J. Phys. Chem. 1996, 100, 15087-15095
15087
Ab Initio and NMR Study of Peroxynitrite and Peroxynitrous Acid: Important Biological Oxidants Hui-Hsu Tsai,† Tracy P. Hamilton,*,† Jyh-Hsin M. Tsai,‡ Mark van der Woerd,§ Joseph G. Harrison,‡ Michael J. Jablonsky,| Joseph S. Beckman,⊥ and Willem H. Koppenol# Department of Chemistry, Department of Physics, Center for Macromolecular Crystallography, ComprehensiVe Cancer Center NMR Core Facility, and Department of Anesthesiology, UniVersity of Alabama at Birmingham, Birmingham, Alabama 35294, and Department of Inorganic Chemistry, ETH, Zurich, Switzerland ReceiVed: April 12, 1996X
The peroxy isomers of nitrate and nitric acid, peroxynitrite and peroxynitrous acid, are studied with ab initio and density functional methods. The results are compared to the observed Raman and 15N NMR spectra. The harmonic vibrational frequencies, NMR chemical shifts, and energies clearly favor cis ONOO- as the most stable and predominant ONOO- isomer. Peroxynitrite has a large rotational barrier of ∼24 kcal/mol because of partial π-bonding in the central bond. This is confirmed by a bond order of 1.5 for cis and trans ONOO- computed by electron density analysis. Electron correlation is critical in accurately predicting the relative energies for this system, as Hartree-Fock predicts a lower triplet state. The intense, broad band in the solution Raman spectrum centered at 642 cm-1 is predicted to be too low by 100-150 cm-1 if the vibration is the cis torsion. Resolution of this discrepancy is attempted by estimating the effects of solvent and anharmonicity. The results on ONOO- are compared to those for ONOOH, which is adequately described by lower levels of theory. The planar cis-cis isomer of ONOOH is the lowest energy structure by 1-2 kcal/mol.
Introduction Peroxynitrite (ONOO-)1 is a biological toxin found by the reaction of nitric oxide1 and the superoxide anion.2 It is also formed by UV-induced rearrangement of the nitrate ion and imparts a yellow color to alkali nitrate crystals.3 Peroxynitrous acid (ONOOH)1 is formed in the body by protonation of ONOO- and has a lifetime of 3 s at neutral pH, whereas ONOO- is stable for weeks in basic solutions.4 ONOOH is also a proposed reaction product of OH and NO2 in the atmosphere.5 Decomposition of ONOOH into HO2 and NO would impact stratospheric ozone chemistry. Early research on peroxynitrite and peroxynitrous acid consists of the UV spectrum in solution,6 the finding that ONOOH forms nitric acid spontaneously,7 and an unsuccessful attempt to detect ONOOH in the gas phase.8 The currently realized importance of ONOO- and ONOOH has now inspired a recent flurry of theoretical and experimental studies. HartreeFock self-consistent-field (HF) calculations were first published on ONOO- in 1990 by Shen et al.9 They also studied the ONOO--water complex and ONOOH at the Hartree-Fock (HF) level of theory. The first HF study of ONOOH was reported by McGrath et al. in 1988, with emphasis on atmospheric chemistry.10 In 1991 Lee et al. subsequently reported detection on ONOOH by matrix isolation IR spectroscopy,11 with the conclusion that the spectra matched those predicted for the isomer of ONOOH that McGrath called cisperp. This configuration had the lowest energy of the six that McGrath et al. examined at the HF/6-31G* level. They were also the first to do correlated calculations on ONOOH, but only †
Department of Chemistry, University of Alabama. Department of Physics, University of Alabama. Center for Macromolecular Crystallography, University of Alabama. | Comprehensive Cancer Center NMR Core Facility, University of Alabama. ⊥ Department of Anesthesiology, University of Alabama. # Department of Inorganic Chemistry, ETH. X Abstract published in AdVance ACS Abstracts, August 15, 1996. ‡ §
S0022-3654(96)01091-X CCC: $12.00
on the cis-perp geometry in their 1988 paper. Koppenol and Klasinc12 studied the rotational barrier for the cis to trans conversion in the anion and in the acid at the HF/6-31G** level of theory. They found that the ONOOH cis to trans isomerization has an activation barrier of 12 kcal/mol, which is consistent with the fact that ONOO- is short-lived at physiological pH and temperature. They also predicted that the anion torsional barrier is 16 kcal/mol. Kinetic studies indicate an overall activation energy of 18 ( 2 kcal/mol for decomposition of ONOO-.13 Some studies on the salts of ONOO- have recently been made, i.e. the synthesis of the tetramethylammonium salt with 97% purity14 and the IR study of ONOOM in a frozen argon matrix (M ) Li, Na, and K) with many different isotopomers.15 McGrath and Rowland (1994) considered nine structures of ONOOH at much higher levels of theory.16 The first lines in the experimental IR spectrum were assigned to the trans-perp form, despite the fact that this structure is 3 kcal/mol higher than their coplanar cis-cis structure (using G2 energies), indicating that at least two forms were trapped in the frozen argon matrix.11 In 1994, Lo and Lee found additional IR lines that were assigned to the planar cis-cis ONOOH.17 In 1994, Krauss employed multiconfiguration SCF (MCSCF) in a theoretical study of the rotational barrier and electronic spectra of ONOO-.18 Krauss also considered different channels for the dissociation of ONOO- in photoisomerization mechanisms. This paper reports the HF, second-order perturbation theory (MP2), coupled cluster, and density functional study of the vibrational frequencies and energetics of ONOO-, for comparison with the Raman spectra reported in 1994 by Tsai et al.19 It will be shown that high levels of electron correlation are essential for a correct description of ONOO-. This is especially evident in the variations of predicted bond lengths. Protonation energies were obtained by computing the energy differences between ONOO- isomers and their related acid forms. The difference in protonation energies will be related © 1996 American Chemical Society
15088 J. Phys. Chem., Vol. 100, No. 37, 1996 to the experimental observation of two pKa values for ONOOH.20 The HF and Møller-Plesset second-order (MP2) perturbation theory 15N NMR chemical shifts of ONOO- are also calculated and compared to the experimental spectrum reported here. Finally, comparisons will be made with the isoelectronic FONO and valence isoelectronic ClONO molecules.
Tsai et al. TABLE 1: Energies in Hartrees and Relative Energies in kcal/mol (with Zero-Point Vibrational Energy Added to Relative Energies) of ONOOHF/6-311+G(d) MP2/6-311+G(d)
Theoretical Methods Standard Pople group basis sets employed in the study were 6-311++G(d,p),21,22 and 6-311+G(2df).24 Another triple-ζ set with two sets of polarization functions (exponents RN ) 1.6, 0.4 and RO ) 1.7, 0.425), a set of f functions (exponents RN ) 1.0 and RO ) 1.4), and an extra set of diffuse s (RN ) 0.0673 and RO ) 0.0898) and p functions (RN ) 0.0496 and RO ) 0.0584) was also used. This latter basis set will be called TZ2PF+diff(s,p). The TZ basis, a standard Huzinaga-Dunning [10s6p/5s3p] set,24 allows for different exponents for the s and p functions, which is potentially significant.25 The diffuse functions were necessary to ensure correct description of the anion. Diffuse functions were also included in the ONOOH calculations for consistency. The d and f functions used were spherical harmonic Gaussians, i.e. 5-d and 7-f function sets. The wave functions computed were HF, MP2,26,27 coupled cluster with single and double substitutions (CCSD),28,29 and CCSD with a perturbative treatment of connected triple excitations known as CCSD(T).30 The 1s core orbitals were frozen in all correlated wave functions. Geometries were optimized using gradient methods for each of the wave functions.31-33 The HF and MP2 calculations were done with the Gaussian 92/DFT suite of computer programs,34 and the coupled cluster calculations were performed with PSI 2.0.35 Harmonic vibrational frequencies were computed analytically at the HF32,36 and MP2 level37 and by finite differences of gradients for CCSD. Room temperature enthalpies and free energies were computed using the G2 procedure.38 The NMR chemical shifts were computed using the gauge-invariant atomic orbital method for the HF39 and MP240 wave functions programmed into the ACES II 2.0 code.41 Density functional theory (DFT) methods were also used in our studies. Three exchange-correlation (XC) density functionals and one hybrid method were employed in this paper. The first exchange-correlation density functional is the BeckeLee, Yang, Parr (B-LYP) functional, which has gradient corrections for exchange and correlation.42,43 The second functional is B-VWN, which combines the Becke 1988 exchange functional with the Vosko, Wilk, and Nusair correlation functional.44 The third combination is Xa-P86, which contains the XR functional45 with Perdew’s 1986 gradient-corrected correlation functional.46 The hybrid method used here is Becke3-LYP (as implemented in Gaussian), which uses Becke’s three-parameter mixing of exchange terms47 with the nonlocal correlation provided by the LYP formula. To account for solvent effects, the self-consistent isodensitypolarizability continuum model (SCI-PCM) in Gaussian 9448 was used. The older solvent model used a spherical cavity in a dielectric medium. The SCI-PCM solvent cavity uses an isodensity contour of the molecule for the cavity (the recommended value of 0.001 was used for the density) and models the interaction of the solvent better by introducing self-consistent charge polarization in the solvent and solute. A dielectric constant of 80.0 was used for the solvent (water). Results and Discussion Energies. Table 1 presents the absolute and relative energies for cis ONOO- and trans ONOO- and the transition state on
MP2/ 6-311+G(2df)a) MP2/ TZ2PF+diff (s,p)a) CCSD/ 6-311+G(d) CCSD(T)/ 6-311+G(d)// CCSD/ 6-311+G(d)b) Becke3-LYP/ 6-311+G(d) B-LYP/ 6-311+G(d) B-VWN/ 6-311+G(d) Xa-P86/ 6-311+G(d) Becke3-LYP + SCI-PCM/ 6-311+G(d)
cis ONOO-
trans ONOO-
transition state
-278.909 814 (0.0) -279.699 999 (0.0) -279.850 184 (0.0) -279.863 960 (0.0) -279.696 269 (0.0) -279.736 316 (0.0)
-278.912 872 (-1.9) -279.694 437 (3.5) -279.843 632 (4.1) -279.857 413 (4.1) -279.693 747 (1.6) -279.731 800 (2.8)
-278.886 232 (14.8) -279.658 219 (26.2)
-280.371 207 (0.0) -280.377 121 (0.0) -282.053 766 (0.0) -278.809 034 (0.0) -280.457 135 (0.0) [53.9]c
-280.365 988 (3.3) -280.369 513 (4.8) -282.046 726 (4.4) -278.798 495 (6.6) -280.449 630 (4.4) [52.5]c
-280.328 306 (26.9)
-279.662 198 (21.4) -279.698 314 (23.8)
a ZPVE from 6-311+G(d) MP2 frequencies. b ZPVE from 6-311+G(d) CCSD frequencies. c Solvation energy in kcal/mol. d Relative energies are in parentheses.
the isomerization pathway that involves twisting of the central N-O bond. The HF results clearly favor trans ONOO-, as concluded by earlier studies.9,12 The highest level correlated treatments predict that cis ONOO- is 3-4 kcal/mol lower in energy than trans ONOO-, which gives equilibrium population ratios that range from 130:1 to 860:1 at room and body temperatures. This has important implications for spectral intensities of the trans species. The DFT calculations also predict that cis ONOO- is more stable than trans ONOO-, with relative energies in agreement with the dynamical electron correlation predictions. The inadequacy of HF in this study was expected beforehand, because anions generally require electron correlation and because molecules containing bonds between the elements N, O, and F are known to have pathological behavior (O3,49 NO3,50 FOOF,51 and F252 for example.) The transition state energies for cis-trans conversion of ONOO- are predicted to be too low by HF theory. Becke3LYP, MP2, and coupled cluster predicted an activation barrier to rotation about the central bond of 21-27 kcal/mol. This hints at significant conjugation of π symmetry orbitals across the central N-O bond. In our computational study on ONOONa,53 abnormal trends in the predicted frequencies led us to perform an instability analysis on ONOONa, which raises the possibility that ONOOmay also have an instability. Indeed ONOO- has a singlettriplet instability at the HF level, and a subsequent search for the triplet state indicated by the stability analysis revealed that the lowest electronic state of ONOO- is a triplet at the HF level. The triplet energies are tabulated in supplementary Table I for only a few levels of theory, because the triplet state is a weak complex of NO and O2- and because the singlet state is lower in energy at levels of theory that include electron correlation. The MP2 calculations may or may not be accurate since they are based on an unstable HF wave function as a reference. The MP2/6-311+(d) results agree with the Becke3-LYP prediction that the singlet state of ONOO- is actually the lowest electronic
Ab Initio Study of Peroxynitrite and Peroxynitrous Acid
J. Phys. Chem., Vol. 100, No. 37, 1996 15089
TABLE 2: Heterolytic O-H Bond Dissociation Energies of ONOOH and HNO3 in the Gas Phase (in kcal/mol)
MP2/6-311++G(d,p) CCSD/6-311++G(d,p) MP2/6-311++(d,p) a
cis-cis ONOOH
cis-perp ONOOH
trans-perp ONOOH
355.1 358.3 HNO3 323.9
356.4 359.2 expta 324.0
358.1 360.3
Reference 54.
state (triplet cis ONOO- is 7.9 and 14.1 kcal/mol above singlet cis ONOO- at those levels, respectively; triplet trans is 13.0 and 9.4 above singlet cis ONOO- at those levels). Supplementary Table II gives the absolute and relative energies for cis-perp ONOOH, trans-perp ONOOH, cis-cis ONOOH, and the transition state for rotation about the central N-O bond. HF predicts that the cis-perp and trans-perp acids are equal in energy, whereas the cis-cis structure is slightly higher by 2 kcal/mol. At correlated levels cis-perp ONOOH is predicted to be marginally lower in energy than the others at 0 K. The MP2 study of McGrath et al. on ONOOH also predicts that all three minima are practically isoenergetic, with the lowest structure being cis-cis at the G2 level of theory.16 Their paper considered all minima and transition states possible from rotation of the OH bond which has a low torsional barrier. All comparisons of ONOOH will involve cis-cis and trans-perp since they are the putative observed forms. Table 2 gives the predicted deprotonation energies of ONOOH and HNO3, along with experimental gas phase values. The difference in the deprotonation energies between cis-cis and trans-perp ONOOH averages 2.5 kcal/mol. Thus the two ONOOH conformers have different gas phase acidities, with the cis-cis acid being more acidic. These results compare favorably to the experimental observation of two pKa values for aqueous ONOOH: 6.8 for cis-cis and 8.0 for trans-perp.20 The insensitivity of the heterolytic bond dissociation energies with respect to levels of theory and the accuracy of the value computed for HNO3 indicates that these values are accurate to within 2 kcal/mol. The gas phase acidities follow the same order expected from aqueous solutions: HNO3 > ONOOH > H2O (water heterolytic bond dissociation energy is 390.0 kcal/ mol).55 The acid rotation barrier is consistently 12 kcal/mol for most levels of theory and agrees very well with the findings of McGrath et al.16 A barrier of 12 kcal/mol is consistent with the fact that ONOO- solutions decompose upon neutralization, if ONOOH dissociates in the trans-perp form. The lower barrier indicates that the π bond is weaker in the acid than in the anion. The strength of the π bond in each of the anion and acid structures will be discussed below in terms of the N-O bond length and by using electron density analysis. Structures. Figure 1 contains the optimized structural parameters for the anion isomers and the ONOO radicals. The angles are more consistently predicted at all levels of theory in contrast to the bond distance trends. This is expected from previous experience, but the amount of variability in the predicted bond lengths is unusually high. As a result, the harmonic vibrational frequencies (see below) will also be expected to change dramatically at different levels of theory. The NdO and O-O bonds are consistently shorter in the cis anion, whereas the central N-O bond is longer. This is probably due to the larger amount of electron correlation in the cis anion, as opposed to effects from the amount of π-bonding or charge polarization (see below). In the CCSD/6-311+G(d) calculations, the NdO bond length is close to the standard NdO double-bond length of 1.21 Å. The central N-O bond has
Figure 1. Optimized ab initio geometries of ONOO- and ONOO minima. The descending order of the geometrical parameters corresponds to the order given at the bottom of the figure. Bond distances are in angstroms.
double-bond character; it is shorter than the standard N-O single bond of 1.40 Å and longer than the standard NdO double bond of 1.21 Å.56 When the peroxynitrite anion is oxidized to form the ONOO radical, one electron is removed from the HOMO, which shortens the NdO and O-O bonds and lengthens the N-O bond. The HOMO is bonding in the N-O region and antibonding for NdO and O-O and has π symmetry. The N-O bond length of the radical is ∼1.5 Å, with little apparent partial double-bond character in it. ONOO can dissociate to O2 + NO in the gas phase.57 Illustrations of the HOMO and LUMO have been published previously.12,19 Charges and bond orders of ONOO- were computed by topological analysis of the MP2/6-311+G(d) electron density.58 Methods such as Mulliken analysis are more theory dependent because of the use of overlap matrices, which are basis set dependent. The charges are -0.63, -0.25, +0.46, and -0.57 for the terminal peroxy O, central peroxy O, N, and doubly bonded O, respectively, in the cis isomer. In the trans structure, the charges (in the same order) are -0.63, -0.23, +0.43, and -0.56. There is little difference in the charges between the cis and the trans forms. The Mulliken charges agree in that the terminal peroxy O atom is the most negative; this is the atom that has the formal negative charge in the best Lewis electron dot structure. The bond orders from the electron density analysis are 1.20 for O-O, 1.55 for N-O, and 1.95 for NdO in cis ONOO-. This indicates significant π-bonding character in cis ONOO-, which is consistent with the rather high rotation barrier of 24 kcal/mol. Trans ONOO- also has similar bond orders of 1.18, 1.54, and 1.90, respectively. Comparison of the Becke3-LYP SCI-PCM/6-311+G(d) results to the Becke3-LYP/6-311+G(d) calculations shows that the solvent effects accounted for by SCI-PCM theory have some effect on the geometry; that is, it shortens the NdO bond and lengthens the other two (see Figure 2). From the trends in the MP2 calculations, increasing the size of the basis set has little effect on the energetics and optimized geometries. Given the importance of electron correlation in the peroxynitrite anion, large differences between the HF calculations and electron correlation methods were expected. The MP2 method has a tendency to overemphasize the contributions from electron correlation, which is observable in the predicted geometries. The CCSD/6-311+G(d) bond lengths are intermediate between the HF/6-311+G(d) bond distances and the MP2/6-311+G(d) bond lengths. The central N-O bond length has no simple dependence on the amount of electron correlation, but inclusion
15090 J. Phys. Chem., Vol. 100, No. 37, 1996
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Figure 2. Optimized DFT geometries of ONOO- minima. The descending order of the geometrical parameters corresponds to the order given at the bottom of the figure. Bond distances are in angstroms.
of electron correlation predicts a shorter bond length than HF does. This could be due to the need for multireference wave functions to properly account for electronic configurations corresponding to important resonance structures. One means for determining the need for nondynamical electron correlation is the T1 diagnostic in CCSD.59 The T1 diagnostics in cis and trans ONOO- are both 0.037, which are above the 0.02 cutoff recommended for considering a problem to be single reference in nature. To allay fears about the reliability of the computations based on Hartree-Fock reference wave functions (due to the singlet-triplet instability and T1 diagnostics discussed above), geometries were also optimized using several density functional methods. CASSCF(8,8)/6-31G** optimizations were performed after the initial study as a further check, and the geometries were in good agreement with the other non-HF structures (it was discovered that the diffuse functions had no qualitative effect for ONOO-, which has a tightly bound electron). Figure 2 contains the optimized DFT geometries. In the DFT/ 6-311+G(d) calculations, the B-LYP/6-311+G(d) and B-VWN/ 6-311+G(d) calculated geometries are similar to each other, but they are not consistent with the Becke3-LYP/6-311+G(d), Xa-P86/6-311+G(d), and correlated calculations. This is further evidence that the B-LYP functional is not uniformly applicable to chemical systems. The central N-O bond is very long in the B-LYP/6-311+G(d) and B-VWN/6-311+G(d) calculations, which indicates almost no partial double character in contrast to the ab initio results. The Becke3-LYP/6-311+G(d) predictions are more consistent with the MP2/6-311+G(d) and CCSD/ 6-311+G(d) values than the other DFT methods used in this study. Becke3-LYP has also been found to outperform HF, MP2, and all other DFT methods for the vibrational frequencies of the related alkali-peroxynitrite salts, a system where Hartree-Fock singlet-triplet instabilities also exist.53 The transition state for interconversion of cis to trans ONOOis displayed in Figure 3. The transition state has a dihedral angle very near to 90°, which means that the p orbitals on the central atoms are practically orthogonal and the central N-O bond has no π-bonding. The N-O bond increases by ∼0.05 Å in the transition state in the absence of π-bonding. Most of the π bond character appears to be in the NdO bond since it shortens and the O-O bond elongates by ∼0.1 Å. The optimized geometries of some ONOOH isomers are shown in Figure 4. The acid molecules have slightly twisted ONOO torsion angles, and the cis-perp and trans-perp structures have almost the same bond lengths. Using differences in hybridization (that is, bonds made with hybrid orbitals having more p character are longer) to explain the difference in the
Figure 3. Optimized ab initio and DFT geometries of ONOO- and ONOOH transition states. The descending order of the geometrical parameters to the order given at the bottom of the figure. Bond distances are in angstroms.
Figure 4. Optimized ab inito and DFT geometries of ONOOH minima. The descending order of the geometrical parameters corresponds to the order given at the bottom of the figure. Bond distances are in angstroms.
anion bond lengths is not valid, because the same argument applies to ONOOH, which does not have different N-O bond
Ab Initio Study of Peroxynitrite and Peroxynitrous Acid
J. Phys. Chem., Vol. 100, No. 37, 1996 15091
TABLE 3: Predicted Ab Initio Harmonic Vibrational Frequencies (in cm-1) for ONOOcis ONOONOO bend ONOO tors O-O stre ONO bend N-O stre NdO stre a
transition state for ONOO- cis-trans isomerization
trans ONOO-
HF
MP2
CCSD
HF
MP2
CCSD
HF
MP2
expta
396 449 797 1024 1300 1779
360 541 844 952 983 1428
362 (0) 493 (7) 802 (4) 913 (7) 1005 (16) 1568 (29)
460 267 663 1077 1317 1766
427 274 663 958 1182 1472
430 (3) 251 (3) 642 (3) 955 (1) 1097 (21) 1557 (29)
336 304i 739 843 1165 1891
278 412i 673 819 883 1562
375 (0) 642 (8) 791 (10) 931 (8) 999 (15) 1564 (28)
Reference 19. b The 6-311+G(d) basis set was used for all wave functions.
c 15N
frequency shifts are given in parentheses.
TABLE 4: Predicted DFT Harmonic Vibrational Frequencies (in cm-1) for ONOOcis ONOO-
trans ONOO-
Becke Becke 3-LYP B-LYP B-VWN Xa-P86 SCI-PCMa 3-LYP B-LYP B-VWN Xa-P86 SCI-PCMa NOO bend ONOO tors O-O stre ONO bend N-O stre NdO stre
332 496 833 969 720 1515
259 449 944 782 356 1474
250 438 941 771 332 1483
349 564 1131 939 703 1618
342 493 830 966 728 1546
421 255 626 1024 852 1487
394 233 701 959 335 1409
380 232 692 953 303 1417
453 287 1154 960 653 1576
416 233 627 1019 835 1541
transition state for ONOOcis-trans isomerization Becke3-LYP exptb 273 616i 756 824 579 1606
375 642 791 931 999 1564
a Self-consistent isodensity surface polarized continuum model with the Becke3-LYP calculation. b Reference 19. c The 6-311+G(d) basis set was used for all functionals.
distances. Furthermore, the O-H bond lengths and O-O-H bond angles do not change from cis-perp to transition state to trans-perp at any level of theory. The major changes upon protonation of ONOO- are that the N-O bond lengths are increased and the OdN bond lengths are decreased, although the change is less for formation of cis-cis ONOOH. In the cis-perp and trans-perp structures the N-O bond is predicted to be longer than the standard N-O single bond.56 The N-O bond is weakened in the transition state (because of reduced π-conjugation), with a comcomitant large N-O distance predicted by methods that incorporate electron correlation. In general, the geometry changes in ONOO- upon protonation to form the acid are similar to those found in ONOO- with hydrogen-bonded water on the peroxy oxygen,60 but greater in magnitude. The larger variations in the N-O bond between levels of theory for ONOOH are due to the large amount of electron correlation. The T1 diagnostics of ∼0.02 indicate that single-reference-based methods are better for ONOOH than for ONOO-. The HF wave function appears to predict a N-O bond distance in ONOOH that is much shorter than the optimized N-O distance in the other methods. Instability analysis revealed that ONOOH HF wave functions have singlet-triplet instabilities also, which means that the Becke3LYP geometries may be the best of those in Figure 4. Vibrational Frequencies. The experimental vibration frequencies and the calculated harmonic vibration frequencies of the peroxynitrite anion are listed in Tables 3 and 4. On the basis of the MP2/6-311+G(d) and CCSD/6-311+G(d) calculations, the vibration frequencies of the cis conformer are in better agreement with the aqueous Raman spectrum than the trans conformation. One vibration that can be used to distinguish cis from trans is the O-O stretch at 791 cm-1, which CCSD/ 6-311+G(d) gives as 802 cm-1 and 642 cm-1 for trans. In the ab initio calculations, dynamical electron correlation was important for accurate prediction of peroxynitrite anion frequencies. The CCSD/6-311+G(d) predictions are better than the MP2/6-311+G(d) calculations except for the problematic ONOO torsion band. The CCSD/6-311+G(d) NdO stretch of 1568 cm-1 fits with the experimental value of 1564 cm-1, while the MP2/6-311+G(d) prediction is 136 cm-1 lower than the experimental value.
Because the geometries from the Becke3-LYP and Xa-P86 optimizations are similar to the high-level ab initio structures, it is not surprising that those functionals also predict vibrational frequencies better than B-LYP and B-VWN. On the basis of the Becke3-LYP/6-311+G(d) and Xa-P86/6-311+G(d) results in addition to the MP2 and CCSD predictions, cis ONOO- is the most likely source of the experimental spectrum, although the differences between the theoretical cis and trans frequencies are less distinctive for Becke3-LYP/6-311+G(d). The N-O stretch is too low in the Becke3-LYP predictions because it has a N-O bond length that is too long. Density functional methods have had more difficulty with anions than with neutral molecules in the past.61 The only band showing poor agreement for all levels of theory is the O-N-O-O torsion. The cis torsion frequency prediction agrees much better with the Raman spectrum than the trans values. Furthermore, the ONOO- frequency shifts caused by 15N-substitution also indicate that the CCSD/6-311+G(d) cis values are more accurate than results on the trans conformer. The predicted torsion bands are 541 cm-1 at MP2/6-311+G(d) and 493 cm-1 at CCSD/6-311+G(d) levels of theory, which are notably lower than the experimental value of 642 cm-1, but much better than the trans frequencies predicted to be ∼250 cm-1. Ab initio harmonic frequencies are generally 5-10% higher than experimental fundamental bands. Several effects were considered as possible reasons for the disagreement between theory and experiment. One possible source of the discrepancy is that f functions are sometimes needed for MP2 vibrational frequencies to be accurate.62 In our case, the MP2 frequencies increased only a little to 559 cm-1 when a 6-311+G(2df) basis was employed. The importance of nondynamical correlation was tested using CASSCF, and the vibrational frequencies were very similar to the HF modes. The unanimity of the methods based on different wave functions or density functionals on the torsion frequency indicates that these methods probably reproduce the quadratic force field. Two other possible factors are anharmonicity of the torsion potential and solvent effects. To estimate anharmonicity, the terms aX4 + bX6 were fitted to the torsional potential, and the vibrational energy correction was estimated using perturbation theory. There are no quadratic
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Tsai et al.
Figure 5. Torsional MP2/6-311+G(d) potential energy curve for ONOO-. Each energy point was obtained by optimization at the MP2/6-311+G(d) level with the dihedral angle constrained. The cofficient of the X2 term is m1, the coefficient of the X4 term is m2, and the coefficient of the X6 term is m3. Chisq is χ2 and R is the regression.
coupling constants between the torsion and the other modes since torsion is the only a′′ mode. Figure 5 shows the fit of the MP2/6-311+G(d) torsion potential curve to even polynomials up to X6. The fit to the fourth-degree polynomial reproduces the potential curve, and the resulting harmonic force constant is slightly lower than the one calculated by analytic methods at the cis minimum. Also the sign of the anharmonic correction is negative, which lowers the predicted vibrational frequency slightly. The peroxynitrite anion has strong interactions with water in the aqueous Raman spectra that are not considered by gas phase calculations. The SCI-PCM model was employed to consider solvent effects, but SCI-PCM does not work well for solvents that hydrogen bond to the solute. Explicit solvation of ONOOhas been studied by Tsai et al.,60 with the conclusion that the O-N-O-O torsion is not significantly shifted by hydrogenbonded water, but there are many high-frequency modes involving the H bond that contribute to the broad, intense torsion band in the spectrum. The experimental width of 200 cm-1 means that the band is not a single mode.63 Supplementary Table III lists the theoretical harmonic vibration frequencies of ONOOH and experimental values. In the Raman and IR experiments, the NdO stretching frequencies of the acid are higher than those of the anion. These results are also supported by higher NdO stretching and shorter NdO bond lengths in ONOOH in our ab initio computations and in those by McGrath and Rowland.16 The O-H stretching frequencies of HOONO are close to the O-H stretch in water. Due to the reduced double-bond character of the N-O bond in ONOOH, the O-N-O torsion and N-O stretch in cis-perp and trans-perp ONOOH are much lower than the corresponding modes in cis and trans ONOO-, whereas the cis-cis ONOOH modes are only slightly lower in frequency. DFT frequencies were computed to assess the uncertainty of previous work based on MP2 results, in light of the potential for Hartree-Fock instabilities. The Becke3-LYP/6-311++G(d,p) frequencies for trans-perp ONOOH agree well with the MP2 values, so the
Figure 6. The 15N NMR spectrum of nitrate, nitrite, and peroxynitrite at pH ) 13, 5 °C (200 µL D2O was used for internal lock).
assignment of the early ONOOH spectra to trans-perp on the basis of MP2 frequencies is still valid. Cheng et al. made the assignment on the basis of the relative intensities of the OO and ONO bands because the cis-perp and trans-perp theoretical frequencies are very similar,11 which is still the case for the Becke3-LYP/6-311++G(d,p) frequencies. This intensity ratio holds for the Becke3-LYP/6-311++G(d,p) frequencies also. The assignment of experimental lines to the trans-perp ONOOH is more likely given that cis-perp can easily rearrange to ciscis. The Becke3-LYP/6-311++G(d,p) NO stretch for cis-cis ONOOH (634 cm-1) matches the experimental band of 629.1 cm-1 even better than the MP2/6-311G(d,p) value of 746 cm-1. 15N NMR Chemical Shifts. The 60.8 MHz 15N NMR spectrum of aqueous peroxynitrite (O15NOO-) at pH 13 and 5 °C is shown in Figure 6. As mentioned above, ONOO- can exist as two planar conformers, the cis and trans configurations. If the two isomers coexist, there should be two O15NOOchemical shift peaks because the activation barrier for rotation is too large to give an average signal. In Figure 6 there is a
Ab Initio Study of Peroxynitrite and Peroxynitrous Acid TABLE 5:
15N
NMR Chemical Shifts (in ppm) of Peroxynitrite exptl values chemical shift
HF/ 6-311+G(d) shielding constant
HF/ 6-311+G(d) chemical shift
MP2/ 6-311+G(d) shielding constants
MP2/ 6-311+G(d) chemical shift
-232.7 -54.7
-239.1 -562.7 -608.9 -625.7
-386.6 -60.0 -16.8 0.0
-70.6 -139.4 -187.4 -182.0
-111.4 -42.6 5.4 0.0
NO3cis ONOOtrans ONOONO2-
0.0
TABLE 6: G2 Atomization Energies and Thermodynamic Parameters of Peroxynitrite, Nitrate, and Nitric Acid ∑D0 cis ONOOtrans ONOOTS of ONOOcis-trans isomerization expt ONOOexpt NO3HNO3 expt HNO3
J. Phys. Chem., Vol. 100, No. 37, 1996 15093
313.3 309.8 282.1
S(298.15 K) 63.5 63.9 63.7
∆Hf(298.15 K) ∆Gf(298.15 K) -27.0 -23.3 4.2
45 (estimate)b -11 (aqueous)b 361.1c 58.8c -74.3c (-49 aqueous)d 373.2 63.6 -34.7 371.2c 63.8c -32.0c
-15.6 -12.1 15.5 10 (aqueous)b -61.6c -20.2 -17.6c
a S in eu; ∆Ec, ∆Hf, and ∆Gf in kcal/mol. b Reference 13. c Reference 54. d Reference 64.
single peak from O15NOO- at 178.0 ppm downfield from nitrate. 15N NMR experiments of O15NOO- at pH from 8 to 12 at 5 and 25 °C were also performed. Because of the fast decomposition of ONOOH at lower pH and the required long integration time (several seconds), no other peak corresponding to ONOO- or ONOOH was observed. The HF/6-311+G(d) and MP2/6-311+G(d) shielding constants and chemical shifts are listed in Table 5. Ab initio NMR calculations give better results if experimental geometries are used, so the CCSD/6-311+G(d) optimized geometries were used in the absence of experimental values, since they were judged to be the most accurate. The absolute values of the chemical shifts are in poor agreement with experimental values because of correlation effects, but the relative 11N shifts are more accurate between species if the bonding around the 15N is comparable, which is the reason that nitrite is used as the reference in our NMR spectrum. The relation of the chemical shifts between cis ONOO- and NO2- is -53 ppm (from the average of the HF and MP2 values) compared to -54.7 ppm from experiment. The corresponding difference in σ is -6 ppm for trans ONOO-. This provides further evidence that cis ONOO- is the predominant isomer in aqueous solution. Thermochemistry. Table 6 collects computed (at the G2 level of theory) and experimental atomization energies, entropies, heats of formation, and free energies of formation for the ONOO- structures, nitrate and nitric acid. G2 values of McGrath and Rowland for ONOOH are published, giving a predicted Gibbs energy of formation at room temperature for cis-cis ONOOH of 8.3 kcal/mol, with cis-perp only 0.4 kcal/ mol higher and trans-perp 2.4 kcal/mol higher.16 Supplementary Table IV shows that, using the complete basis set-atomic pair natural orbital (CBS-APNO) method,65 the spacing between the relative Gibbs energies of these ONOOH structures is 2 kcal/ mol with the same ordering. The CBS-APNO method has a mean absolute deviation of 0.5 kcal/mol for the energies computed in the G2 series of tests. The CBS-APNO Gibbs energy and enthalpy of formation of 8.8 and -3.8 kcal/mol, respectively, are in good agreement with the 7 and -6 kcal/ mol derived from experiment (see below). The cis to trans rotation barrier is 12 kcal/mol for ONOOH at almost all levels of theory. Gas phase HNO3 is more stable than ONOOH by 27 kcal/mol from experiment and theory. G2 theory predicts that cis ONOO- is more stable than trans ONOO- by 3.5 kcal/mol using either the enthalpy of formation
or Gibbs energy of formation. The G2 barrier for rotation of cis to trans ONOO- is predicted to be 31 kcal/mol, notably higher than the 21-27 kcal/mol from DFT and straightforward electron correlation calculations. The enthalpy difference between cis ONOO- and nitrate is predicted to be 47.3 kcal/ mol in the gas phase, whereas the experimental enthalpy difference in solution is only 38 kcal/mol. Since the G2 method has an accuracy of 2 kcal/mol for energies of formation, the discrepancy is most likely due to differences in solvation energy. The SCI-PCM model does not predict a significant difference in the solvation energies, so differences in hydrogen bonding to water should be important. The values for the thermodynamic properties of ONOOH calculated by ab initio methods are supported by the following independent considerations. From the known enthalpy of formation of ONOO-, -10.7 kcal/mol,67,68 and an estimated S° of 44.6 eu,13 one calculates a ∆Gf(ONOO-aq) of 9.4 kcal/ mol. Given a pKa value of 6.8 of ONOOH,13 ∆Gf(ONOOHaq) ) 0 kcal/mol. To arrive at values for thermodynamic parameters of peroxynitrite in the gas phase, we will now consider the homolysis of ONOOH. ∆Gf(ONOOHg) is not known. We estimate ∆Gsolv(ONOOH) to be slightly less than the -7.8 kcal/mol of hydrogen peroxide,69 namely, -7 kcal/mol. This amount reflects the ability to create a cavity in water (4 kcal/mol) and to form approximately six hydrogen bridges, each -2 kcal/mol.70 Thus, ∆Gf(ONOOHg) ) 7 kcal/mol. Given the Gibbs energies of formation of the OH and NO2 radicals in the gas phase, 8.2 and 12.3 kcal/mol respectively,71 the Gibbs energy of homolysis is 13.5 kcal/mol. The T∆S term of this reaction is estimated at 9.7 kcal/mol, in between that of hydrogen peroxide (10.5 kcal/ mol) and alkylhydroperoxides (9.0 kcal/mol). This yields a ∆Hrxn of 23.2 kcal/mol for homolysis in the gas phase. With the known enthalpies of formation for OH and NO2 radicals, 7.9 and 9.3 kcal/mol respectively,70 a ∆Hf(ONOOHg) of -6.0 kcal/mol is calculated. Finally, the T∆S term of 9.7 kcal/mol, combined with the standard entropies of the OH and NO2 radicals, 43.9 and 57.4 eu, respectively,70 results in a S°(ONOOHg) of 69 eu. With estimated error of 2 kcal/mol in the T∆S term, the errors in ∆Gf(ONOOHg), ∆Hf(ONOOHg), and S°(ONOOHg) are 2 kcal/mol, 2 kcal/mol, and 7 eu, respectively. A recent paper dealing with the rearrangement of ONOOH predicted a Gibbs energy for the O-O bond to be 3 kcal/mol using MP4SDQ/6-31G*//MP2/6-31G*.72 This is considerably smaller than our homolytic Gibbs dissociation energy of 13.5 kcal/mol, which is lowered by 2 kcal/mol using solvation energy computed using Becke3-LYP(SCIPCM)/6-31G**. Also, there may be additional activation energy required for O-O bond dissociation. The conclusion of Cameron et al.72 with respect to the very high barrier to unimolecular rearrangement to nitric acid is still valid. Comparison to FONO and ClONO. High-level ab initio studies of the FONO system give results that are quite similar to those for the isoelectronic ONOO- molecular ion. The isomer analogous to nitrate is lower than cis FONO by 37 kcal/ mol, and trans FONO is 2.5 kcal/mol higher in energy than cis FONO.73 FONO has more π-bonding in the NdO bond and
15094 J. Phys. Chem., Vol. 100, No. 37, 1996 less in the other bonds, resulting in lower torsion and N-O stretching frequencies. The ClONO system is also predicted to be cis by 3 kcal/mol when compared to trans, and cis ClONO has a higher torsion frequency.74 In this case the CCSD(T)/ TZ2P frequencies agree with experiment extremely well. The primary dissimilarity of ClONO from ONOO- is the fact that the nitrate analog is only 11 kcal/mol lower in energy than cis ClONO. Conclusions Cis ONOO- is more stable than trans ONOO- by 3-4 kcal/ mol and is the only apparent isomer present in base solutions on the basis of comparisons of Raman and NMR spectra with ab initio calculations. The only problematic vibrational frequency is the intense and broad Raman band centered at 642 cm-1, which is assigned to the torsional mode of cis ONOOeven though the theoretical values are too low by 100 cm-1. Non-hydrogen-bonding solvent effects and anharmonicity of the torsion potential are not causes for the disagreement. The torsional barrier is predicted to be quite high in ONOO-, ranging from 21 to 27 kcal/mol for various ab initio and DFT methods. The G2 barrier is quite a bit higher at 31 kcal/mol using ab initio Gibbs energy differences at room temperature, and this may indicate that very high levels of theory are needed to resolve the discrepancy between experiment and theory for the torsion frequency. The other likely possibility is that a large part of the broad band at 642 cm-1 involves significant vibrations involving hydrogen bonds, although this peak is also high in the Raman spectra of irradiated nitrate crystals. Cis ONOOH is more stable than trans ONOOH by 2 kcal/mol at the CBSAPNO level of theory. The torsional barrier for ONOOH is much lower (12 kcal/mol) at almost all levels of theory. Acknowledgment. This work is supported through grants from NIH and Cray Research. We appreciate the generous amounts of computer time allocated by the Alabama Supercomputer Center and the Pittsburgh Supercomputer Center. We also thank Prof. Jerzy Cioslowski of Florida State for the charges and bond orders derived from electron density analysis, and Zhi Chen for calculations on triplet states. Supporting Information Available: Tables of energies, vibrational frequencies, and thermodynamic parameters (4 pages). Ordering information is given on any current masthead page. References and Notes (1) The names recommended by IUPAC are oxoperoxonitrate(1-) for ONOO-, hydrogen oxoperoxonitrate for ONOOH, and nitrogen monoxide for NO. (2) Beckman, J. S.; Beckman, T. W.; Chen, J.; Marshall, P. M.; Freeman, B. A. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 1620. (3) King, P. A.; Anderson, V. E.; Edwards, J. O.; Gustafson, G.; Plumb, R. C.; Suggs, J. W. J. Am. Chem. Soc. 1992, 114, 5430. (4) Hughes, M. N.; Nicklin, H. G. J. Chem. Soc. A 1968, 450. (5) Finlayson-Pitts, B. J.; Pitts, J. N. Atmospheric Chemistry: Fundamentals and Experimental Techniques; Wiley: New York, 1992. (6) Kortu¨m, G.; Finckh, B. Z. Phys. Chem. 1940, B48, 32. (7) Benton, D. J.; Moore, P. J. Chem. Soc. A 1970, 3179. (8) Burkholder, J. B.; Hammer, P. D.; Howard, C. J. J. Phys. Chem. 1987, 91, 2136. (9) Shen, M.; Xie, Y.; Schaefer, H. F.; Deakyne, C. A. J. Chem. Phys. 1990, 93, 3379. (10) McGrath, M. P.; Francl, M. M.; Rowland, F. S.; Hehre, W. J. J. Phys. Chem. 1988, 92, 5352. (11) Cheng, B.-M.; Lee, J.-W.; Lee, Y.-P. J. Phys. Chem. 1991, 95, 2814. (12) Koppenol, W. H.; Klasinc, L. Int. J. Quantum Chem. Symp. 1993, 20, 1.
Tsai et al. (13) Koppenol, W. H.; Moreno, J. J.; Pryor, W. A.; Ischiropoulos, H.; Beckman, J. S. Chem. Res. Toxicol. 1992, 5, 6834. (14) Bohle, D. S.; Hansert, B.; Paulson, S. C.; Smith, B. D. J. Am. Chem. Soc. 1994, 116, 7423. (15) Lo, W.-J.; Lee, Y.-P.; Tsai, J.-H.; Tsai, H.-H.; Hamilton, T. P.; Harrison, J. G.; Beckman, J. S. J. Chem. Phys. 1995, 103, 4026. (16) McGrath, M. P.; Rowland, F. S. J. Phys. Chem. 1994, 98, 1061. (17) Lo, W.-J.; Lee, Y.-P. J. Chem. Phys. 1994, 101, 5494. (18) Krauss, M. Chem. Phys. Lett. 1994, 222, 513. (19) Tsai, J.-H. M.; Harrison, J. G.; Martin, J. C.; Hamilton, T. P.; van der Woerd, M.; Jablonsky, M. J.; Beckman, J. S. J. Am. Chem. Soc. 1994, 116, 4115. (20) Crow, J. P.; Spruell, C.; Chen, J.; Gunn, C.; Ischiropoulos, H.; Tsai, M., Smith, C. D.; Radi, R.; Koppenol, W. H.; Beckman, J. S. Free Radical Biol. Med. 1994, 16, 331. (21) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (22) Clark, T.; Chandrasekhar, J.; Spitznagel, G. W.; Schleyer, P. v. R. J. Comput. Chem. 1983, 4, 294. (23) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (24) Dunning, T. H. J. Chem. Phys. 1971, 55, 716. (25) Grev, R. S.; Schaefer, H. F. J. Chem. Phys. 1989, 91, 7305. (26) Bartlett, R. J.; Silver, D. M. J. Chem. Phys. 1975, 65, 3258. (27) Møller, C.; Plesset, M. S. Phys. ReV. 1934, 4, 618. (28) Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (29) Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F. J. Chem. Phys. 1988, 89, 7382. (30) (a) Raghavachari, K.; Pople, J. A.; Replogle, E. S.; Head-Gordon, M. J. Chem. Phys. 1990, 94, 5579. (b) Bartlett, R. J.; Watts, J. D.; Kucharski, S. A.; Noga, J. Chem. Phys. Lett. 1990, 165, 513. (31) Pulay, P. Mol. Phys. 1969, 17, 197. (32) Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., Symp. 1979, 13, 325. (33) Scheiner, A. C.; Scuseria, G. E.; Rice, J. E.; Lee, T. J.; Schaefer, H. F. J. Chem. Phys. 1987, 87, 5361. (34) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian 92/DFT, Revision G2; Gaussian, Inc.: Pittsburgh, PA, 1993. (35) Janssen, C. L.; Seidl, E. T.; Scuseria, G. E.; Hamilton, T. P.; Yamaguchi, Y.; Remington, R. B.; Xie, Y.; Vacek, G.; Sherrill, C. D.; Crawford, T. D.; Fermann, J. T.; Allen, W. D.; Brooks, B. R.; Fitzgerald, G. B.; Fox, D. J.; Gaw, J. F.; Handy, N. C.; Laidig, W. D.; Lee, T. J.; Pitzer, R. M.; Rice, J. E.; Saxe, P.; Scheiner, A. C.; Schaefer, H. F. PSI 2.0.8; PSITECH, Inc.: Watkinsville, GA 30677, 1994. (36) Saxe, P.; Yamaguchi, Y.; Schaefer, H. F. J. Chem. Phys. 1982, 77, 5647. (37) Handy, N. C.; Amos, R. D.; Gaw, J. F.; Rice, J. E.; Simandiras, E. D. Chem. Phys. Lett. 1985, 120, 151. (38) Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94, 7221. (39) Wolinski, K.; Hinton, J. F.; Pulay, P. J. Am. Chem. Soc. 1990, 112, 8251. (40) Gauss, J. Chem. Phys. Lett. 1992, 191, 614. (41) ACES II, an ab initio program system authored by Stanton, J. F.; Gauss, J.; Watts, J. D.; Lauderdale, W. J.; Bartlett, R. J. The package also contains modified versions of the MOLECULE Gaussian integral program of Almlo¨f, J.; Taylor, P. R.; the ABACUS integrals derivative program of Helgaker, T. U.; Jensen, H. J. A.; Jørgensen, P.; Taylor, P. R.; and the PROPS property integral package of Taylor, P. R. (42) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (43) Lee, C.; Yang. W.; Parr, R. G. Phys. ReV. B 1993, 98, 5648. (44) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 90, 1007. (45) Hohenberg, P.; Kohn, W. Phys. ReV. B 1964, 136, 846. (46) Perdew, J. P. Phys. ReV. 1986, B33, 8822. (47) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (48) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B.; Nanayakkar, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision A.1; Gaussian, Inc.: Pittsburgh, PA, 1995. (49) Lee, T. J.; Rice, J. E. J. Chem. Phys. 1992, 97, 4223. (50) Davy, R. D.; Schaefer, H. F. J. Chem. Phys. 1989, 91, 4410. (51) Bhatia, S. C.; Hall, J. H. J. Chem. Phys. 1985, 82, 1991. (52) Hamilton, T. P.; Pulay, P. J. Chem. Phys. 1986, 84, 5728. (53) Tsai, H.-H.; Hamilton, T. P.; Tsai, J.-H. M.; Beckman, J. S. J. Phys. Chem. 1996, 100, 6942.
Ab Initio Study of Peroxynitrite and Peroxynitrous Acid (54) Gurvich, L. V.; Veyts, I. V.; Alcock, C. B. Thermodynamic Properties of IndiVidual Substances; 4th Hemisphere Publishing Corp.: New York, 1989. (55) Morrison, R. T.; Boyd, R. N. Organic Chemistry, 6th ed.; PrenticeHall, Inc.: Englewood Cliffs, NJ, 1992. (56) Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry, 4th ed.; Harper Collins: New York, 1993. (57) Guillory, W. A.; Johnston, H. S. J. Chem. Phys. 1965, 42, 2457. (58) Cioslowski, J.; Mixon, S. T. J. Am. Chem. Soc. 1991, 113, 4142. (59) Lee, T. J.; Taylor, P. R. Int. J. Quantum Chem. Symp. 1989, 23, 199. (60) Tsai, H.-H.; Hamilton, T. P.; Tsai, J.-H. M.; Beckman, J. S. Struct. Chem. 1995, 6, 323. (61) Kawai, R. Private communication. (62) Simandiras, E. D.; Rice, J. E.; Lee, T. J.; Amos, R. D.; Handy, N. C. J. Chem. Phys. 1988, 88, 3187. (63) Goodman, L. Private communication. (64) Alberty, R. A. Physical Chemistry, 7th ed.; John Wiley & Sons: New York, 1987.
J. Phys. Chem., Vol. 100, No. 37, 1996 15095 (65) Montgomery, J. A.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys. 1994, 101, 5900. (66) Leigh, G. J., Ed. Nomenclature of Inorganic Chemistry; Blackwell Scientific Publications: Oxford, 1990. (67) Ray, J. D. J. Inorg. Nucl. Chem. 1962, 24, 1159. (68) Manuszak, M.; Koppenol, W. H. Thermochim. Acta 1996, 273, 11. (69) Koppenol, W. H. In Focus on Membrane Lipid Oxidation; VigoPelfrey, C., Ed.; CRC Press: Boca Raton, FL, 1989; Vol. 1, p 1. (70) Schwartz, H. A.; Dodson, R. W. J. Phys. Chem. 1984, 88, 3643. (71) Wagman, D. D.; Evans, W. H.; Parker, V. B.; Schumm, R. H.; Halow, I.; Bailey, S. M.; Churney, K. L.; Nuttal, R. L. J. Phys. Chem. Ref. Data 1982, 11, Suppl. 2, 37. (72) Cameron, D. R.; Borrajo, A. M. P.; Bennett, B. M.; Thatcher, G. R. J. Can. J. Chem. 1995, 73, 1627. (73) Lee, T. J.; Rice, J. E. J. Chem. Phys. 1992, 97, 4223. (74) Lee, T. J. J. Chem. Phys. 1994, 98, 111.
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