Mechanism of the oxidation reaction of Cu with N2O via nonadiabatic electron transfer

Mechanism of the Oxidation Reaction ofCu with N2O via Nonadiabatic ElectronTransfer

EUGENE S. KRYACHKO,1,2 OKSANA TISHCHENKO,1

MINH THO NGUYEN1

1Department of Chemistry, University of Leuven, Celestijnenlaan 200 F, B-3001 Leuven, Belgium2Bogoliubov Institute for Theoretical Physics, Kiev 03143, Ukraine

Received 1 October 2001; accepted 1 October 2001Published online 9 July 2002 in Wiley InterScience (www.interscience.wiley.com).DOI 10.1002/qua.10296

ABSTRACT: We treat the present work as an attempt to elucidate the mechanism of theoxidation reaction of the Cu atom by nitrous oxide based on our recent work (Kryachko,E. S.; Vinckier, C.; Nguyen, M. T. J Chem Phys 2001, 114, 7911) on the electron attachmentto this molecule. We suggest that the title reaction in its Arrhenius regime occurs via thenonadiabatic electron transfer from Cu to the oxygen atom at the crossing of the potentialenergy surfaces Cu(4s 2S1/2) � N2O(X 1��) and Cu� � N2O�, where the latter is linked tothe complex N2O� originated from the higher-energy T-shape N2O molecule anddiscovered in the aforementioned work. The calculations performed in the present workusing a variety of quantum chemical methods support the proposed model. We also showthe existence of other reaction pathways of the title reaction that, we believe, contribute toits non-Arrhenius behavior observed experimentally at T � 1190 K. © 2002 WileyPeriodicals, Inc. Int J Quantum Chem 89: 329–340, 2002

Key words: nitrous oxide; oxidation reaction of Cu with N2O; crossing of potentialenergy surfaces; Arrhenius regime

1. Introduction

N itrous oxide (N2O) is an important long-livedgas whose increasing concentration in the at-

mosphere and known ability to deplete the ozone

layer and contribute to the greenhouse effect hasrecently become a subject of intensive study anddebate [1] mainly focusing on the mechanisms reg-ulating N2O production and balancing it with theconsumption of N2O. The latter task opens a widearea of modeling and understanding the favorablemechanisms of the reduction of the N2O emission.One of them leading actually to the decompositionof N2O is to use heterogeneous catalysts includingtransition metals, copper in particular [2, 3]. As iswell known, the oxidation reaction of N2O withmetal atom resulting in the metal oxide and N2 as

Correspondence to: E. S. Kryacko; e-mail: [email protected]

This article is dedicated to the memory of Professor IvanZhelyaskov Petkov who, together with Professor Mario Stoitsovand one the authors (E. S. K.) proposed nearly 20 years ago thelocal-scaling density functional theory for many-electron sys-tems.

International Journal of Quantum Chemistry, Vol 89, 329–340 (2002)© 2002 Wiley Periodicals, Inc.

the products proceeds via the following schemetaken, for example, for the Cu atom [4]:

Cu�4s2S1/ 2� � N2O�X1��f

CuO�X2�� N2�X1�g��. (1)

It is worth mentioning that the reactions of thesimilar type with alkali, alkali earth, and transitionmetal atoms are interesting on their own due to thefact [4–9] they are usually highly exothermic andexhibit complex kinetic behaviors because the metaloxide products are often formed on the energeti-cally accessible lower-lying excited-state potentialenergy surfaces (PESs). This, on the one hand, givesrise to a strong chemiluminescence and, on theother, provides a wide opportunity in theoreticalmodeling.

Reaction (1) is characterized by a large exother-micity of 27.1 kcal/mol [10] thanks to the oxygenatom, which, on the one hand, strongly binds theCu atom and, on the other, is weakly bonded to N2in nitrous oxide [9d], and, moreover, shows theexistence of two different regimes [4]. One is atypical Arrhenius whose rate constant kA(T) is de-termined by the equation

kA�T� � kA�o�exp��EA/RT�, (2)

where the preexponential factor kA(o) � 1.70 10�10

(470 K T 1190 K) [4a] or (2.4 � 0.6) 10�10 (458K T 980 K) [4b] and the activation barrier(actually the enthalpy) EA � 5129 K � 10.2 kcal/mol [4a] or 11.6 � 0.3 kcal/mol [4b]. The otherregime is non-Arrhenius, which takes place at tem-peratures above 1190 K and whose rate constantobeys the following empirical fit [4b]:

knon-A�T� � knon-A�o� T�exp��Enon-A/RT�, (3)

where knon-A(o) � 3.04 10�20, � � 2.97, and Enon-A �

6.1 kcal/mol. An appearance of a non-Arrheniusbehavior of the reaction (1) usually suggests anopening of another reaction pathway (see Ref. [6c]and references therein). What is the mechanismunderlying reaction (1)? How does then structur-ally the non-Arrhenius reaction channel look like?These questions will be addressed in the next sec-tions.

2. Theoretical Model of Reaction (1)

Two models have been proposed to describe theArrhenius regime of the types of reactions (1). Ac-cording to the electron-hopping model [7], theground-state Cu atom hops its 4sth valence electronto N2O that causes its bending and weakening ofthe NOO bond. Within this model [7a–c], the acti-vation energy EA of the oxidation reaction (1) iscertainly determined by the ionization energy IECuof Cu equal to 178.2 kcal/mol [11], although suchdependence has been recently questioned [7d–f,9d]. However, as we have recently shown [12], theelectron affinity (EA) of the ground-state N2O mol-ecule is negative by ca. �6.0 kcal/mol, meaningthat the electron hopping from Cu to the ground-state N2O must be ruled out.

The second, so-called resonance interactionmodel proposed by Fontijn and coworkers [1a, 8] isbased on the suggestion that there exists an empir-ical correlation between the experimental activationbarrier EA of reaction (1) with alkali, alkali earth,and transition metal atoms and the sum of theirionization energy and the electron s � p promotionenergy (PE). The PE of Cu is equal to 365 kJ/mol[8a]. The Fontijn model assumes that the reaction ofany of the aforementioned metal atoms Z with N2Ois governed by an activated complex (AC) com-posed of three resonating structures—S1, S2, andS3—described by the corresponding wave func-tions �1, �2, and �3. S1 is primarily formed by thecovalent interaction between the oxygen atom ofN2O and the s bonding orbital of Z. The structure S2is analogous to S1 where the covalent interaction isrealized throughout the p bonding orbital of Zwhereas the third one, S3, is suggested to be ionicand composed of the anion N2O� interacting withthe cation Z�. Therefore, the total wave function�AC of the activated complex is expressed as alinear combination of those three wave functions:

�AC � �i�1

3

ci�i, (4)

with real variational parameters ci, i � 1, 2, 3 subjectto the normalization condition ¥i�1

3 ci2 � 1, chosen

under the assumption of the mutual orthogonalityof the wave functions corresponding to the differ-ent resonating structures. �AC is then defined as theeigenfunction corresponding to the lowest eigenen-ergy of the 3 3 Hamiltonian matrix

KRYACHKO, TISHCHENKO, AND NGUYEN

330 VOL. 89, NO. 4

� H11 H12 H13

H21 H22 H23

H31 H32 H33

� , (5)

where the diagonal elements are the following:H11 � V is the barrier of the formation of S1 treatedas a model parameter, H22 � PE � V/2, and H33 isapproximated as

H33�1� � IEZ � EAN2O �

e2

Ro�

�e2

2Ro4 �

BRo

� (6)

or

H33�2� � IEZ � EAN2O �

e2�� 1�

�Ro, (7)

including in particular the attractive Coulomb andpolarization potentials and the repulsive Born-typepotential. In Eqs. (6) and (7), e is the proton charge,Ro is the sum of the univalent radii of Z� and O�, �is the sum of their polarizabilities, and � is theaveraged Born exponent. As mentioned above, theelectron affinity of the ground-state N2O molecule

is slightly negative and we may put it equal to zeroin these equations. The application of the Fontijnmodel to reaction (1) based on the present calcula-tions will be further discussed in Section 5.

The main purpose of the present work is to pro-pose a new mechanism of reaction (1) whose basicfeatures, as we believe, are valid for all reactions oftype (1) with atoms Z containing a single ns valenceelectron and that will answer the questions raised atthe end of Section 1. This mechanism is groundedon our recent theoretical study [12] of the electronattachment to nitrous oxide, whose main results arebriefly the following (partly summarized in Table Iand Fig. 1; for computational details see Section 3):

1. The electron attachment to the linear NNOmolecule N1 in its ground electronic stateN2O(X 1��) leads to the bent structure A1 ofthe N2O� with the NNO angle varying within130–140°. A1 is unstable to the either asymp-tote of N2O(X 1��) � e� with the energy offsetof about 6.0 kcal/mol or to N2 � O�.

2. There exists another anionic complex A2 ofN2O� originating from the T-shape neutral

TABLE I ______________________________________________________________________________________________Control calculations of the ground-state structures and harmonic vibrational frequencies of N2O, CuO, and N2

and anionic structures of the N2O molecule displayed in Figure 1.

Neutral N2O CuO N2

r(NON) 1.124 (1.126 [15a]) 1.094 (1.094 [15b])r(NOO) 1.184 (1.186 [15a])r(CuOO) 1.785 (1.724 [15b])NNO bend 595 (589 [15a])NO stretch 1326 (1277 [15a])NN stretch 2347 (2224 [15a]) 2456 (2359.61 [15b])CuO stretch 563 (640.17 [15b])

Anionic MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ MP2/aug-cc-pVQZ MP2/TZVP

A1 17.2 15.3 14.3 9.7A2 0.0 0.0 0.0 0.0ATS 27.2 26.5 26.5 22.0

AnionicQCISD(T)/

aug-cc-pVDZCCSD(T)/

aug-cc-pVTZCCSD(T)/

aug-cc-pVQZCCSD(T)/

TZVP

A1 7.9 6.2 5.3 5.5A2 0.0 0.0 0.0 0.0ATS 11.5 11.2 11.2 11.5

The calculations with TZVP basis set are compared with the other basis sets taken at the QCISD(T)/aug-cc-pVDZ-optimizedgeometry [12]. Bond lengths in Å, frequencies in cm�1, energies in kcal/mol after ZPVE. Experimental values are given inparentheses.

OXIDATION REACTION OF N2O WITH CU

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 331

structure N2 lying above N1 by 62.6 kcal/moland exhibiting, due to a somewhat looselybonded oxygen atom, the significant electronaffinity of ca. 2.68 eV with respect to its parentneutral species N2. A2 is placed by 3.8 kcal/mol beneath the ground-state asymptote N2 �O� and is more stable than A1 by ca. 5.3kcal/mol.

3. The anionic structure A2 has a finite lifetimewithin the detachment channel N2O(X 1��) �e� thanks to the existence of the transitionstructure ATS between A2 and A1 with thebarrier energy of about 12.0 kcal/mol.

The proposed model suggests that reaction (1) inthe Arrhenius regime proceeds in four stages that,as will be discussed in Section 5, partly reconcile theelectron-hopping and Fontijn models. It begins onthe entrance PES correlating with the ground-stateCu(4s 2S1/2) atom and N1, which embodies theirweak complexation in a variety of structures de-pending on the mutual angle of attack. These struc-tures are treated in Section 4. Nevertheless, one ofthem is so particular that it deserves a few words. Itresides on the pathway of this PES that can be

interpreted as the entrance “moat” of reaction (1) ina sense that it leads to the crossing with the lower-lying ionic PES Cu� � A2. The second stage con-sists in the nonadiabatic electron transfer from theCu chiefly to the oxygen atom of N2 occurringalong the crossing seam. Such nonadiabatic electrontransfer results, at the third stage, in the key struc-ture N2OCuOO located on the exit moat of reac-tion (1) and reported in the present work for thefirst time. It accomplishes this stage of reaction (1)that further proceeds to the fourth product stage,yielding CuO(X 2�) � N2(X 1�g

�). Within thepresent model, the non-Arrhenius regime is linkedto the other reaction pathways on the crossing PESsdiscussed in Section 4 and/or the other higher-lying PES(s). Calculations elaborated in Section 4provide a support for the proposed mechanism.The computational methodology chosen for thispurpose is outlined below.

3. Computational Methodology andControl Calculations

All calculations were performed using theGaussian 98 suite of programs [13]. The Ahlrichstriple-� (TZV) basis set augmented by one polariza-tion function [14] (TZVP) was chosen for our com-putational purpose for a couple of reasons. The firstis that, within the framework of the second-orderMøller–Plesset perturbation approach (MP2) takenat the frozen core approximation, TZVP accuratelydescribes the dissociation pathway of anionic N2O�

species [12]. Because the electron attachment pro-cess is, as we thought, the essential feature of reac-tion (1), we preliminarily performed a series ofcontrol calculations with the neutral and anionicstructures of N2O discussed in Section 2 to comparethem with the coupled-cluster/aug-cc-pVQZ basisset data [12]. Table I and Figure 1 firmly demon-strate a sufficient accuracy of the chosen basis set.Second, the hybrid density-functional B3LYP inconjunction with the TZVP basis set reasonablywell describes the activation barrier separating theentrance and exit moats of the reaction (1) [9d].

In the present work, the optimized geometriesand harmonic vibrational frequencies of theCuNNO system were determined using theB3LYP/TZVP computational level. The frequencieswere retained unscaled. The zero-point vibrationalenergies (ZPVE) were used to correct the electronicenergies of the optimized structures. To locate shal-low energetic minima, the “tight” convergence cri-

FIGURE 1. Lower-energy portions of the PESs of theneutral and anionic nitrous oxide calculated at a varietyof computational levels: MP2/TZVP, CCSD(T)/TZVP (in-dicated by �), and QCISD(T)/aug-cc-pVDZ (in paren-theses). The relative energies in kcal/mol refer to thelatter method. Bond lengths in Å, bond angles in °.


332 VOL. 89, NO. 4

terion was used in all optimizations and a numer-ical integration was performed employing the“ultrafine” grid of points. For further refinement,single-point calculations using the coupled-clusterCCSD(T) method of all studied structures were alsocarried out. The lowest-energy reaction path map-pings starting at the saddle structures of the firstand second orders were also calculated in thepresent work to determine the landscape of thestudied PESs. Natural bond analysis (NBO) [16]was conducted to verify the electronic configura-tion of the studied structures.

4. Computational Modeling ofReaction (1)

The PES of the ground-state reactants Cu(4s 2S1/2)� N2O(X 1��) representing the entrance channel ofreaction (1) comprises of two energy minima thatmirror two attacking pathways of the reactants(Figs. 2 and 3). One was briefly discussed in Section2 and actually represents the entrance moat of re-action (1). Here, Cu approaches the N2O moleculenearly perpendicular to the oxygen and, at theCuOO distance of 3.695 Å, forms a typical van derWaals complex I characterized by the B3LYP/TZVP binding energy of 0.24 kcal/mol (only 0.04kcal/mol predicted by CCSD(T)/TZVP) and by thebond angle �NOCu � 88.7°. Notice that there ob-viously exist two energetically equivalent struc-tures of the type I, the left and right ones withrespect to the NNO axis. On the oxygen side, theyare separated by the linear second-order saddlestructure Saddle1, where Cu is aligned with theNNO axis and distanced from the oxygen atom by3.631 Å. Table II demonstrates that Cu is completelyneutral in I and, for this reason, the geometry andharmonic vibrational frequencies of its NNO moe-ity resemble those inherent to N1 rather than an-ionic nitrous oxide, implying thus that no chargetransfer occurs in the entrance moat.

The other pathway on this ground-state PES islinked to Cu approaching the N2O molecule on theN side. It is characterized by a van der Waals com-plex II displayed in Figure 2 and having the follow-ing geometric parameters: the CuON distance isequal to 3.313 Å and the NONOCu angle to 119.6°;the N2O linearity inherent for N1 is slightly de-formed by 0.7°. The B3LYP/TZVP energy of forma-

tion of II amounts to 0.32 kcal/mol. Another struc-ture III is also located there and shown in Figure 2.1

The product side of reaction (1) lies on the exitmoat of the ionic PES Cu� � A2 and in particularincludes the key structure IV residing at its globalminimum. Interestingly, IV is not only stable, by20.2 kcal/mol [B3LYP; 20.8 kcal/mol by CCSD(T)],relative to its parent product asymptote CuO(X2�) � N2(X 1�g

�) of reaction (1), but also stable, by41.8 [B3LYP; 37.3 by CCSD(T)] kcal/mol, with re-

1We also reveal two following structures located along thispathway which might be an artefact of the present computa-tional methods because of the discrepancy in their energiesobtained using the different methods. Approaching further N2Ofrom II, at the distance of 2.854 Å to the neighboring nitrogenatom, Cu meets the transition structure TS1 whose B3LYP/TZVP activation barrier of 31 cm�1 is rather negligible showingthus a flatness of the studied portion of the PES. Therefore, Cupasses it practically freely and finally arrives at the minimumenergy structure III which is characterized by a slightly largerbinding energy (0.70 kcal/mol at B3LYP/TZVP) and a shorterCuON distance (2.191 Å) compared to the structure II.

FIGURE 2. B3LYP/TZVP-optimized geometries of thestudied CuNNO structures. Bond lengths in Å, bondangles in °.



spect to the reactant one. As seen in Figure 2, theCOO and NON bond lengths are 1.793 and 1.099Å, respectively, and thus are slightly longer thanthose in the isolated ground-state CuO and N2 mol-ecules (see Table I). The central CuON bond isshort: 1.844 Å. IV is a typical ionic structure: underits formation, Cu loses 0.75e of its electronic chargewhere 0.44e flows out from the 4s orbital and 0.31efrom the 3d one, as demonstrated in Table II on thebasis of the NBO analysis (compare with Mullikencharges given there as well). This electron chargemainly transfers to the oxygen atom. The formationof IV is also accompanied by substantial frequencyshifts (cf. Tables I and II). For example, the CuOOstretching vibration is blue shifted by 41 cm�1 com-pared to that in the ground-state CuO molecule,implying a slightly stronger bonding between Cuand O atoms arising likely from a “pushing” effectof Cu by the neighboring N atom. On the otherhand, the latter results in a red shift of the NONstretching mode by 71 cm�1.

Before proceeding to a further discussion of thelandscape of the ionic PES Cu� � A2, which is farfrom being exhausted by structure IV and opensanother reaction pathway leading likely to the non-Arrhenius regime of (1) (see the insert in Fig. 3), letus briefly summarize the computational results. Wetherefore reveal two moats, the entrance and exitones, of reaction (1) lying on the two PESs correlat-ing with the asymptotes Cu(4s 2S1/2) � N2O(X 1��)and CuO(X 2�) � N2(X 1�g

�), respectively. Theformer determines the CuNNO structure I, whichshows no sign of the electron transfer. The latter,where structure IV is located, on the contrary, does.Therefore, these two moats cross each other at thecrossing seam where the electron transfer related tothe Arrhenius regime of reaction (1) actually takesplace and can only occur nonadiabatically. Struc-turally speaking, the electronic charge transfersnonadiabatically along two different nonadiabaticpathways composed of two following transition-state linker structures named in Figure 3 as TS2 and

FIGURE 3. Lower-energy PESs profiles of reaction (1). Relative CCSD(T)/TZVP and B3LYP/TZVP (in parentheses)energies (in kcal/mol) based on the B3LYP/TZVP geometries are indicated.


334 VOL. 89, NO. 4

TABLE II ______________________________________________________________________________________________Variety of CuNNO structures related to reaction (1).

Energy Frequency Vibrational assignment

Mullikenchargeon Cu

Electronicconfiguration

of Cu

I �0.24 9 CuON stretch, CuOO stretch 0.0 4s1.003d10.00

�0.20 34 CuOO stretch, CuON stretch�0.04 585 NNO in-plane bend

593 NNO out-of-plane bend1326 NNO sym stretch2346 NNO asym stretch

II �0.32 12 CuOO stretch, CuON stretch �0.01 4s1.003d10.00

�0.29 29 CuON stretch0.06 587 NNO in-plane bend


TS1 �0.29 30� CuON stretch 0.00 4s0.993d9.99

�0.29 49 CuOO stretch�0.61 575 NNO in-plane bend


III �0.70 76 CuOO stretch �0.01 4s0.973d9.93

�0.79 126 CuON stretch3.36 484 NNO in-plane bend


Saddle1 �0.19 4� CuON end 0.00 4s1.003d10.00

�0.16 4� CuON bend�0.16 26 CuOO stretch

595 NNO bend595 NNO bend

1322 NNO sym stretch2345 NNO asym stretch

TS2 11.0 593� NOO stretch, NNO bend �0.85 4s0.513d9.85

8.5 99 CuON stretch, NNO bend8.7 207 NNO out-of-plane bend

394 NNO in-plane bend, CuOO stretch504 CuOO stretch, NNO bend

1909 NON stretchTS3 17.2 567� NOO stretch, NNO bend �0.88 4s0.733d9.90

15.0 19 CuON in-plane bend22.1 110 NNO out-of-plane bend

404 CuOO stretch, NOO stretch740 NOO stretch

2026 NON stretchIV �36.1 99 CuNNO bend �0.63 4s0.563d9.69

�37.3 288 CuNNO bend�41.8 303 CuNNO bend

352 CuON stretch604 CuOO stretch

2385 NON stretch(continued)



TS3, both located along the seam. TS2 and TS3possess the imaginary frequencies 593� and 567�cm�1, respectively, associated with the coupledNOO stretching and NNO bending vibrationalmodes (Table II).

The lowest intersection linker TS2 correspondsto a cis orientation of the CuOO and NON bondswhereas the higher one, TS3, corresponds to thetrans orientation. If in the former linker, the CuOO,OON, and NON distances are equal to 1.860, 1.519,and 1.141 Å, respectively, and the NNO bond anglecomprises of 123.9° (cf. Ref. [9d]); the latter is char-acterized by a larger CuOO distance (1.990 Å) andless perturbed distances OON (1.309 Å) and NON(1.136 Å) and the NNO bond angle (145.7°). That iswhy, speaking geometrically, it appears at an “ear-lier” stage although its higher-energy position be-comes clear comparing the charges transferred

from Cu to NNO in these structures (4s0.513d9.85 forTS2 vs. 4s0.733d9.90 for TS3; note that their Mullikencharges are nearly equal and overestimate the NBOcharges): the less charge that is transferred, the lessstable it is. Figure 4 plots the nonadiabatic electrontransfer q along the nonadiabatic reaction pathwaypassing through the transition-state linker TS2 to-gether with the corresponding changes of the NNOangle and the total dipole moment, which resem-bles the q-plot and can be used in evaluating theadiabatic-to-diabatic mixing angle for the two-stateproblem [17]. As seen from the structural snapshotsin Figure 4, the electron transfer starts to occurwhen the NNO moeity becomes sufficiently bentand the NOO bond elongated or, in other words,when Cu is ready to “feel” the oxygen atom in thestructure similar to A2. The transition-state linkerTS2 actually bifunctions as the bond breaker and

TABLE II ______________________________________________________________________________________________(Continued)

Energy Frequency Vibrational assignment

Mullikenchargeon Cu

Electronicconfiguration

of Cu

TS4 �19.1 124� CuN asym stretch �0.67 4s0.523d9.75

�21.4 88 OCuN in-plane bend�29.0 113 OCuN out-of-plane bend

184 CuN sym stretch575 CuOO stretch

2330 NON stretchV �22.7 106 OCuN in-plane bend �0.67 4s0.503d9.71

�24.5 134 OCuN out-of-plane bend�28.6 235 CuN asym stretch

246 CuN sym stretch609 CuOO stretch

2253 NON stretchTS5 �14.5 18� CuON out-of-plane bend �0.80 4s0.573d9.78

�17.0 14 CuON in-plane bend�22.6 36 NO sym stretch

48 ONN asym stretch565 CuOO stretch

2458 NON stretchSaddle2 �14.5 19� CuON in-plane bend �0.80 4s0.573d9.78

�17.0 11� CuON out-of-plane bend�22.6 35 CuON stretch

55 CuON stretch564 CuOO stretch

2457 NON stretch

The relative energies (in kcal/mol) are taken with respect to the ground-state reactant asymptote and ordered (from the top) in thefollowing manner: B3LYP/TZVP, B3LYP/TZVP � ZPVE, and CCSD(T)/TZVP � ZPVE. Harmonic vibrational frequencies in cm�1 areobtained at the B3LYP/TZVP computational level. Mulliken charges on Cu are calculated using the B3LYP/TZVP method. Theelectronic configuration of the Cu atom is determined on the basis of the NBO analysis (B3LYP/TZVP).


336 VOL. 89, NO. 4

bond creator: it breaks the NOO bond and formsthe CuOO that is accompanied by the charge trans-fer of 0.64e (NBO) from Cu to O. After that, the restof the nonadiabatic pathway pertains to the ionicPES. Along its ionic portion, the electron chargecontinues to be transferred from Cu to O and thusCu accommodates to a better geometry of NNOalong a smooth variation of the NNO bond angle inthe vicinity of A2.

Energetically, both TS2 and TS3 correlate withthe entrance asymptote Cu(4s 2S1/2) � N2O(X 1��)as follows: on the one hand, the activation energyEA

(2) of the pathway I f TS2 f IV of reaction (1)

amounts to 8.8 [B3LYP; 8.7 by CCSD(T)] kcal/mol.Bearing in mind that, in fact, the enthalpy of reac-tion (1) has been experimentally measured, we es-timate its theoretical magnitude related to this path-way and obtain 9.7 kcal/mol, which agrees wellwith the experimental data [4] discussed in Section1. On the other hand, the activation energy EA

(3) ofthe pathway I f TS3 f IV lying on the higher-energy sheet of the diabatic PES is equal to 17.2[B3LYP; 22.1 CCSD(T)] kcal/mol (the enthalpy is16.3 kcal/mol) and, therefore, this pathway appearsto be less energetically accessible. However, it maybe accessible at higher temperatures. It is then rea-

FIGURE 4. Nonadiabatic electron transfer in terms of Mulliken charge and the corresponding changes of the totaldipole moment and the NNO angle in the vicinity of the transition-state linker TS2.



sonable to suggest that it can contribute to thenon-Arrhenius regime of reaction (1) experimen-tally observed by Fontijn and coworkers [4a].

Let us now return to the ionic PES Cu� � A2. Itssubtle patterns are displayed in the insert of Figure3. First, it is worth mentioning that this PES pos-sesses another minimum energy structure V lyingby 13.4 [B3LYP; 13.2 by CCSD(T)] kcal/mol abovethe global minimum IV. The reaction pathway IVf V shown in the insert passes along the followingstructures:

IV f17.0

TS4f TS5f�8.2

V, (8)

where the quantity above the arrow indicates theenergy difference between the B3LYP/TZVP ener-gies corresponding to the left and right structuresbracketing this arrow. Some key properties of theintermediate structures shown in (8) are collected inTable II. Note that they can be partitioned into twoclasses: One is with Cu approaching the weak bondbetween O and N2 in A2 whereas the other origi-nates from Cu approaching O of A2 perpendicularto the NON bond. In fact, the reaction pathway (8)establishes another channel of reaction (1) thatmight also contribute to its non-Arrhenius behav-ior. Note after all that the studied reaction path-ways finally exit without barrier to the productCuO(X 2�) � N2(X 1�g

�).

5. Summary

Summarizing the present work, we would like tostress the following key conclusions. We proposeda new mechanism of reaction (1) as proceeding viathe nonadiabatic electron transfer at the crossing ofthe neutral Cu(4s 2S1/2) � N2O(X 1��) and the ionicCu� � A2 PESs and approved its functionalitycomputationally using a variety of quantum chem-ical methods and thoroughly analyzing all its pos-sible lower-energy reaction pathways. We have alsoshown how and where such nonadiabatic electrontransfer from Cu to the oxygen atom occurs byidentifying the transition-state linkers located alongthe crossing seam. There are actually four reactionpathways of reaction (1):

Cu�4s 2S1/ 2� � N2O�X 1��f If TS2f IV

f CuO�X 2�� N2�X 1�g�� (9)

Cu�4s 2S1/ 2� � N2O�X 1��f If TS3f IVf

CuO�X 2�� N2�X 1�g�� (10)


TS4f Saddle2f TS5f Vf

CuO�X 2�� N2�X 2�g�� (11)


TS4f Saddle2f TS5f Vf

CuO�X 2�� N2�X 1�g��, (12)

where the last two are only accessible with theinitial kinetic energies of the reactants or at highertemperatures. Obviously, the reaction pathway (9)is the most favorable. We have shown that its acti-vation enthalpy EA

(2) amounts to 9.7 kcal/mol,which satisfactorily matches the experimental value[4]. In general, the pathway (9) of reaction (1) rec-onciles, to a certain extent, the electron-hopping [7]and Fontijn models [1a, 8]. Regarding the former,the electron hop actually takes place along the path-way (9) but, as persuasively demonstrated, non-adiabatically: precisely in the vicinity of the transi-tion-state linker TS2 located along the crossingseam of the entrance and ionic PESs, where theionic PES is related to A2, rather than, as suggestedby this model, on the ionic PES correlated with theground state of Cu atom and A1, which is lessstable than A2 [12]. Interestingly, the proposedmechanism resembles the harpooning mechanism[18] occurring at the covalent–ionic intersection. Onthe other hand, our mechanism bears some featuresof the Fontijn model, in particular the most impor-tant one: that the activated complex AC or, in ourterminology, the transition-state linker is partly at-tributed to the ionic resonance structure S3 origi-nated from the ionic PES Cu� � A2 rather thanfrom the entrance one. What is actually the origin ofthe transition-state linker in the reaction pathway(9) and how large is its ionic contribution?

We suggest that, in contrast to the aforemen-tioned models, the formation of the transition-statelinker TS2 is mostly determined by the transitionstructure ATS that can be interpreted as the linkeras well in the nonadiabatic electron transfer N1 �e� f ATS f A2 taking place solely on the NNOPESs displayed in Figure 1. This suggestion is basedon the following arguments. First is the energeticone: The energies of ATS and TS2 are close al-though we have certainly taken into account that


338 VOL. 89, NO. 4

the bonding of Cu to ATS lowers the energy of TS2compared to the asymptote Cu � ATS. Second isthe structural argument: A simple comparison ofthe NNO geometries in ATS and TS2 shown inFigures 1 and 2 firmly demonstrates that they areclose, in particular the NON distance and the NNObond angle. A slight elongation of the NOO bondlength in TS2 compared to that in ATS is againattributed to the CuOO bonding.

A further comparative analysis of the Fontijnmodel with the present one reveals that, first, reac-tion (1) is barrierless along the entrance moat, im-plying thus that the parameter V must be zero, and,second, there is absolutely no computational evi-dence of the s � p promotion along the pathway (9).Together, this means that the 3 3 Hamiltonianmatrix (5) must be therefore reduced to the 2 2one with the matrix elements H11, H13 � H31, andH33. Diagonalizing it and applying then Eq. (7) toevaluate H33 (see Table I in Ref. [8a]), we obtain theeigenenergies E1 (open circle) and E2 (open square)plotted in Figure 5 as the functions of the parameterV together with the similar plots for the expansioncoefficients c1 (dark rhombus) and c3 (dark triangle)(c2 � 0). Inspecting the E-plot in Figure 5, we con-

clude that the lowest eigenenergy that corresponds,according to the Fontijn model, to the energy of theactivated complex is always E2 within the interval0 V 100 kcal/mol and it becomes equal to�200.36 kcal/mol at V � 0. Together with the c-plot, this implies, first, that within the mentionedinterval of V the ionic component plays a major rolein the formation of the activated complex (c3 1)and, second, that the analytic part of the Fontijnmodel is unable to predict the correct value of theactivation energy of reaction (1) that does not pos-sess any barrier (i.e., V � 0) on its entrance moat.

A comparison of the energetic features of theother possible pathways of reaction (1) listed in Eqs.(10)–(12) shows that the pathway (10) is likely themost favorable among them and can govern thenon-Arrhenius regime of reaction (1). However, wethink that a more affirmative answer demands aconduction of additional kinetic experiments at T �1190 K.

We conclude the present work with the wordsthat the proposed mechanism convincingly demon-strates still another “wisdom of the conical intersec-tion” [19].

ACKNOWLEDGMENTS

The authors thank Chris Vinckier for valuablediscussions. The present work was partly sup-ported by the KU Leuven Research Council (GOAProgram).

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Mechanism of the oxidation reaction of Cu with N2O via nonadiabatic electron transfer

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