a new N O isomer, which involves2 4the coupling of two NO groups through oxygen2

w xatoms 11 . But the geometrical structures of otherpossible isomers of ONOONO and their relativestabilities remain not well understood. These iso-

Ž .mers with peroxide —O—O— linkage are ex-pected to photolyze more easily in the 290]400 nmrange, and this behavior is of great significance inthe photochemistry of atmospheric pollutants.

Ž .Ab initio and density functional theory DFThave been successfully applied to determining theaccurate molecular properties of nitrogen oxides.The well-studied N O isomers, N—N bonded2 4

( )International Journal of Quantum Chemistry, Vol. 76, 77]82 2000Q 2000 John Wiley & Sons, Inc. CCC 0020-7608 / 00 / 010077-06

WANG AND QIN

O N—NO and N—O bonded ONONO struc-2 2 2tures, have been calculated previously withHartree]Fock theory and DFT method, giving the

w xbest agreement with experiment 11]14 . To get adeep insight into the chemistry of ONOONO iso-mers, we have carried out ab initio and DFT stud-ies on the structures, vibrational frequencies, andhypervalency of the oxygen atoms for these iso-mers. Our calculation results show that two newisomers, cis-perp-cis and cis-perp-trans ONOONO,are local minima on the potential energy hyper-surface.

COMPUTATIONAL METHOD

All calculations have been carried out with thew xGaussian 94 Program package 15 . The ab initio

and DFT methods have been applied in this study.The methods used to optimize the geometries andto calculate the energies involve the second-order

Ž .Møller]Plesset perturbation MP2 theory, anddensity functional theory described as Becke3LYP,

Ža variation of Becke’s three-parameter local, non-.local, Hartree]Fock hybrid exchange functional

using the Lee]Yang]Parr correlation functionalw x16, 17 , and Becke3P86, a method using Becke’sthree-parameter hybrid exchange functional withPerdew’s 1986 gradient-corrected correlation func-

w x Ž . Žtional 18, 19 . The 6-311G d and cc-PDVZ Dun-ning’s correlation-consistent polarized valence

w x.double-zeta 20 basis sets are used in MP2 andDFT calculations, respectively. Geometries wereoptimized using analytic gradients, and vibra-tional frequencies were calculated analytically atthe optimized structures. At optimized MP2r6-

Ž .311G d geometries, single-point energies were de-Ž .termined at MP4 level with 6-311G 2d basis set.

Results and Discussion

The geometry optimizations of the peroxideN O isomers with peroxide linkage were per-2 4

Ž .formed at MP2 level with 6-311G d basis set, andBecke3LYP and Becke3P86 levels with cc-PVDZbasis sets for most possible N O peroxide iso-2 4

Ž .mers. Two new peroxide N O isomers Fig. 12 4cis-perp-cis and cis-perp-trans isomeric forms, werelocated on the potential energy hypersurface. Thecis-perp-cis has C symmetry while cis-perp-trans2has C symmetry. Vibrational frequency analysesshave been carried out for two new isomers, and

they are verified to be true local minima. To com-pare the properties of all peroxides of N O ,2 4trans-perp-trans form, which had been calculated

w xby McKee 11 , has also been considered in thisstudy. The results of the structure parameters,relative energies and vibrational frequencies ofthree ONOONO isomers are given in Tables I, II,and III.

The cis-perp-cis isomer has an unusual struc-ture as compared with other nitrogen oxides. It iswell-known that the N O molecules have strongx yNO bonds with bond lengths ranging from 1.15 to

˚ 1 11.23 A. The N O bond lengths outside cis-perp-cis˚are about 1.15]1.17 A calculated at MP2, B3LYP,

and B3P86 levels, which is similar to the NO bondof common N O . However, the N1O2 bondx y

˚lengths inside the isomer are 1.55 A at B3LYP and˚1.51 A at B3P86 levels, respectively, but these

˚bonds are estimated to be 2.31 A at MP2 level. Thecalculated O—O bond length in this isomer ranged

˚from 1.3 to 1.4 A at B3LYP and B3P86 levels,˚which is 0.1]0.2 A shorter than that in the well-

known peroxides, such as HOOH, CH OOH, and3CH OOCH . However, at MP2 level the O—O3 3

˚bond length is 1.23 A, which is close to that of free˚Ž .O molecule 1.21 A . The NOON dihedral angle2

Žin cis-perp-cis is quite close to 908 e.g., 86.78 at.B3LYP, 92.28 at MP2 while the OONO dihedral

Žangle is close to 08 e.g., y2.928 at B3LYP, 0.58 at.MP2 , which means that OONO is kept in the

same plane. It is noted the structure parameters ofcis-perp-cis isomer are somewhat scattered de-pending on methods used.

The cis-perp-trans isomer is also a local mini-mum of the peroxides. As shown in Table II, DFTcalculations at B3LYP and B3P86 levels show thatthe structure parameters are similar to that ofcis-perp-cis except that one of the OONO dihedralangle is close to 08 and another is close to 1808. Inaddition the MP2 calculations for this isomer arevery close to DFT results. The third isomeric formof N O peroxide, as shown in Table III, is trans-2 4perp-trans N O with C symmetry, in which both2 4 2OONO dihedral angles are close to 1808. Our cal-culated results for this isomer at DFT and MP2levels are basically in agreement with the report of

w xMcKee 11 .The total energies of three N O peroxide iso-2 4

Ž .mers and relative energies to sym-N O D cal-2 4 2 hculated at various levels are listed in Table IV. Toconfirm the stability orders, single-point energies

Ž .were calculated at the MP4 level with 6-311G 2dŽ .at optimized MP2r6-311G d geometries. The

VOL. 76, NO. 178

PEROXIDE LINKAGE N O MOLECULE2 4

FIGURE 1. Structures of N O isomers.2 4

calculated results show that the relative ordersof energy are similar in all calculations. Themost stable form is N—N bonded planar sym-

Ž .N O D whereas the trans-perp-trans N O ,2 4 2 h 2 4the highest one in energy, lies approximately

Ž .40]50 kcalrmol above N O D estimated at2 4 2 hŽ .DFT, MP2, and MP4 SDTQ levels, which is in

agreement with the calculations at same levels byw xMcKee 11 . The cis-perp-cis and cis-perp-trans

forms are more stable than trans-perp-trans struc-ture while the cis-perp-cis form is the most stableone in all three N O peroxide isomers. The rela-2 4tive energy of cis-perp-cis form is 31.1 kcalrmol

Ž .over N O D at MP2 level, which is close to2 4 2 h

DFT calculations, but the value decreases to 21.1Ž .kcalrmol determined at MP4 SDTQ level. It is

obvious that the relative energies for these isomersin Hartree]Fock theory are sensitive to electroncorrelation. As we noted the estimated energies for

Žthree peroxides at DFT level are very close only 2.kcalrmol separation while at MP2 and

Ž .MP4 SDTQ levels the cis-perp-trans and trans-perp-trans isomers are also close in energy, but thecis-perp-cis form is predicted to be about 20kcalrmol more stable than trans-perp-trans iso-mer.

TABLE Ia ( y1)Equilibrium structure and harmonic frequencies cm of cis-perp-cis ONOONO.

MP2 Becke3LYP Becke3P86( )Parameter 6-311G d cc-PVDZ cc-PVDZ

1 1( )R N O 1.1753 1.1531 1.15361 2( )R N O 2.3072 1.5562 1.51172 3( )R O O 1.2460 1.3789 1.3771

1 1 2( )a O N O 84.88 113.03 113.481 2 3( )a N O O 88.66 110.59 111.251 1 2 3( )d O N O O 0.46 y2.92 y3.021 2 3 2( )d N O O N 92.17 86.68 84.89

b( ) ( ) ( )A NO s-str 1753.4 5.3 1887.0 181.1 1894.2 175.2( ) ( ) ( )OO str 1445.9 5.1 955.6 1.8 967.7 0.6

( ) ( ) ( )NO s-str 752.0 46.9 769.3 23.6 790.5 27.2( ) ( ) ( )O N—O bend 566.9 2.5 414.7 22.7 424.6 17.6( ) ( ) ( )OON bend 514.1 1.9 360.4 53.2 371.6 69.7( ) ( ) ( )NOON torsion 194.2 0.0 211.7 3.7 215.4 5.5( ) ( ) ( )OONO torsion 131.5 3.7 79.5 0.0 84.6 0.1

( ) ( ) ( )B N O a-str 2813.6 49046.6 1838.6 396.0 1848.4 340.0( ) ( ) ( )N—O a-str 604.7 2.2 894.6 61.6 928.5 65.3( ) ( ) ( )OON bend 437.9 7.6 475.2 174.9 496.0 186.5( ) ( ) ( )O N—O bend 279.4 4.4 368.5 47.0 384.6 46.3( ) ( ) ( )OONO torsion 218.3 0.5 220.3 1.5 229.9 1.4

aBond lengths in angstroms, angles in degrees.b ( ) y 1IR absorption intensities in parentheses in km mol .

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WANG AND QIN

TABLE IIa ( y1)Equilibrium structure and harmonic frequencies cm of cis-perp-trans ONOONO.

MP2 Becke3LYP Becke3P86( )Parameter 6-311G d cc-PVDZ cc-PVDZ

1 1( )R N O 1.1548 1.1570 1.15641 2( )R N O 1.5751 1.5276 1.49472 3( )R O O 1.3873 1.3869 1.37893 2( )R O N 1.5585 1.5543 1.52432 4( )R N O 1.1565 1.1531 1.15221 1 2( )a O N O 112.68 113.46 113.721 2 3( )a N O O 108.50 111.10 111.452 3 2( )a O O N 106.18 107.04 106.933 2 4( )a O N O 109.21 108.71 108.751 1 2 3( )d O N O O y5.38 y5.08 y5.141 2 3 2( )d N O O N 85.58 83.50 82.212 3 2 4( )d O O N O 177.29 178.42 178.79

b( ) ( ) ( )A N O s-str 1804.2 236.5 1884.9 253.1 1900.9 248.6( ) ( ) ( )N O a-str 1748.7 567.4 1834.7 363.8 1850.8 325.4

( ) ( ) ( )OO str 952.4 33.8 995.7 33.5 1018.3 32.2( ) ( ) ( )N—O a-str 773.9 11.0 894.0 22.5 921.2 24.4( ) ( ) ( )N—O s-str 693.4 80.8 738.9 162.7 756.0 174.1( ) ( ) ( )ONO bend 414.6 77.8 439.1 72.4 459.1 100.1( ) ( ) ( )ONO bend 376.5 1.0 430.2 108.9 449.5 83.4( ) ( ) ( )OON bend 312.0 30.6 398.6 88.5 420.7 98.6( ) ( ) ( )OON bend 277.5 0.9 331.0 1.7 344.3 1.3( ) ( ) ( )NOON torsion 194.2 0.3 226.1 0.9 234.1 1.0( ) ( ) ( )OONO torsion 171.7 0.4 186.9 0.0 196.2 0.1

( ) ( ) ( )OONO torsion 76.1 0.2 82.6 0.2 86.7 0.1

aBond lengths in angstroms, angles in degrees.b ( ) y 1IR absorption intensities in parentheses in km mol .

The origin of the energy difference of threeN O peroxides is due to the long-range bonding2 4overlap between pairs of cis-oxygen atoms. Thetwo terminal O atoms of the ONOONO chain areweakly bonded with central O—O, which shouldbe responsible for the stability order. This type ofinteraction is known to exist in several nitrogen

Ž .oxides. The planar D structure of the symmet-2 hric N O molecule, for instance, is stabilized by the2 4p orbitals overlap between the cis-oxygen atoms,giving rise to an appreciable barrier of internal

w xrotation 21 . As another example for the terminalO—O bonding interacting calculations on threedifferent conformers of the ONNNO moleculeshow that the cis isomer is also energetically fa-

w xvored due to O—O orbital overlaps 22 . It isnoted that there are two pairs of cis-oxygen atoms

Ž 1 3 2 4in cis-perp-cis O —O and O —O shown in Fig-.ure 1 , which obtains stronger additional stabili-

zation energy. Only one pair of cis-oxygen atomsŽ 1 3.O —O in cis-perp-trans, however, gives relative

weaker stabilization energy, while there is no suchkind of overlap in the trans-perp-trans structure.

Although the ONOONO isomers have neverbeen observed experimentally, the other O—Obonded peroxide molecules such as HOONO andits isomers have been well characterized by vi-

w xbrational spectroscopy 23]26 . Our calculatedvibrational frequencies and infrared intensities forthe three isomers of ONOONO are also listed inTables I]III. Their most intense bands are N O

y1 Žantisymmetric stretching mode, 1838.6 cm cis-. y1 Ž .perp-cis , 1834.7 cm cis-perp-trans , and 1844.5

y1 Ž .cm trans-perp-trans at the B3LYPrcc-PVDZlevel. At MP2 level the N O antisymmetricstretching modes of cis-perp-trans and trans-perp-trans forms are 1748.7 and 1753.8 cmy1, respec-tively, however, for cis-perp-cis isomer this modeis 2813.6 cmy1, much higher than DFT estimation.Recently our group has studied the infrared spec-troscopy of dinitrogen trioxides theoreticaly and

w xexperimentally 27]29 and found the DFT calcula-

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PEROXIDE LINKAGE N O MOLECULE2 4

TABLE IIIa ( y1) bEquilibrium structure and harmonic frequencies cm of trans-perp-trans ONOONO .

MP2 Becke3LYP Becke3P86( )Parameter 6-311G d cc-PVDZ cc-PVDZ

1 1( )R N O 1.1785 1.1627 1.15511 2( )R N O 1.5338 1.5333 1.50662 3( )R O O 1.4264 1.3891 1.3785

1 1 2( )a O N O 108.64 108.94 109.021 2 3( )a N O O 104.76 106.84 106.741 1 2 3( )d O N O O 178.14 179.34 179.881 2 3 2( )d N O O N 83.49 75.81 73.74

c( ) ( ) ( )A NO s-str 1773.4 50.9 1878.0 62.9 1897.5 62.0( ) ( ) ( )OO str 1012.0 21.7 1032.2 31.7 1058.6 31.5

( ) ( ) ( )NO s-str 746.7 68.8 753.4 53.9 775.9 63.3( ) ( ) ( )O N—O bend 373.6 12.5 402.6 16.9 421.5 19.4( ) ( ) ( )OON bend 327.4 26.4 334.9 6.3 349.5 4.9( ) ( ) ( )NOON torsion 208.3 0.1 208.9 0.3 219.1 0.3

( ) ( ) ( )OONO torsion 85.1 0.4 75.5 0.1 79.4 0.0( ) ( ) ( )B N O a-str 1753.8 440.5 1844.5 668.1 1864.8 637.2

( ) ( ) ( )N—O a-str 850.1 194.0 868.5 232.0 889.1 231.3( ) ( ) ( )OON bend 387.2 50.8 448.0 292.2 470.9 301.1( ) ( ) ( )O N—O bend 354.4 397.7 394.2 2.6 411.7 4.6( ) ( ) ( )OONO torsion 162.3 2.8 169.5 0.6 176.4 0.7

aBond lengths in angstroms, angles in degrees.b [ ]McKee also studied this species in Ref. 11 .c ( ) y 1IR absorption intensities in parentheses in km mol .

TABLE IV( ) ( y1)Total energies hartree and relative energies kcal mol for N O isomers.2 4

Level of theory sym-N O cis-perp-cis N O cis-perp-trans N O trans-perp-trans N O2 4 2 4 2 4 2 4

Becke3LYP / cc-PVDZ y410.21024 y410.15784 y410.15457 y410.15118Becke3P86 / cc-PVDZ y411.02392 y410.96399 y410.96063 y410.95715

( )MP2 / 6-311G d y409.34928 y409.29977 y409.26998 y409.26590( )MP4 / 6-311G 2d / / y409.50479 y409.47109 y409.44127 y409.43517( )MP2 / 6-311G d

y1( )Relative energies kcal molBecke3LYP / cc-PVDZ 0.0 32.9 34.9 37.1Becke3P86 / cc-PVDZ 0.0 37.6 39.7 41.9

( )MP2 / 6-311G d 0.0 31.1 49.8 52.3( )MP4 / 6-311G 2d / / 0.0 21.1 39.9 43.7( )MP2 / 6-311G d

tions can be effective in reproducing the vibra-tional frequencies of N O . Here DFT calculationsx yare also expected to reproduce the frequencies ofN O peroxides well. Taking account of the high2 4fundamentals of N O antisymmetric stretch, it

Žmight be helpful to compare with X—N O X s.Cl, OH, OOH, etc. in which the bond order of the

nitrogen]oxygen bond is two, or greater, depend-

ing on the ionic character of the nitrogen]oxygenbond is two, or greater, depending on the ioniccharacter of the X—N bond; i.e., on the electroneg-ativity of X. The nitrogen-oxygen stretch vibrationis found to be 1600]1700 cmy1 in the HOONO

w x y1molecule 23 and appears at 1750]1850 cm inw xClOONO 24 . It is well known that the electroneg-

ativity of the NO group is close to that of the Cl

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 81

WANG AND QIN

atom. Thus we predict with reasonable confidencethat the nitrogen]oxygen stretching vibration fre-quency of ONOONO is in the range 1800]1850 cmy1. The calculated O—O stretches vibra-tion for the three isomers of ONOONO are found

y1 Ž . y1to be 950]970 cm cis-perp-cis , 995]1025 cmŽ . y1 Žcis-perp-trans and 1030]1070 cm trans-perp-

.trans , respectively. These frequencies are largerŽthan the experimental O—O stretch in HOOH 863

y1 . w xcm 25 but smaller than the experimental O—OŽ y1 . w xstretch in FOOF 1210 cm 26 . If these three

ONOONO isomers can be produced and stabilizedin a special experimental condition, the structuresof three isomers could not easily be identified bythe predicted infrared spectra since the vibrationalbands in all region for three isomers are very closeto each other. It would be possible to identify thestructures of three isomers by studying the iso-topic shifts and comparing the relative intensitiesof N O antisymmetric and symmetric stretchingvibrations.

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