2037
Strong Complex Formation by HOn Radical 25, 318 (1974); (b) E. Herbst, T. A. Patterson, and W. C. Lineberger, J. Chem. Phys., 61, 1300 (1974). (3) R. M. Hochstrasser and A. P. Marchetti, J. Chem. Phys., 50, 1727 (1969). (4)R. R. Sardzewski and W. E. Fox, Jr., J. Am. Chem. SOC., 96, 304 (1974). (5) (a) N. G. Adams, D. K. Bohme, D. B. Dunkin, F. C. Fehsenfeld, and E A . Ferguson, J. Chem. Phys., 52,3133 (1970); (b) E. E. Ferguson, D. B. Dunkin, and F. C. Fehsenfeld, ibid., 57, 1459 (1972). (6) P.K. Pearson, H. F. Schaefer, ill, J. H. Richardson, L. M. Stephenson, and J. I. Erauman, J. Am. Chem. SOC., 96, 6778 (1974). , (7) For an example of the importance of nitrogen oxides in the atmosphere,
see G. Brasseur and M. Nicoiet, Planet. Space Sci., 21, 939 (1973). (8) S.Huzinaga, J. Chem. Phys., 42, 1293 (1965). (9) T. H. Dunning, J. Chem. Phys., 53, 2823 (1970). (IO) G. Herzberg, “Spectra of Diatomic Molecules”, Van Nostrand-Reinhold, New York, N.Y., 1950. (11) H. F. Schaefer, “The Electronic Structure of Atoms and Molecules”, Addison-Wesley, Reading, Mass., 1972. (12) S. Rothenberg and H. F. Schaefer, Mol. Phys., 21, 317 (1971). (13) G. D. Gillispie, A. U. Khan, A. C. Wahl, R. P. Hosteny, and M. Krauss, J. Chem. Phys., 63,3425 (1975). (14) G. Herzberg, “Electronic Spectra of Polyatomic Molecules”, Van Nostrand-Reinhold, New York, N.Y., 1966.
Theoretical Calculation of Strong Complex Formation by the H02 Radical: H02*H20and H02*NHsia E. J. Hamilton, Jr.,+lb and C. A. Naleway Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received February 20, 1976) Publication costs assisted by Argonne National Laboratory
Exploratory ab initio calculations using a minimal basis set support the existence of the H02*H20 and HO2. NH3 complexes, as proposed earlier by experiment. For the minimum energy configurations having HO2 as the H donor within a linear H-bond structure, electronic stabilization energies of 9.1 and 12.0 kcal/mol are calculated for HOyH20 and HOz-NHs, respectively, compared with 5.3 kcal/mol for ( H 2 0 ) ~Values . of AH” and AS’ for the complex formations are estimated and found consistent with available experimental data. A plausible model is proposed to explain the reactivity of these complexes. These calculations indicate that in the troposphere a significant fraction of the HO2 is complexed with H2O.
Introduction Recent experiments in this laboratory2 have revealed that the observed rate of the atmospherically i m p ~ r t a n tself~,~ reaction of HO2 in the gas phase is increased by up to a factor of -2.5 (at -298 K) in the presence of a few Torr of H2O or NH3. Various considerations have led to the inference that this phenomenon is due to the formation of 1:l complexes HO2 + H2O e HO2 * H20
(1)
HO2 + NH3 e HO2 NH3 (2) which are more reactive than uncomplexed HO2 toward a second uncomplexed HO2 r a d i ~ a lBased . ~ on a kinetic model for this system, a preliminary equilibrium constant for (2) of K p 95 (based on a Po = 1atm standard state) at -298 K has been derived from the data.5 In connection with this proposed explanation of the data, ab initio calculations on hydrogen-bonded HOyH20 and HOyNH3 complexes have been carried out and equilibrium thermodynamic parameters for (1)and (2) estimated.
-
Ab Initio Calculations In the Hartree-Fock calculations reported here, a minimal Gaussian basis set [3s lp/ls] expansion was employed. The primitive basis consisted of a (10s 5p) expansion on the oxygen and nitrogen sites, while a (5s) expansion was used on the hydrogens. This primitive basis set is of essentially atomic double-l quality. The contraction scheme, composed from a
concatenation of Whitten’$ s-type orbitals with Huzinaga’s7 p-orbital set, has been outlined in detail earlier.x An effective Slater exponent of { = 1.2 for all hydrogen orbitals was found to be near optimum for each monomer. This basis set is equivalent to that employed in previous studies of hydrogen bonding in the molecular series HF, HzO, and N H S . This ~ basis set expansion yields a stabilization energy in good agreement with experiment (see next section) for the closedshell (H2O)z sy~tem,~JO although the approximate character of this basis expansion dictates that this agreement is partially due to a cancellation of errors. It has been the authors’ premise that agreement such as that found earlier could be extended to complexes between an uncharged radical and a neutral polar molecule wherein the open shell system is primarily removed from the region of H bonding. Essentially experimental monomer geometries were held rigid for all calculations. The geometry used for the water monomer has an 0-H bond length of 0.957 A and an H-0-H angle of 104.52’. The ammonia geometry has an N-H bond length of 1.012 A and an H-N-H angle of 106.7’. The HOz geometryll has an 0-0 bond length of 1.34 A, an 0-H bond length of 0.96 A, and an 0-0-H angle of 100.0’. Self-consistent field molecular orbital calculations were performed following Roothaan’s formalism for open-shell systems1* using the MOLE LCAO-MO program package. The SCF energies for the H20, “3, and HO2 monomers were calculated as -75.976 221 3, -56.142 436 9, and -150.101 432 0 hartrees, respectively. The Journal of Physical Chemistry, Vol. 80,No. 18, 1976
2030
E. J. Hamilton and C. A.
0
TABLE I HOzmH20 Geometric Search
n
.... .... ................................ ................................
&? H
64-80
I
(b)
...........
H
RN0+
Flgure 1. Calculated minimum energy geometries. (a)H02.H20: Roo = 5.246 bohr, 0 = 176O, $ = 9 0 ' . (Note that when d, = 0 or 180°,the Hopplane contains the C2 axis of H 2 0 for all values of 0.) (b) HO2-NH3: RNO= 5.196 bohr, $ = .'0 (The HO2 plane contains one N-H bond.)
Population Differences -0.02740
H t0.0183
?lo.............."... f0.0330 .. ,/
-0.0185
H-
-0.0230
H'+ 0.0 I76 -0.041 1
N.................+0.0365 ...H-
H < ~ ~ ~ 9 , 4
/
0
I
-0.0326
-00107
...............+O ...0262 0.. H-
/
0, deg
5.386 5.386 5.386 5.386 5.386 5.386 5.386 5.386
120 125 130 135 145 155 180 185
0 0 0 0 0 0 0 0
-8.81
4.786 4.986 5.186 5.246 5.386 5.586
180 180 180 180 180 180
0 0 0 0 0 0
-7.15 -8.36 -8.92 -8.95 -8.84" -8.48
5.246 5.246 5.246 5.246 5.246
165 170 175 180 185
0 0 0 0 0
-8.90 -8.94 -8.96 -8.95" -8.92
5.246 5.246 5.246 5.246 5.246 5.246 5.246 5.246 5.246 5.246 5.246
175 175 175 175 175 1'75 175 175
180 150 135 120 100 90 80
175
45 30
-8.92" -8.80 -8.91 -8.89 -8.93 -9.07 -8.94 -8.91 -8.94 -8.84 -8.96"
4, deg
aEoelec,kcal mol-1
-6.76 -7.18 -7.55 -7.84 -8.30 -8.60 -8.84
60
175 175
0
HOyNHs Geometric Search
0
Htoo184
-00118
Roo, bohr
I
+--Roo-+ o-------ROo-+
.b
Naleway
H
I
0
-0 0223
H -0 0 0 9 3 Figure 2. Population
for equilibrium configurations. These difference maps correspond to changes in charge distribution upon complexing. For comparison, (H20)2 at the same basis set level is included. [Note that in both the H02-NH3 and (H20)2 representations, one H atom of the proton acceptor is hidden.] The Mulliked5 atomic charges on the monomer atoms were calculated as: HO2-H, +0.43, O(central), -0.37, O(end), -0.06; HzO-H, +0.36,0, -0.73; NHB-H, +0.30, N, -0.91. {Jsing such calculated Mulliken15 atomic charges, Kollman and Allen9J6have found that for hydrogen-bonded complexes involving first-row hydrides, greater stabilization energy was correlated with greater positive charge on the atom in the proton donor and with greater negative charge on the heteroatom in the proton acceptor. Thus, for HOz-HzO and H02.NH3, the most stable structures should have HOz as the proton donor. This conclusion is also experimentally supported by the equality of the extinction coefficients a t 230 nm for HOz and the complexe~.~~5J7 A potential energy surface search was carried out for each complex to obtain the equilibrium configuration, within the The Journal of Physical Chemistry, Vol. 80, No. 18, 1976
RNO, bohr
4, deg
AEoelec, kcal molt1
4.946 5.046 5.196 5.246 5.446 5.646
0 0 0 0 0 0
-11.30 -11.74 -11.96 -11.95 -11.58 -10.99
5.196 5.196 5.196 5.196
0
20 40 60
-11.96" -11.86 -11.86 -11.83
a Duplication of equivalent geometries in this table is done as an aid t o the reader.
restriction of a linear hydrogen-bond structure with HO:!as the H donor; for HOrHzO, there was the additional restriction that the linear H-bond axis be contained in the a; plane of the HzO that is perpendicular to the HzO molecular plane; for HOyNH3, there was the additional restriction of collinearity of the C3 axis of NH3 and the linear H-bond axis. Optimization of the HOz-HzO complex required the variation of one intermolecular distance (Roo)and two intermolecular angles (0 and 4),while for the HOyNH3 structure this required the variation of one intermolecular distance (RNo)and one rotational angle ($1 about the H bond. These coordinate representations are defined in Figure 1. For each complex, a geometry of lowest computed energy was obtained by successive variation of the above intermo-
Strong Complex Formation by HO:, Radical
2039
H2O + H2O =+ (H20)z
TABLE 11: Calculated AHo Contributions at 298.16 K (kcal mol-')
Separation of hEo into translational, rotational, vibrational, and electronic components leads to21
AE" vib
Reaction
intra6 AH" molec intermolec AEoelec (ca1cd)f AH" (exptl)
-3.6 -3.8g 4.2 (3)b -5.27d -9.07e -7.4 4.05c -11.96e -10.3 a From frequencies in tin Nz matrix from ref 23. An estimate based on the results of several theoretical calculations; see text. Approximated as equal to a o v l b for (3). From ref 10. e This work. f From (4). g From ref 30 and 31; see text. 3
'
(3)
AE" + A(PV) = A E O t r a n s + AE'rot f A E O v l b + AEoelec4- A ( P V )= -4RT + A E o v l h + AEoelec = -2.370 kcal mol-l + A E o v l b -t hEoelec (4)
AH" =
-0.150a
1 2
lecular coordinates as shown in Table I. A minimum geometry for the HOyH20 complex was found (interpolated) a t Roo = 5.246 bohr, 0 = 176", and 4 = 90" with a stabilization energy ( 3 AE"elec) of -9.07 kcal/mol,lg while the optimized geometry for the H02.NH3 complex was calculated to be RNO= 5.196 bohr, 4 = Oo, with A E o e l e c = -11.96 kcal/mol. Considerable electronic relaxation (relative to the monomers) is evident from examination of the electronic structure of the complex. As a means of illustrating the extent of this electronic migration, a Mulliken population difference analysis15 is shown in Figure 2 for the two optimized complex configurations. A further analysis of the wave functions associated with the complexes indicates that the electron density of the unpaired electron remains primarily localized on the thus supporting our initial premterminal oxygen of ise. The restraints of a minimal basis set were examined in relation to a pair of calculations performed on the H02.H20 system using a somewhat larger (split-out) basis [5s 2p/2s]. The results of these two calculations a t Roo = 5.246 bohr, 0 = 175", a n d 4 = 90 and 0" yielded stabilization energies of -11.86 and -11.76 kcal/mol, respectively. These higher stabilization energies (by 2.8 kcal/mol) are consistent with the basis set characteristics observed with (H20)2, for which extension of the basis set as described above increased the stabilization energy from -5.3 to -7.5 kcal/mol.lO This suggests comparable reliability for the minimal basis set results on HOyH20 and (HzO),. Estimation of AH"a n d A S o In this section, AH" and AS" (units are per mole of complex) at 298.16 K are estimated for (l),(2), and the reaction
for (1)-(3), where RT/2 has been allotted to each degree of translational and rotational freedom. The AE"elec values were calculated above for the HO2 complexes and in ref 10 for (H20)2.Within the harmonic oscillator approximation, each normal vibration (vi) will contribute22 hvi[l/2
+
- 1)-l]
(ehvl/RT
2 RT
(5)
to the internal energy. Of the 3n - 6 vibrational modes in each complex, six "intermolecular" modes are expected to be low frequency due to relative motion of the two entire component molecules; the remaining 3n - 1 2 ("intramolecular7') frequencies should be similar to the equal number of vibrational frequencies of the two isolated component molecules. Separating A E o v l b in this manner, A E o v l b = A E O l n t r a + A E " 6 Inter. From the fundamental frequencies observed for HzO and (H20)2 in an N2 matrix,23AEolntrais approximately -0.150 kcal mol-l for (3). The intermolecular normal mode frequencies of (H20)z have not been experimentally determined but have been theoretically predicted from several ab initio and empirical potential^.^^-^^ These predictions lead to values of A E 0 6 Inte; for (3) in the range 4.0-5.1 kcal mol-l (the classical, lower limit is 6RT = 3.555 kcal mol-1);28 from consideration of the reliabilities of the various theoretical treatments based upon the accuracy of prediction of other (H20)z proper tie^,^^ we estimate A E o 6 ,nter = 4.2(3) kcal mol-l in Table 11. For both (1)and (2), AE"vib is set equal to that for (3), which should be reasonable approximation^;^^ the AH" values then calculated from (4) are listed in Table 11. For (3), AH" (calcd) is consistent with the value AH" (exptl) = -3.8 kcal/mol obtained in two recent studies",31 (which assumed AH" constant over the temperature ranges 423-673jn and 285-400 K3l). Separation of the translational, rotational (external), vibrational, and electronic contributions to the total entropy gives22 Sotot
= Sotrans
+ S o r o t f S'vih + S'elec
(6)
In the rigid rotor and harmonic oscillator approximations,
TABLE 111: Calculated Entropiesa at 298.16 K (cal mol-' K-l) S'vih
SotranS Sorotb intramolec
6 intermolec
Soelec
Sotot(calcd)k
Sototiexptl)
__
HzO
34.611 10.453 0.008d 0 0 45.072 45.11' 11.433 0.128d 0 0 46.004 46.011 34.443 36.416 16.868 0.082e 0 HOz 1.377 54.743 21.227c 0.015f 12.5 (20)h (HzO)2 36.677 0 70.4 69.6,m72.zn HOyH20 37.714 23.607 0.09og 12.5L 1.377 75.3 HOyNH3 37.656 23.624 0.210s 11.71 1.377 74.6 a. Gaseous standard state, P = 1 atm. From geometries used or determined in this work. From geometry measured in ref 32. From the fundamental frequencies given in ref 33. e From the fundamental frequencies given in ref 34. f Assuming frequencies shifted from those of HzO by the same shifts as observed in an N2 matrix (ref 23). Approximated as equal to the sum of the corresponding values for the two separate molecules. An estimate based on the results of several theoretical calculations;see text. Approximated as equal to the corresponding quantity for (HzO)z. Approximated as equal to the corresponding quantity for (H2O)z minus R(1n 3 - In 2); see text. From (6). From ref 35. From ref 30. From ref 31. "3
'
J
The Journal of Physical Chemistry, Vol. 80, No. 18, 1976
2040
E. J. Hamilton and C. A. Naleway
standard formulas are available for the' above contributions,22 and the calculated results for the species involved in (1)-(3) are shown in Table 111. As with AE0,ib above, S o v i b = Sointra f S O 6 Inter. For the complexes, the S O 6 inter are large and uncertain. The various theoretical predi~tions2~-~7 of the six intermolecular vibrations for (H20)2lead to values of S O 6 in the range 8.4-14.0 cal mol-l K-1;28 as above for the internal energy, we estimate S O 6 inter = 12.5(20)cal mol-l K-l in Table 111. S06interfor H02sH20 is approximated also as 12.5 cal mol-' K-l, while for H02-NH3this figure is reduced by R (In 3 - In 2) because of the increased effective symmetry of the internal rotation (about the H-bond axis) motion which is probably occurring in these c o m p l e x e ~As . ~ shown ~ in Table 111,the calculated total entropies of H2O and NH3 are in excellent agreement with experiment, while for (H20)2 the calculated value is consistent with the two experimental measurements.30,31 The above calculations give for (2) at 298.16 K the value AGO = -2.5 kcal mol-', while the preliminary experimental value for the equilibrium constant mentioned earlier corresponds to AGO = -2.7 kcal mol-l. This small disagreement is certainly less than the uncertainty one would associate with the theoretical value. Nevertheless, the apparent accuracy of the theoretical calculations for (2) and (3) suggests that the results for (11,for which experimental thermodynamic data are as yet unavailable, are reliable. We note, then, the atmospherically relevant prediction of this work that at 298.16 K and 100% relative humidity ( p ~ =~ 23.76 0 Torr), approximately 3.5%of the HO2 is calculated to be complexed with HzO.
for a longer time (due to enhanced hydrogen-bonding possibilities), during which a reactive orientation of the two HO2 may be realized. This speculation is supported by the calculated electron migration in going from the monomers to the complexes (Figure 2), which would seem to favor further hydrogen bonding, and by the very low barrier to rotation about the hydrogen bond in each complex (Table I), suggesting some flexibility in the reactant encounter pairs of (7).
Acknowledgment. We thank A. C. Wahl for his active interest and support of this program. We are also grateful to L. L. Shipman for pointing out several references and for constructive criticism of our original manuscript, to C. D. Jonah for providing a moment of intertia program, to M. E. Schwartz for his assistance in establishing the MOLE program package at Argonne, and to J. M. Williams for use of his ORTEP-based plotting system. References a n d Notes (1)(a) Based on work performed under the auspices of the U.S. Energy Research and Development Adminlstration. (b) Present address: Research Staff, Ford Motor Company, Dearborn, Mich. 48121. (2)E. J. Hamllton, Jr., J. Chem. Phys., 63, 3682 (1975). J. G. Calvert and R. D. McQuigg, Int. J. Chem. Klnet., 7 (Symp. l),113 ._
(1975). H. Levy (I, Adv. Photochem., 9,369 (1974). E. J. Hamilton, Jr. and R. R. Lii, to be submitted for publication. J. L. Whitten, J. Chem. Phys., 44,359 (1966). S.Huzinaga, J. Chem. Phys., 42, 1293 (1965). M. E. Schwartz, Chem. Phys. Lett., 6, 631 (1970). P. A. Kollman and L. C. Allen, J. Am. Chem. Soc., 93, 4991 (1971). P. A. Kollman and L. C. Allen, J. Chem. Phys., 51, 3286 (1969). The 0-0bond length was taken from ref 12;the graph In ref 13 was then used to obtain the two other parameters. H. E. Hunziker and H. R. Wendt, J. Chem. Phys., 60, 4622 (1974). J. T. Hougen, H. E. Radford, K. M. Evenson, and C. J. Howard, J. Mol. Spectrosc., 56,210 (1975). C. C. J. Roothaan, Rev. Mod. Phys., 32, 179 (1960). R. S.Mulliken, J. Chem. Phys., 23, 1833 (1955). P. Kollman, J. McKelvey, A. Johansson, and S.Rothenberg, J. Am. Chem. Soc., 97,955 (1975). This observation suggests that the complexing site in HOZ is not at the chromophore (the 0 end of the radical). From ORTEP plots (C. K. Johnson, ORNL). A few calculations on the "inverse" hydrogen bond structure H20 (donor)-H02(acceptor), where the terminal oxygen of HOZ is Involved in H bonding, showed only marginal electronic stabilization of the order of 1.0 kcal mol-'. The Mulliken atomic population associated with the open-shell orbital of HOPchanged by less than 1 % upon complexation. L. J. Schaad, "Theory of the Hydrogen Bond", in "Hydrogen Bonding", M. D. Joesten and L. J. Schaad, Ed., Marcel Dekker, New York. N.Y., 1974, p 88. G. N. Lewis and M. Randall (revised by K. S.Pitzer and L. Brewer), "Thermodynamics", 2nd ed, McGraw-Hili, New York, N.Y., 1961,Chapter 27. A. J. Tursi and E. R. Nixon, J. Chem. Phys., 52, 1521 (1970). The present work does not include calculation of intermolecular force constants because of the excessive computer time required and because of the sensitivity of results to the basis set (ref 26). J. C. Owickl, L. L. Shipman, and H. A. Scheraga, J. Phys. Chem., 79,1794
Discussion a n d Conclusions The theoretical results reported here constitute strong, independent support for the explanation of reported2 and concurrent5 experimental results in terms of H02sH20 and HOYNH3 complexes, since the experimental evidence for these complexes is quite indirect. Specifically, the calculated and experimental values of AGO at ~ 2 9 K 8 for (2) agreed closely; also, a greater stability of H02.NH3 than H02.Hz0, which is experimentally suggested by a larger NH3 than H2O effect on the reaction rate, is calculated in this work. From this work, it is strongly indicated that at temperatures and humidities relevant to the troposphere, a significant fraction of the HO2 is complexed with H2O. This substantially affects the rate of the HOz s e l f - r e a c t i ~ n ,which ~ . ~ is a very important chain termination process in the t r ~ p o s p h e r e . ~ , ~ The HOyH20 species, which will likely exhibit reactivity different from HO2 in other reactions as well, must be included in a complete model of the lower atmosphere. In the calculated geometries of H02mH20 and H O Y N H ~the , H of the HO2 is hydrogen bonded. Thus, due to steric hindrance, the reaction probability for transfer of this H atom would be expected to be reduced. Yet, as stated in the Introduction, it has been inferred from experiment5 that the reactions
+ HO2 HOa + HO2 HO2
*
H20
(74
+
NHB
(7b)
+
are faster than the reaction H02
+ HO2
+
H202 + 0
2
(8)
We speculate that this is because the steric hindrance to the transfer of the H atom of one HOz is outweighed by the following effect: relative to the situation for (a),a reactant encounter in (7) should hold two H 0 2 radicals in close proximity The Journal of Physical Chemistry, Vo/. 80, No. 18, 1976
(1975).
L. A. Curtiss and J. A. Pople, J. Mol. Spectrosc., 55, 1 (1975). C. Braun and H. Leidecker, J. Chem. Phys., 61, 3104 (1974). As Owicki et al. have discussed for (H20)z,25the harmonic oscillator model is expected to be only a crude representation of reality for the six intermolecular vibrations-by not taking into account vibrational anharmonicities and the low barriers to interconversion among isoenergetic minima, this model should underestimate the stability of (H20)2in the calculation of both the enthalpy and the entropy. In support of these approximations, we note the opposite signs of two major effects on the six intermolecular frequencies (vi) in going from4HzO)p to H02.Hz0 and H02.NH3: the increased electronic interactions should give generally Increased force constants and higher vi, while the change in Droton donor from H20 to H02 should give generally increased effective masses and lower PI. (30) G. S.Kell and G. E. McLaurln, J. Chem. Phys., 51,4345 (1969). (31)F. T. Greene, J. Beachey, and T. A. Milne, U S . Office of Saline Water, Research and Development Progress Report, No. 772 (1972). (32)T. R. Dyke and J. S.Muenter, J. Chem. Phys., 60, 2929 (1974). 1331 D. R. Stull and H. ProDhet, 2d ed Natl. Std. Ref. Data Ser., Natl. Bur. Stand., No. 37, (1971). (34)T. T. Paukert and H. S.Johnston, J. Chem. Phys., 56, 2824 (1972). (35)R. C. Weast, Ed., "Handbook of Chemistry and Physics", 56th ed, The Chemical Rubber Co., Cleveland, Ohio, 1975. I
,
