Gibbs energies of reactive species involved in peroxynitrite chemistry calculated by density functional theory

Gibbs energies of reactive species involved in peroxynitrite

chemistry calculated by density functional theory

Silvia Pfeiffera, Bernd Mayera, Rudolf Janoschekb,*

aContribution from the Institut fur Pharmakologie und Toxikologie, Karl-Franzens Universitat Graz, Universitatsplatz 2, A-8010 Graz, AustriabInstitut fur Chemie (Theoretische Chemie), Karl-Franzens Universitat Graz, Strassoldogasse 10, A-8010 Graz, Austria

Received 6 July 2002; accepted 3 September 2002

Abstract

The wide-spread biological messenger nitric oxide (zNO) reacts at nearly diffusion-controlled rates with superoxide anion

ðOz22 Þ to give the potent cytotoxin peroxynitrite (ONOO2). We applied density functional theory to various neutral as well as

ionic and free radical species involved in the complex biological chemistry of ONOO2 in aqueous solution. The solvation

effects were considered by the addition of a water molecule to anions to take strong hydrogen-bonding in anion-water

complexes into account and, subsequently, by the polarized continuum model PCM (for bulk solvent effects) to achieve realistic

values for total Gibbs energies G o(aq.). From these results standard reaction Gibbs energies were calculated for a series of

reactions involved in peroxynitrite chemistry. In particular, the Gibbs energy change for peroxynitrous acid homolysis,

ONOOH ! zNO2 þzOH, was calculated at the G3MP2B3//PCM/B3LYP/cc-pvtz level of theory to be DG o(aq.) ¼ 46.4

kJ mol21 which is in good agreement with the experimentally determined value of 56.9 ^ 1.7 kJ mol21 (Merenyi, G.; Lind, J.;

Goldstein, S.; Czapski, G. Chem. Res. Toxicol.1998, 11, 712–713), calculated from experimentally determined DfGo values.

For peroxynitrite homolysis, ONOO2 ! zNO2 þ Oz22 ;the calculated value of DG o(aq.) ¼ 72.0 kJ mol21 was obtained when the

ionic species were replaced by ion-water complexes. Comparison with the experimental value of 87.4 kJ mol21 is satisfying

(Merenyi, G.; Lind, J.; Goldstein, S.; Czapski, G. J. Phys. Chem.1999, 103, 5685–5691). For an alternative peroxynitrite

homolysis, ONOO2 ! zNO þ Oz22 ; the calculated value of DG o(aq.) ¼ 54.4 kJ mol21 was obtained only when ion-water

complexes were included. This is in reasonable agreement with the experimental value of 64.4 kJ mol21, based on DfGo(aq.)

values (Merenyi, G.; Lind, J. Chem. Res. Toxicol. 1998, 11, 243–246).

q 2003 Elsevier Science B.V. All rights reserved.

Keywords: Gibbs energy; Density functional theory; Homolysis

1. Introduction

The free radical nitric oxide (zNO) plays an

important role as a signalling molecule in a wide

variety of biological systems [1]. Many of the

cytotoxic effects of zNO are thought to be caused by

its reaction with superoxide anion radicals ðOz22 Þ;

yielding the potent oxidant peroxynitrite (ONOO2)

(Eq. (1)).

Oz22 þ zNO ! ONOO2 ð1Þ

0166-1280/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved.

PII: S0 16 6 -1 28 0 (0 2) 00 6 74 -7

Journal of Molecular Structure (Theochem) 623 (2003) 95–103

www.elsevier.com/locate/theochem

* Corresponding author.

E-mail address: [email protected] (R.

Janoschek).

http://www.elsevier.com/locate/theochem

Formation of peroxynitrite occurs at a nearly diffusion-

controlled rate of ,2x1010 M21s21, which is about

10-fold faster than dismutation of Oz22 by superoxide

dismutase [2,3]. As a potent cellular oxidant that reacts

with virtually all classes of biomolecules, peroxyni-

trite may essentially contribute to tissue injury in a

number of pathophysiological conditions associated

with increased oxidative stress, including athero-

sclerosis, congestive heart failure, and stroke [4].

In aqueous solution peroxynitrite undergoes two

different pathways of decay: at low pH, protonation of

peroxynitrite anion (pKa of 6.8 at 37 8C) [4], which

isomerizes to nitric acid, HNO3, whereas decompo-

sition of peroxynitrite yielding NO22 and O2 in a 2:1

ratio is predominant at pH values $ 7.0 [5,6]. The

isomerization reaction involves homolysis of

ONOOH to yield caged zNO2 and zOH radicals (Eq.

(2)) [7–9]. About 30% of the radicals can escape the

cage before recombination and isomerization,

explaining the observed radical properties of perox-

ynitrous acid [10].

ONOOH O {zNO2;zOH} O

zNO2 þzOH ð2Þ

Thirty years ago, Mahoney suggested that the

decomposition of ONOOH yields about 30% freezNO2 and zOH radicals, [11] but nevertheless homo-

lysis of peroxynitrite has recently been questioned

because of both, calculations implying that this

reaction is “thermodynamically impossible“ and

data showing that neither NO22 (a product of zNO2

hydrolysis) nor H2O2 (the product of zOH dimeriza-

tion) are formed from peroxynitrite at acidic pH

[12,13]. However, the thermodynamics of peroxyni-

trite has recently been revised and the lack of NO22

and H2O2 formation has been explained by a rapid

electron transfer reaction occurring between NO22 and

zOH yielding OH2 and zNO2 (Eq. (3)) [14]. Thus

initially formed NO22 and zOH are rapidly consumed

to recycle zNO2, such that NO23 is finally formed as

exclusive product of the overall reaction without

concomitant production of H2O2.

zOH þ NO22 ! OH2 þ zNO2 ð3Þ

At increasing pH ($7), decomposition of ONOO2 to

yield NO22 and O2 in a 2:1 ratio prevails over

homolysis and isomerization, [5] presumably due to

decreasing equilibrium concentrations of ONOOH

(pKa ¼ 6.8). It has been suggested that the key

reactions initiating ONOO2 decomposition at

pH ¼ 14 are reactions (1A) (the reverse of reaction

1) and 4,

ONOO2 ! zNO þ Oz22 ð1AÞ

ONOO2O

zNO2 þ Oz2 ð4Þ

followed by a sequence of reactions leading to the

consumption of two molecules of ONOO2 for every

homolysis via reaction 4 [7,8]. The published

equilibrium constant for reaction (4) is

(5.9 ^ 2.9) £ 10216 M with a corresponding Df-

G o(aq) of 86.6 kJ mol21 [9]. This proposed mechan-

ism of decomposition results in formation of both zNO

and zNO2 as intermediates, indicating that reactions

(5–7) are involved in NO22 and O2 formation [6,7,15].

zNO þ zNO2 ! N2O3 ð5Þ

N2O3 þ H2O ! 2NO22 þ 2Hþ ð6Þ

ONOO2 þ N2O3 ! 2zNO2 þ NO22 ð7Þ

In the present paper we have used computational

methods, based on density functional theory (DFT),

for the calculation of total Gibbs energies G o for a

series of reactive species involved in peroxynitrite

chemistry. Our data should be useful for the

calculation of Gibbs energies of reaction DG o of

biologically relevant processes occurring in aqueous

solution.

2. Former calculations

Quantum chemical calculations on nitric acid

(HONO2) and peroxynitrous acid (HOONO) have

been performed in the past [16]. The conformations of

the peroxynitrite anion (ONOO2) were studied by the

coupled cluster singles and doubles method (CCSD)

[17,18] which predicted that the cis isomer is

12.6 kJ mol21 more stable than the trans isomer.

Calculations indicate that a 88–100 kJ mol21 barrier

limits isomerization between the cis and trans anions,

but in contrast to the cis isomer, the terminal oxygen

in the trans isomer can directly rearrange to nitrate

[19]. Ab initio methods as well as density functional

theory at the B3LYP level were applied to peroxyni-

trite molecules and to the ONOO2.H2O complex [20].

Ab initio calculations (MP2 and CCSD(T)) as well as

S. Pfeiffer et al. / Journal of Molecular Structure (Theochem) 623 (2003) 95–10396

different density functional theory (DFT) methods

were applied to spectroscopic properties (geometry,

IR, Raman, and NMR data) of peroxynitrite and

peroxynitrous acid [21]. Thermochemical properties

were studied at the G2 level, and to account for

solvent effects, the self-consistent isodensity polar-

ized continuum model (SCIPCM) was used. However,

the most important effect for solvation energies,

caused by hydrogen bonding, was ignored. In

particular, the experimental enthalpy difference in

solution between ONOO2 and NO23 (nitrate) is

159 kJ mol21, but the SCIPCM method predicted

198 kJ mol21. The authors concluded that “differ-

ences in hydrogen bonding to water should be

important“ [21]. Mechanisms of peroxynitrite and

peroxynitrous acid oxidations have been investigated

with density functional theory methods using the

B3LYP functional [22,23].

3. Strategy of calculations

A great part of computational efforts so far suffer

from the lack of physiological conditions. These are

mainly strong chemical interactions between ionic

reactants or products and water molecules. In order to

consider the most important effects of ions in solution,

at least one water molecule per ion is involved in this

study. Thus, ionic reactants and products, as they are

usually written in chemical equations (for example

NO22 ), are replaced by the corresponding ion-water

complexes ðNO22 :H2OÞ and are investigated in the

sense of the super-molecule-approach. Geometry

optimizations, vibrational wavenumbers, and thermo-

chemical corrections for reaction energies are based,

therefore, on ion-water complexes. For comparison,

weak H-bonds between neutral species and water are

ignored in this study. Finally, the remaining effect of

the liquid phase is taken into account by single-point

polarized continuum model (PCM) calculations [24].

More details can be found in the following section

entitled ‘Exploratory calculations…’.

Thermochemical corrections were calculated at

standard states T ¼ 298 K, p ¼ 1 atm. In the PCM

approach, where water is the dielectric medium,

the calculated Gibbs energies correspond to pH ¼ 0.

Standard rigid-rotor harmonic oscillator partition

function expressions are used throughout. Gas-phase

calculations, such as relative enthalpies DH o(gas) as

well as changes in Gibbs energies DG o(gas), are

uniformly based on the successful G3MP2B3 pro-

cedure [25] which is able to produce heats of

formation with experimental accuracy. For a list of

32 radicals, for example, a mean absolute deviation

between experimental and calculated DfHo(gas)

values of 4.2 kJ mol21 has been obtained which is

close to the average experimental uncertainty of

^2.9 kJ mol21 [26]. PCM calculations for bulk

solvent effects are not included in the G3MP2B3

procedure. Therefore, density functional theory in the

framework of B3LYP [27,28] was applied with the

correlation consistent polarized valence triple zeta

(cc-pvtz) basis sets; in standard notation: 3s,2p,1d (for

H) and 4s,3p,2d, 1f (for the heavy atoms C,N,and O).

Then, the Gibbs energy corrections of the solvent and

the investigated systems, based on PCM/B3LYP/cc-

pvtz and B3LYP/cc-pvtz calculations, respectively,

are combined with the G3MP2B3 relative energies as

follows:

DHoðaq:Þ ¼DHoðgasÞðG3MP2B3Þþ ½DEðaq:ÞðPCMÞ

2DEðgasÞðB3LYPÞ� or

DGoðaq:Þ ¼DGoðgasÞðG3MP2B3Þþ ½DGoðaq:ÞðPCMÞ

2DGoðgasÞðB3LYPÞ�

This procedure is abbreviated in the following by the

acronym G3MP2B3//PCM/B3LYP/cc-pvtz. PCM

means a single point calculation PCM/B3LYP/cc-

pvtz at B3LYP/cc-pvtz optimized geometries. The

standard radius of each atomic sphere is determined by

multiplying the van der Waals radius by 1.2. It should

be noted that the PCM method yields the Gibbs energy

of the solvent, and the contribution from vibrations

and rotations of the investigated system should be

added to complete the term DG o(aq.)(PCM) in the

above equation. Calculations have been performed

with the GAUSSIAN 98 suite of programs [29].

4. Exploratory calculations on strong H-bonds inion-water complexes

Exploratory calculations are necessary for two

reasons. On one hand, a well-known example should

S. Pfeiffer et al. / Journal of Molecular Structure (Theochem) 623 (2003) 95–103 97

be studied to find out the least number of water

molecules for qualitatively correct descriptions of

the hydrated oxonium ion and small anions. We

have chosen the well established standard

enthalpy of neutralization which can be found in

textbooks as H3Oþ þ OH2 ! 2H2O ðDHoðaq:Þ ¼

257:3kJ mol21Þ. On the other hand, the successively

increased number of water molecules demonstrates

nicely how meaningless are calculations of gas-phase

mechanisms for understanding aqueous-phase pro-

cesses where ionic species are involved. A body of

evidence, derived mainly from solution chemistry

studies, indicates that the central ion in solution is

H3Oþ and its primary coordination sphere can

contain one, two or three H2O molecules, and

H3Oþ.3 H2O (H9O4þ) is considered the dominant

species [30,31]. In Table 1 the stepwise increased

number of water molecules from (b) to (e) exhibits

H-bond stabilization, summed up over the hydrated

oxonium ion H3Oþ.3 H2O and hydroxide OH2.3

H2O, of DHH o(gas) ¼ 2561.9 kJ mol21. Compari-

son of (f) and (g) shows that for a reduced number of

water molecules (f) bulk solvent effects of the

remaining infinite number of water molecules,

treated as dielectric medium, cannot fit the DH o

value properly. A second stabilizing effect of ions is

caused by bulk solvent effects (aqueous solution,

dielectric constant e ¼ 78.39) which can be found in

Table 1 when going from (e) to (g) with an amount

of DsolvH o(aq.) ¼ 2241.9 kJ mol21. The grand total

of calculated stabilizing contributions to the ions

yields a reaction enthalpy DH o(aq.) of the neutral-

ization reaction of 2 146.0 kJ mol21. Although this

value seems to be still far from the experimental

value of 2 57.3 kJ mol21, the series of calculations

shows unequivocally the importance of ion-water

complexes for reaction energies in aqueous solution.

Unfortunately, both ions in the equation of neutral-

ization are on the same side so that the missing

energy of incomplete hydration of ions is acumu-

lated. Fortunately, in the reactions of interest in this

study anions are present on both sides of the reaction

equations so that deficiencies in the description of

anions in solution can be compensated to some

extent. Moreover, anion-water complexes show

lower H-bond strengths than cation-water complexes

as is evident from the values in Table 2. Therefore, a

single water molecule attached to an anion should be

sufficient to give reasonable measure of H-bond

effects in Gibbs energy changes for reactions.

Table 1

G3MP2B3 calculated standard enthalpies of neutralization, DH o/kJ mol21, in the supermolecule-approach. (a)-(e) different degrees of proton

hydration and hydroxide hydration in the gas phase; (f) and (g) bulk solvent effects (aqueous solution, dielectric constant e ¼ 78.39) considered

by PCM/B3LYP/cc-pvtz calculations; (h) experiment

Equation DH o

(a) HO2 þ Hþ ! H2O 21635.9

(b) HO2 þ H3Oþ ! 2 H2O 2949.8

(c) HO2 þ H3Oþ.H2O ! 3 H2O 2811.1

(d) HO2.H2O þ H3Oþ.H2O ! 4 H2O 2696.5

(e) HO2.3H2O þ H3Oþ.3 H2O ! 8 H2O 2387.9

(f) HO2.H2O(aq.) þ H3Oþ.H2O(aq.) ! 4 H2O(aq.) 2164.4

(g) HO2.3H2O(aq.) þ H3Oþ.3H2O(aq.) ! 8 H2O(aq.) 2146.0

(h) HO2.aq. þ H3Oþ.aq. ! 2 H2O.(aq.). 257.3

Table 2

B3LYP/cc-pvtz calculated symmetries and H-bond lengths,

re(O· · ·O)/A, of ion-water complexes. H-bond strengths DH-

H o(gas)/kJ mol21 for ion-water complexes, A^.n H2O ! A^ þ

n H2O, are taken from G3MP2B3 calculations

Ion-water complex Symmetry re(O· · ·O) DHH o(gas)

H3Oþ.H2O C2 2.401 138.7

OH2.H2O C2 2.453 114.6

NO22 :H2O C2v 2.852 66.5

Oz22 :H2O C2v 2.695 82.0

Oz2.H2O Cs 2.517 117.2

ONOO2.H2O C1 2.700 69.9

H3Oþ.3H2O C3 2.556 297.1

HO2.3H2O C3 2.623 264.4


5. Results and discussions

Since entropic effects are known to be a dominant

factor for the reactivity of weakly interacting systems,

[32] enthalpy lowering by hydration might be offset

by the TDS term. This is obviously the case for the

well-known water dimer (H2O)2 [33]. However, it

should be pointed out that some systems investigated

here contain many low-frequency modes. These are,

in particular, H3Oþ.3 H2O and HO2.3 H2O where 15

low-frequency modes are in the range of 60–

600 cm21. In such cases a statistical thermodynamic

analysis based on the harmonic oscillator approxi-

mation may result in significant errors [34]. Even

more problematic appears to be the use of the ideal-

gas-phase rigid-rotor harmonic-oscillator partition

function expressions to describe molecules in sol-

utions where many intermolecular interactions are

likely to be significant. However, it appears to have

become common practice to use DG o values not only

in the gas phase but also in combination with self-

consistent-reaction-field (SCRF) models of bulk

solvent effects [35,36]. Therefore, for the sake of

completeness and comparability, we have also

included DG o(aq.) values in Tables 3–7 for the

equations of interest, (Eqs. (1A, 2, 3, 4, and 7)) and

aquated analogues.

The evaluation of the calculated reaction energies

could be performed, in principle, from experimental

data, however, these are rare. For example, the

experimental Gibbs energy change DG o(aq.) for the

reaction zNO þ zNO2 ! N2O3 (Eq. (5)) is reported as

216.7 kJ mol21, without giving a range of uncer-

tainty [37]. This value is reasonably approximated at

the G3MP2B3//PCM/B3LYP/cc-pvtz level of theory

by 26.7 kJ mol21. For comparison, the experimental

value [38 – 42] of DG o(gas), þ 3.5 kJ mol21, is

almost perfectly reproduced at the G3MP2B3 level

with DG o(gas) ¼ þ3.8 kJ mol21. In the following,

the computational results of Eqs (1A,2, 3, 4 and 7) are

presented and compared with experimental data

where this is possible.

ONOO2 !z NO þ Oz22 One of the suggested reac-

tions initiating ONOO2 decomposition is the reverse

Table 3

ReactionenthalpyandGibbsenergychanges(kJ mol21)atG3MP2B3

(DH o(gas) and DG o(gas)) and G3MP2B3//PCM/B3LYP/cc-pvtz

(DG o(aq.)) computational levels for reactions ONOO2! zNOþOz22

(Eq. (1A)) and ONOO2:H2O! zNOþOz22 :H2O

ONOO2 ONOO2.H2O

DH o(gas) 148.5 136.0

DG o(gas) 106.3 89.5

DG o(aq.) 136.4 54.4

Table 4

Reaction enthalpy and Gibbs energy changes (kJ mol21) at

G3MP2B3 (DH o(gas) and DG o(gas)) and G3MP2B3//PCM/

B3LYP/cc-pvtz (DG o(aq.)) computational levels for two ONOOH

conformers for homolysis ONOOH ! · · ·NO2 þ· · ·OH (Eq. (2)).

The shallow minimum on the energy hypersurface for the cis-perp

conformer could not be detected at the B3LYP/6-31G(d) level

implemented in G3MP2B3. Therefore, the B3LYP/cc-pvtz elec-

tronic energy difference of conformers is used. Dipole moment m

(D) in the gas phase and Gibbs energy of the solvent DG(solv.)

ONOOH ONOOH

cis-cis cis-perp

DH o(gas) 77.8 70.7

DG o(gas) 34.7 31.0

DG o(aq.) 28.5 46.4

m 0.95 1.69

DG(solv.) 211.2 229.0

Table 5



B3LYP/cc-pvtz (DG o(aq.)) computational levels for homolysis

ONOO2 ! · · ·NO2 þ O· · ·2 (Eq. (4)) and ONOO2.H2O ! · · ·

NO2 þ O· · ·2.H2O

ONOO2 ONOO2.H2O

DH o(gas) 244.8 197.1

DG o(gas) 208.8 150.6

DG o(aq.) 25.1 72.0

Table 6



B3LYP/cc-pvtz (DG o(aq.)) computational levels for electron

transfer reactions zOH þ NO22 ! OH2 þ zNO2 (Eq. (3)) and

zOH þ NO22 :H2O ! OH2:H2O þ zNO2

Without H2O With H2O

DH o(gas) 47.7 20.4

DG o(gas) 48.1 25.0

DG o(aq.) 2123.4 262.8


of reaction 1. Strong hydrogen bonding is expected for

the ionic species in aqueous solution. In particular, the

H-bond strength (DH o(gas)) of the Oz22 :H2O complex

(82.0 kJ mol21) is slightly higher than that of the

ONOO2.H2O complex (69.9 kJ mol21; Table 2).

Thus, we can expect that inclusion of a water

molecule to the anions might facilitate this kind of

homolysis of peroxynitrite. As can be seen in Table 3,

this effect predominates only after bulk solvent effects

are taken into account, where DG o(aq.) for homolysis

is reduced from 136.4 to 54.4 kJ mol21. The exper-

imental value of DG o(aq.) ¼ 64.4 kJ mol21 is

obtained from Gibbs energy of formation DfGo(aq.)

values of the contributing species which are summar-

ized in Table 8.

ONOOH !z NO2 þz OH Since homolysis of per-

oxynitrous acid is still controversial, the Gibbs energy

of reaction of this process is revisited here. Exper-

imental evidence suggested the Gibbs energy change

of homolysis in the gas phase of DG o(gas) ¼

46.0 ^ 12.6 kJ mol21, and an enthalpy of

DH o(gas) ¼ 87.9 ^ 12.6 kJ mol21[12]. (In the fig. 6

as well as in the abstract of Ref. [12] these DG and DH

values are obviously exchanged by mistake). More

recent studies arrived at a Gibbs energy change of

DG o(aq.) ¼ 53.1 ^ 15.5 kJ mol21, [43] and some-

what later DG o(aq.) ¼ 56.9 ^ 1.7 kJ mol21 [7].

Alternative values are DG o(gas) ¼ 30.1 and

DG o(aq.) ¼ 66.9 kJ mol21 [44]. Very recently a

DH o(aq.) value of 88.7 kJ mol21 has been measured

for the activation enthalpy of ONOOH decomposition

[9]. In a careful earlier computational study two

different conformers for ONOOH were considered,

cis-cis and cis-perp, and the thermochemical

corrections of homolysis were based at the G2 level

of theory [21]. Although the authors

presented calculated enthalpies H o and Gibbs ener-

gies G o of formation for ONOOH, the final answer for

homolysis is based solely on experiments. These

yielded the Gibbs energy for homolysis of

DG o(gas) ¼ 56.5 and DH o(gas) ¼ 97.1 kJ mol21. A

complete computational investigation of homolysis at

the B3LYP/6-31G* level of theory provided

DG o(gas) ¼ 37.7 and DH o(gas) ¼ 94.1 kJ mol21,

[22]. and quite similar data at a more advanced

method [23].

Meanwhile, improved computational procedures

became available, and therefore, we applied

G3MP2B3 instead of G2, and PCM instead of

SCIPCM for bulk solvent effects. The most important

result can be seen in Table 4: When going from

DH o(gas) or DG o(gas) to DG o(aq.), the energetic

sequence of the conformers, cis-cis more stable than

cis-perp, is reversed. This reversion can be explained

by the different dipole moments of 0.95 and 1.69 D of

the cis-cis and cis-perp conformers of ONOOH,

respectively, which might cause different Gibbs

energies of the solvent DG(solv.) of 211.2 and

229.0 kJ mol21, respectively. In addition, when

going from DG o(gas) to DG o(aq.), the Gibbs energy

change of homolysis is slightly decreased for

Table 7



B3LYP/cc-pvtz (DG o(aq.)) computational levels for reactions

ONOO2 þ N2O3 ! 2zNO2 þ NO22 (Eq. (7)) and ONOO2:H2O þ

N2O3 ! 2zNO2 þ NO22 :H2O

ONOO2 ONOO2.H2O

DH o(gas) 2111.3 2108.4

DG o(gas) 2156.1 2152.3a

DG o(aq.) 2165.7 2152.3a

a These values turned out to be accidentally equal within the

chosen accuracy.

Table 8

Experimental standard Gibbs energies of formation Df-

G o(aq.)/kJ mol21 in aqueous solution, rough estimates in parenth-

eses. Standard Gibbs energies of formation (T ¼ 298.15 K,

p ¼ 1 bar, pH ¼ 0) can be transformed to a specified pH [45]

System DfGo(aq.) Ref.

Oz2 93.7 [9]

Oz22 31.8 [7]

zOH 25.9 ^ 0.4 [7]

OHþ (443.5 ^ 41.8) [12]

OH2 2157.3 [38–42]

H2O 2237.1 [38–42]zNO 102.1 [7]zNO2 63.2 [7]

NOþ2 217.6 [12]

NO22 232.2 [38–42]

ONOOz (83.7 ^ 8.4) [12]

ONOO2 69.5 ^ 1.7 [7]

NO23 2111.3 [38–42]

ONOOH 31.5 ^ 2.3 [7,9]


the conformer cis-cis, but increased for the conformer

cis-perp. Since the cis-perp conformer is at present

not available at the G3MP2B3 level due to the shallow

energy minimum, the electronic energy difference of

conformers is taken from B3LYP/cc-pvtz

calculations.

Summarizing, we suggest DG o(gas) ¼ 34.7

kJ mol21 for the Gibbs energy change of homolysis.

This value is supported by the following Gibbs

energies of formation DfGo(gas) which have been

calculated at the G3MP2B3 level (experimental

values in parentheses) [38–42]: zNO2 48.7 (51.3);zOH 28.8 (34.3); ONOOH 42.8 (-) kJ mol21. From

these calculated values, the Gibbs energy of reaction

for homolysis of ONOOH (cis-cis ) turned out to be

DG o(gas) ¼ 34.7 kJ mol21, which is identical with

the value of the direct calculation by means of total

Gibbs energies (Table 4). The most relevant calcu-

lated value for homolysis of ONOOH in aqueous

solution, based on the cis-perp conformer, is

DG o(aq.) ¼ 46.4 kJ mol21.

We suggest for the future not to treat the two

energetically closely spaced conformers (rotamers)

independently. Instead, a common treatment based on

the anharmonicity of the energy hypersurface should

be performed.

ONOO2 ! zNO2 þ Oz2 The mechanism of homo-

lysis of ONOO2 into zNO2 þ Oz2 was discussed

recently and the equilibrium constant was obtained

[9]. In order to complete our knowledge of this

reaction, the G3MP2B3//PCM/B3LYP/cc-pvtz com-

putational procedures were applied to calculate the

Gibbs energy of reaction. Strong hydrogen bonding of

the anionic species is expected in aqueous solution.

At the G3MP2B3 level, the H-bond strength for

Oz2.H2O ! Oz2 þ H2O with DH o(gas) ¼ 117.2

and DG o(gas) ¼ 90.4 kJ mol21 (see Table 2)

turned out to be significantly stronger than

that for ONOO2.H2O ! ONOO2 þ H2O with

DH o(gas) ¼ 69.9 and DG o(gas) ¼ 32.6 kJ mol21,

where the electronic excess charge at the proton

acceptor is delocalized. Therefore, strongly bonded

water molecules at ionic species ONOO2 and Oz2

facilitate homolysis in the gas-phase as can be seen in

Table 5. Surprisingly, the effect of strong H-bonds is

reversed when going from DG o(gas) to DG o(aq.).

The experimental Gibbs energy change of homolysis

of ONOO2 in water can be evaluated from the Gibbs

energies of formation of the contributing systems.

The DfGo(aq.) values of interesting systems in this

context, which are widely distributed in the literature,

are collected in Table 8. The agreement between the

G3MP2B3//PCM/B3LYP/cc-pvtz calculated (72.0)

and the experimentally determined Gibbs energy

change DG o(aq.) (87.4 kJ mol21) [9] of homolysis

is satisfying. The meaning of the calculations,

however, is not only to reproduce experimental data.

Calculations are able to compose the final energy

values from electronic effects, chemical interactions

(strong H-bonds), thermochemical corrections, and

bulk solvent effects, as can be learned from Table 5.zOH þ NO2

2 ! OH2 þ zNO2 The suggested rapid

electron transfer reaction occurring between NO22 and

zOH can be understood in the gas-phase by the

ionization energies of NO22 and OH2 which are

known to be 2.27 and 1.83 eV, respectively [38–42].

This difference of ionization energies of 42.5 kJ mol21

is close to the DH o and DG o values shown in Table 6.

The attachment of a water molecule to each anion

compensates for the above difference of ionization

potentials as can be seen from the H-bond strengths of

NO22 :H2O and OH2.H2O which are 66.5 and

114.6 kJ mol21, respectively (Table 2). Bulk solvent

effects facilitate the reaction, but the neglect of strong

H-bonds exaggerates this trend (cf. DG o(gas) and

DG o(aq.) inTable6).ThefinalGibbs energyof reaction

is calculated to be DG o(aq.) ¼ 262.8 kJ mol21.

ONOO2 þ N2O3 ! 2zNO2 þ NO22 An additional

reaction vital for the decomposition of peroxynitrite

was studied theoretically. This reaction must be

exothermic in the gas-phase as well as in aqueous

solution. Comparison of the calculated change of

Gibbs energies DG o(gas) and DG o(aq.) without and

with consideration of strong H-bonds shows that the

DG o value is affected neither by the attached water

molecule at anions nor by bulk solvent effects. The H-

bond strengths for both anion-water complexes

are almost equal according to Table 2. The

calculated Gibbs energy of reaction is

DG o(aq.) ¼ 2152.3 kJ mol21.

6. Conclusions

For the calculation of Gibbs energies of reaction

in aqueous solution, the combination of methods


abbreviated by G3MP2B3//PCM/B3LYP/cc-pvtz was

found to be suitable for the suggested series of

elementary processes. In particular, for

different homolysis and isomerization processes of

peroxynitrite, ONOO2 ! zNO þ Oz22 (Eq. (1A)) or

zNO2 þ Oz2 (Eq. (4)) or NO23 (not discussed here), the

calculated DG o(aq.) values of reaction differ from the

experimental values 64.4, 87.4, 2 180.8 kJ mol21,

respectively, by þ 72.0,262.3,223.8 kJ mol21,

respectively, if the contributing anions are treated as

isolated systems in the polarized continuum;

however, the addition of a water molecule to

anions decrease the corresponding uncertainty

to 2 10.0, 2 15.4, 2 11.9 kJ mol21, respectively.

These results reflect the unrealistic model for isolated

anions in a polarized continuum. At least one water

molecule is necessary to consider strong chemical H-

bond to each anion to obtain realistic Gibbs energies

of reaction. The computational procedure G3MP2B3//

PCM/B3LYP/cc-pvtz is a useful tool for the calcu-

lation of Gibbs energies of reaction for the case of

lacking or uncertain experimental values.

Acknowledgements

S. Pfeiffer and B. Mayer gratefully acknowledge

the support of this work by grant 13784-MED from

the “Fonds zur Forderung der Wissenschaftlichen

Forschung” in Austria. Silvia Pfeiffer is a recipient of

an Austrian Academy of Sciences APART fellowship

(APART 7/98).

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Gibbs energies of reactive species involved in peroxynitrite chemistry calculated by density functional theory