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Valence formulae and the oxidation of nitric oxide to nitrogen dioxide
JixmaZ of MoIecufar
Structure
Elsevier Publishing Company, Amsterdam. Printed in the Netherlands
VALENCE FORMULAE NITROGEN DIOXIDE
AND THE OXIDATIT)N
OF NITRTC OXIDE
TO
R. D. HARCOURT Department of Chemistry,
Unit;ersity of Melbomne, ParkoiZZe,Vkforia 3O.Q (Australia1
(Received August 27th, 1971)
ABSTRACT
‘Three-electron bond’ and ‘increased-valence’ formulae are described for NO, 02, N03, O3 and NO2 . These species occur in the HeickIen and Cohen mechanism for the atmospheric oxidation of nitric oxide to nitrogen dioxide. By using these valence formulae, 0, is predicted to be formed as the 3Xi electronic state in the reaction NO-I- 0, --, NO2 + Oz. SimiIar conclusions pertain for the reaction HO + 0, -+ HO2 + 02, and for some other radical transfer reactions which involve the formation of Oz. Use of NO as a Lewis base in the NO/O, reaction can generate 0, either as 1x:+ g or as ]-AS’
The oxidation of nitric oxide to nitrogen dioxide is an important reaction which occurs in poIIuted atmospheres. Various mechanisms have been proposed for this reaction, one of which involves the following steps%: NO-+-O, --+ ON00 ON00
-+ ONOO*
ONOO* + N02+0 oto,
--* 03
(9 (2) (3) (4)
In daytime Los Angeles, the time required to generate NO2 from NO by means of this mechanism has been estimated1 to be approximately 1 hour. In this paper it is not our intention to attempt to justify or reject the mechanism, but only to use it in order to illustrate some new aspects of elementary valence theory. We shall &xamine the bonding for all of the molecular species that pertain to this mechanism, and then indicate the electronic- rearrangements which might occur J. Mol. &%wctures 11 (1972)
1
for the reaction steps (l)-(4), and also for the reactions H+ 0s ---, HO+ O2 and NO + 0s -+ NO2 + Oz. The ‘three-electron bond’ valence formulae2 and the newly developed ‘increased-valence’ formulae3 were used to describe the bonding for diatomic and polyatomic systems respectively.
THREE-ELECTRON
BONDS
AND
INCREASED-VALENCE
FORMULAE
Pauling’, in 1931, introduced the three-electron bond to describe aspects of the bonding of paramagnetic molecules such as NO and 02, writing their valence formulae as (1) and (2), which have one and two three-electron bonds respectively. He showed that the three-electron bond structure (3) summarized the resonance of i
;A
‘A’
i,
There is one unpaired electron in each of these two structures. Therefore, for the Ot valence formula (2), there are two unpaired electrons. If these unpaired electrons have parallel spins, then the O2 is paramagnetic. At room temperature, NO is also paramagnetic. :N*-o: (1)
:o@s$& *me
A***B
i
(3)
(7)
0
(2)
4 (4)
(61
In 1960, Linnett and Green4 generated valence formulae with three-electron bonds from the molecular orbital configurations for the NO and O2 ground states. Each three-electron bond developed from the presence of two bonding and one antibonding electron occupying orthogonal molecular orbitals which are constructed from the same two atomic orbitals. Their proof is very simple, and we shall now examine it. Let a and b be two overlapping atomic orbitals on two atoms. From them, the orthogonal bonding and antibonding molecular orbitals $+ = a+b and 4-- = a-b may be constructed. Linnett and Green4 (and earlier, Linnett’) demonstrated that the determinantal wave-functions I@“+$5 and l$$t,@l are equivalent to kl&b”l and kldbsl, in which k is a constant and o!and j3 are spin wavefunctions. These results are easily obtained by expanding either determinantal wave-function. Thus, omitting normalization,
2
J_ Mol.
Structure,
11 (1972)
I#“+*I
= ~+,(l)a(1)~-(2)a(2)-~-(l)a(l)J/+(2)a(2) = Ml) + w)hm@)
= -2{a(l)cr(l)b(2)cr(2)= - 21n”b”l
- fQ)W) - W) - w)MQ~42) + W)l(2b b(l)a(l)u(2)r(2))
It follows that if we have the molecular orbital configuration I@+t+C$$.I involving two bonding and one antibonding electrons, then this configuration is equivalent to klti&,&l, for which two electrons occupy atomic orbitals and the third electron (with opposite spin) occupies the bonding molecular orbital. The Pauli principle keeps electrons with the same spins in different spatial orbitals. Linnett and Green have recommended that the resuhing electron distribution be written as (4) rather than as the Pauling structure (3). Structure (4) shows clearly that there is only one bonding electron in the three-electron bond. Linnett and Green wrote the NO and O2 valence formulae as (5) and (6), which indicate better than do (1) and (2) that these molecules have bond-orders of 2.3 and2 respectively*. If we indicate the electron spins of a three-electron bond, then (4) is equivalent either to (7) or to (S), in which the crosses and circles represent electrons with o! and j? spin functions. It is usually considered that the three-electron bond is restricted to a small number of paramagnetic molecular systems. However, it is possible to incorporate the three-electron bond structure (4) into the valence formulae for a very large number of diamagnetic, triatomic and polyatomic systems3. To do this for a triatomic system, a Y atom with one unpaired electron is introduced into valence formulae (7) and (8). Valence formulae (9) and (10) are obtained if there are a total of two CYand two /? electrons.
Y-A*& (11)
‘B’ -vxE3
Y-A 02)
03)
When the atomic orbitals on Y and A overlap appreciably, we may represent these two atoms as bonded together. We thereby obtain valence formula (1 l), in which the electron spins are not specified. This valence formula summarizes the resonance3 between the valence formulae (12) and (13). Since (13) does not have a YA bond, the YA bond of (11) must be longer and weaker than the YA bond of (12). Therefore, we use” a light line to represent the YA bond of (11). We have called3 valence formula (11) an increased-valence formula, because in it, more * The NO bond order has been calculated from the bond length6 of 1.150 A by using the Pauling formula3”*7 R(rr) = 1.44 -0.8 log N, in which tt is the bond order. J_
Mol.
Sfructure,
11 (1972)
3
electrons participate in bonding than occurs in either of the electron-pair bond formulae (12) or (13). The wave-function for (11) may be shown to represent a singIet spin state3=w3b, and therefore it is appropriate for diamagnetic systems. Nitrogen
trioxide (Fig.
I)
Some IR studies show that one NO, isomer is an unsymmetrical peroxides, with an ON00 structure. The nitrosyl stretching frequencies of NO3 and NO are bond, with a disand 1876 cm-r respectively, and the ON -0, 1840 cm-’ sociation energy of 742 kcal/moIe*, is very weak. GuilIory and Johnston’ have described the bonding in terms of the spin pairing of the unpaired eIectron of NO formula for with one of the two unpaired electrons of 0,. An increased-valence NO, corresponding to this description may be generated from valence formulae (5) and (6) for NO and Oz. This valence structure is compatible with the observed bond properties, because it shows that the electronic structure of NO need be little Oz bond is weak. modified on bonding to 02, and that the ON-
Fig, 1. NO-i-O2
+ ONGO.
The calculated’ 00 stretching frequency for ONOO, 1400 cm- ‘, is rather Iess than the 1556 cm-l for free 02, and could arise because of unequal sharing of the four bonding electrons by the two oxygen atoms of NOa. On bonding of O2 to NO, the electronegativities of the two oxygen atoms of O2 must be altered relative to each other. Increased-valence formulae for ONNO, XNO (with X = halogen), FOOF, FSSF, F$S and FzSO may be similarly constructed3, i.e. from the three-electron bond formulae (5), (6), (14) and (15) for NO, 02, Sz and SO. Each of these polyatomic molecules has bond properties which are similar to those of the diatomic molecules, and long or weak NN, XN, OF or SF bonds. The observed properties are compatible with those which are implied by the increased-valence formulae. Cl bond, and an Dichtoiine dioxide, OCICIO, however, has a very weak CIincreased-valence formula which is constructed from the three-electron bond formufa (16) for CIO shows this adequatefyg. The 00, SS and NO bonds of HOOH, HSSH and HNO Iengthen relative to those of free O,, S2 and NO, and 4
J. Mol.
Structure,
11 (1972)
the familiar Lewis formulae HO -OH, provide HSSH and HN--0 satisfactory representations of the electronic structures of these molecules. Hydrogen atoms are not able to stabilize three-electron bonds of increased-valence bonding units; we shall use this result when we discuss the H+O, reaction.
Ozone (Fig. 2) Oxygen atoms react rapidly with molecular oxygen to form ozone’ ‘. By spin pairing the unpaired electrons of the 0 and O2 ground states, we obtain an increasedvalence formula for 0, _ In Fig. 2, we also show a Lewis formula for O,, which may be obtained
from
excited
states
(:d
and :I!=@)
of 0
and
02,
each
of
which has no unpaired electrons. This Lewis formula has net positive and negative charges on the central atom and on one terminal oxygen atom. These net charges may be reduced in magnitude by delocalizing two lone-pair electrons of the Ointo two bonding orbitals of O-O+ which are vacant in the Lewis structure. These delocalizations are shown (Fig. 2) by means of two curly arrows with single barbs. The resulting valence formula is an increased-valence formula. It is easy to show that the increased-valence formula summarizes resonance between the Lewis structure and three long-bond structures. Therefore, the increased-valence formula mzrst have a Iower energy than has the Lewis formula. Further, by delocalizing lone-pair electrons of a Lewis formula, it is always possible to generate an increased-valence formula from Lewis formulae of types (17) and (18), provided that the three atomic orbitals on Y, A and B overlap3. From (17) and (18), the increased-valence formula (11) is generated by delocalizing a lone-pair electron of B
Fig. 2. 0+02 J. Mol.
+ OS, and Lewis and increased-valence formulae for OZ.
Structure, I1 (1972)
5
of (17) into a bonding AB orbital, and by delocalizing a Y lone-pair electron of (18)
into an antibonding AB orbitaL FuIler details of these delocalizations are described elsewhere3. For OS, the molecular symmetry requires a description of the electronic structure to involve resonance between a number of increased-valence structures, two of which are shown in Fig. 2. Equivalent valence structures are omitted from the NO2 discussions but it is to be understood that they exist, and that they participate in resonance with the structures that are shown.
Nitrogen dioxide (Fig. 3) The reaction O+NO generates N02; the initial step could involve the formation of a weak NO single bond, as in Fig. 3(a).
(b)
(e)
Fig. 3. O+NO
-+ NOz*
+ NOz.
Valence formula (a) is an increased-valence formula, with seven bonding electrons. However, the structure may be stabilized by increasing the number of
bonding electrons to eight, if one of the nitrogen lone-pair eIectrons of (a) is delocalized into a bonding NO orbital, thereby generating (b). ESR measuremerits” detected a fractional unpaired-electron charge on the nitrogen atom of NO,. The structure for NO= obtained in the reactions above is the increased-
valence formula (b), which may be further stabilized by delocalizations, which reduce the magnitudes of the formal charges on the oxygen atoms and generate increased-valence formula (c). We have shown3’ that (c) is compatible with the measured NO bond lengths. Increased-valence formulae, compatible with the experimental bond lengths3’; may be constructed for r\r,O,, N,O,, XN02 and CX3N02 (X = halogen) using structure (c), together with structure (5) for NO, 6
J. Mol. Structure, 11 (1972)
halogen atoms or trihalomethane radicals. It is to be understood that we may generate (c) from the valence formulae of type (b) which are produced in the reactions shown in Figs. 4 and 6. We may also generate (c) by starting with the NO excited state (e) which has three unpaired electron charges on the nitrogen atoms. Two of these charges are then spin-paired with the two unpaired electrons on the oxygen atom. The NO excited state (e) is obtained from the ground-state by promoting one of the nitrogen lone-pair electrons into an antibonding NO orbital, as we show in (d). The reaction O+NO + NO2 is accompanied by chemiluminescence12, which possibly arises from the transition of (b) to (c).
RADICAL
TRANSFER REACTIONS
A radical transfer reaction involves a redistribution of unpaired electrons between reactants and products_ In the atmosphere, many examples are known’ 3_ By using increased-valence formulae it is possible to devise simple mechanisms for quite a number of them. As yet, the full consequences of these mechanisms have not been worked through, and therefore what we describe probably represents only a beginning in this subject. The reactions considered are ONOO* --, NO2 + 0, H+O, + HO+O, and NO+O, --, NO,+O,. (a) NO3 + NO2 + 0 (Fig. 4) In Fig. 1, we have displayed the formation of ON00 from NO+ Oz. Here, we shall indicate the formation of NO2 + 0 from the excited state ONOO*. We suggest that ONOO* corresponds to the formation of an 00 single
Fig. 4.ONOO J. Mol.
-+ ONOO*
Structure,
-+ NOz+O.
1I (1972)
7
bond together with the delocalization of a nitrogen lone-pair electron into a bonding NO orbital’- The appropriate electron transfers are shown in Fig. 4, and the delocalization of the nitrogen electron into the bonding NO orbital must weaken the 00 bond. When this bond breaks, NO, + 0 are formed. The oxygen atom can react (Fig. 2) with an oxygen molecule to produce 0s , which then reacts with NO to form NO, + 0,. If we obtain an initial bonding of O2 to N03, as has also been suggested by Heicklen and Cohen’, the NOz0s bond will be weak, and on breaking, generates NO= + 0s. (b) H-I-O,
+ HO+O,
(Fig. 5)
This reaction is described here in order to illustrate the principles which are also involved in the NO+O, reaction. The electronic structure of 0, is assumed adequately represented by its increased-valence following
Fig. 5. H+03
structures of Fig. 2. In Fig. 5, the
steps in the reaction are shown.
-+ HO3 + HO+O~
(‘2;).
(i) A hydrogen atom approaches Os, and stabilizes one increased-valence structure relative to the others. By this we mean that the electronic structure of 0, resembles the stabilized structure more than it resembles any of the other structures. (ii) The hydrogen atom forms a weak electron-pair bond with one of the unpaired electrons on the adjacent terminal oxygen atom of OX++_ (iii) We now assume that the two unpaired bonding electrons of w-0 transfer into oxygen atomic orbitals. An O---O single bond is thereby formed, and the Hbonding O bond is strengthened. We have now formed an HO -0 scheme which is similar to that of HO--OH for hydrogen peroxide. In both, t This nitrogen delocalizationcould
also occur appreciably in the unexcited ON00 of Fig. 1; if so, then it would be partially responsible for the reduction of the 00 stretching frequency. tt A very small amount of energy is needed to break the weak long bond which is formed between this unpaired electron and an electron on the other terminal oxygen atom. 8
J. Mol. Strucrure,
11 (1972)
the hydrogen atoms are not able to stabilize the three-electron bonds of OZ. One other result of these electron transfers is the breaking of one of the weak bonds of O--0, thereby forming an unpaired electron on the terminal oxygen atom.
The electronic structure of HO? has now lost its increased-valence character; its structure is HO---O---O, and involves only singfe bonds.
(iv) Increased-valence is now restored by delocalizing two oxygen lone pair electrons into two vacant bonding 00 weakens the adjacent HO--O bond.
(v) The weakened HO -0
orbitals.
One
of these delocalizations
bond breaks to form the products HO and Oz.
(c) NO -HI3 -+ N&-I- 0, (Fig. 6) By using valence formula (3) for NO, and the increased-valence formula of Fig. 2 for Os, we may construct the mechanism of Fig. 6 for NO t 03, which closely resembles that of Fig. 5 for Hi- O3 _ The 0 -0 bond of the second NOB structure has been weakened by delocalizing a nitrogen lone-pair electron into a vacant bonding NO orbital. This type of deIocalization has also been used in Figs.
3 and 4.
Fig. 6. NOtO
+ NO4 + NOz-+-O+ (3x:,).
The NO-t0, reaction is a bimolecular reaction which proceeds along two paths’““. One of these produces electronically excited NO,. The radiation that is emitted might arise from the Ioss of energy which is generated when the NOz formed in Fig. 6 returns to the ground-state structure (G) of Fig. 3. Increased-valence mechanisms for many other radical transfer reactions, such as NO+NO, + 2NOt, NO,+O, -P NOs+O,, O,+O, + 202+0, CIOz + NO 3 Cl0 + NOa and 2H02 -+ H202 + O2 may be described in a similar manner to that of (b) and (c). For the last of these reactions, the HOOOOH is predicted to decompose as 02+20H, and the two OH radicals then combine to
forXrl J&o, * 9
ELECTRONIC
STATES OF 0,
We shall now consider the nature of the electronic state of the 0, which is produced in the HO -t-O, and NO t 0s reactions. ff spin is conserved in these reactions, the HO3 and NO4 radical intermediates will have doublet (S = +) sp in states. Each of HO, and NO4 (Figs. 5, 6) generates an O2 molecule with two three-electron bonds, and therefore with two unpaired electrons. The “XL ground state and one ‘4 excited state have molecular orbital configurations with two unpaired electrons occupying antibonding xelectron orbitals16. If z+, IL-, ~2 and zc*_ are the bonding and antibonding n-electron molecular orbitals, the x*-electron configurations for these “2; and ‘A9 states are 16
In the increased-valence formulae shown in Figs. 5,6 for HO, and NO,, O2 has spin-paired one of its unpaired electrons with the unpaired electron of either HO or NO,. If we label the orbital for the latter electron by the symbol 4, and for simplicity, retain the n$ and R? notations for the 0, antibonding orbitals, then we may construct two orthogonal spin eigenfunctions which involve unpaired electrons in the zz, n*, and C$orbitals17. For Sz = -++, these spin eigenfunctions are
and
(There are also two doublet functions with Sz = -f, which we need not write down here.) By separating the 0, from the NO, or HO without in any way changing the spin coupling18, we may extract 0, valence states from 2*x and 2$2. Using the theory of Craig and Thi~~amac~n~an’*, we obtain
and 10
.J. Mol..Strucrure,11
(1972)
= -$ (23ZZ, (S= = 1) +JZe’*
“Xi (S= = 0))
in which eie is an arbitrary phase factor. Only one of nr and ~3 can overlap with (p. If we assume for example that n*_ overlaps with 4, then neither 2$1 nor ‘14~ involves perfect spin-pairing of the k!! and C#Jelectrons; in both functions, the determinant IxT8 z*_” @I
indicates parallel spins for the IT? and @electrons. But by forming the linear combination
we can eliminate this determinant, and thus obtain perfect spin-pairing and 4 eIectrons. 2~b3 generates the 0, valence-state configuration 2$3(02)
=
$1
=
+(“Z;
of the n?
7r~7r*_sj + eie17ry7r*,j)
(S= = 0)+ IA, (S= = 0))
+ --L eie “E,J (S, = 1) J2 When HO3 and NO4 dissociate to generate HO+O, and NO2 +02, a query arises about the electronic state of the 02. To answer this question we must examine the behaviour at large HO-O2 and N02-O2 distances (R) of the general linear combination 2!P = Cl 2f#!G~+c23k2. When
R is large,
the overlap
between
x*_ and q5 is small.
To a good
appro-
ximation, we may evaIuate the Hamiltonian matrix elements by assuming that these orbitals are orthogonal. The Hamiltonian matrix elements are then given by
Hll =
<‘ihw?‘~l,>
H22
=
<“ti21=W2ti2>
H12
=
<2+11W2ti2>
J. Mol. Structure, 11 (1972)
in which k is a constant, and the K(zT, K*_), K(z? , 4) and K(z? , #) are (positivedefinite) exchange integrals. As R --+ co, both IC(z*+, #) and K(~E*, , #) - 0; in the limit, H,, = k,tK(zT, n*_),I-I,, = k,-K(x%, n*_)and H,, = 0. It follows
thatasR-tw,2#-+2@ 2, and thereby generates O2 as “X~_Therefore, the HO + O3 and NO + 0, reactions are here predicted to generate ground-state Oz. For the NO + O3 reaction, we may also devise the mechanism of Fig. 7, which uses a Lewis fonnuIa for OS5 and NO as a Lewis base. The O2 is generated a double bond consisting of two electron-pair bonds. For this to occur, the bonding IE~ and n*_ orbitals must be either vacant or doubly occupied. excited efectronic states satisfy this requirement, namely ‘Ez and one ‘A, whose wave-functions arez6
with antiTwo state,
Therefore, Lewis and increased-valence theories predict different electronic states for the 0, product. Ciough and Thrush”, Pitts19*20 and Wayne2’ have tormented that so far no singlet O2 has been detected in the NO +O, reaction, and Wayne has suggested that this reaction should be written as NO-I-O, -+ NOT-i- 0; rather than as NO+ 0, --, NO, + 0:. Wayne’s suggestion agrees with the conclusions which we have obtained from the increased-valence mechanrsm
Fig. 7. NO 4-0~ --;FNO2-l-O2+. (An increased-valence forndation of the reaction)
12
J.
Mol.
Slrrrcrtfre,
11 (1972)
of Fig. 6. However the possibility” is not precluded here of subsequent formation of 0; by collision of NO; with Oz. For the H-+0, reaction, we cannot use the hydrogen atom as a Lewis base in the manner which we have done for NO in Fig. 7. If we use the Lewis formula for O3 it is necessary to unpair two of its bonding electrons in order that it may form a bond with the hydrogen atom. Therefore, in contrast to the increasedvaIence theory, the Lewis theory involves two different types of electronic processes to occur for the NO + O3 and H+ 0, reactions. Generally, we expect singlet O1 to be generated in those reactions which proceed by means of a Lewis acid-base mechanism. Some well known examples’ 6slg are CIO- + H,O, + Of + Cl- + H,O, and 20H- +peroxyacetyl nitrate --, CH&OO-+H20+N0,-+O;. ACKNOWLEDGEMENT
I express my thanks to Dr. D. P. Kelly, Department of Melbourne, for initiating my interest in this subject.
of Chemistry,
University
REFERENCES
J. HEICKLEN AND N. COHEN, in W. A. NOYES, JR., G. S. HAMMOND AND J. N. Prrrs, JR. (Editors), Adcances in Photochemistry, Vol. 5, Interscience-Wiley, New York, 1968, p. 157. 2 L. PAULING, J. Amer. Chem. Sot., 53 (1931) 1367, 3225. 3 R. D. HARCOURT, (a) J. CJxem.Edac., 45 (1968) 779, errata, 46 (1969) 856; (b) Arcst. J. Chem., 22 (1969) 279; (c) J. Mol. Stracfrtre, 5 (1970) 199; (d) ht. J- Q uantum Clrem., 5 (1971) 479: (e) J. Mol. Sfracture, 8 (1971) 11; (f) J. Mol. Strrccrwe, 9 (1971) 221; (g) unpublished results. 4 M. L. GREEN AND J. W. LINNJXT, J. Chem. Sac., (1960) 4959. 1
J. Chem. Sot., (1956) 756. 5 J. W. LINNE~, 6 J. H. SHAW, J. CJlem. Pilys., 24 (1956) 399. 7 L. PAULING, The Nature of the Chemical Bond, Cornell
Univ. Press, Ithaca, New York, 1960, pp_ 239, 344. 8 W. A. GUILLORY AND J. S. JOHNSTON,J. Chem. Phys., 42 (1965) 2457. 9 J. W. LINNETT, private communication. IO A. P. ALTSHULLER AND J. J. BUFALINI, Enuiron. Sci. Technol., 5 (1971) 39. 11 P. W. ATKINS AND M. C. R. SYMONS, J. Chem. Sot., (1962) 4794.
12 C. A. FONTIJN, C. B. MEYER AND H. I. SCHIFF, J. Clrem. Phys., 40 (1964) 64. 13 H. S. JOHNSON,J. LEWIS AND L. ZAFONTE, AtmospJzeric CJzemistry and PJaysics,Task Force 14 15 16 17 18 19 20 21
No. 7, Preliminary Report, University of California, June 30th, 1970. M. A. A. CLYNE, B. A. THRUSH AND R. P. WAYNE, Trans. Faraday Sot., 60 (1964) 3.59. P. N. CLOUGH AND B. A. THRUSH, Trans. Faraday Sot., 63 (1967) 915 and 65 (1969) 23. M. K.ASHAAND A. U. KHAN, Ann. N. Y. Acad. Sci., 171 (1970) 1. F. L. PILAR, Elementary Quantum Chemistry, McGraw-Hill, New York, 1968, p. 292. D. P. CRAIG AND T. THIRUNAMACHANDRAN, Proc. Roy. Sot. (London), A303 (1968) 233. J. N. Prrrs, Ann N. Y. Acad. Sci., 171 (1970) 239. J. N. Prm, R. P. WAYNE,
J. Air PolZar. Contr. Ass., 19 (1969) 658. Ann. N. Y. Acad. Sci., 171 (1970) 295.
1. Mol. Structure, 11 (1972)
13
Structure
Elsevier Publishing Company, Amsterdam. Printed in the Netherlands
VALENCE FORMULAE NITROGEN DIOXIDE
AND THE OXIDATIT)N
OF NITRTC OXIDE
TO
R. D. HARCOURT Department of Chemistry,
Unit;ersity of Melbomne, ParkoiZZe,Vkforia 3O.Q (Australia1
(Received August 27th, 1971)
ABSTRACT
‘Three-electron bond’ and ‘increased-valence’ formulae are described for NO, 02, N03, O3 and NO2 . These species occur in the HeickIen and Cohen mechanism for the atmospheric oxidation of nitric oxide to nitrogen dioxide. By using these valence formulae, 0, is predicted to be formed as the 3Xi electronic state in the reaction NO-I- 0, --, NO2 + Oz. SimiIar conclusions pertain for the reaction HO + 0, -+ HO2 + 02, and for some other radical transfer reactions which involve the formation of Oz. Use of NO as a Lewis base in the NO/O, reaction can generate 0, either as 1x:+ g or as ]-AS’
The oxidation of nitric oxide to nitrogen dioxide is an important reaction which occurs in poIIuted atmospheres. Various mechanisms have been proposed for this reaction, one of which involves the following steps%: NO-+-O, --+ ON00 ON00
-+ ONOO*
ONOO* + N02+0 oto,
--* 03
(9 (2) (3) (4)
In daytime Los Angeles, the time required to generate NO2 from NO by means of this mechanism has been estimated1 to be approximately 1 hour. In this paper it is not our intention to attempt to justify or reject the mechanism, but only to use it in order to illustrate some new aspects of elementary valence theory. We shall &xamine the bonding for all of the molecular species that pertain to this mechanism, and then indicate the electronic- rearrangements which might occur J. Mol. &%wctures 11 (1972)
1
for the reaction steps (l)-(4), and also for the reactions H+ 0s ---, HO+ O2 and NO + 0s -+ NO2 + Oz. The ‘three-electron bond’ valence formulae2 and the newly developed ‘increased-valence’ formulae3 were used to describe the bonding for diatomic and polyatomic systems respectively.
THREE-ELECTRON
BONDS
AND
INCREASED-VALENCE
FORMULAE
Pauling’, in 1931, introduced the three-electron bond to describe aspects of the bonding of paramagnetic molecules such as NO and 02, writing their valence formulae as (1) and (2), which have one and two three-electron bonds respectively. He showed that the three-electron bond structure (3) summarized the resonance of i
;A
‘A’
i,
There is one unpaired electron in each of these two structures. Therefore, for the Ot valence formula (2), there are two unpaired electrons. If these unpaired electrons have parallel spins, then the O2 is paramagnetic. At room temperature, NO is also paramagnetic. :N*-o: (1)
:o@s$& *me
A***B
i
(3)
(7)
0
(2)
4 (4)
(61
In 1960, Linnett and Green4 generated valence formulae with three-electron bonds from the molecular orbital configurations for the NO and O2 ground states. Each three-electron bond developed from the presence of two bonding and one antibonding electron occupying orthogonal molecular orbitals which are constructed from the same two atomic orbitals. Their proof is very simple, and we shall now examine it. Let a and b be two overlapping atomic orbitals on two atoms. From them, the orthogonal bonding and antibonding molecular orbitals $+ = a+b and 4-- = a-b may be constructed. Linnett and Green4 (and earlier, Linnett’) demonstrated that the determinantal wave-functions I@“+$5 and l$$t,@l are equivalent to kl&b”l and kldbsl, in which k is a constant and o!and j3 are spin wavefunctions. These results are easily obtained by expanding either determinantal wave-function. Thus, omitting normalization,
2
J_ Mol.
Structure,
11 (1972)
I#“+*I
= ~+,(l)a(1)~-(2)a(2)-~-(l)a(l)J/+(2)a(2) = Ml) + w)hm@)
= -2{a(l)cr(l)b(2)cr(2)= - 21n”b”l
- fQ)W) - W) - w)MQ~42) + W)l(2b b(l)a(l)u(2)r(2))
It follows that if we have the molecular orbital configuration I@+t+C$$.I involving two bonding and one antibonding electrons, then this configuration is equivalent to klti&,&l, for which two electrons occupy atomic orbitals and the third electron (with opposite spin) occupies the bonding molecular orbital. The Pauli principle keeps electrons with the same spins in different spatial orbitals. Linnett and Green have recommended that the resuhing electron distribution be written as (4) rather than as the Pauling structure (3). Structure (4) shows clearly that there is only one bonding electron in the three-electron bond. Linnett and Green wrote the NO and O2 valence formulae as (5) and (6), which indicate better than do (1) and (2) that these molecules have bond-orders of 2.3 and2 respectively*. If we indicate the electron spins of a three-electron bond, then (4) is equivalent either to (7) or to (S), in which the crosses and circles represent electrons with o! and j? spin functions. It is usually considered that the three-electron bond is restricted to a small number of paramagnetic molecular systems. However, it is possible to incorporate the three-electron bond structure (4) into the valence formulae for a very large number of diamagnetic, triatomic and polyatomic systems3. To do this for a triatomic system, a Y atom with one unpaired electron is introduced into valence formulae (7) and (8). Valence formulae (9) and (10) are obtained if there are a total of two CYand two /? electrons.
Y-A*& (11)
‘B’ -vxE3
Y-A 02)
03)
When the atomic orbitals on Y and A overlap appreciably, we may represent these two atoms as bonded together. We thereby obtain valence formula (1 l), in which the electron spins are not specified. This valence formula summarizes the resonance3 between the valence formulae (12) and (13). Since (13) does not have a YA bond, the YA bond of (11) must be longer and weaker than the YA bond of (12). Therefore, we use” a light line to represent the YA bond of (11). We have called3 valence formula (11) an increased-valence formula, because in it, more * The NO bond order has been calculated from the bond length6 of 1.150 A by using the Pauling formula3”*7 R(rr) = 1.44 -0.8 log N, in which tt is the bond order. J_
Mol.
Sfructure,
11 (1972)
3
electrons participate in bonding than occurs in either of the electron-pair bond formulae (12) or (13). The wave-function for (11) may be shown to represent a singIet spin state3=w3b, and therefore it is appropriate for diamagnetic systems. Nitrogen
trioxide (Fig.
I)
Some IR studies show that one NO, isomer is an unsymmetrical peroxides, with an ON00 structure. The nitrosyl stretching frequencies of NO3 and NO are bond, with a disand 1876 cm-r respectively, and the ON -0, 1840 cm-’ sociation energy of 742 kcal/moIe*, is very weak. GuilIory and Johnston’ have described the bonding in terms of the spin pairing of the unpaired eIectron of NO formula for with one of the two unpaired electrons of 0,. An increased-valence NO, corresponding to this description may be generated from valence formulae (5) and (6) for NO and Oz. This valence structure is compatible with the observed bond properties, because it shows that the electronic structure of NO need be little Oz bond is weak. modified on bonding to 02, and that the ON-
Fig, 1. NO-i-O2
+ ONGO.
The calculated’ 00 stretching frequency for ONOO, 1400 cm- ‘, is rather Iess than the 1556 cm-l for free 02, and could arise because of unequal sharing of the four bonding electrons by the two oxygen atoms of NOa. On bonding of O2 to NO, the electronegativities of the two oxygen atoms of O2 must be altered relative to each other. Increased-valence formulae for ONNO, XNO (with X = halogen), FOOF, FSSF, F$S and FzSO may be similarly constructed3, i.e. from the three-electron bond formulae (5), (6), (14) and (15) for NO, 02, Sz and SO. Each of these polyatomic molecules has bond properties which are similar to those of the diatomic molecules, and long or weak NN, XN, OF or SF bonds. The observed properties are compatible with those which are implied by the increased-valence formulae. Cl bond, and an Dichtoiine dioxide, OCICIO, however, has a very weak CIincreased-valence formula which is constructed from the three-electron bond formufa (16) for CIO shows this adequatefyg. The 00, SS and NO bonds of HOOH, HSSH and HNO Iengthen relative to those of free O,, S2 and NO, and 4
J. Mol.
Structure,
11 (1972)
the familiar Lewis formulae HO -OH, provide HSSH and HN--0 satisfactory representations of the electronic structures of these molecules. Hydrogen atoms are not able to stabilize three-electron bonds of increased-valence bonding units; we shall use this result when we discuss the H+O, reaction.
Ozone (Fig. 2) Oxygen atoms react rapidly with molecular oxygen to form ozone’ ‘. By spin pairing the unpaired electrons of the 0 and O2 ground states, we obtain an increasedvalence formula for 0, _ In Fig. 2, we also show a Lewis formula for O,, which may be obtained
from
excited
states
(:d
and :I!=@)
of 0
and
02,
each
of
which has no unpaired electrons. This Lewis formula has net positive and negative charges on the central atom and on one terminal oxygen atom. These net charges may be reduced in magnitude by delocalizing two lone-pair electrons of the Ointo two bonding orbitals of O-O+ which are vacant in the Lewis structure. These delocalizations are shown (Fig. 2) by means of two curly arrows with single barbs. The resulting valence formula is an increased-valence formula. It is easy to show that the increased-valence formula summarizes resonance between the Lewis structure and three long-bond structures. Therefore, the increased-valence formula mzrst have a Iower energy than has the Lewis formula. Further, by delocalizing lone-pair electrons of a Lewis formula, it is always possible to generate an increased-valence formula from Lewis formulae of types (17) and (18), provided that the three atomic orbitals on Y, A and B overlap3. From (17) and (18), the increased-valence formula (11) is generated by delocalizing a lone-pair electron of B
Fig. 2. 0+02 J. Mol.
+ OS, and Lewis and increased-valence formulae for OZ.
Structure, I1 (1972)
5
of (17) into a bonding AB orbital, and by delocalizing a Y lone-pair electron of (18)
into an antibonding AB orbitaL FuIler details of these delocalizations are described elsewhere3. For OS, the molecular symmetry requires a description of the electronic structure to involve resonance between a number of increased-valence structures, two of which are shown in Fig. 2. Equivalent valence structures are omitted from the NO2 discussions but it is to be understood that they exist, and that they participate in resonance with the structures that are shown.
Nitrogen dioxide (Fig. 3) The reaction O+NO generates N02; the initial step could involve the formation of a weak NO single bond, as in Fig. 3(a).
(b)
(e)
Fig. 3. O+NO
-+ NOz*
+ NOz.
Valence formula (a) is an increased-valence formula, with seven bonding electrons. However, the structure may be stabilized by increasing the number of
bonding electrons to eight, if one of the nitrogen lone-pair eIectrons of (a) is delocalized into a bonding NO orbital, thereby generating (b). ESR measuremerits” detected a fractional unpaired-electron charge on the nitrogen atom of NO,. The structure for NO= obtained in the reactions above is the increased-
valence formula (b), which may be further stabilized by delocalizations, which reduce the magnitudes of the formal charges on the oxygen atoms and generate increased-valence formula (c). We have shown3’ that (c) is compatible with the measured NO bond lengths. Increased-valence formulae, compatible with the experimental bond lengths3’; may be constructed for r\r,O,, N,O,, XN02 and CX3N02 (X = halogen) using structure (c), together with structure (5) for NO, 6
J. Mol. Structure, 11 (1972)
halogen atoms or trihalomethane radicals. It is to be understood that we may generate (c) from the valence formulae of type (b) which are produced in the reactions shown in Figs. 4 and 6. We may also generate (c) by starting with the NO excited state (e) which has three unpaired electron charges on the nitrogen atoms. Two of these charges are then spin-paired with the two unpaired electrons on the oxygen atom. The NO excited state (e) is obtained from the ground-state by promoting one of the nitrogen lone-pair electrons into an antibonding NO orbital, as we show in (d). The reaction O+NO + NO2 is accompanied by chemiluminescence12, which possibly arises from the transition of (b) to (c).
RADICAL
TRANSFER REACTIONS
A radical transfer reaction involves a redistribution of unpaired electrons between reactants and products_ In the atmosphere, many examples are known’ 3_ By using increased-valence formulae it is possible to devise simple mechanisms for quite a number of them. As yet, the full consequences of these mechanisms have not been worked through, and therefore what we describe probably represents only a beginning in this subject. The reactions considered are ONOO* --, NO2 + 0, H+O, + HO+O, and NO+O, --, NO,+O,. (a) NO3 + NO2 + 0 (Fig. 4) In Fig. 1, we have displayed the formation of ON00 from NO+ Oz. Here, we shall indicate the formation of NO2 + 0 from the excited state ONOO*. We suggest that ONOO* corresponds to the formation of an 00 single
Fig. 4.ONOO J. Mol.
-+ ONOO*
Structure,
-+ NOz+O.
1I (1972)
7
bond together with the delocalization of a nitrogen lone-pair electron into a bonding NO orbital’- The appropriate electron transfers are shown in Fig. 4, and the delocalization of the nitrogen electron into the bonding NO orbital must weaken the 00 bond. When this bond breaks, NO, + 0 are formed. The oxygen atom can react (Fig. 2) with an oxygen molecule to produce 0s , which then reacts with NO to form NO, + 0,. If we obtain an initial bonding of O2 to N03, as has also been suggested by Heicklen and Cohen’, the NOz0s bond will be weak, and on breaking, generates NO= + 0s. (b) H-I-O,
+ HO+O,
(Fig. 5)
This reaction is described here in order to illustrate the principles which are also involved in the NO+O, reaction. The electronic structure of 0, is assumed adequately represented by its increased-valence following
Fig. 5. H+03
structures of Fig. 2. In Fig. 5, the
steps in the reaction are shown.
-+ HO3 + HO+O~
(‘2;).
(i) A hydrogen atom approaches Os, and stabilizes one increased-valence structure relative to the others. By this we mean that the electronic structure of 0, resembles the stabilized structure more than it resembles any of the other structures. (ii) The hydrogen atom forms a weak electron-pair bond with one of the unpaired electrons on the adjacent terminal oxygen atom of OX++_ (iii) We now assume that the two unpaired bonding electrons of w-0 transfer into oxygen atomic orbitals. An O---O single bond is thereby formed, and the Hbonding O bond is strengthened. We have now formed an HO -0 scheme which is similar to that of HO--OH for hydrogen peroxide. In both, t This nitrogen delocalizationcould
also occur appreciably in the unexcited ON00 of Fig. 1; if so, then it would be partially responsible for the reduction of the 00 stretching frequency. tt A very small amount of energy is needed to break the weak long bond which is formed between this unpaired electron and an electron on the other terminal oxygen atom. 8
J. Mol. Strucrure,
11 (1972)
the hydrogen atoms are not able to stabilize the three-electron bonds of OZ. One other result of these electron transfers is the breaking of one of the weak bonds of O--0, thereby forming an unpaired electron on the terminal oxygen atom.
The electronic structure of HO? has now lost its increased-valence character; its structure is HO---O---O, and involves only singfe bonds.
(iv) Increased-valence is now restored by delocalizing two oxygen lone pair electrons into two vacant bonding 00 weakens the adjacent HO--O bond.
(v) The weakened HO -0
orbitals.
One
of these delocalizations
bond breaks to form the products HO and Oz.
(c) NO -HI3 -+ N&-I- 0, (Fig. 6) By using valence formula (3) for NO, and the increased-valence formula of Fig. 2 for Os, we may construct the mechanism of Fig. 6 for NO t 03, which closely resembles that of Fig. 5 for Hi- O3 _ The 0 -0 bond of the second NOB structure has been weakened by delocalizing a nitrogen lone-pair electron into a vacant bonding NO orbital. This type of deIocalization has also been used in Figs.
3 and 4.
Fig. 6. NOtO
+ NO4 + NOz-+-O+ (3x:,).
The NO-t0, reaction is a bimolecular reaction which proceeds along two paths’““. One of these produces electronically excited NO,. The radiation that is emitted might arise from the Ioss of energy which is generated when the NOz formed in Fig. 6 returns to the ground-state structure (G) of Fig. 3. Increased-valence mechanisms for many other radical transfer reactions, such as NO+NO, + 2NOt, NO,+O, -P NOs+O,, O,+O, + 202+0, CIOz + NO 3 Cl0 + NOa and 2H02 -+ H202 + O2 may be described in a similar manner to that of (b) and (c). For the last of these reactions, the HOOOOH is predicted to decompose as 02+20H, and the two OH radicals then combine to
forXrl J&o, * 9
ELECTRONIC
STATES OF 0,
We shall now consider the nature of the electronic state of the 0, which is produced in the HO -t-O, and NO t 0s reactions. ff spin is conserved in these reactions, the HO3 and NO4 radical intermediates will have doublet (S = +) sp in states. Each of HO, and NO4 (Figs. 5, 6) generates an O2 molecule with two three-electron bonds, and therefore with two unpaired electrons. The “XL ground state and one ‘4 excited state have molecular orbital configurations with two unpaired electrons occupying antibonding xelectron orbitals16. If z+, IL-, ~2 and zc*_ are the bonding and antibonding n-electron molecular orbitals, the x*-electron configurations for these “2; and ‘A9 states are 16
In the increased-valence formulae shown in Figs. 5,6 for HO, and NO,, O2 has spin-paired one of its unpaired electrons with the unpaired electron of either HO or NO,. If we label the orbital for the latter electron by the symbol 4, and for simplicity, retain the n$ and R? notations for the 0, antibonding orbitals, then we may construct two orthogonal spin eigenfunctions which involve unpaired electrons in the zz, n*, and C$orbitals17. For Sz = -++, these spin eigenfunctions are
and
(There are also two doublet functions with Sz = -f, which we need not write down here.) By separating the 0, from the NO, or HO without in any way changing the spin coupling18, we may extract 0, valence states from 2*x and 2$2. Using the theory of Craig and Thi~~amac~n~an’*, we obtain
and 10
.J. Mol..Strucrure,11
(1972)
= -$ (23ZZ, (S= = 1) +JZe’*
“Xi (S= = 0))
in which eie is an arbitrary phase factor. Only one of nr and ~3 can overlap with (p. If we assume for example that n*_ overlaps with 4, then neither 2$1 nor ‘14~ involves perfect spin-pairing of the k!! and C#Jelectrons; in both functions, the determinant IxT8 z*_” @I
indicates parallel spins for the IT? and @electrons. But by forming the linear combination
we can eliminate this determinant, and thus obtain perfect spin-pairing and 4 eIectrons. 2~b3 generates the 0, valence-state configuration 2$3(02)
=
$1
=
+(“Z;
of the n?
7r~7r*_sj + eie17ry7r*,j)
(S= = 0)+ IA, (S= = 0))
+ --L eie “E,J (S, = 1) J2 When HO3 and NO4 dissociate to generate HO+O, and NO2 +02, a query arises about the electronic state of the 02. To answer this question we must examine the behaviour at large HO-O2 and N02-O2 distances (R) of the general linear combination 2!P = Cl 2f#!G~+c23k2. When
R is large,
the overlap
between
x*_ and q5 is small.
To a good
appro-
ximation, we may evaIuate the Hamiltonian matrix elements by assuming that these orbitals are orthogonal. The Hamiltonian matrix elements are then given by
Hll =
<‘ihw?‘~l,>
H22
=
<“ti21=W2ti2>
H12
=
<2+11W2ti2>
J. Mol. Structure, 11 (1972)
in which k is a constant, and the K(zT, K*_), K(z? , 4) and K(z? , #) are (positivedefinite) exchange integrals. As R --+ co, both IC(z*+, #) and K(~E*, , #) - 0; in the limit, H,, = k,tK(zT, n*_),I-I,, = k,-K(x%, n*_)and H,, = 0. It follows
thatasR-tw,2#-+2@ 2, and thereby generates O2 as “X~_Therefore, the HO + O3 and NO + 0, reactions are here predicted to generate ground-state Oz. For the NO + O3 reaction, we may also devise the mechanism of Fig. 7, which uses a Lewis fonnuIa for OS5 and NO as a Lewis base. The O2 is generated a double bond consisting of two electron-pair bonds. For this to occur, the bonding IE~ and n*_ orbitals must be either vacant or doubly occupied. excited efectronic states satisfy this requirement, namely ‘Ez and one ‘A, whose wave-functions arez6
with antiTwo state,
Therefore, Lewis and increased-valence theories predict different electronic states for the 0, product. Ciough and Thrush”, Pitts19*20 and Wayne2’ have tormented that so far no singlet O2 has been detected in the NO +O, reaction, and Wayne has suggested that this reaction should be written as NO-I-O, -+ NOT-i- 0; rather than as NO+ 0, --, NO, + 0:. Wayne’s suggestion agrees with the conclusions which we have obtained from the increased-valence mechanrsm
Fig. 7. NO 4-0~ --;FNO2-l-O2+. (An increased-valence forndation of the reaction)
12
J.
Mol.
Slrrrcrtfre,
11 (1972)
of Fig. 6. However the possibility” is not precluded here of subsequent formation of 0; by collision of NO; with Oz. For the H-+0, reaction, we cannot use the hydrogen atom as a Lewis base in the manner which we have done for NO in Fig. 7. If we use the Lewis formula for O3 it is necessary to unpair two of its bonding electrons in order that it may form a bond with the hydrogen atom. Therefore, in contrast to the increasedvaIence theory, the Lewis theory involves two different types of electronic processes to occur for the NO + O3 and H+ 0, reactions. Generally, we expect singlet O1 to be generated in those reactions which proceed by means of a Lewis acid-base mechanism. Some well known examples’ 6slg are CIO- + H,O, + Of + Cl- + H,O, and 20H- +peroxyacetyl nitrate --, CH&OO-+H20+N0,-+O;. ACKNOWLEDGEMENT
I express my thanks to Dr. D. P. Kelly, Department of Melbourne, for initiating my interest in this subject.
of Chemistry,
University
REFERENCES
J. HEICKLEN AND N. COHEN, in W. A. NOYES, JR., G. S. HAMMOND AND J. N. Prrrs, JR. (Editors), Adcances in Photochemistry, Vol. 5, Interscience-Wiley, New York, 1968, p. 157. 2 L. PAULING, J. Amer. Chem. Sot., 53 (1931) 1367, 3225. 3 R. D. HARCOURT, (a) J. CJxem.Edac., 45 (1968) 779, errata, 46 (1969) 856; (b) Arcst. J. Chem., 22 (1969) 279; (c) J. Mol. Stracfrtre, 5 (1970) 199; (d) ht. J- Q uantum Clrem., 5 (1971) 479: (e) J. Mol. Sfracture, 8 (1971) 11; (f) J. Mol. Strrccrwe, 9 (1971) 221; (g) unpublished results. 4 M. L. GREEN AND J. W. LINNJXT, J. Chem. Sac., (1960) 4959. 1
J. Chem. Sot., (1956) 756. 5 J. W. LINNE~, 6 J. H. SHAW, J. CJlem. Pilys., 24 (1956) 399. 7 L. PAULING, The Nature of the Chemical Bond, Cornell
Univ. Press, Ithaca, New York, 1960, pp_ 239, 344. 8 W. A. GUILLORY AND J. S. JOHNSTON,J. Chem. Phys., 42 (1965) 2457. 9 J. W. LINNETT, private communication. IO A. P. ALTSHULLER AND J. J. BUFALINI, Enuiron. Sci. Technol., 5 (1971) 39. 11 P. W. ATKINS AND M. C. R. SYMONS, J. Chem. Sot., (1962) 4794.
12 C. A. FONTIJN, C. B. MEYER AND H. I. SCHIFF, J. Clrem. Phys., 40 (1964) 64. 13 H. S. JOHNSON,J. LEWIS AND L. ZAFONTE, AtmospJzeric CJzemistry and PJaysics,Task Force 14 15 16 17 18 19 20 21
No. 7, Preliminary Report, University of California, June 30th, 1970. M. A. A. CLYNE, B. A. THRUSH AND R. P. WAYNE, Trans. Faraday Sot., 60 (1964) 3.59. P. N. CLOUGH AND B. A. THRUSH, Trans. Faraday Sot., 63 (1967) 915 and 65 (1969) 23. M. K.ASHAAND A. U. KHAN, Ann. N. Y. Acad. Sci., 171 (1970) 1. F. L. PILAR, Elementary Quantum Chemistry, McGraw-Hill, New York, 1968, p. 292. D. P. CRAIG AND T. THIRUNAMACHANDRAN, Proc. Roy. Sot. (London), A303 (1968) 233. J. N. Prrrs, Ann N. Y. Acad. Sci., 171 (1970) 239. J. N. Prm, R. P. WAYNE,
J. Air PolZar. Contr. Ass., 19 (1969) 658. Ann. N. Y. Acad. Sci., 171 (1970) 295.
1. Mol. Structure, 11 (1972)
13