H02(g2A ) Potential Energy Surface from the Double Many-Body

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H02(g2A ) Potential Energy Surface from the Double Many-Body

Transcript Of H02(g2A ) Potential Energy Surface from the Double Many-Body


J. Phys. Chem. 1988, 92, 3132-3742

nuclei interacting with Ln3+ions (in which case y in eq 3 refers to the nucleus and r to the electron-nuclear distance). As part of an NMR study of lanthanidebound micelles,we have measured the proton Ti relaxation times for SDS micelles (0.07 M surfactant) to which a variety of Ln3+ ions (0.002 M) had been added.22 The quantity of interest, plotted as hollow squares in Figure 1, is the relaxation enhancement for the CH, group in SDS
bound directly to the sulfate, defined as (l/Tl(L))- (l/Tl(’)),
where TI(La)nd are the proton spin-lattice relaxation times in the presence and absence of lanthanide, respectively. (Gd3+ was not included because it produced line widths too broad to measure properly.) For Ln3+ions the dipolar interaction typically dominates the Fermi contact term.19,23 Note that the pattern



(22) In this concentration regime TI-’ was not linear with Ln” concentration. Therefore, all measurements were carried out at the same concentration.
(23) Alsaadi, B.; Rossotti, F.; Williams, R. J . Chem. SOC.,Chem. Commun. 1980, 2147.

of dipolar Ti enhancements (hollow squares) does not match the pattern of k, values (filled squares). This argues against a significant dipolar contribution to k,.
We have measured bimolecular quenching rate constants k, for interaction of lanthanide ions with the 1,9-biradical 2. The evidence so far suggests that spin exchange is the principal quenching mechanism. The dipolar mechanism does not appear to have a major influence on the quenching. Further investigations, including the magnetic field dependence and chain length dependence of k,, and lanthanide effect on intramolecular product ratios, are in progress.
Acknowledgment. The authors thank the National Science Foundation and Air Force Office of Scientific Research for support. C.D. thanks the N S F (CHE-84-21140) for support. K.C.W. thanks the National Institutes of Health for a postdoctoral fellowship, NCI-NIH No. CA07957.

A Realistlc H02(g2A”)Potential Energy Surface from the Double Many-Body Expansion Method
A. J. C. Varandas,* J. BrandHo, and L. A. M. Quintalest
Departamento de Quimica, Universidade de Coimbra. 3049 Coimbra Codex, Portugal (Received: July 21, 1987; In Final Form: December 29, 1987)
+ - + A double many-body expansion potential energy surface reported previously for H02(R2A”)and referred to here as DMBE
I is modified to produce thermal rate coefficients for the reaction 0 OH O2 H in good agreement with experiment. This new potential energy surface will be referred to as DMBE 11. By the further imposition that the potential function should reproduce the experimentalspectroscopicforce field data for the hydroperoxylradical, another potential energy surface has been obtained, DMBE 111. Both of these improved DMBE I1 and DMBE 111 potential energy surfaces preserve the functional form used previously for DMBE I except for the long-range 0.-.OH electrostatic interaction, which is defined in the spirit of a more satisfactory adiabatic theory.

1. Introduction

The potential energy surface fo_r the electronic ground state of the hydroperoxyl radical, H02(X2A”), is important in under-
+ - + standing the chain-branching reaction (i) H O2 OH 0 + - of many combustion processesi and its reverse (ii) 0 OH
+ 0, H, both of which are also important in the HO, cycle of

atm are

ospheri studies

c c of

hemi~ isotope

try exc

. ~C. ~onnected hange4in 0

+with reactions OH and the

( v

i i

) b

an rat

d (ii) ional

relaxation5 of O2in collisions with H. It is also important for

theoretical studies of the vibrational-rotational spectroscopy of H02(R2A”) and, as a building block, for construction of the

potential energy functions of larger polyatomics (which have
ground-state H 0 2as a dissociation fragment) from the many-body expansion (MBE)6 and double many-body expansion (DMBE)’-*

methods. Thus, it is not surprising that there has been a considerable theoretical effort to arrive at a reliable potential energy surface for the electronic ground state of the hydroperoxyl radical, with use of both a b initiog-14and semiempiri~al’~-’m’ ethods.
On the experimental side, the dissociation en erg^,'^,'^ the ge-
ometry,6s20-2a1nd the quadratic force constants6-20of the hydroperoxyl radical have also been reported. An extensive list of references to spectroscopic studies by a variety of techniques

covering a wide range of the spectra can be found in ref 14. Once a reliable three-dimensional (3D) working potential energy
surface is available, it can be used for dynamics calculations by

‘Permanent address: Facultad de Quhica, Universidad de Salamanca, 37008 Salamanca, Spain.


using either the classical trajectory method4,5,22-2o9r approximate quantum mechanical t h e o r i e ~ ~ ’a.n~d~for variational transition
(1) Benson, S . W.; Nangia, P. S. Acc. Chem. Res. 1979, 12, 223. (2) Rowland, F. S.; Molina, M. Rev. Geophys. Space Phys. 1975, 13, 1. (3) Lee, Y. P.; Howard, C. J. J . Chem. Phys. 1982, 77, 756. (4) Miller, J. A. J . Chem. Phys. 1981, 75, 5349. (5) Miller, J. A. J. Chem. Phys. 1981, 74, 5120. (6) Murrell, J. N.; Carter, S.; Farantos, S.C.; Huxley, P.; Varandas, A. J. C. Molecular Potential Energy Functions; Wiley: Chichester, 1984. (7) Varandas, A. J. C. Mol. Phys. 1984, 53, 1303. (8) Varandas, A. J. C. THEOCHEM 1985, 120, 401. (9) Melius, C. F.; Blint, R. J. Chem. Phys. Lett. 1979, 64, 183. (10) Langhoff, S. R.; Jaffe, R. L. J . Chem. Phys. 1979, 71, 1475. (11) Dunning, T. H., Jr.; Walch, S. P.; Wagner, A. C. In Potential Energy Surfaces and Dynamics Calculations; Truhlar, D. G.,Ed.; Plenum: New York, 1981; p 329. (12) Dunning, T. H., Jr.; Walch, S. P.; Goodgame, M. M. J . Chem. Phys. 1981, 74, 3482. (13) Metz, J. Y.; Lievin, J. Theor. Chim. Acta 1983, 62, 195. (14) Vazquez, G.J.; Peyerimhoff,S. D.; Buenker, R. J. Chem. Phys. 1985, 99, 239. (15) Farantos, S. C.; Leisegang, E. C.; Murrell, J. N.; Sorbie, K. S.; Teixeira Dias, J. J. C.; Varandas, A. J. C. Mol. Phys. 1977, 34, 947. (16) Gauss, A., Jr. Chem. Phys. Lett. 1977, 52, 252. (17) Varandas, A. J. C.; Brandlo, J. Mol. Phys. 1986, 57, 387. (18) Howard, C. J. J. A m . Chem. SOC.1980, 102, 6937. Foner, S . N.; Hudson, R. L. J. Chem. Phys. 1962, 36, 2681. (19) Ogilvie, J. F. Can. J. Spectrosc. 1973, 19, 171. (20) Beers, Y.; Howard, C. J. J . Chem. Phys. 1976, 64, 1541. (21) Tuckett, R. P.; Freedman, P. A,; Jones, W. J. Mol. Phys. 1979, 37, 379, 403. (22) Gauss, A,, Jr. J . Chem. Phys. 1978, 68, 1689.
0 1988 American Chemical Society

A Realistic HO2(WZA") Potential Energy Surface

state3, and adiabatic ~ h a n n e ltr~ea~tm. ~en~ts; ref 34 reports also

simplified 1D short-range/long-range switching models for the

radial and angular interaction 0-OH potential in the context of

the adiabatic channel model.

Ab initio electronic structure calculations of the ground-state

H 0 2potential energy have been carried out by Melius and Blint:

Langhoff and Jaffi5,'O Dunning et al.,l'*lzMetz and Lievin,13and

Vazquez et al.I4; for references to earlier work see ref 9. Some

of these a r t i ~ l e s ' ~ *h'a~veJ ~also considered excited states of HO,.

Melius and Blintgcarried out MCSCF C I calculations and defined

a global HOzsurface by fitting the calculated points to an ad hoc

funct mol-'


ona for

l t

fo he

rm H

. +

This O2a

s d

u d

rface ition

gives reacti

a on

b .

arrier Using

of a

abo mor

u e

t 2.3 kcal extensive

C I wave function, Langhoff and JaffE'O reported no barrier for

this addition step. Dunning et a1.1'q12carried out generalized

valence bond calculations and concluded that by taking the

computational deficiencies into account, it is likely that there is

no barrier to the addition reaction. Metz and LievinI3 and

Vazquez et al.I4 concentrate on the electronic spectra and UV

photodissociation of HOzand hence do not address this barrier

problem on the ground-state potential surface of H02.

In a recent articleI7 (hereafter referred to 5s article I), we

reported a potential energy surface for HOz(X2A") using the

DMBE method. This HOZDMBE I potential surface conforms

with the a b initio data of Melius and Blintg for the three-body

energy and shows reasonable agreement with available spectro-

+ - + scopic data for the energy and geometry of the minima referring
to the equilibrium triatomic. In agreement with the best ab initio estimates, it also shows no barrier for the H O2 OH 0 reaction. In addition, the H02DMBE I potential energy surface

predicts two secondary minima that have chemical interest. One

refers to a T-shaped (C2J H-O2 weakly bound complex, while

the other is related to a linear (C-J weak hydrogen-bonded 0.6-HO

structure. Moreover, it shows the appropriate long-range behavior

of the H-O2 and 0-OH asymptotic channels being the electro-

static energy defined in the spirit of an adiabatic theory recently

proposed by Clary and Werner.31 This is particularly significant since Clary30$3h1as shown that the long-range forces are major
+ - factors in determining the rate constant for the 0 O H O2
+ H reaction. Such importance has most recently been stressed

by T r ~ ine hi~s s~tatistical adiabatic channel model. Along the

+ same direction, Wagner35has explicitly considered coupling be-
tween the long-range 0 OH spin-orbit potential curves. Despite the fact that the HO, DMBE I potential energy surface

+ - + shows some definite improvement over previous functions, it is
not completely satisfactory. For example, exploratory trajectory resultsz9for the 0 OH O2 H reaction have yielded thermal rate coefficients that significantly underestimate the best available

experimental measurements (for a critical review, see ref 36). In

contrast, similar calculations carried out on the Melius-Blint fitg

agree wellz8with the experimental results. The aim of this work

is ther_eforeto report a new DMBE potential energy surface for

H02(X2A") that overcomes such difficulty. In addition we suggest

an alternative, perhaps more satisfactory, adiabatic description

of the long-range O-OH electrostatic interaction. Finally, we show

how to make the potential reproduce the complete quadratic force

field of the hydroperoxyl radical as surveyed in ref 6 and 21, while

maintaining a good description of the rate coefficient measure-

(23) Blint, R. J. J . Chem. Phys. 1980, 73, 765. (24) Bottomley, M.; Bradley, J. N.; Gilbert, J. R. Int. J . Chem. Kinet. 1981. 13. 957. (25) Gallucci, C. S.; Schatz, G. C. J . Phys. Chem. 1982, 86, 2352. (26) Brown, N. J.; Miller, J. A. J . Chem. Phys. 1984, 80, 5568. (27) Kleinermanns, K.; Schinke, R. J . Chem. Phys. 1984, 80,1440. (28) Miller, J. A. J. Chem. Phys. 1986, 84, 6170.
(29) Quintales, L. A. M.; Varandas, A. J. C.; Alvarifio, J. M. J . Phys. Chem., in press.
(30) Clary, D. C. Mol. Phys. 1984, 53, 3. (31) Clary, D. C.; Werner, H. J. Chem. Phys. Lett. 1984, 112, 346.
(32) Rai, S. N.; Truhlar, D. G. J . Chem. Phys. 1983, 79, 6046. (33) Cobos, C. J.; Hippler, H.; Troe, J. J . Phys. Chem. 1985, 89, 342. (34) Troe, J. J. Phys. Chem. 1986, 90, 3485. (35) Wagner, A,, private communication.
(36) Cohen, N.; Westberg, K. R. J . Phys. Chem. ReJ Data 1983, 12, 531.

The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3733

n U

v n

+ - + Figure 1. Coordinates used to define the HOzpotential energy surface.
ments for the 0 O H Oz H reaction. This article is organized as follows: Section 2 outlines the
mathematical form of the energy terms in the DMBE and describes the approach used to obtain the numerical values of the parameters they contain from available ab initiogand spectroscopic6,21data. Section 3 presents a discussion of the results. The conclusions are gathered in section 4.

2. New DMBE H 0 2 Potentials
The DMBE of the potential energy for ground-state HOz has the form37,38

I/ = VEHF(R)+ Vwrr(R)


where E H F denotes an extended-Hartree-Fock-type energy that includes the nondynamical correlation due to degeneracies or near-degeneracies of the valence orbitals, and corr is the dynamical correlation energy due to the true dynamic correlation of the electrons; R = R,, R2,R3is a collective variable of the internuclear separations, which are defined in Figure 1. In eq 1, both the E H F and corr energy terms are written as a many-body expansion+

vEHF(R) = i- 1GzAF,i(Ri) + %?lF(R1,R2,R3) (2)


Vcorr(R) = fl!!r,i(Ri) + G%(R18Z?R3)



where all two-body and three-body fragments are assumed to be

in their ground-electronic states as predicted from the Wigner-

Witmer spin-spatial correlation rules; i = 1 is taken to label the

homonuclear 00 bond, and i = 2 and 3 label the two OH bonds.

A detailed review of the theory has been given e l s e ~ h e r aend~ ~ ~ ~ ~ ~ ~

will not be repeated here. Instead, we refer only to those aspects

that are essential for this work. The notation is mainly that of

article I; for further clarity, we use the initials EHF37,38rather

than HF7,s,17to represent the extended-Hartree-Fock-typeenergy.

In article I the two-body energy terms assumed the form of the

realistic EHFACE

and are thus kept unchanged in the

current work. They have the general form

+ 3

V&(R) = DR"(1 C a d ) exp(-yr)


i= 1

C v!;r(R) = -




where = - Rm is the


from the

equilibrium diatomic geometry. In eq 5, xnare dispersion damping

(37) Varandas, A. J. C. In Structure and Dynamics of Weakly Bound Complexes; Weber, A., Ed.; D. Reidel: Dordrecht, 1987; p 357.
(38) Varandas, A . J. C. Adv. Chem. Phys., in press. (39) Varandas, A. J. C.;Dias da Silva, J. J . Chem. SOC.F, araday Trans. 2 1986, 82, 593.

3734 The Journal of Physical Chemistry, Vol. 92. No. 13, 1988

Varandas et al.

TABLE I: Coefficients Used for the Ground-StateO2and OH Potentials"




0.14291 3.64459 3.92812 2.09867 3.35225 0 5.66169 2.2818 15.40 235.22 4066.24

0.13825 2.65648 1.74505 0.71014 2.54533 0 6.29489 1.8344 10.00 180.45 3685.26

nCalculated from equations 4 and 5; see also text. All values are in atomic units. bCalculated from eq 6a with ( r H 2 )= 3a: and43( r o 2 ) =

TABLE I 1 Coefficients for the Three-Body Correlation Energy"

k6 = 2.46501 (-2) 76 = k'6 = 0.68758

OH bondb*'
ks = 5.03696 (-2) 78 = k', = 0.82542

klo = 6.29438 (-2) 710 = k'lo = 0.94034

k6 = -?.7_8478 (-1)
76 = k 6 - 0.95274

00 bondsbed ks = -4.68155 (-1)
78 = k'8 = 0.94148

klo = -1.20507 (0) 710 = k'lo = 0.72379

Calculated from eq 7; units are as in Table I. Given in parentheses

are the powers of 10 by which the numbers should be multiplied, e.g.,

2.46501 (-2) = 2.46501 X

b9',, (n = 6, 8, 10) are taken equal to

unity for all diatomic fragments. c R o = 1.8344 ao. d R o = 2.2818 ao.

functions (for recent references to earlier work on dispersion damping see ref 38 and 40) defined bySv4l

XfltR) = [1 - exp(-(A,R/p) - (B"R2/P2))1" (6a)


A, =


+ B, = POexp(-P14


p = (R, 2.5Ro)/2


Ro = + 2((rX2)'l2 (rY2)'l2)


is the Le Roy42distance for the onset of breakdown of the as-
ymptotic R-"perturbation series expansion, X and Y label the
two interacting atoms, (rX2)and (ry2) are the corresponding expectation values for the squared radii of the outer orbitals of
X and Y , and ai and p i (i = 0, 1) are dimensionless universal
constants8for all isotropic interactions: a,, = 25.9528, al= 1.1868,
Bo = 15.7381, and = 0.09729. (Unless mentioned otherwise,
all values reported are in atomic units: 1 hartree ( E h )= 1 au of energy = 4.359 821 5 aJ; 1 bohr (ao) = 1 au of length = 0.529 177
A = 0.052 917 7 nm.) Table I define? the numerictl values of
the coefficients in eq 4-6 for the OH(X211) and 02(X3Z-,) dia-
tomic fragments.
Also the three-body dynamical correlation energy, which is calculated semiempirically within the DMBE framework, is defined as in article I. It is written as37938944


I3 E X R ) = C

CnXn(Ri)(l- %kn(Ri+l(mrx13)) X

i=l n=6.8,10

hn(Ri+z(mod3)) + gn(Ri+2(md 3)) hn(Ri+l(mod 3))IRT"I (7a)

gn(Ri)= 1 + k,(i) exp[-k',(')(R, - R i O ) ] (7b)

h,(Ri) = [tanh (7,,(i)R,)]q'2)


and R: is a reference geometry; for the numerical values of the

40) Knowles, P. J.; Meath, W. J. Mol. Phys. 1987, 60, 1143. 41) Varandas, A. J. C.; BrandHo, J. Mol. Phys. 1982, 45, 857.
42) Le Roy, R. J. Mol. Spectrosc. Chem. Soc. (London) 1973, I, 113.
43) Desclaux, J. P. At. Data 1973, 12, 311. 44) Varandas, A. J. C.; Brown, F. B.; Mead, C. A.; Truhlar, D. G.;Blais, C. J. Chem. Phys. 1987, 86, 6258.

TABLE III: Coefficients for the Three-Body Electrostatic Energy Term"

OH bondsb K4 = K5= 0.O883lc Kb = K; = q4 = v 5 = 2.54533

00 bondb K4 = K , = 0.0

k h = K', = 74 = 7, = 3.35225

Calculated from eq 8, with 6 = 4; all quantities are in atomic units.
bq'n (n = 4, 5) are taken equal to unity for all diatomic fragments. cK4 = K5= ( l / R 0 ) 4 with R o = R, = 1.8344 ao.

coefficients in eq 7, see Table 11.

Modifications that lead to the improved DMBE potentials of

the current work refer therefore only to the three-body E H F

energy term and to the description of the 0-OH electrostatic

energy, which is treated" separately from the rest of the three-body

E H F term. We therefore begin our discussion with this elec-

trostatic energy term.

2.1. Three-Body Electrostatic Energy. As in previous ~ o r k , ' ~ , ~ ~

the three-body electrostatic energy term is similarly represented


c?j(R1)/2c c 3


[CnGn(Ri+l(mod3)) hn(Ri+2(mod3)) +

1=1 fl=4,5

C'~Gn(~i+Z(mo3d)) hn(Ri+l(mod3))I Xn(Ri)Rr" (8a)

where ele stands for electrostatic

G,(R,) = K,R; exp[-K',(')(R, - R i O ) ]


and h, is defined by eq 7c. Note that C, represents the long-range

+ electrostatic coefficient for the atom-diatom interaction involving
the i l(mod 3) diatomic and the remaining atom of the ith pair
+ (that associated with Ri),and C',, has a similar meaning but refers
to the other atom of the ith pair with the i 2(mod 3) diatomic.
Similarly, x,,denotes the damping function of order n for the ith

diatomic fragment, which has been defined by eq 6a. Since there

is no H-00 long-range electrostatic interaction, one must have

G,(Rl) = 0; see Table 111.

F$;i As for the K,, and K',, coefficients, they are determined from

the requirement that given values for 7, and v,',


reproduce the long-range electrostatic energy that results from
the interaction between the permanent quadrupole moment (e,)

of the 0 atom and the dipole (&) and quadrupole (0,) moments

of OH; a labels the 0 center, while b stands for the center of mass of OH. Note that the quadrupoledipole interaction (ea-&) leads

to an energy contribution that varies as C4r-4,while that for the
quadrupole-quadrupole (e,+,) interaction varies as CSis,where
C4and C, are defined by4s

c4 = 74/,8,Fb[COS8b(3 COS2 8, - 1) -

2 sin 8, sin 8b cos 8, cos dab] (9)

+ cs = 3/168,8b(1 - 5 cos2 8, - 5 cos2 8b 17 cos2 8, cos2 o b +
+, 2 sin28, sin2 8, cos2 -
16 sin 8, sin eb cos 8, cos 8, cos +ab) (10)

where r is the S O H center-of-mass separation, 8, and 8b are the
angles made by the axis of the electric multipole moments with
r, and +ab is the dihedral angle between those axes; in the present calculations, the electric multipole moments for the 0 atom and O H diatomic are given the values468, = -1.60 eao2and47& = 0.656 eao and480, = 1.37 euo2,respectively. Note especially that the C,and C, coefficients depend on the atom-diatom orientation though they vanish when averaged (for a fixed atom-center of mass of the diatomic separation) over the angles 8,, Bb, and +ab
= 6,- 4b.4s
To define C4and C,, we have, in article I, followed the adiabatic theory of Clary and Werner,31which constrains the angle 8, at 0, = 0 such as to give the lowest value for the dipole-quadrupole and quadrupole-quadrupole electrostatic energies. However, Clary's approach assumes that the quadrupole axis of the 0 atom always lies along the vector connecting the atom to the center of

(45) Hirschfelder, J. 0.C;urtiss, C. F.; Bird, R. B. The Molecular Theory of Gases and Liquids, 2nd ed.; Wiley: New York, 1964.
(46) Fisher, C. F. At. Data 1973, 12, 87. (47) Meerts, W. L.; Dymanus, A. Chem. Phys. Lett. 1973, 23, 45. (48) Chu, S. I.; Yoshimine, M.; Liu, B. J . Chem. Phys. 1974, 62, 5389.

A Realistic H02(g2A") Potential Energy Surface

The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3135



N! , ,

,,.,,.,,,, ,


e , / I
0.' ' '36. ' ' 6 6 . ' '3d. ' '!go:

'150.' 'l#O*~ '2i'On' '2d0.' 'Z?Om' ,300.' '33'0: '360.

d e g r e e s

Figure 2. Optimum values of the C, and C, 0-OH long-range electrostatic coefficients as a function of the angle Ob (this may be either O2 or
O3 in the notation of Figure l ) , the angle formed by the OH axis with the line connecting the remaining 0 atom with the center of mass of OH. The three-term Fourier analysis of eq 11 is essentially indistinguishable
within the scale of the figure, and hence it is not shown.

TABLE IV: Values of the Expansion Coefficients in the Fourier
Series Analysis of Eq 11"



bo b, b2 b,
max. dev (three terms), % max. dev (four terms), %

-1.987 67 -0.393 61 -0.195 76
0.009 78
-0.000 94 1.1 0.1

-1.043 70
-0.1 15 02
0.01672 1.7 0.1

Units are


for C., and c,, respectively. Smaller in

absolute value than 0.0001 au.

mass of the OH molecule. As a result, there is a change of sign of the potential as the angle of approach of the 0 atom changes from head on with the 0 end of OH to head on with the H end of OH.
A more satisfactory adiabatic description of the long-range
electrostatic interaction is to let the electronic distribution on the 0 atom instantaneously adjust to the OH electronic charge distribution, whatever the angle of approach, so as to produce the lowest potential energy. We will follow this approach in the
present work. Since a quadrupole can be thought of as having one charge on each comer of a square with the charges alternating in sign around the square, this would correspond to a change in its angle of approach by 180'. Thus, the negatively charged
diagonal axis of the quadrupole square will be coincident with the OH axis when 0 approaches the H end of OH, b u t t h e positively charged diagonal will be coincident if the 0 end is approached. W e choose therefore, for a fixed value of ob, the value of Oa that gives the lowest interaction potential energy. Figure 2 shows the optimum values of C, and C, obtained from this procedure. They can be described in terms of a Fourier expansion:

where the coefficients for N = 6 are given in Table IV. Note

XI;, Figure 3. Contours of the electrostatic energy, eq 8, for an 0 atom
moving around an equilibrium OH with the center of mass fixed at the
origin. Contours are equally spaced by 0.01 E,, starting at A = -0.20

i <\)\\\ , I / j , c.



, ,

, I ,\

-5.0 -4.0 -3.0 -2.0 -!,l-0.o ! . O 2,o 3.0 4,O 5.0

Figure 4. Same as in Figure 3 but for a H atom moving around an equilibrium 02.

that sine terms in the Fourier series expansion vanish due to symmetry reasons. Note especially that a three-term Fourier
analysis reproduces the calculated data within 1-2% and that a conversion to the (R1,R2,R3se)t of coordinates can be made by using the pseudoangular coordinate reported in eq 11 of article
I; see also ref 38. However, rather than using qp'w,e adopt a
simpler approach that is similar to that employed for the dispersion
coefficient^.^^^^^^^ Accordingly, we parametrize eq 8 so as to
reproduce the spherically averaged values of these optimum long-range coefficients for the 0. -OHelectrostatic interaction energy. To perform numerically the sine-weighted O b averaging,
we have used a Gauss-Legendre quadrature technique, having
obtained ( e 4=) -0.929Ehao4and (C,) = -1.790Ehao5.
Figure 3 shows contours of the electrostatic energy, as predicted from eq 8, for an 0 atom moving around an equilibrium OH diatomic. A similar contour plot for the H atom moving around an equilibrium O2 is shown in Figure 4. In contrast to the electrostatic energy from article I that shows, as a polar plot in 0-OH radial distance and angle of approach, a sign change at the line corresponding approximately to a 90' insertion of 0 into
the middle of OH, the current approach produces long-range electrostatic potentials that are attractive at every angle of approach though they are least attractive for the perpendicular insertion of 0 into OH.
Although the change of sign in C, and C5of article I might affect the dynamics at low collision energies, it is hardly expected
from the magnitude of the energies involved that this sign change
may significantly alter the dynamics at high energies. Indeed, exploratory dynamics studies29on the H 0 2 DMBE I potential
+ + energy surface have shown that a small energy barrier along the
minimum energy path for the 0 OH -+ O2 H reaction was responsible for the poor agreement between the calculated thermal rate coefficients and e ~ p e r i m e n t . ~ ~ ~T~h' ~is' barrier, which also

(49) Lewis, R. S.;Watson, R. T. J . Phys. Chem. 1980, 84, 3495. (50) Howard, M. J.; Smith, I . W. M. J . Chem. SOC.F, araday Trans. 2 1981, 77, 997. ( 5 1) Deleted in proof.
(52) Frank, P.; Just, Th. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 181.

3736 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988

appears on the 0-OH spherically averaged interaction energy


curve, must therefore be removed. For this purpose a further


least-squares fit to the three-body ab initio E H F energies has been

carried out as described in the following subsection.

2.2. Nonelectrostatic Three-Body EHF Energy. As in article

I, the remainder of the three-body E H F energy assumes the form

Varandas et al.

where the prime denotes that the electrostatic energy is left out, and Qi ( i = 1-3) are the D3*symmetry coordinates defined by

Also as in article I we define yo(’) = - yl(‘)RYr,where RIref(i =

1-3) is a reference C, geometry defined through the experimental

equilibrium H 0 2geometry (denoted R: (i = 1-3); note that the

+ latter differs slightly numerically from that
follows: Rlref= Rleand Rzref= R F f = (R:

used in R3e)/2.

ref 17) as Moreover,

the value of yl(’)has been taken from the nonlinear least-squares

fit carried out in article I, while those of yl(2)= yl(3)have been

obtained through a trial-and-error procedure by carrying out linear

least-squares fits (the least-squares parameters being VO and c,,

with i = 1-33) to the remainder three-body energies which are

obtained by subtracting the sum of the three-body dynamical

correlation energy (see ref 17) and the three-body electrostatic

energy from the three-body correlated ab initio energies of Melius

and B l i ~ ~(tA. l~though the ab initio surface of Melius and Blint

gives inaccurate dissociation energies and hence is questionable

for dynamics studies, we believet7that due to a cancellation of

errors the ab initio three-body energy contributions have greater

reliability. By combining the latter with accurate semiempirical

curves for the diatomic fragments, one should therefore get an

improved description of the complete triatomic potential energy

surface.) Thus, least-squares fits to the 365 data points so obtained

have been generated until no nonphysical minima appeared in the

final potential energy function, and the corresponding barrier in
+ the 0 OH minimum energy reaction path (or alternatively in
the spherically averaged component Voof the O-OH interaction
+ potential; see later) was below the 0 OH dissociation limit; see

Figure 5. Note that this barrier separates the shallow minimum

associated with the 0...HO hydrogen-bonded structure from the

deep chemical minimum corresponding to equilibrium H02. In

our previous HO, DMBE I potential the minimum associated with

this 0. .HO hydrogen-bonded structure was separated from the

deep H 0 2chemical well by an energy barrier of at least 0.13 kcal
mol-’ (relative to 0 + O H ) located at R l = 4.60ao, R2 = 1.84ao,

+ R3 = 4.63ao. A simple way to remove the positive barrier in the 0 OH minimum energy reaction path has been to allow small adjustments
into the poo and DOH range-determining parameters of the two-

body Morse potentials used by Melius and Blintg (which are then

subtracted from the H 0 2energies to calculate the three-body ab

initio energies) while yl(2)= y1(3w) ere varied freely as discussed

above to yield the best least-squares fit. To improve the reliability

of our prediction at the equilibrium geometry of the hydroperoxyl

i:I‘I ,


Figure 5. Potential along the minimum energy reaction path as a function of the separation, in angstroms, between the 0 atom and the center of mass of OH: (-*-) Melius-Blint9 potential surface; (---) MBE”
potential surface; (-- -) DMBE I” potential surface; (. .) this work
DMBE I1 potential surface; (-) this work DMBE I11 potential surface.

TABLE V Weights Used for the Least-Squares Fitting Procedures
Related to the H 0 2 DMBE Potentials of This Worko




initio W, =

1 99

(i = exp

1-365): [-lOO~







special point







366 5.521 810 1.906955 3.614856 -0.178 168 100’

DMBE 111 ab initio points (i = 1-365): W, = 1 - e x p [ - l O O ~ ~ ~ , -( RR,:)]’
suecial uoints







366 367 368 369 370 371-373 374-379

5.521 810 2.512 1.85 2.226 492 2.283 606 2.512 2.512

1.906955 1.843 1.8344 4.542 893 7.263427 1.843 1.843

3.614856 3.457 0.99 4.542 893 7.263 427 3.457 3.457

-0.178168 -0.27 47
0.34 097 -0.20 1568 -0.19 2700 1st der
2nd der

1 Ob 1 OOOC
1000d 1000d 10000‘ 10/Fz;f

“Units are as in Table I. bOH...O hydrogen-bonded structure. Experimental binding energy of H02.6J8-21dEstimated energy from the H 0 2 DMBE I1 potential surface of the present work. e Condition of zero first derivativeat the equilibriumgeometry of H 0 2 . /Condition to impose the quadratic force constants of H 0 2 : FI1= 13’V/dR2~;F22 = a2v/aR22;F,, = a2v/aff2F; , =~ a2v/aR,aR2;F,, = a2v/aR,affF; ~~ = a2vja~~a~.

radical, we considered a least-squares weight function in fitting
+ + the nonelectrostatic three-body residual E H F energies, namely, W = 1 + 99 exp[g((Rl - RIe), (R, - R2e))Z (R3 - R3’)*)];
see Table V. Note that the diatomic Morse parameters (poo and
POH) were not specified by Melius and Blint’ for the ab initio
energies, and we adopted, somewhat arbitrarily, the values Boo
= 1.45ao-’ and POH = 1.38ao-’ in article I. To reduce the current
least-squares fitting procedure to a two-variable trial-and-error
search, we have forced the poo/@oH ratio to be equal to thats3

(53) Huber, K. P.: Herzberg, G. Molecular Spectra and Molecular Structure: Constants of Diatomic Molecules: van Nostrand: New York, 1979.

A Realistic HOZ(R2A") Potential Energy Surface

The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3737


Coefficients for the Residual Three-Body Extended-Hartree-Fock Energy Term"sb

VO = 5.8472 (0) CI = -9.8340 (-1) c2 = -2.1836 (0) cj = 3.8540 (-1) cq = 3.8215 (-2) c5 = 1.9349 (0) ~6 = -5.5602 (-1) CT = -7.1609 (-2) cg = -7.0660 (-2) cg = 6.5073 (-2)

cIO = -6.2814 (-1) c ~ I= 3.8207 (-1) c12 = 1.0142 (-1) c13 = 6.0124 (-3) c14 = 2.5117 (-2) CIS = -5.7318 (-2) ~ 1 =6 -2.0818 (-2) c17 = 8.8011 (-2)

c1g = -8.5610 (-2) ~ 1 =9 -2.7164 (-2) ~ 2 =0 -1.1228 (-2) c2I = 2.7195 (-2) ~ 2 =2 -1.5328 (-4) ~ 2 =3 -2.4537 (-3) c24 = 1.1601 (-2) ~ 2 =5 1.3576 (-3)

c26 = 7.5568 (-3) ~ 2 7= -4.4659 (-3) c2g = 6.0668 (-3) c29 = 2.0637 (-3) c3g = 1.8701 (-3) cjl = -3.9858 (-3) ~ 3 =2 2.7786 (-3) cj3 = -2.5483 (-4)

1(O(I) = -2.46683 (0) yo(') = -1.64300 (0) yl(')= 0.98202 (0) y1(2'= 0.62 (0)

yo(3)= -1.64300 (0) yl(') = 0.62 (0)

VO = 2.0245 (1) CI = -1.0827 (0) ~2 = -1.5532 (0) cj = 4.8201 (-1) cq = 9.9026 (-2) c5 = 1.2977 (0)
c6 = -4.0758 (-1) ~7 = -1.0942 (-1) cg -5.1977 (-2) ~9 = -6.5829 (-4)

~ 1 =0 -4.0323 (-1) c11 = 2.5285 (-1) c12 = -3.3377 (-3) ~ 1 =3 1.2622 (-2) ~ 1 =4 8.4826 (-3) CIS = -1.0826 (-2) ~ 1 =6 8.0499 (-4) ~ 1 =7 5.5122 (-2)

DMBE 111
c1g = -5.1866 (-2) ~ 1 =9 1.9565 (-3) ~ 2 =0 -4.6763 (-3) c ~ I = 7.6118 (-3) ~ 2 =2 -5.8673 (-4) ~ 2 =3 -3.8808 (-4) ~ 2 =4 2.1401 (-3) ~ 2 =5 -1.3589 (-4)

C26 = 1.8273 (-3) ~ 2 7= -2.7984 (-3) c2g = 3.4617 (-3)
~ 2 9 1.8739 (-4) c30 = 9.4458 (-4) cjl = -1.1727 (-3) ~ 3 =2 -9.5638 (-4) ~ 3 =3 -3.7996 (-4)

yo(') = -2.46683 (0) yo(') = -1.64300 (0) yl(l)= 0.98202 (0) yl(') = 0.62 (0)

= -1.64300 (0) yl(j)= 0.62 (0)

'Calculated from eq 12; units are as in Table I. bGiven in parentheses are the powers of 10 by which the numbers should be multiplied, e.g., 5.8472 (0) =
5.8472 X 10'.

TABLE VII: Spectroscopic Properties of the Hydroperoxyl Radical (C,Mirima)"



ab initio9 MBEI5qb



Rdao Rzlao Rdao

1.83 3.51

2.570 1.861

2.543 1.893 3.525 104.28

2.584 1.870 3.530 103.70

2.512 1.843 3.457 104.02

2.52 1.85



2.512 f 0.001


1.843 f 0.004


104.02 iz 0.24

Dissociation Energy







-0.2747 * 0.003

F,lIEhao-2 F22/EhaO-*
Fl2 I Ehao-2
F e u / EhaO-l
FZu/ Ehall-l

0.452 0.497 -0.0172 0.277 0.0941

0.375 0.418 0.0064 0.240
0.0482 -0.0607

0.522 0.329 0.0264 0.445 0.138 0.0068

Force Constants
0.426 0.273 0.0186 0.393 0.1 16 -0.0202

0.375 0.417 0.0060 0.241 0.0482 -0.0600

0.375 0.418 0.0064 0.240 0.0482 -0.0607

'The dissociation energy, in Eh, is taken relative to the three isolated atoms. R Ilabels the 00 bond distance, in ao. *The force field has been fitted to the experimental data reported in this table.

experimentally found for the isolated diatomic fragments, Le.,
&,o//~oH= 1.15. Thus, only DOH and yl(,)= y1(3w) ere system-
+ atically varied until the isotropic component of the 0-OH in-
teraction potential and the 0 OH minimum energy path were
barrier free. This procedure gave POH = 1.42ao-' and Boo =
1.633ao-' for the final fit. The DMBE potential energy surface (denoted hereafter as
DMBE 11) obtained from the above procedure is numerically defined in Table VI,while the spectroscopic force field it predicts for the hydroperoxyl radical is reported in Table VII. We note
+ - + the reasonably good agreement with the best available empirical
estimates and our own force field data from article I. Moreover, quasiclassical trajectories for the 0 OH 0, H reaction
run on this potential surface have produced thermal rate coefficients in good agreement with the best reported experimental v a l ~ e s ;a~de~tai,le~d ~des~cr~iption of these trajectory calculations
as well as those obtained on the DMBE I11 potential surface reported next will be presented el~ewhere.,~
Although the DMBE I1 potential surface shows a definite improvement over the ad hoc potential of Melius and Blint: which was fitted to their own ab initio data, it would be desirable for spectroscopic studies to have a H 0 2 potential function (DMBE 111) that reproduces the experimental quadratic force field reported

elsewhere6*21for this species. This has been accomplished by
having 10 extra conditions imposed (namely, the well depth, three first derivatives, and six quadratic force constants at the HO, equilibrium geometry) as further items in the least-squares minimization procedure. For example, a first derivative is con-
sidered as an extra data point for which the model function is the gradient of the potential energy surface with respect to a given internuclear coordinate; in the present case, such gradient will
be evaluated at the triatomic equilibrium geometry and hence is equal to zero. Thus, we suggest a least-squares fitting procedure where the ab initio energies and the experimental data are dealt with on an equal footing. To ensure that the calculated and experimental values agreed within error bars, we attributed special weights to the various items as summarized in Table V. Since the resulting function showed a tendency to develop nonphysical minima at the strong interaction region where ab initio data points are unavailable, a further point had to be given to guide the potential at such regions. We have estimated this point from the HOz DMBE I1 potential energy surface reported above. In ad-
dition, two extra points (numbers 369 and 370 of Table V) were added to prevent the DMBE I11 potential surface from developing
a small barrier (<1 kcal mol-') at the H + O2asymptotic channel;
the associated energies have also been estimated from the DMBE

3738 T h e Journal of Physical Chemistry, Vol. 92, No. 13, 1988

Varandas et al.

x de
Figure 6. Contour plots for an 0 atom moving around an equilibrium OH that lies along the x axis with the 0 end on the negative part of this axis and the center of the bond fixed at the origin. In this figure, as well as in Figure 7 , the upper plot refers to the DMBE I1 potential energy surface, while the other is for the DMBE 111 potential surface. Contours
+ are equally spaced by 0.01 Eh,starting at A = -0.277 Eh. Shown by the
dashed line (contour a) is the energy contour corresponding to the 0 OH dissociation limit.
I1 potential energy surface from the current work. We conclude this section by reporting the unweighted root-mean-square deviations for the two DMBE potential surfaces with respect to the three-body residual E H F a b initio energies of Melius and Blint: 0.0073 and 0.0121 E, for the DMBE I1 and DMBE 111potential surfaces, respectively. These values may be compared with those for the ad hoc Melius-Blint9 form and our previous DMBE I surface,17respectively 0.0116 and 0.0073 Eh. Note that the larger root-mean-square deviation for the DMBE 111 potential surface is mainly due to the form chosen for the weighting function that weights least the ab initio points near the equilibrium HO, geometry.
3. Results and Discussion
The HO, DMBE (I1 and 111) potential surfaces from the present work are numerically defined in Tables 1-111 and VI. Note that the coefficients for the three-body electrostatic energy term and the residual three-body E H F term (which are reported in Tables 111and VI, respectively) are the only ones that differ from those reported in article I; the coefficients of Tables I and I1 have therefore been given here only for completeness.
Figure 6 displays equipotential energy contours of the final HO, DMBE (I1 and 111) potential surfaces for an 0 atom moving around an equilibrium OH diatomic. Similar equipotential energy contours but for H moving around an equilibrium O2are shown in Figure 7. Note the absence of an energy barrier in the plots of Figures 6 and 7 and hence absent for both 0 approaching O H and H approaching 0,.
In Figure 8 we show equipotential energy contours for the 00 and OH stretching in HO, with the HOO angle kept fixed at the corresponding equilibrium value, while Figure 9 shows contours
- for the stretching of the two O H bonds in linear OHO. Apparent
from Figure 9 are the two minima associated with the OH. -0 and 0...HO equivalent hydrogen-bonded structures. Note, however, that the seemingly Dmhminimum at short OH distances is an artifact of the dimensionality of the graphical representation being truly a saddle point for the motion of 0 around the H end of OH. Despite the similar topographies of the DMBE I1 and

7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 l . C 2.0 3.0 4.G 5 ~ 5 6,O /.C
Figure 7. Contour plots for a H atom moving around an equilibrium O2
+ molecule with the center of the bond fixed at the origin. Contours are
as in Figure 6 , except for contour a, which refers now to the H 0, dissociation limit.

- + DMBE 111 potential surfaces at these regions of configuration
space, they show some noticeable differences, particularly con-
cerning the height of the barrier for the 0 + O H OH 0
H atom exchange reaction. Accurate ab initio calculations for

the H atom migration between the two 0 atoms would therefore

provide an important way of settling this issue.

Figure 10 shows contours for the C2, insertion of H into 0,.

Again, the DMBE I1 and DMBE 111potential surfaces show some

quantitative differences mainly near the collinear 0-H-0 geom-

etries referred to in the previous paragraph.

Figures 11 and 12 show the leading terms in the Legendre

analysis of the 0-OH and H-0, interaction potentials with the

diatomics kept fixed at their equilibrium geometries, while Figure

13 compares the V, for the 0-OH interaction with that obtained

from other treatments. Again, we have reported the results ob-

tained from both the H0, DMBE I1 and 111potential surfaces.

Note the absence of a positive barrier in the spherically symmetric

component of the O-OH interaction potential for both the DMBE

I1 and Melius-Blint potentials; see also Figure 5. For the HO,

DMBE 111potential energy surface this barrier exists, though it

is small. Note especially that the condition of no barrier in V,

+ (or, if existing, a small barrier) has been considered in the present
work a key feature for a good 0 O H dynamics.

The properties of the C, chemical minima for both the HO,

DMBE I1 and 111potential energy surfaces are gathered in Table

VII. Also shown for comparison in this table are the attributes

of the H 0 2D M B E I potential surface," those of the Melius-Blint9

ad hoc functional form, and the experimental


ticularly striking is the good agreement between the properties

from potential I1 and experiment. Table VI11 summarizes the

properties of other stationary points in the H 0 2 ground-state

potential energy surface. It is seen that all relevant chemical

structures associated with stationary points in article I remain in

the new potential, although they differ somehow quantitatively.

4. Concluding Remarks
The properties of the HO, DMBE potentials derived in the present work have been carefully analyzed by numerical methods and by graphical techniques. Whenever available, experimental information has been used to parametrize the present functions. In addition, a least-squares fitting procedure has been adopted

A Realistic H 0 2 ( ~ 2 A ”P) otential Energy Surface
0 h

The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3139


0 LD

0 M


0 .-.

















Figure 8. Contour plots for the stretching of the 00 and OH bonds in H02(g2A”)with the HOO angle fixed at 103.7’. In this figure, as well as in Figures 9-12, the plot in the left-hand side refers to the DMBE I1 potential energy surface, while the other is for the DMBE 111potential surface.
Contours are as in Figure 6 .









1n o













R2/ a0

Figure 9. Contours for the stretching of the OH bonds in O H 0 (g2A”)showing the two equivalent OH.-.O and O.--HO hydrogen-bonded structures.

Contours are as in Figure 6 .

to derive the H 0 2DMBE I11 potential energy surface that takes
the a b initio energies of Melius and Blint9 and the available
experimental spectroscopic force field data for the hydroperoxyl
radica16J8-21on an equal footing, perhaps yielding the most realistic
global representation currently available for that surface. The H 0 2DMBE I1 and I11 potentials derived in this work have
+ also been used for extensive quasiclassical trajectory calculations
of the 0 OH -+ O2+ H reaction with good success. Since a
detailed description of these calculations is presented el~ewhere?~ we refer to only the results for the thermal rate constant at T = 500 and 2000 K based on the H 0 2DMBE I11 potential surface. At T = 500 K one gets k(500) = 1.55 (f0.12) X 1013cm3mol-’ s-l, a result that is in good agreement with the best available experimental e s t i m a t e ~ ~(1~.4v5~(f~O.05) X lOI3and 1.68 (f0.06) X 1013cm3 mol-I s-l, respectively), while at T = 2000 K one obtains k(2000) = 8.58 (f0.10) X 10l2cm3 mol-’ s-l, which is

in reasonably good agreement with the experimental correlation

of Cohen and W e ~ t b e r g(k~(2~000) = 1.02 (f0.36) X l O I 3 cm3

mol-’ s-l) but somewhat too low in comparison with the most

recent estimate of Frank and Justs2 (k(2000) = 1.39 (50.38) X

1013cm3 mol-’ s-’).

Neither the DMBE I1 nor DMBE I11 potential energy surfaces

+ from the present work explicitly treat all the fine-structure states
of O(3P) OH(211). Indeed, no representations so far published

for this system have done so, including ones4that has just recently

appeared. Quantum mechanically, this can be done by a Gen-

+ try-GieseSs type analysis of
applied to 0 OH produces

th a

e long-range matrix of 36

force which when states. The diago-

nalization of this matrix as a function of angle of approach and

(54) Lemon, W. J.; Hase, W. L. J . Phys. Chem. 1987, 91, 1596. (55) Gentry, W. R.; Giese, C. F.J . Chem. Phys. 1977, 67, 2 3 5 5 .

3740 The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 ? .-t

0 W

0 LD

0 U

0 N

- 0








Figure 10. Contour plots for the C,, insertion of H into 02.Contours are as in Figure 7 .

ln I

Varandas et al. 6,5


ru -
W \
0 id-
-' 1

, m




'4. '5.






'2. '3.




'7. '8.



Figure 11. Isotropic (V,) and anisotropic (VI, V,, V,, V,, and V,) components of the 0-OH interaction potential, with the molecule ilxed at the

v,; v,; v,. v,; equilibrium diatomic geometry, for 1 Ir I9 q,. Note that r is now the distance from the 0 atom to the center of mass of OH: (-) V,; (---) V,;


(*..) ( - - - ) (-.-)

A Realistic HO2(a2A'') Potential Energy Surface 2

- N


The Journal of Physical Chemistry, Vol. 92, No. 13, 1988 3741


W \
N m

w I




. m I



'4 a



'7 a

'8 a


. '2.


'4 *



7. '8.



Figure 12. Isotropic (Vo)and anisotropic (V2,V4,V,,V,,and Vlo) components of the H a 2interaction potential, with the molecule fixed at the equilibrium diatomic geometry, for 1 5 r 5 9 ao: (-) Vo;(---) V2;(---) V4;(.-a) V,;( - - - ) V,;( - e - ) VI,,,

. '2.

'3. ' A .

3m '6.


'8. '9.


Figure 13. Comparison of Vofor the 0-OH interaction with that ob-
tained from other models. Symbols are as in Figure 5.

distance of 0 from OH [email protected] 18 doubly degenerate potential energy surfaces that include the coupling and the quadrupole axis orientation effects mentioned in section 2.1; the lowest doubly degenerate potential energy surface so obtained is therefore the adiabatic potential that should go smoothly to the Melius-Blint electronic structure calculations. Yet, although spin-orbit coupling

+ - TABLE VIII: Geometries and Energies of the Metastable Minima
+ and Saddle Points hedicted by the DMBE Potentials for the
H O2 OH 0 and Isomerization Reactionsa DMBE





T-Shaped H-O2 Structure














- -0.2012

-0.205 0

Hydrogen-Bonded OH. e 0 Structure














2.267 4.824 4.824 76.41 -0.2039
5.808 1.863 3.945 0 -0.1807

Saddle Point Structure for the H + O2Reaction




















Saddle Point Structure for the H 0 2 Isomerization














5 1.16




-0.2 332


Energies, in Eh, are taken realtive to three isolated atoms.

+ may be important and should ultimately be included in any
representation of the 0 OH interaction, it is also possible that for calculations of thermal rate constants and other macroscopic observables an explicit treatment of spin-orbit coupling may be
PhysChemEnergy SurfaceSurfaceEnergy