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Reaction rates of the hydrated electron with N2O in high temperature water and potential surface of the N2O− anion

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Reaction rates of the hydrated electron with N2O in high temperature water and potential surface of the N2O− anion
  Reaction rates of the hydrated electron with N 2 O in hightemperature water and potential surface of the N 2 O  anion  q Kenji Takahashi  a,*,1 , Shintaro Ohgami  a , Yasushi Koyama  a , Sadashi Sawamura  a ,Timothy W. Marin  b , David M. Bartels  b,*,2 , Charles D. Jonah  b a Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan b Chemistry Division, Argonne National Laboratory, Argonne, IL 60439, USA Received 10 June 2003; in final form 4 November 2003 Abstract The reaction rate of hydrated electrons, (e  ) aq , with N 2 O can be fitted with an Arrhenius-type temperature dependence up to300   C with an activation energy of 15.5 kJ/mol. At higher temperatures, the rate constant decreases to give a local minimum at380   C. Ab initio calculations of the N 2 O  anion suggest a possible dissociation path of N 2 O  in water. The calculated free energiesfor electron transfer suggest the (e  ) aq  reaction with N 2 O should fall on the   normal   part of the Marcus parabola, and for thisreason the reaction is not diffusion limited.   2003 Elsevier B.V. All rights reserved. 1. Introduction Hydrated electrons, (e  ) aq , and hydroxyl radicals,OH, represent two of the primary species formed inwater radiolysis. The reaction of nitrous oxide, N 2 O,with (e  ) aq  has been widely used to convert (e  ) aq  to OHradicals in water [1]. The reduction of N 2 O produces theN 2 O  anion, which dissociates to give O  and N 2 . TheO  anion immediately reacts with a water molecule togive OH radicals and OH  .While there has been considerable interesting re-search on the electron attachment to N 2 O in the gasphase [2–12], the presence of solvent molecules will sig-nificantly alter the electron affinity, molecular structureand chemical reactivity of N 2 O. One cannot apply thegas phase data to an N 2 O solution. A thermal electron isvery unreactive with an isolated N 2 O molecule in the gasphase [13], while in the condensed phase, this reaction isclose to diffusion controlled. Thus, the effects that ac-celerate the gas phase-reaction are probably not relevantfor the condensed-phase reaction. The differences be-tween gas and condensed phase are not confined to N 2 Osolutions. For e.g., we have demonstrated for CO 2 molecules that the CO   2  anion is unstable in the gasphase while the CO   2  anion is stable in water and CO 2 dimer anion is stable in supercritical CO 2  [14,15]. Thereactivity of CO 2  and the CO   2  anion in a high-densitysupercritical CO 2  is significantly different from that ingas phase [15].In recent pulse radiolysis/optical absorption work, thereaction of N 2 O with (e  ) aq  was used to study reactionsof OH radicals with several solutes under both sub- andsupercritical water conditions [16–19]. It is widely ac-knowledged that OH radical reactions play an importantrole in supercritical water oxidation [20]. To make intel-ligent use of N 2 O as an (e  ) aq  scavenger and a source of OH radicals, knowledge of the reaction rate constant of (e  ) aq  with N 2 O is necessary over a wide range of tem-peratures, exceeding the critical temperature of water. Chemical Physics Letters 383 (2004) 445–450www.elsevier.com/locate/cplett q Work at Argonne performed under the auspices of the Office of Science, Division of Chemical Science, US-DOE under contractnumber W-31-109-ENG-38. * Corresponding authors. Fax: +81762344829. E-mail addresses:  ktkenji@t.kanazawa-u.ac.jp (K. Takahashi),bartels@anl.gov (D.M. Bartels). 1 Present address: Department of Chemistry and Chemical Engi-neering, Kanazawa University, 2-40-20 Kodatsuno, Kanazawa 920-8667, Japan. 2 Present address: Radiation Laboratory, University of Notre Dame,Notre Dame, IN 46556.0009-2614/$ - see front matter    2003 Elsevier B.V. All rights reserved.doi:10.1016/j.cplett.2003.11.050  In this Letter, we report the reaction rate of (e  ) aq  with N 2 O in high temperature water, includingthe supercritical regime. We also report ab initio calcu-lations used to explore the potential energy curves of theN 2 O  anion in water. A possible dissociation path of the N 2 O  anion and its energetics in water will bediscussed. 2. Experimental The experimental system is basically the same aspreviously described [21] except for the electron accel-erator used. We shall only give an outline of the ex-perimental system; please see the cited references forfurther details.Electron pulse radiolysis experiments were carriedout using the 45 MeV Linac installed at HokkaidoUniversity. Kinetics were measured by injecting a 10 nselectron pulse and monitoring the optical absorption of (e  ) aq  at 800 nm. A pulsed 300 W xenon-arc lampprovided the probe light, and the wavelength was iso-lated using a 10 nm bandwidth interference filter. Theprobe light was detected with a reverse-biased photodi-ode (EG&G FND100), and data were acquired using adigital oscilloscope (LeCroy model 9362). Data analysiswas carried out using standard non-linear least-square-fitting techniques.The high-pressure cell used for these measurementshas been previously described [21]. Stock solutions of water purged with N 2 O at 1 atm were mixed with de-gassed pure water using two separate HPLC pumps(JASCO PU-980). The flow rates of the pumps at highpressurewerecalibratedbyweighingtheamountofwaterpumped over the course of 1 min. The total flow rate waskept constant (normally 4 ml/min) to maintain a stabletemperature and pressure in the sample cell. Five totwenty decay signals of the hydrated electrons were av-eraged, depending on the temperature. Examples of the(e  ) aq  decay signals in 300   C water are shown in Fig. 1.Solid lines are pseudo-first-order fits to the observed de-cay signals. The pseudo-first-order reaction rates weremeasured using four or five different N 2 O concentrations(ranging from 10 to 400  l M, see inset of Fig. 1). Themolal scavenger concentration was calculated from therelative flow rates of the HPLC pumps. The final molarconcentration was calculated from the density of water atthe experimental temperature and pressure. 3. Results and discussion 3.1. Reaction rate as a function of temperature Fig. 2 shows an Arrhenius plot for the reaction of (e  ) aq  with N 2 O at a constant pressure of 260 bar. Therate constant essentially shows Arrhenius behavior up to300   C. Above 300   C, the rate constant gradually de-creases and gives a very sharp   dip   at 380   C, afterwhich it increases again. This behavior can be explainedby considering the nature of solvent clustering and localdensity enhancements in supercritical water. Near thecritical region, the entropic driving force that favorsvaporization roughly balances the attractive potentialbetween the solvent molecules responsible for conden-sation. Microclusters of molecules are constantly form-       A      b     s     o     r     p      t      i     o     n 4003002001000 Time / s (x10 -9  ) 6040200       k      /     s    -      1       (    x      1      0       6       ) 3002001000 [N 2 O] / M (x10 -6  ) Fig. 1. Sample decay signals for hydrated electron scavenging by N 2 Oin 300   C and 260 bar. Solid lines are fits. Inset: pseudo-first-order plotillustrating the concentration dependence of the observed scavengingrate at 300   C. 9 10 1023456789 10 1123    k   /   M   -   1     s   -   1 1/T /K -1   (x10 -3  )  N 2 O O 2 Fig. 2. Arrhenius plot for the reaction of the hydrated electron withN 2 O. The solid line indicates a fit up to 300   C, and the dashed line is afit up to 150   C. Reaction rates of the hydrated electron with O 2  [23]are also plotted for comparison.446  K. Takahashi et al. / Chemical Physics Letters 383 (2004) 445–450  ing and dissipating. In this environment, solute mole-cules with attractive potential relative to the solvent willtend to form the nucleus of a cluster and be found in aregion of local density enhancement relative to the bulkaverage. A solute with repulsive potential can be ex-pected to be found more often in the voids between thedynamic solvent clusters [22]. In our previous work [23],we interpreted our results by assuming that the hydratedelectron in 380   C water will strongly solvate withinwater clusters while hydrophobic molecules will be seg-regated in the voids between dynamic water clusters. Onaverage, a potential of mean force develops to preventreactive contact between the hydrated electron and hy-drophobic species.Fitting the rate constants over the temperature rangefrom 30 to 300   C gives an activation energy of 15.5  1.5 kJ/mol. The slight curvature in the Arrheniusplot will give a higher activation energy if we fit thelower temperature data. A fit of the rate constants be-tween room temperature and 150   C gives an activationenergy of 18.6  1.5 kJ/mol (0.19 eV). The reaction rateconstants are summarized in Table 1.A similar activation energy for the reaction of (e  ) aq with oxygen (14.0 kJ/mol) was previously obtained [23].In Fig. 2, the rate constant for the reaction of (e  ) aq  withoxygen (at 250 bar) is also plotted for comparison. Upto 300   C, the reaction rate constant of (e  ) aq  with N 2 Ois slightly smaller than that for oxygen. The activationenergy for the diffusion of (e  ) aq  in water measured upto 100   C is 20.3 kJ/mol [24], and previous studies of thereaction of (e  ) aq  with nitrobenzene indicate an activa-tion energy of 20.8 kJ/mol up to 300   C [25]. Hence, thereaction of (e  ) aq  with N 2 O at higher temperatures isnot diffusion-limited. 3.2. Potential energy curve of N  2 O  anion in water There are several questions regarding the nature of the N 2 O  anion. These include: (1) the threshold fordissociative electron attachment and (2) the electronaffinity. Even though established thermodynamic mea-surements calculate a value for the threshold for disso-ciative electron of 0.26 eV, most gas phase experimentsobserve an O  signal at 0 eV [6]. This disparity wasresolved by Chantry [26], who showed that the resultsdepend on pressure. While the adiabatic electron affinityof N 2 O in the gas phase is assigned to be +0.22 eV [8],there are both experimental and theoretical results onthe electron affinity that disagree with this value (fore.g., [9–11]), and the reason for this disparity has notbeen determined.For N 2 O  formed in water, our understanding is verylimited. There is no information on the electron affinity,structure of the anion, and the potential curves for dis-sociation of the anion. For this reason, we examined thesolvent effect on stability and dissociation of the N 2 O  anion rather than explaining the temperature effect onthe reaction rates.Ab initio calculations of the N 2 O  anion were per-formed using G AUSSIANAUSSIAN  98 [27]. The geometries wereinitially optimized using B3LYP/(aug)-cc-pVDZ meth-ods. The energies were further refined using quadraticconfiguration interaction, QCISD(T), in conjunctionwith the (aug)-cc-pVDZ basis set. Solvation effects weresimulated using the polarized continuum model (PCM)of Tomashi [28], which is available as a self-consistentreaction field (SCRF) theory in G AUSSIANAUSSIAN  98.It is known that the N 2 O  anion has a bent formwith an N–N–O bond angle of about 133   in the gasphase [12]. The bond lengths of N–O and N–N arestretched as compared with the neutral species. Re-cently, Kryachko et al. [12] performed extensive abinitio calculations on N 2 O and N 2 O  using a aug-cc-pVQZ basis set at the coupled-cluster level, CCSD(T).According to their calculations, the N 2 O  anion lies0.26 eV above neutral N 2 O in gas phase. They foundtwo transition states of the N 2 O  anion as shown inFig. 3 (ATS and ATT  ).We have confirmed the negative (adiabatic) electronaffinity of N 2 O in gas phase at the QCISD(T)/aug-cc-pVDZ level. Fig. 4 shows the potential energy of theN 2 O  anion in the gas phase and in PCM water as afunction of the N–N–O bond angle. The zero of energywas defined as the ground state of N 2 O in the gas phase.The N–N and N–O bond lengths were fixed as 1.185 and1.302  AA, respectively. In the gas phase, the energy of theN 2 O  anion in its relaxed (bent) form is 0.16 eV  above the ground state of linear neutral N 2 O. The lowest pointof crossing between the energy curves of the N 2 O  an-ion and N 2 O occurs at a bond angle of about 150  . Thepotential barrier for the electron autodetachment is Table 1Reaction rates between N 2 O and (e  ) aq  at 260 bar T   (K)k(M  1 s  1 )299  0.5 9.36E+09  1.50E+07302  0.5 1.05E+10  6.82E+08373  0.5 3.24E+10  1.97E+09424  0.5 7.26E+10  4.52E+09424  0.5 7.94E+10  6.63E+09448  0.5 1.15E+11  2.44E+09448  0.5 9.11E+10  2.29E+09473  0.5 1.06E+11  2.38E+09498  0.5 1.46E+11  3.48E+09533  0.5 1.64E+11  8.40E+09554  0.5 2.20E+11  8.72E+09583  0.5 2.26E+11  8.91E+09603  0.5 2.30E+11  1.08E+10623  0.5 1.92E+11  1.25E+10653  0.5 7.27E+10  4.04E+09668  0.5 1.51E+11  2.45E+09674  0.5 1.16E+11  3.35E+09 K. Takahashi et al. / Chemical Physics Letters 383 (2004) 445–450  447  0.45 eV. Conversely, in water the energy of the bentN 2 O  anion is 2.5 eV  below  the ground state of neutralN 2 O with bond lengths N–N ¼ 1.196   AA andN–O ¼ 1.311  AA. Even in a non-relaxed linear form of theN 2 O  anion, the energy is 0.7 eV  below  the ground stateof N 2 O. Hence in water the electron attachment to N 2 Ois energetically favorable.In both the gas phase and in water, it is known thatthe N 2 O  anion dissociates into N 2  and O  after elec-tron attachment [1]. Consequently, we now turn to thepotential energy of the N 2 O  anion as a function of theN–O bond length. We calculated the potential energycurves for two selected N–N–O bond angles of 180   and132  . The results are shown in Fig. 5. Let us first con-sider the potential energy curve of the N 2 O  anion inwater. For the potential energy with N–N–O ¼ 180  , aminimum ( ) 0.33 eV) is located at a N–O bond length of 1.3  AA. With increasing bond length, the energy increases,and then sharply drops at a bond length of 1.45   AA. Theenergy difference between the local minimum and thesharp   peak   is 0.23 eV. If the vibrational excitation en-ergy exceeds this potential barrier, the N 2 O anion willeasily dissociate into N 2  and O  .For the potential energy curve with a N–N–O angleof 132  , a broad potential barrier for dissociation intoN 2  and O  was found at a bond length of about 1.7   AA,and a local minimum was found at a bond length of about 1.3   AA. The energy difference between the localminimum and the broad potential barrier is 0.28 eV.Both of the bond angles selected for calculations indi-cate that only a small energy (0.21–0.28 eV) is requiredto overcome the potential barrier for the dissociation of the N 2 O  anion in water.Kryachko et al. [12] reported two different geometriesfor the N 2 O  anion in the gas phase. One is a well-knownbent form (A1 in Fig. 3), and another is a cyclic structurewith long N–O bond lengths (A2 in Fig. 3). They sug-gested that following electron attachment, the N 2 O sys-tem undergoes a facile dissociation process through thecyclic isomer to the final fragments, e  +N 2 O ! A1(0.26 eV) ! ATS (0.52 eV) ! A2 (0.03 eV) ! N 2  +O  .The numbers in parentheses are energies relative to theground state of neutral N 2 O.In case of the N 2 O  anion in water, an optimizedcyclic geometry was obtained. However, the bond lengthof N–O is 3.5   AA, suggesting that the O  is almost dis-sociated from the N 2 O system at this geometry. There-fore, we think that following the electron attachment inwater, the N 2 O  anion will change geometry to the bentform and then dissociate through the small potentialbarrier shown in Fig. 5. 3.3. Thermochemistry and energetics of the N  2 O  anion Using the calculated solvation energies, we canelucidate the free energy of formation of the N 2 O  anion at 298.15 K in water. After the standard statecorrection of the SCRF [29] and considering the con-vention that the free energy of formation of solvated OOOON NN NN NNN 1.2091.331.1581.6731.124 2.7481.1232.720133.2130.1 A1ATSATS*A2  Fig. 3. Optimized geometries of the N 2 O  anion in the gas phase.Bond lengths and angles shown are values reported by Kryachko et al. 3210-1-2-3    R  e   l  a   t   i  v  e   E  n  e  r  g  y   /  e   V 180160140120100 N-N-O Angle Gas phase N 2 O N 2 O -  anion In water N 2 O N 2 O - anion  Fig. 4. Potential energy curves of N 2 O and the N 2 O  anion in the gasphase and water as a function of N–N–O angle. The potential curve forN 2 O in water (dashed line) is nearly indistinguishable from the po-tential surface of N 2 O in gas phase (filled circle).448  K. Takahashi et al. / Chemical Physics Letters 383 (2004) 445–450  protons is zero [29], the free energy of formation canbe written as D G  0f  ð N 2 O  ð aq ÞÞ¼ D G  0SCRF ð N 2 O  Þþ D G  0f  ð N 2 O  ð g ÞÞþ 425 : 5 kJ = mol ¼ 276 : 6 þ 90 : 8 þ 425 : 5 ¼ 239 : 7 kJ = mol :  ð 1 Þ Including the free energy of formation of hydratedelectron,  D G  0f   (e  (aq)), the free energy of the reaction, D G  0rxn , can be calculated as D G  0rxn ¼ D G  0f  ð N 2 O  ð aq ÞÞ D G  0f  ð e  ð aq ÞÞ D G  0f  ð N 2 O ð aq ÞÞ¼ 239 : 7  275 : 7  100 : 8 ¼ 136 : 8 kJ = mol ;  ð 2 Þ where  D G  0f  (e  (aq)) is estimated from [30]. The gas-phaseenthalpy and entropy of N 2 O are obtained from experi-mental references [31], and the solvation energy of N 2 O iscalculated using the SCRF. These values are useful inconsidering the reduction of N 2 O on an electrode.It is well known that Marcus theory predicts a max-imum in the electron transfer rate when the free energychange balances the reorganization energy  E  r , that is,when  D G  0rxn þ  E  r  ¼ 0. In the case of    D G  0rxn  >  E  r , thereaction falls in the so-called Marcus   inverted region  [32]. The results of Marcus theory and its extensionsincorporating quantum vibrational degrees of freedomis an electron-transfer rate expression taking the form[33] w ð  R ; T  Þ¼j V   j 2  h  ffiffiffiffiffiffiffiffiffiffiffiffi ffi p  E  r k  B T  r  X n f  S   0 ; n f  ð Þ exp   D G  0rxn þ  E  r þ n f  x   2 4  E  r k  B T  " # ;  ð 3 Þ where  V    is the matrix element for electron transfer, S   (0 ; n f  ) is the Frank–Condon overlap factor for thetransition from the ground state of acceptor to a vib-rationally excited state of the reduced product, and thesum is taken over quantized vibrational states of prod-uct with energies  n f  x .Two effects contribute to the total reorganizationenergy. The first is the solvent reorganization energywhere the reactants are assumed to be spherical mole-cules surrounded by a dielectric continuum. The secondcontribution is the energy for structural changes in thereactants, or internal reorganization energy. The solventreorganization energy  k s  can be calculated using thefollowing well-known equation: k s  ¼  1 e opt     1 e s   12 r  a   þ  12 r  b  1  R  ;  ð 4 Þ where  e opt  and  e s  are the optical and static dielectricconstants of the solvent, respectively, and  r  a ; r  b  and  R are radii of reactants and intermolecular reaction dis-tance. The internal reorganization energy may be cal-culated from the difference in energy between the linearand bent N 2 O  anions (1.8 eV).In Table 2, the calculated total reorganization en-ergies are summarized for several different reactiondistances  R . The radius of the hydrated electron wasestimated from moment analysis modeling of the tem-perature-dependent absorption spectra of the hydrated Table 2Reaction distances and solvent reorganization energies for the(e  ) aq  +N 2 O reaction r  ð e  aq Þ (  AA) r  (N 2 O)(  AA)  R (  AA) k s (eV)  E  r (eV)2.43 2.0 6 2.3 4.12.43 2.0 8 2.6 4.42.43 2.0 10 2.8 4.62.43 2.0  1  3.6 5.4 1086420-2-4      R    e     l    a     t     i    v    e     E    n    e    r    g    y     /    e     V Bond Length ofN-O Gas PhaseN 2 O(NNO=180)N 2 O - anion (NNO=133)In waterN 2 O - anion (NNO=132)N 2 O - anion (NNO=180)-3-2- Bond Length ofN-O0.23 eV0.28 eV Fig. 5. The potential energy curves of N 2 O and the N 2 O  anion in the gas phase and water as a function of N–O bond length. K. Takahashi et al. / Chemical Physics Letters 383 (2004) 445–450  449
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