Coral Getino et al- Ab Initio Study of Stretch-Bend Coupling in HOOH

8/3/2019 Coral Getino et al- Ab Initio Study of Stretch-Bend Coupling in HOOH

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J . Phys. Chem. 1990, 94, 3995-4000Ab Initio Study of Stretch-Bend Coupling in HOOH

3995

Coral Getino: Bobby G . Sumpter,* Jesus Santamaria,+ and Gregory S . Ezra**$Department of Chemistry, Cornell University, Ithaca, New Yor k 14853 (Received: Septembe r 25, 1989)

Ab initio calculations are used to investigate the dependence of th e OO H bend force constants on the 00 and OH bondlengths in HOOH. The calculations were performed using second-order Mdle r-Plesset perturb ation theory with a split-valencetriple-< basis set augmented with multiple polarization functions on both the oxygen and hydrogen atom s [6-311G(3d,2p )].Analytical functions describing the variation of the bending force constants with the bond lengths are obtained by fittingthe ab initio data and are found to be significantly different from the switching functions previously used in trajectory studiesof HOOH.

I . IntroductionThere has been considerable experimental' and theoreticalZinterest in the vibrational overtone induced decomposition ofpolyatomic molecules. Th e possibility of inducing unimoleculardissociation in state-specific fashion has provided the stimulus formany of the studies. Hydrogen peroxide is an attractive poly-atomic molecule for study of overtone-induced unimoleculard i s ~ o c i a t i o n . ~ ~he 0-H bonds are good local modes and providewell-defined sites for overtone excitation; classical trajectorysimulation^^-'^ are feasible, and the relatively small size (fouratoms) makes it possible to perform ab initio calculations withlarge basisEarly work on the spectroscopy of HOOH established thenonplanar geometry and the existence of a hindered internalrotational mode.z6-30 Some of the earlier studies indicated theimportan ce of torsion-vibration interactions and the depend enceof the torsional potential on the degree of excitation of the O H~ t r e t c h . ~ + ~ *everal valence force fields were proposed whichgave reasonable fits to th e experimental data,16J3 and some abi n i t i o ~ a l c u l a t i o n s ' ~ - ~ ~ere also performed.Mo re recently, several experimental studies of the vibrationalovertone initiated decomposition of HOOH have been reported.&*The vibrationally mediated photodissociation of HOOH andHOODj4 and UV-induced photodissociation of hydrogen per-oxidej5 have also been investigated.On the theoretical side, both ab initio and semiempiricalquantu m mechanical potential surface calcu latio ns'z ~~6 ~z4 ~25ndclassical trajectory calculations of the O H overtone induceddis ~o cia tio n" ~ ave been carried out. We briefly discuss someof the more recent studies below.The equilibrium structure of hydrogen peroxide has been thesubject of controversy for several years.30,31-364zAlthough it isknown tha t th e equilibrium dihedral angle is between 110' an d120', the exact value has not been well established until veryrecently.38 Khachkuruzov and Prz hev al~ kii~ 'eported a dihedralangle of 119.1' obtain ed by fitting rotational constan ts frommicrowave studies, whi le Hunt and c o - ~ o r k e r s ~ ~btained a valueof 1 1 1 .5 ' by f it ti ng t or siona l f requencie s. K o p ~ t ~ ~etermineda value of 111.83' by solving the torsional Schrodinger equ ationfor a fixed O H bond distance of 0.965 A and then fitting thesolution to the experimental dat a. Koput argues that the valuereported by Khachkuruzov and Przhevalskii corresponds to anaverage dihedral angle for the torsional ground state and that

1 11.83' is the correct equilibrium dihedral angle. Mo re recently,experim ental s t ~ d i e s ~ ~ < ~ *lso indicate that the dihedral ang le inH O O H is near the value reported by Koput.There is a long history of a b initio calculations on the stru ctureand torsional barriers of HO OH . A comprehensive account ofthe a b initio studies of H O O H before 1978 can be found in refs18 and 19, while more recent work is discussed in refs 22 and 23.Departamento de Quimica Fisica, Faculdad de C C Quimicas, Universidad

*Present address: Chemistry Division, Oak Ridge National Laboratory,8 Alfred P. Sloan Fellow; Camille and H enry Dreyfus Teacher-Scholar.

Complutense de Madrid, 28040 Madrid, Spain.Oak Ridge, TN 37831-6182.

0022-3654/90/2094-3995$02.50/0

The ab initio studies of Dunning and Winter18 provided areasonable account of the torsional barriers and equilibrium(1) Crim, F. F. Annu. Rev. Phys. Chem. 1984, 35, 657.(2) Uzer, T. Ado. Ar. Mol. Phys. 1988, 25, 417.(3) Rizzo, T. R.; Hayden, C. C.; Crim, F. F.Faraday Discuss. Chem. Soc.1983, 75, 112; J . Chem. Phys. 1984, 81 , 4501.(4) Butler, L. J. ; Ticich, T. M. ; Likar, M. D.; Crim, F. F. J . Chem. Phys.1986,85, 2331.( 5 ) Scherer, N. F.; Doany, F. E.; Zewail, A . H.; Perry, J. W. J. Chem.Phys. 1986, 84, 1932. Scherer, N. F.;Zewail, A . H. J . Chem. Phys. 1987,87 , 97 .(6) Luo, X.; Rieger, P. T.; Perry, D. S.;Rizzo, T. R. J . Chem. Phys. 1988,89 , 4448.(7) Diibal, H.-R.; Crim, F. F. J . Chem. Phys. 1985, 83 , 3863.(8 ) Ticich, T. M.; Likar, D. M.; Diibal, H.-R .; Butler, L. J.; Crim, F. F.J . Chem. Phys. 1987,87, 5820. Likar, M. D.; Baggot, J. E.; Sinha, A.; Ticich,T. M.; Vander Wal, R. L.; Crim, F. F. J . Chem.Soc.,Faraday Tram. 2 1988,84 , 1483. Likar, M . D.; Sinha, A ,; Ticich, T. M .; Vander W al, R. L.; Crim,F. F. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 289.(9) Uzer, T.; Hynes, J. T.; Reinhardt, W. P. Chem. Phys. L e f f . 985, 117,600: J . Chem. Phvs. 1986. 85 . 5791.(10) Uzer, T.; MacDonald, B. D.; Guan, Y . ;Thompson, D. L. Chem. Phys.(1 1) Sum pter, B. G.; Thompson, D. L. J . Chem. Phys. 1985,82,4557;J .(12) Sumute r, B. G. Ph.D. Thesis. Oklahoma Stat e Universitv. 1986.

Lett. 1988, 152, 405.Chem. Phys. 1987, 86, 2805; Chem. Phys. Lett . 1988, 153, 243.

(13) Getino, C.; Sumpter, B. G.; Santamaria, J.; Ezra, G. S. 1 Syner-gefics, Order and Chaos; Velarde, M. G., Ed.; World Scientific: Singap ore,1987; p 499.(14) Getino, C.; Sumpter, B. G.; Santamaria, J.; Ezra, G. S. J . Phys .Chem. 1989, 93, 3877.(15) Getino, C.; Sumpter, B. G.; Santamaria, J. ; Ezra, G. S. To be sub-mitted for publication.(16) Botschwina, P.; Meyer, W .; Semkow, A . M. Chem. Phys. 1976,15,25. (17) Veillard, A . Theor. Chim. Acta 1970,18, 21; Chem. Phys. Len. 1969,4, 51.(18) Dunning, T. H.; Winter, N. W . Chem. Phys. Lefr. 1971, 11 , 1 9 4 ;J .Chem. Phys. 1975, 63, 1847.(19) Cremer, D. J . Chem. Phys. 1978, 69, 4440.(20) Rogers, J. D.; Hillman, J . J. J . Chem. Phys. 1981, 75, 1085; 1982,76, 4046. Rogers, J. D. J . Phys. Chem. 1984, 88 , 526.(21) Bair, R. A. ; Gcddard, W. A. , 111 J . Am . Chem. SOC.1982, 204, 2719.(22) Block, R.; Jansen, L. J . Chem. Phys. 1985, 82, 3322.(23) Carpenter, J. E.; Weinhold, F. J . J . Phys. Chem. 1986, 90, 6405;

(24) Willetts, A.; Gaw, J. F.; Handy, N . C. J . Mol. Specfrosc. 1989, 135,(25) Harding, L. B. J . Phys. Chem. 1989, 93, 8004.(26) Zumwalt, L. R.; Gigutre, P. A. J. Chem. Phys. 1941,9,458. Gigutre,P. A. J . Chem. Phys. 1950, 18 , 88 .(27) Giguere, P. A.; Bain, 0. J . Phys. Chem. 1952, 56 , 340. Bain, 0.;Gigutre, P. A. Can. J . Chem. 1955, 33, 527. Chin, D.; Gigutre, P. A. J .Chem. Phys. 1961, 3 4 , 6 9 0 .(28) GiguBre, P. A .; Srinivasan, T. K. K. J . Raman Specfrosc . 1974, 2,125; J . Mol. Specfrosc . 1977, 66, 168.(29) H elminger, P.; Bowman, W . C.; De Lucia, F. C. J . M ol . Specfrosc .1981, 85 , 120. Bowman, W. C.; De Lucia, F. C.; Helminger, P. J . M ol .Specfrosc .1981, 87, 571. Hillman, J. J . J . Mol. Specfrosc . 1982, 95, 236.(30) Redington, R. L.; Olson, W. B.; Cross, P. C . J . Chem. Phys. 1962,36 , 1311.(31) Hunt, R . H.; Leacock, R . A,; Peters, C. W.; Hecht, K. T. J . Chem.Phys. 1965,42, 1931. Hunt, R. H.; Leacock, R. A . J . Chem. Phys. 1966,45,3141.(32) Hirota, E. J . Chem. Phys. 1958, 28, 839.(33) Przhevalskii, I. N.; Krachkuruzov, G. . Opt . Specfrosc . 1974, 36 ,175. Krachkuruzov, G. A,; Przhevalskii, I. N. Op t . Specfrosc. 1972, 33 , 127,434; 1973, 35, 216; 1976, 41, 323.

1988, 92, 4295, 4306.370.

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3996 The Journal of Physical Chemistry, Vol. 94 , N o . 10, 1990 Getino et al.structure of HOO H. They employed the Hartree-Fock ap-proximation using a [4s3pld/2slp] basis set and showed thenecessity of using geometry optimization and polarization functionsi n order to obtain good geometries and torsional barr ier heights.Cremer19 undertook a syste matic study of the dependence ofthe torsional barriers and molecular geometry on the basis set andlevel of theory and made a critical comparison of theory andexperimental results. He concluded that 2p polarization functionsat the H are important to accurately describe the cis configuration,and inclusion of correlation is necessary to obtain good agreementwith the experimental geometry.

Bair and Go ddard2 ' calculated the equilibrium geometry forHO OH using the generalized valence bond (GV B) plus CI me-thod. They obtained a geometry in good agreement with thatreported by Cremerigand stressed the importance of inclusionof electron correlation i n obtaining the correct equilibrium ge-ometry.Botschwina, Meyer, and Semkow (BM S)I6 derived the first abinitio quadratic force field for HO O H using a small basis set andthen scaled the diagonal F matrix to obtain estimated vibrationalfrequencies. The B MS semiempirical global surface was subse-quently used i n modified form in classical trajectory studies byUzer et aI.9si0C ar pe nte r and W e i n h ~ l d ~ ~ave carried out high-level ab initiocalculations to characterize the O H overtone vibration-torsionpotential coupling on the ground -state potential surfac e. Theyhave provided a detailed analysis of the effect of the level of theoryand basis set on the equilibrium structure an d torsional barrierheights, and their results support the conclusions presented byKoput. Carpen ter and Weinhold find that the trans torsionalbarrier increases with each O H stretch quan tum of excitation,in good agreement with the experimental measurements of Diibaland Crim,7 and provide an exp lanation for this trend.Willetts et a l.24 ave carried out ab initio calculations usingthe double- and triple-{ DZP . DZZP, and TZ2 P+ f basis sets tocharacterize the quartic force field (Dun ham form) for H OO H.MP2 perturbation theory was used to estimate electron correlation.A six-dimensional variational calculation using th e quartic forcefield was carried out to determine the vibrational energy levels,and good agr eemen t with experiment was obtained for levels upto 6000 cm- ' .Hardin gZ5 as carried out the most extensive ab initio calcu-lations on the ground -state potential energy sur face of hydrogenperoxide to dat e, employing a (4s 3p2dl f/2s7p) basis set and usingGVB+ 1+2 calculations with a correction for quadruple excitations.From a f i t to the 480 calculated ab initio energies as a functionof internal coordinates, Harding carried o ut a normal-coordinateanalysis and reexpanded the potential i n terms of normal coor-d i n a t e ~ . ~ ~he calculated normal-mode frequencies w ere i n verygood agreement with the experimental values. The geometricparam eters obtained from the a b initio calculations were also ingood agreement with experiment. A reaction path analysis of the

(34) Brouard, M.; Martinez. M. T.; O'Mahoney, J.; Simons, J. P. Chem.Phys. Lett. 1988, 150, 6; J . Chem. Soc., Faraday Trans. 2, in press.( 3 5 ) Docker, M. P.; Hodgson, A.; Simons, J. P. Chem. Phys. Let t . 1986,128,264;Faraday Discuss.Chem. Soc. 1986,82,25. Jacobs, A ,; Wahl, M.;Weller, R.; Wolfrum, J. Appl. Phys. B 1987, 42, 173. Gericke, K.-H.; Kice,S.; Comes, F. J. ; Dixon, R. N . J . Chem. Phys. 1986, 85 , 4463. Comes, F. J. ;Gericke, K.-H.; Grunew ald, A. U.; lee, S. er. Bunsen-Ges. Phys. C hem.1988, 92, 273. Klee. S.;Gericke, K.- H. ; Comes. F. J. Ber. Bunsen-Ges. Phys.Chem. 1988, 92. 429.(36) Oelfke, W . C.; Gordy, W. J . Chem. Phys. 1969, 51 , 5336 .( 37 ) Khachkuruzov, G . A.; Przhevalskii, I. N . Opt. Spectrosc. 1974, 36,172; 1989, 46 , 586; 1988, 63, 685 .(38) Koput, J. J . Mol . Spectrosc. 1986, 115, 438.(39) Cremer. D.; Cristen, D. J . Mol . Spectrosc. 1979, 74 , 480.(40) Hillman, J . J.; Jennings, D. F. ; Olson, W. B.; Goldman, A. J . Mol.Snectrosc 1986. 117. 46, ~- J ~ ~~~ ~(41) Olson, W: B.; Hunt, R. H.; Young, B. W .; Maki. A. G.; Brault, J.

(42) Flaud, J . -M . ;Camy-Peyret, C .; Johns, J . W . C.; Carli, B. J . Chem.W . J . M ol . Spectrosc. 1988, 127, 12 .P h v r 1989. 9 / . I504~ -,-(43) Harding, L. B.; Ermler, W. C. J . Comput . Chem. 1985,6, 13 . Erm-ler, W. C .: Hsiuchin, C. H. ; Harding, L. B. Comput . Phys. Commun . 1988,51 , 251 .

torsional mode was also performed, and quantitatively accuratetorsional energy levels were obtained.There have been several classical trajectory calculations of theovertone-induced decomposition of hydrogen p e r~ x id e. ~ -l ~hesestudies have shown the importance of the bending degrees offreedom in the flow of energy out of the initially excited O Hstretch o vertone and also provided some evidence for incompleteredistribution of energy on the time scale for disso~iation.~Uzer et aL9J0have carried ou t several classical trajectory stud iesof the unimolecular decomposition of HOOH, using a potentialenergy surface that incorporated spectroscop ic and thermo dynamicda t a . The O H and 00 bond stretches were modeled as Morseoscillators and the OOH bends as harmo nic oscillators. Potentialcoupling between the various modes was taken into account byoff-diagonal F matrix elements (linear coupling) and by switchingfunctions describing the attenuation of the OOH bend forceconstants by the 00 and O H stretches (nonlinear coupling). Thetorsional motion was found to play an insignificant role in theintramole cular dynam ics of nonrota ting hydrogen peroxide. T heunimolecular decay rate calculated by Uzer et al. for an overtoneexcitation of vOH = 6 was consistent with statistical calculation^,^^although vibrational energy redistribution was not complete inthe time scale for dissociation. In p articular, the initially unexcitedO H bond remain s unexcited and does not receive a statisticalproportion of the total energy prior to reaction.While the classical trajectories of Uzer et al. indicate that th etorsional mode plays an insignificant role in the vO H = 6 over-tone-induced dissociation of rotationless HOOH molecules, thework of Sumpter and Thompson" has shown that internal rotationbecomes more importan t for higher excitation energies. Theimportance of coupling of internal rotation to stretching andbending modes has also been stressed by Spears and Hutchinson."Moreover, overall molecular rotation has been shown to induceboth rotation-vibration and vibration-vibration sug-gesting the possibility of increased dynamical activity of thetorsional mode at higher total angular momenta.We have recently studied the classical dynamics of H O O H forvarious potential energy surfaces and initial excitations (uOH =4, 5 , 6, 7).I3-l5 Unimolecular decay lifetimes of H O O H werefound to be sensitive to deta ils of the potential energy surfaces.I n the case of C H overtone relaxation in benzene, it is known tha tit is impo rtant to include switching functions in th e potential toattenuate the CCH bending force constants as a function of theC H bond length.46 Such attenuation induces a potential couplingwhich leads to increased localization of energy in the C H bondby an effective cancellation of the kinetic and potential couplings.47Similarly, we have found that the overtone-induced unimoleculardecay lifetime of HOOH is strongly dependent on the rate a t whichthe H O O bend force constant is attenuated by 00 s t r e t ~ h i n g . l ~ - ' ~It is therefore important to determine an accurate switching

(44) Spears, L. G.; Hutchinson, J. S. J . Chem. Phys. 1988, 88 , 250.(45) Bunker, D. L. J . Chem. Phys. 1967,91,6106. Hung, N . C.; Wilson,D. J. f. Chem. Phys. 1963,38,828. Hung, N . C. J . Chem. Phys. 1972,57,332. Parr, C . A,; Kupperman, A,; Porter, R. N . J . Chem. Phys. 1977, 66,2914. Rolfe, T. J. ; Rice, S. A . J . Chem. Phys. 1983, 79, 4863. Clodius, W.B.; Shirts, R. B. J . Chem. Phys. 1984,81, 6244. Shirts, R. B. J . Chem. Phys.1986,85,4949. Shirts, R. B. In!. J . Quantum Chem. 1987, 31, 199. Combs,J . A,; Hoover, W . G. J . Chem. Phys. 1984, 80, 2243. Uzer, T.; Natanson,G. A,; Hynes, J. T. Chem. Phys. Lett. 1985, 122, 12. Stace, A. J . Ber.Bunsen-Ges. Phys. C hem. 1977, 81 , 200. Quack, M.; Troe, J . Ber. Bunsen-Ges. Phys. Chem. 1974, 78, 240. Schlier, Ch. G. Mol. Phys. 1987, 62, 1009.Wolf, R. J .; Hase, W. L. J . Chem. Phys. 1980, 73, 3779; 1981, 75, 3809.Hovingh, W J. ; Parson, R. Chem. Phys. Lett. 1989, 158, 222. Frederick, J .H.; M cClelland, G. M.; Brumer, P. J . Chem. Phys. 1985, 83, 190. Frederick,J. H.; McClelland, G. M . J . Chem. Phys. 1986, 84, 4347. McClelland, G .M.; Nathanson, G. M .; Frederick, J. H. ; Farley, F. W . n Excired Stares; Lim,E. C., Innes, K. K ., Eds.; Academic: London, 1987;Vol. 7. Ezra, G. S. Chem.Phys. Lett. 1986, 127, 492. Sumpter, B. G.; Martens, C. C.; Ezra, G. S. J .Phys. Chem. 1988, 92, 7193. Sumpter, B. G.; Ezra, G. S. Chem. Phys. Lett.1987, 144, 144. To be submitted. Nathanson, G. .; McClelland, G. M . J .Chem. Phys. 1986,85,4311;1984,81,629;1986,84,3170Chem. Phys. Lett.1985, 114, 441; 1985, 118, 228. Farley, F. W. ; Novakoski, L. V. ; Dubey, M.;Nathanson, G. M.; McClelland, G. M. J . Chem. Phys. 1988, 88, 1460.(46) Lu , D.-H.; Hase, W. L. J . Phys. Chem. 1988, 92 , 3217 .(47) Garcia-Ayllon, A ,; Santam aria, J.; Ezra, G. S. J . Chem. Phys. 1988,89, 801.


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3998 The Journal of Physical Chemistry, Vol. 94 , No. 10 , 1990 Getino et ai.TABLE 11: Harmonic Force Constants, Calculated Harmonic Normal-Mode Frequencies, and Rotational Constants for Hydrogen Peroxide'

HF/II HF/IV HF/V M P 2 / I MP2/III M P 2 / I V MP2/V GVB+OCbF rr 9.626FRR 6.912Fh, 1.149F4 c 0.0389Frr, -0.0085FCR -0.0704Fr, -0.01 12Fr,, 0.0083FRa 0.654Fa d 0.104FR# -0.024Fr, 0.015F** 0.041

9.5877.0591.1650.0453-0.0027-0.0601-0.01780.00830.6590.094-0.0180.0160.041

9.6597.1281.1770.048-0.0038-0.0440-0.01 160.00500.6690.088-0.0100.0160.038

7.7774.7641.0020.0353-0.01 33-0.1354-0.0 12 40.01000.6250.096-0.0180.0150.039

7.2733.5430.9010.0048-0.0241-0.21430.10320.02150.5740.199-0.000010.000020.00004

8.1834.8690.9650.0391-0,001 8-0.1515-0.00370.01210.6330.0850.0160.036-0.0 13

8.2244.8080.9880.0427-0.005 1-0.14940.00430.00500.6500.075-0.0050.0160.03 1

8.1334.3470.9570.039-0.014-0.092-0.0280.0030.5750.076-0.001 20.0200.026

W , (sym O H s t ) 4152 4145 4160 3731 3602 3830 3839 3816w 2 (sym bend) 1615 1619 I625 1462 I466 1442 1455 1429u3 00 t re tch) 1149 I162 1166 928 786 932 921 887o4 torsion) 387 42 3 44 0 357 I36 371 404 383w 5 (asym OH s t ) 4153 4144 4160 3734 3614 3828 3838 3820u6 asym bend) 1474 1500 1518 1328 1143 1322 1357 1328ABC

10.7615 10.8289 10.8968 9.7903 9.6786 10.02 73 10.1 1810.9476 0.9532 0.9566 0.8698 0.8007 0.8852 0.88520.91 35 0.9242 0.93 14 0.8344 0.7241 0.8593 0.8593'Uni t s of force are mdyne, units of length angstroms, angles radians, frequencies an d rotational constants wavenumbers. The basis sets used ar eas follows: I , 6-31G*; 11, 6-31G**; 111, 6-311G; IV, 6-311G(2d,p); V , 6-311G(3d,2p). bReference25 .20 I

!0 00 0 50 1 0 0 1 5081 , ,Q) 50 a.

Figure 1 . Minimum-energy paths along 00 (circles) and OH (stars)bond stretch coordinates. Potential energy is calculated at the M P 2 / 6 -31 l G ( 3 d . 2 ~ )evel with full optimization of all geometric parameters forfixed 00 or OH bond lengths. Energies ar e in hartrees an d bond dis-placements in angstroms.as calculated by second-order Merller-Plesset perturbation theory,which also leads to an 00 equilibrium bond length which is tooshort (see Table I ) .111. Switch ing Funct ions

Figure I shows the M P2/6-31 IG (3d,2p) p otential energy alongthe minimum-energy paths (M EP's) for dissociation along the00 (circles) and O H (stars) bond stretch coordinates, obta inedby f u l l optimization of al l of the geometric parameters for fixed00 or OH bond lengths, respectively. Th e 00 MEP is ener-getically more favorable and is the reaction c oordinate pathw ayfor overtone-induced unimo lecular dissociation of HOOH;3weare interested in accurately describing the potential couplings alongthis coordinate. The OH stretch-bend potential coupling is alsoimportant in determining overtone decay dynamics,14and the OHstretch-OO H bend coupling is therefo re also of interest.The OO H bending potential is determined from energiescalculated by varying one of the bend angles over 20 about the

(53) Wahl, A. C . J . Chem. Phys. 196441 , 2600. Nesbet, R. . J . Chem.P hy s . 1962, 36, 1518.

'-0 0 0 0 6 022 0 39 0 5 5 0 1 O S 7 1 0 4 1 2 0Arm

Figure 2. Quartic bending force constant as a function of the 00 bondlength. Force constants are in hartree/rad:equilibrium angle for fixed values of the 00 or OH bond lengthsalong the M EP s. (The remaining geometric parameters are fullyoptimized.) Th e energies obtained ar e fit by using the nonlinearleast-squares method to a quadratic

v,= o.x,(e - e0)2vo = o s ~ , ( e eo12 +&(e eo14

( l a )or a quadratic-quartic function

( I b)The force constants calculated as a function of the bond lengthsare then fit to a suitable functional form. Figure 2 shows thequartic force constant CfJ dependence on the 00 bond length.Quadratic force constants (K,) obtained from both fits (eqs laan d 1b) ar e very similar, and the small magn itude of the quarticcorrection suggests tha t deviations from harmonicity are smallfor the bending angle displacements studied here.Figure 3 shows the calculated switching function (a ) for the00 bond compared to that used in previous dynamics calculationsof HOOH.9-15 In this figure, the circles are the ab initio data( K / K o ,where KO s the force constant at equilibrium) and the solidline is the fit given by

S(ro0) = exp[-1.468Aroo] (2 )


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Stretch-Bend Coupling in HOOH The Journal of Physical Chemistry, Vol. 94 , No. 10 , 1990 3999I2 0

!0 0 4 I , , , I , I , ,- C 5 0 000 5 50 30 1 5 0 2 50

A Z3Figure 3. Switching functions describing variation of HOO bend forceconstant with the 00 bond length: (a) MP2/6-311G(3d,2p) a b initioresults (this paper; the circles are the ab initio points, and the solid lineis th e fi t given by eq 2); (b) function describing HCH attenuation inCH4;48 c) a b initio results a t HF/6-31G** level.l*The second switching function (b) describes the H C H bend at-tenuation for methane4* and corresponds to

S(roo) = 1 - anh [1.531 X 10-7Aroo(roo + 4.67)*] (3)This function has been used by Uz er et al. in classical trajecto rystudies of HOOH.9910The third switching function (c) was ob-tained by a b initio calculations at the Hartree-Fock level for a6- 3 IG** basis12

S(roo) = 1 - anh [0.1205ArooS] (4)We have previously used this function in a study of the dissociationdynamics of HOOH.l3-l5There are substantial differences between the various switchingfunctions. Th e switching function (Fig ure 3a) calculated in thepresent pap er shows very strong stretch-bend coupling in theregion of small bond displacemen ts (-0. 5 < Ar < 0.5) as comparedto the other functions but decreases relatively slowly at largedistances. On the oth er hand, curve c of Figure 3 shows very weakcoupling for moderate bond displacements and abruptly decreasesto zero at larger displacements. The stretch-bend coupling de-scribed by Figure 3 b is of a type intermed iate between the oth ertwo; this function was, however, derived for the H C H bend ofmethan e and not for HO OH . The transferability of switchingfunctions from one molecule to another has been seriouslyquestioned by several authors.I1-IS As the intramolecular dynam icsof HOOH and other polyatomic molecule^^^^^^^^^ is sensitive tochanges i n the rate of attenuation of bending force constants asdescribed by switching functions of the type shown in Figure 3,it is clearly important to use functions that correctly describe thistype of stretch-bend coupling.Figure 4 illustrates the switching function for the O H bondstretch. Curv e a is the best fit to the a b initio points (stars) andcorres pond s to a function of the formS(rOH) = 0.076(1 - t anh [5 . 752 Aro ~ 0 .4501)+0.892 exp(-0.364AroH3) (Sa)although a simpler function

S(rOH) = 1 - a nh [ 0 . 0 0 8 2 3 A r o ~ ( r o ~ 1 .7 57 )3 ] (5b)was found to give a reasonable fit. Th e switching function usedby Uzer et al.48(curve b)

S(rOH) = 1 - anh [1.531 x 1 0 - 7 A r o ~ ( r o ~4.67)8] (6 )a nd on e a pp ro pr ia te for th e hy dropero xyl r a d i ~ a l ~ ~ . ~ ~curve c)

S(rOH) = 1 - tanh [ 1 . 0 2 7 9 A r o ~ ( r o ~0.797)2] (7 )are also shown in Figure 4. The param eters in eqs 2-7 areapprop riate for distances measured in angstroms.

Ii-0 50 000 0 50 00 1 50 2 00 2 50

0 OHFigure 4. Switching functions describing variation of HOO bend forceconstant with th e OH bond length: (a) M P2/6-311G(3d ,2p) ab initioresults (this paper; the stars are th e ab initio points, and the solid lineis the fit given by eq 5a); (b ) function describing HCH attenuation inCH4;48 c) function appropriate for HOO r a d i ~ a l . ~ ~ J ~

The differences between these switching functions are not asstriking as for the 00 bond coordinate. Th e ra te of attenua tionof curve a (Fig ure 4) is slower for the larg e bond displacementsthan either curve b or c.In the simplest statistical adiabatic channel (S AC ) approach54to unimolecular bond fission and the reverse association reaction,the shape of the potential surface governing dissociation dependson two parameters. The first parame ter, 6 , s the usual Morseparamete r describing th e radial interaction potential, while thesecond parameter, a, etermines the function used to interpolatethe adia batic channel eigenvalues between their equilibrium andasymptotic eigenvalues.ss In fact, a s directly related t o the radialdependence of the bending force constanP

(cf. eq 2; note the factor of 2).Application of SAC theory to a large number of neutral radicalreactions56 eads to an approximately consta nt value of the ra tioa/P close to 0.5, implying a correlation between the range of th eradial interaction potential and the switching function (8). Wolfet al.49have recently pointed out such a correlation for the H Obond rupture in the hydroperoxyl radical. Th e short range of theswitching function (Figure 4c) correlates with the short-rangeinteraction of the H + 0, association potential, where th e lattercan be understood by noting that the double bond in O2must bebroken to form the O H bond. Th e bending switching functionfor HO O H (Figure 4a) has a longer range than the function (c),which is consistent with the longer range radial interaction ex-pected for the association of H and H 0 2 adicals to form hydrogenperoxide.From th e switching function exponent 2 a = 1.4683 A-1 (cf.eq 2) and a fit of the M EP for 00 dissociation to a Mo rse functionwith 6 = 2.005 A-1,we obtain a ratio a//3= 0.37. T his numbershould be compared with th e value (0.44) used in the S AC cal-culation of the HOOH dissociation rate of ref 57.IV . Conclusions

We have reported a b initio calculations of the 00 and OH bondlength dependence of HO O bending force constants in H OO Hat th e MP 2/6- 3 11G(3d,2p) level and have determined switchingfunctio ns describing the stretch-bend potentia l couplings. Theswitching functio ns differ markedly from those used previouslyin classical trajectory calculations of HO OH d i s s ~ c ia ti o n .~ ~nparticular, the attenuation of the bending force constant by 00

K(r) = K , exp[-2aAr] (8)

( 5 4 ) Troe, J . J . Chem. Phys.( 5 5 ) Troe, J . J . Phys. Chem.(56) Cobos, C . J. ; Troe, J . J .(57) Brouwer, L. ; Cobos, C.Let t . 1985, 113, 419.Chem. Phys. 1987, 86, 6171.

1981, 75, 226.1986, 90 , 3485.Chem. Phys. 1985, 8 3, 1010; Chem.J . ; Troe, J .; Diibal, H.-R.; Crim, F.

Phys.F. J .


6/6

4000 J . Phys. Chem. 1990, 94, 4000-4006bond stretching is of BEBO forms8 and is more rapid than forthe functions previously used.We believe that the present a b initio results give an acc uratedescription of the stretch-bend coupling in HO O H . As theHOOH dissociation rate is strongly dependent on the rate ofatten uatio n of the bending force constants,14 it will be impo rtantto study the unimolecular reaction dynamics using the switchingfunctions determin ed here. Preliminary classical trajectorycalculations for rotationless HOOH, using the switching functionsof the present p ape r in the potential surfa ce of refs 14 and 15,give a lifetime for vOH = 6 of around 8 ps. Furt her details of both

(58) Johnston, H. S. Gas Phase Reaction Rate Theory; Ronald Press:New York, 1966.

the a b initio potential surface and t he classical trajectory calcu -lations will be given elsewhere.Acknowledgment. This work was supported by N SF Gr antCHE-87 04632 and by the US.-Spain Cooperative Program inBasic Sciences. Com putation s reported here were in part per-formed on the Cornell National Supercomputer Facility, whichis supported by the N S F and IB M Corp. Oth er calculations wereperformed on the University of Tennessee (UTCC) IBM 3090computer. We thank Dr. L. Harding for providing us with apreprint of his work on HO OH , Dr. W . Ha se for useful discussions

on switching functions, and Dr. J. Bloor for helpful discussionson a b initio calculations.Registry No. H202,7722-84-1.

Dipolar-Chemical Shift NMR Spectra of the Carbon-Nitrogen Linkage inBenzyiideneanlllne. Carbon and Nitrogen Chemical Shielding Anisotropies

Ronald D. Curtis, Glenn H . Penner,+William P. Power, and Roderick E. Wasylishen*Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3(Received: Septemb er 26 , 1989)

The m agnitu des and orientations of the principal components of the carb on and nitrogen chem ical shift tensors for the localizedimine moiety of the Schiff base benzylideneaniline have been determined by the analysis of dipolar-chemical shift NMRspectra. The carbon chemical shift anisotropy was determined to be 156 f ppm with 7 = 0.88 f 0.02 whereas the nitrogenshift anisotropy was found to be 545 f ppm with 7 = 0.92 f .01. The most shielded component of both th e carbon andnitrogen shift tensors is approximately perpendicular to the im ine fragment. For the imine carbon the interm ediate componentof the shift tensor is approxima tely along the C=N axis. The corresponding componen t of the nitrogen chemical shift tensoris oriented along the direction of the nitrogen lone pair. These results are compared to those available in the literature forrelated molecules. For the I3C,l4Nspin pair, the I3Cdipolar-chemical shift NMR spectrum cannot be accurately simulatedif the high-field approximation for the I4N nucleus is assumed. To circumvent this problem, a general equation is describedthat can be used to calculate the dipolar-chem ical shift NM R spectrum of a spin nucleus dipole coupled to a spin 1 nucleuswhere the high-field approximation is not invoked.

IntroductionIn the past 10-1 5 years information about the anisotropic natureof chemical shielding has become a vailable for carbon nuclei,a n d t o a le sse r e xt en t fo r n itr og en n ~ c l e i * ~ ~ ~ , ~n a variety ofmolecular environments. Generally th e principal components ofthe chemical shift tensor for any given functional group arereasonably constant or typical for the particular functional groupunder c o n s i d e r a t i ~ n . l ~ ~ ~ ~ , ~or examp le, in a series of 1 0 relativelyunstrained molecules containing olefinic carbons, Orendt et al.8cfound tha t t he most shielded compo nent of the 13C chemical shifttensor, b,,, varied between 5 an d 51 ppm; similarly, the inter-mediate component, 822, varied between 85 and 152 ppm and th eleast shielded co mpon ent, b , , , varied between 214 and 288 ppm .I n this same series of molecules the isotropic chemical shift, 6,,,

= ( b , , + 62 2 + b33)/3, has a smaller range, 116-149 ppm. Po-tentially much more information about the mechanism or originof magnetic chemical shielding at a nuclear site is available fromthe principal components of the shift tensor than from the isotropicchemical shift, particularly i f the orientation of the principal axissystem of the tensor in the molecular framew ork is known. On eof the simplest experimental techniques available for obtaininginformation about the orientatio n of the chemical shift tensor isdipolar-chemical shift N M R spectroscopy.lOJ Th e techniqueinvolves measuring the static N M R powder p attern for a spinwhich is dipolar coupled to a neighboring spin.~~*Author to whom correspondence should be addressed.Present address: Department of Chemistry, University of Guelph, Guelph,Ontario, Canada NIG 2W1.

0022-3654/90/2094-4000%02.50O

In order to characterize the carbon and nitrogen chemical shifttensors of the im ine fragment, we have analyzed the I3C and ISNdipolar-chemical shift N M R powder spectra of the I3C=l4N andl3C=I5N spin pairs in benzylideneaniline (1). This compoundwas chosen since it is easy to p repare with selective enrichmen tat either th e imine carbon or nitrogen or both simultaneously.Also, the availability of X-ray diffraction data greatly facilitates(1 ) Mehring, M. High Resolution N M R in Solids, 2nd ed.; Springer-Verlag: Berlin, 1983.(2) Spiess, H. W . In N M R Basic Principles and Progress;Diehl, P., Fluck,E. , Kosfeld, R. , Eds.; Springer -Verlag: New York, 1978; Vol. 15, p 55.(3) Veeman, W. S. Prog. Nucl. Magn. Reson. Spectrosc. 1984, 16 , 193.(4 ) Duncan, T. M . J . Phys. Chem. Ref Data 1987, 16 , 125.( 5 ) Facelli, J. C.; Grant, D. M.; Michl, J. Acc. Chem. Res . 1987, 20, 152.(6) Jameson, C. J . In Specialist Periodic Repo rt-NM R Spectroscopy;Webb, G . A,, Ed.;The Chemical Society: London, 1989; Vol. 18 and previousvolumes of this annual review.(7 ) Mason, J . In MulIinuclear NM R; Mason, J ., Ed.; Plenum Press: NewYork. 1987: OD 337-340r r ~- - -. ~( 8 j ( a ) Beeler, A. J.; Orendt, A . M. ; Grant, D. M. ; Cutts, P. W. ; Michl,J.; Zilm, K. W.; Downing, J. W .; Facelli, J. C.; Schindler, M. S.;Kutzelnigg,W. J . Am . Chem. SOC.1984, 106, 7672. (b) Facelli, J. C.; Orendt, A. M.;Beeler, A. J.; Solum, M. S.; Depke, G. ; Malsch, K. D.; Downing, J. W .;Murthy, P. S.; Grant, D. M.; Michl, J . J. Am. Chem. Soc. 1985, 107, 6749.(c) Facelli, J . C.; Orendt, A. M. ; Solum, M. S.; epke, G.; Grant, D. M. ;Michl, J. J . Am . Chem. SOC.1986, 108,4268. (d) Solum , M. S.; Facelli, J.C.; Michl, J.; Grant, D. M. J. Am . Chem.SOC. 986, 108,6464. (e) Orendt,A. M.; Facelli, J. C.; Beeler, A. J.; Reuter, K.; Horton, W. J.; Cutts, P.:Grant,D. M.; Michl, J. J . A m . Ch em . S O C.1988, 110, 3386.(9) Sardashti, M.; Maciel, G. E. J. Phys. Chem. 1988, 92, 4620.(10) VanderHart, D. L.; Gutowsky, H. S. J . Chem. Phys. 1968, 49 , 261.(11) Zilm, K. W. ; Grant, D. M . J . Am . Chem. SOC.1981, 103. 2913.

0 1990 American Chemical Societv

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Coral Getino et al- Ab Initio Study of Stretch-Bend Coupling in HOOH