J . Phys. Chem. 1990, 94, 7007-7012 This latter reaction has been shown to occur with near diffusion controlled rate,14 and both reactions 7.5e/2 and 3.3/3 were important in modeling the FT-ICR experiments.’*
Acknowledgment. This work was supported in part through the grants from the Environics Division of the United State Air
7007
Force Engineering and Service Center, Tyndall AFB, FL (M. C.Z.), and through a PRF-Type B 20313-BS award (B.W., C.W., D.H.). We gratefully acknowledge useful discussions with Dr. John Eyler, University of Florida, and the Penn State Computation Center for the generous amount of computer time on their IBM 3090-4008 and IBM 3090-6008.
Nonemplrlcal Valence Bond Studles of the Origin of the Rotation Barrier for N,O, Richard D. Harcourt* and Frances L. Skrezenek Department of Physical Chemistry, University of Melbourne, Parkville, Victoria 3052, Australia (Received: February 9, 1990)
The origin of the barrier to rotation around the N-N bond of N204is examined by means of nonempirical valence bond calculations with 34 valence shell electrons. Particular attention is focussed on the electrons that are considered to be primarily associated with this phenomenon, namely, two N-N u-bonding electrons and four sets of oxygen lone-pair electrons, whose orbitals overlap appreciably with those of the N-N u bond. In agreement with the conclusion obtained from previous molecular orbital studies, it is calculated that overlap between atomic orbitals located on pairs of cis oxygen atoms in the planar conformer is primarily responsible for the stabilization of this conformer relative to the perpendicular conformer. The “cis 0-0overlap” stabilization only manifests itself when there is some delocalization of the oxygen lone-pair electrons into the atomic orbitals that form the N-N u bond and is mostly associated with covalent-ionic resonance, Le., N02-N02 NO2+NO2- NO< NO2+ with an important involvement by covalent and ionic Lewis structures of types A and B. It is also calculated that N-N A bonding in the planar conformer is too weak to account for the existence of an appreciable rotation barrier. Q
A
Introduction
The planar ( D Z h )isomer of N 2 0 4 has a barrier to rotation around the N-N bond of 8-12 kJ mol-’.1v2 On occasions, the planarity has been associated primarily with the presence of some N-N A b ~ n d i n g . ~ - ~However, the results of a number of semiempirical and ab initio molecular orbital (MO) studies6-I5 and semiempirical valence bond (VB) calculations10,16indicate that an important contribution to the rotation barrier arises from the existence of long-range bonding overlap (or cis 0-0overlap2.6) in the planar conformer. This overlap occurs between u-type atomic orbitals (AOs) that are located on pairs of cis oxygen atoms; its magnitude decreases as rotation around the N-N bond proceeds, and the perpendicular conformer is approached. When the AOs that form the N-N and N - 0 u bonds are assumed to be oriented as in Figure 1, the relevant oxygen AOs that are required to provide a VB description of the cis 0-0 overlap effect are the 2pii AOs of this figure. These orbitals are doubly occupied in the standard Lewis structures of types 1 and 11 of Figures 2 and 3, but because they overlap with the nitrogen AOs that help form the N-N u bond of these structures (Figure I ) , the latter AOs need also to be included in a VB treatment of the cis 0-0 overlap effect. Together, the six orbitals have been designated as mobile a-electron A O S . ~ ’ . ~Each ~ of the cis 0-0 overlap integrals ( ~ ~ 1 % and ~ ) ( ii51ii6)for the planar conformer has an STO-SGvalue of 0.01 I , which is reduced to 0.001 in the perpendicular conformer. Several conclusions were obtained from the VB calculations of refs I O and 16, namely: (a) Cis 0-0overlap stabilization of the planar conformer only manifests itself when there is some delocalization of the iio electrons into the hz and h3 AOs of the N-N u bond.
* Author to whom correspondence
should be addressed.
Q
0
(b) When the iio electron delocalization occurs, a substantial cis 0-0 overlap stabilization energy is only obtained through resonance between covalent (N02NOz-type)VB structures, such as 1-4 of Figure 2, and ionic (NO2+NO2- N02-N02+ type) VB structures. In particular, it was also found that the (long) cis 0-0 covalent bond (0-- -0)in covalent structures of type 4 is too weak to stabilize the planar conformer. The above conclusions were obtained by using semiempirical VB techniques. The purpose of the present paper is to provide further support for them by means of nonempirical VB calculations
+
(1) Snyder, R. G.; Hisatsune, I. C. J . Mol. Spectrosc. 1957, I, 139. (2) Bibart, C.H.;Ewing, G. E. J . Chem. Phys. 1974, 61,1284. (3) Pauling, L. The Nature ofthe Chemical Bond; Cornell: Ithaca, NY, 1960;p 350. (4) Green, M.; Linnett, J. W. Trans. Faraday SOC.1961, 57, 10. (5) Bauschlicher, C. W.; Komornicki, A,; Roos, B. J . Am. Chem. SOC. 1983, 105, 745. See also: Roos, B. Advances in Chemical Physics; Wiley: New York, 1987;Vol. LXIX, p 399. (6) Redmond, T. F.; Wayland, B. B. J . Phys. Chem. 1968, 72, 3038. (7) Epiotis, N. D.; Cherry, W. R.; Shaik, S.; Yates, R.; Bernardi, F. Top. Curr. Chem. 1977, 70, 63. (8) Gimarc, B. M.; Khan, S.A.; Kohn, M. C. J. Am. Chem. SOC.1978, 100, 1996. (9) Kishner, S.;Whitehead, M. A,; Gopinathan, M. S.J . Am. Chem. Soc. 1978, 100, 1365. (10)Harcourt, R. D. Ausf. J. Chem. 1981, 34, 231. Some additional semiempirical studies were also made with Volkoff, C., 1983. ( I 1) Harcourt, R. D.; Smith, 8.; Marsden, C. J. Aust. J. Chem. 1984, 37, 1553. (12) Howell, J. M.; van Wazer, J. R. J . Am. Chem. SOC.1974, 96,7902. (13)Ahlrichs, R.; Keil, F. J . Am. Chem. SOC.1974, 96,7615. (14)Clark, T.;Schleyer, P. v. R. J . Compuf. Chem. 1981, 2, 20. (15) Del Re, G . ; Berthier, G.; Serre, J. Lecfure Nores in Chemistry; Springer-Verlag: Berlin, 1980;Vol. 13, p 166. (16)Harcourt, R. D. Ausf. J. Chem. 1978, 31, 1635. (17) Brown, R. D.; Harcourt, R. D. Proc. Chem. SOC.1961, 216. (18) Brown, R.D.; Harcourt, R. D. (a) Aust. J . Chem. 1963. 16,737;(b) 1965, 18, I 1 15.
0n32-7654/90/2094-7007~02.S0/0 0 1990 American Chemical Societv
7008
Harcourt and Skrezenek
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990
05
Figure 3. Trans N-0 type VB structures
6' N2
N3
01
04
Figure 1. Orientations for in-plane oxygen p and nitrogen AOs for planar N204,N20,,and N202.The four iio and two hN AOs for NzO,are designated as "mobile u electron" A*, their occupation numbers differ in the various Lewis VB structures of Figures 2-4. The *-electron AOs
Figure 4. Additional trans N-0 type V B structures.
have their axes perpendicular to the molecular planes.
MOs.Isb The approach adopted here involves the simplest qualitative model that may be used to provide a VB study of the cis 0-0 overlap effect. Valence Bond Structures
Figure 2. Cis N-0 type VB structures.
for the ten mobile Q electrons of Figure 1, together with the remaining 24 valence shell electrons, which are assumed to form a core for the mobile u electrons. The analysis is more detailed than that reported previously and brings out some additional factors that do not arise when the zero differential overlap assumption of ref 10 is invoked. It will also be demonstrated that the barrier does not arise from N-N A bonding in the planar conformer. The status of the present N2O4calculations, with 34 valence shell electrons, resembles closely those of some recent nonempirical VB studies of the origin of the antiferromagnetism of Cu(I1) carboxylate dimers, in which similar types of VB structures (but fewer electrons) have been explicitly con~idered.'~Both sets of calculations are intended to be illustrative of VB aspects of the cis 0-0overlap contribution to either rotation barriers or antiferromagnetism, rather than a priori attempts to calculate exactly the magnitudes of the rotation barriers and the magnetic exchange parameters. We note also that Shaik and Hibertym have also used model VB calculations to illustrate certain aspects of bonding theory, Le., they have treated explicitly the electrons and orbitals that were considered to be primarily associated with the phenomenon that was being studied. As well as restricting our attention to the valence shell electrons and specific sets of VB structures, various other simplifications have been made in the present calculations. For example, the energy-optimized orientations of the hfN,2paO, and iio AOs will not correspond to those of Figure 1, and we have ignored the small degree of 50-delocalization that can occur into antibonding u * (19) Harcourt, R. D.; Skrezenek, F. L.; Maclagan, R. G . A. R. J . Am. Chem. SOC.1986, 108, 5403. (20) Shaik, S. S.; Hiberty, P. C. J . Am. Chem. SOC.1985, 107, 3089.
~
In the Lewis structures 1-10 of Figure 2 and 11-20 of Figure 3, the N-O double bonds are located cis and trans relative to each other. In the subsequent discussion, we shall designate these VB structures as "cis" and "trans* structures, respectively. For either type of N - 0 double-bond arrangement, there are 21 S = 0 spin Lewis structures that differ in the locations of ten electrons amongst the six mobile u electron AOs of Figure I . We were unable to include all structures simultaneously in the VB calculations with 34 valence shell electrons and therefore calculations with smaller sets of structures were performed. These structures were selected by using the following considerations. The tendency for the iio electrons to delocalize is assisted by the appreciable electronegativity of the N+ relative to the 0- in the Lewis structures 1 and 11. (Delocalizations from the 0-rather than from the 0 reduce the magnitudes of the formal charges on two of the oxygen atoms as well as those for the nitrogen atoms.) In Figures 2 and 3, the covalent structures 2-4 and 12-14 arise from iio- electron delocalizations into the hN+AOs. In Figure 2, structures 5-10 are the cis ionic structures that partner the four covalent structures. The trans ionic structures 15-20 of Figure 3 correspond to structures 5 1 0 in Figure 2. Rotation around the N-N bond of one NOz moiety relative to the other generates identical perpendicular structures from the cis and trans structures of Figures 2 and 3. These sets of structures are those that have been included in most of the VB calculations with 34 valence shell electrons. We have also performed some calculations with the trans ionic structures 21-24 replacing 17-20, in order that a cis 0-0 overlap effect (see later) may manifest itself through resonance between a set of trans Structures. Because substantial electronic reorganization is required to convert the structures of Figures 2 and 3 into their mirror images, little interaction can occur between these sets of structures. Therefore, to keep the size of the VB calculations manageable, we have excluded the mirror image structures, Le., we have invoked either c, or C2h symmetry rather than Dzh symmetry for the VB calculations. To demonstrate that this type of simplification is reasonable, we have performed some Dzh VB calculations with smaller sets of structures. The results of these latter calculations ~(Table 1) show mostly that the barriers obtained by taking either one or two equivalent structures from Figures 2 and 3 are almost identical with those obtained when the mirror image structures are included. The only exception involves the trans structure 11 and its mirror image, and 11 is calculated (cf. Table V) to be
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7009
Origin of the Rotation Barrier for N204 TABLE I: Rotation Barriers (kJ mol-') for Resonance between Sets of Structures with Mirror Image Structures (l', Il', etc.) Included and (in Parentheses) Excluded structures k=O k = 0.45 I , 1' -67.8 (-68.2) -32.6 (-38.7) 11, 11' 2. 3, 2', 3' 2, 3, 7, 8, 2'. 3', 7'. 8' 4, 4' 4, 9, 10, 4', 9', 10' 1, 11, l', 11'
13.7 20.4 40.9 -3.1 -0.5 -21.5
(24.1) (20.1) (41.1) (-3.1) (-0.5) (-27.0)"
TABLE 11: Energies ( E , au; E", kJ mol-') for Resonance between the Cis Lewis Structures 1-10
k
-8.2 (1.5) 29.5 (29.0) 48.7 (49.0) -14.2 (-14.2) -1 1.8 (-I 1.8) -18.3 (-20.4)"
- -
"Arithmetical average of barriers for 1 1' and 11 11'. Here and in Tables 11-VII, k is the polarity parameter for the N-0 r-electron MOs of the general form +No = TO + krN.
unimportant when it participates in resonance with structures 12-20. It may be noted also that variational calculations for resonance between 1, 11, and their mirror images give barriers (Table I) that are close to those obtained by arithmetical averaging of the separate barriers for 1 mirror image and 11 + mirror image. Due to *-electron delocalization-in particular from the doubly occupied rv AOs of each of the Lewis structures-VB structures with *-electron distributions that differ from those of structures 1-24 also contribute to the VB resonance ~ c h e m e . ~ . ~Such '-~~ structures increase the K electron charge on the nitrogen atoms. (Molecular orbital estimates of these charges on all larger than unity; see for example refs 5, 9, and 12-14. Our GAUSSIAN goz6 M O estimate, with an 6-31G basis, is 1.07.) In most of the VB calculations, we have taken account of this effect by locating the eight A electrons in four N-O bonding MOs, instead of two N-O bonding MOs and two lone-pair TO- AOs.
1.o 0.45" 0.45b
Geometry. The bond lengths and 0-N-0 bond angles of ref
1
(25)
Orbitals. Due to the size of the VB calculations, we were only able to include the 34 valence shell electrons in them. Our experience with VB calculations for S2N2, Sq2+, 03,and HCONH229-34shows that exclusion of the Is electrons affects only (21) Harcourt, R. D. J . Mol. Struct. 1971, 9, 221. (22) Harcourt, R. D. J . Am. Chem. Soc. 1980,100,5195; 1981,101,5623. (23) Harcourt, R. D. Lecture Notes in Chemistry; Springer-Verlag, Berlin, 1982; Vol. 30, p 131. (24) Harcourt, R. D. In Valence Bond Theory and Chemical Structure; Klein, D. J., Trinajstif, N., Eds.; Elsevier, 1990; p 251. (25) Harcourt, R. D. J . Mol. Struct. (Theochem) 1988, 169, 193. (26) Binkley, J. S.; Whiteside, R. A., Krishnan, R.; Seeger, R.; DeFrees, D. J.; Schlegel, H. B.; Topiol, S . ; Kahn, L. R.; Pople, J. A. QCPE 1981, 13, 406. (27) McClelland, B. W.; Gundersen, G.; Hedberg, K. J. Chem. Phys. 1972, 56, 4541. A more recent geometry is provided in ref 28. (28) Kvick, A.; McMullan, R. K.; Newton, M. D. J . Chem. Phys. 1982, 76, 3154. (29) Skrezenek, F. L.; Harcourt, R. D. J. Am, Chem. Soc. 1984,106,3934. (30) Skrezenek, F. L.; Harcourt, R. D. Theoret. Chim. Acta 1985.67, 271; 1986, 70, 287. (31) Harcourt, R. D.; Skrezenek, F. L. J . Mol. Sfruct. (Theochem) 1987, 151, 203. (32) Harcourt, R. D.; Skrezenek, F. L.; Wilson, R. M.; Flegg, R. H . J . Chem. Soc. Faraday 11, 1986, 82, 495.
E"' 13.2 15.9 16.3 16.7 12.6 5.6 11.1
TABLE 111: Energies ( E , au; E", kJ mol-') for Resonance between Trans Lewis Structures
k
E(vlanar) -90.15965 -90.298 64 -90.300 76 -90.299 9 1 -90.185 52 -90.15434 -90.291 37
0" 0.4" 0.45"
0.5" I .O" Ob
0.45b
Eberv) -90.158 62 -90.296 26 -90.297 99 -90.296 72 -90. I77 51 -90.15266 -90.286 88
"Structures 11-20. bStructures 11-16
ErOl
2.7 6.3 7.3 8.4 21.0 4.4 11.8
+ 21-24.
TABLE IV: Coulson-Chirgwin Weights for Resonance between the Cis Covalent and Ionic Structures 1-10" k=O k = 0.45 structure
planar 0.010 (0.009) 0.100 10.097) 0.747 (0.796j 0.001 0.017 0.004
1 2=3 4
5=6 7 =8 9 = 10
27 were used in the VB calculations for both conformers. How-
ever, for one set of calculations (see Appendix) with average *-electron distributions, as in structure 25, for example, the effect of N-N bond-length variation in both conformers has been examined. The results of these calculations show that use of the same bond lengths in both conformers does not alter the qualitative conclusions of this work. It may be noted that in ref 13, the N-N bond len th for the perpendicular conformer was estimated to be -0.06 shorter than it is in the planar conformer.
E(verv) -90.158 62 -90.296 26 -90.297 99 -90.296 72 -90.1 77 5 1 -90.286 01 -90.295 60
"Structures 7 and 8 omitted. bStructures 5, 6, 9, and 10 omitted.
+
Method of Calculation
E(vlanar) -90. I63 66 -90.302 30 -90.304 19 -90.303 07 -90.182 3 I -90.288 13 -90.299 8 1
0 0.4 0.45 0.5
LI
perp 0.010 (0.009) 0.096 (0.094) 0.767 (0.802j 0.001 0.013 0.001
planar PerP 0.027 (0.025) 0.027 (0.024) 0.153 (0.152) 0.146 (0.144) 0.584 (0.671j 0.617 ( o m j 0.002 0.002 0.034 0.027 0.002 0.005
Values in parentheses are for resonance between the covalent structures
1-4.
slightly the values of the structural weights; even though the valence shell u AOs are mostly not orthogonal to the Is AOs. The hybridization for the nitrogen AOs was determined via the one-center orthogonality requirement and the experimental bond angles of ref 27; p:s ratios of 1.2 and 2.2 for the hlN and hN AOs of the N - 0 and N-N u bonds (Figure 1) are thereby obtained. The latter ratio is similar to the CNDO/MO estimate9 of 1.9. The 24 electrons that form the core for the ten mobile u electrons were accommodated in the following orbitals: (a) Four 2s0 AOs. (b) Four N - O a-bonding MOs of the general form uN0 = h'N K2pUo, for which hlN and 2pu0 are directed along the N - O bond axis, and the p:s ratio for hlN is 1.2. These MOs have been assumed to be homopolar (Le., K = I ) , as they are in each of the N - 0 u bonds in the Lewis structures of Figures 2 and 3. (c) Two N-0 ?r-bonding MOs of the general form = rN r0. These orbitals accommodate the four A electrons that form the two homopolar K bonds which are present in each of the Lewis structures. (d) Two N-0 x-bonding MOs of the general form dNo= xo + k r N . When k = 0, the a-electron distribution for each of the Lewis structures of Figures 2-4, namely, ( T ~ O ) ~ ( K @is) ~obtained. , However, an energy-optimized value for k was determined to allow for some delocalization of the xo- electrons. Polarization of the N-0 u bonds was not treated explicitly, but the optimized value of k indirectly takes some account of this effect. The resulting core configuration for the mobile u electrons is then ( 2 s O ) 8 ( ( r N 0 ) 8 ( A N 0 ) 4 ( ~ N 0 ) 4 . The use of eight doubly occupied bonding MOs to accommodate 16 of the core electrons simplifies the S = 0 spin formulation of the total wave function for a VB
+
+
~
~~
~
(33) Harcourt, R. D.; Roso, W. Can. J . Chem. 1978,56, 1093. (34) Flegg, R. H.; Harcourt, R. D. J . Mol. Struct. (Theochem) 1988, 164, 67.
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Harcourt and Skrezenek
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990
TABLE V: CoulsonChirgwinWcights for Resonance between the Trans Covalent and Ionic Structures 11-20" k=O k = 0.45 structure
olanar
DerD
vlanar
verv
0 010 (0 009) 0095 (0093) 0 767 (0 804) 0001
0 010 (0 009)
0014 0001
0013
0 027 (0 024) 0 141 (0 140) 0 626 (0 696) 0 002 0 027 0 002
0 027 (0 024) 0 146 (0 144) 0 617 (0 687) 0 002 0 027 0 002
TABLE VII: Rotation Barriers (kJ mol-') for Resonance between Sets of Cis and Trans Covalent and Ionic Structures structure k=O k = 0.45 1, 2. 3, 4 1, 5 , 6 2, 3, 7,8 4, 9, 10 11, 15, 16 12, 13, 17, 18 14, 19, 20 12, 13, 21, 22 14, 23, 24
~
11 12 = 14 15 = 17= 19 =
13 16 18
20
0 0 9 6 (0094) 0 767 (0 802) 0 001 0 001
"Values In parentheses are for resonance between the covalent structures 11-14
TABLE VI: Rotation Barriers (kJ mo1-I) When Structures Are Omitted from the Cis Structure Calculations omitted structures k=O k = 0.45 5-10 I . 5. 6 2, 3. 7. 8 4, 9, IO
2.7 13.3 -0.5 31.3
1.1 15.4 - 1 1.6 37.8
structure, which then involves either one or two Slater determinants according to whether zero or two mobile u-electron AOs are singly occupied (cf. refs 29-35). The VB calculations were performed by using the program written by Roso33335 (cf. also refs 29-32 and 34), with Stewart's STO-5G bas@ and neutral atom Slater exponents. Results
I n Tables I I and 111, the energies and rotation barriers are reported for various values of the polarity parameter k in the dN0 MOs. For each set of cis, trans, and perpendicular structures that obtains to Figures 2 and 3, an energy minimum is obtained when k = 0.45. For this and smaller values of k , the cis energy lies below the trans energy, but the energy difference decreases as the k value increases. Also, for small values of k , the cis rotation barrier is substantially larger than the trans barrier. Taken together, these results indicate that the rotation barrier is associated much more with the properties of the cis structures than with those of the trans structures. In Tables I V and V, we report the Coul~on-Chirgwin~' weights for the various sets of VB structures when k = 0 and k = 0.45 in the For each case, the sum of the weights for structures 2-4 7-10 and 12-14 + 17-20 exceeds 0.8, Le., the extent of iio electron delocalization is calculated to be very substantial. It is probable that 0.8 is an overestimate, but as is discussed below, it is accompanied by physically reasonable estimates of the rotation barrier. Without the ire- electron delocalization, the calculated barrier is negative; resonance between structures 1, I f , 11, and 11' generates barriers of -21.5 and -18.3 kJ mol-' for k = 0 and k = 0.45 (Table I). When k = 0, which corresponds to what occurs in the structures displayed in Figure 2 and 3, the Lewis structures 4 and 14 with zero formal charges on all atoms, are calculated to have the largest weights. Allowance for delocalization of the ire- electrons via the k = 0.45 calculations reduces the extent of to-electron delocalization, but the calculated barriers of 16.3 and 11.8 kJ mol-' for either the cis structures alone, or the nonvariational average for the cis + trans structures, are close to the experimental estimate'**of 8-1 2 kJ mol-'. For further support of the earlier findingi0.l6that resonance between covalent and ionic structures with the mobile cr-electron distributions of 2. 3, 7, and 8 is primarily responsible for the cis 0-0 contribution to the rotation barrier, the following sets of structures were omitted from the VB calculations for the planar cis and perpendicular structures: (a) the ionic structures 5-10; (b) structures 1, 5 , and 6; (c) structures 2, 3, 7, and 8; (d) structures 4,9, and 10. The resulting barriers are reported in Table
+
(35) Harcourt, R. D.; Roso, W. Int. J . Quuntum Chem. 1979, 16, 1033. (36) Stewart, R. F. J . Chem. Phys. 1970, 52, 431. (37) Chirgwin. B. H.: Coulson, C. A . Pror. R . SOC.London 1950, AZO], 196.
2.7 -66.5 41.1 -0.5 25.8 -7.5 2.2 -7.4 4.0
1.1 -37.0 49.0 - 1 1.8
3.2 -13.0 13.6 -11.5 16.4
VI. Of these, only those for the b and d calculations, which retain structures 2, 3, 7, and 8, give appreciable rotation barriers. In Table VII, rotation barriers are reported for resonance between each of the three sets of cis structures of b-d of the previous paragraph, and also for the corresponding sets of trans structures, namely, (e) 11, 15, and 16; (f) 12, 13, 17, and 18; (9) 14, 19, and 20. Of these, the calculations for c and e when k = 0 provide the largest rotation barriers. However, because structures 11, 15, and 16 make a rather smaller contribution to the resonance scheme for the ten trans structures than do 2, 3, 7, and 8 for the ten cis structures (cf. Tables IV and V), resonance between the cis structures 1-10 generates a larger rotation barrier than does resonance between the trans structures 11-20 (cf. Tables I1 and 111). To conclude this section, we give further VB consideration to the origin of the long, weak N-N bond in N204. It has been indicated previouslyIBathat the ito electron delocalization is also appreciable when the N-N distance is close to the 1.45 A for a normal N-N single bond. This effect may be demonstrated here via VB calculations for resonance between the cis Lewis structures 1-10 when r(NN) = 1.45 A. The resulting minimum energy for this resonance is -89.8972 au, which occurs when k = 0.7. The sum of the weights for structures 2-4 and 7-10, which arise when the 7r0 electrons delocalize, is then 0.772. When r(NN) = 1.45 A, the N-N overlap inte ral (h2lh3) has a value of 0.513 (cf. 0.348 when r(NN) = 1.782 ), and therefore for this distance, the substantial iio electron delocalization must produce strong antibonding N-N repulsions. This factor, together with the reduced N-N u bond order, lengthens and weakens the N-N bond. The presence of nitrogen lone-pair electrons in structures 4 and 14 produces antibonding N-N repulsions in these s t r u c t ~ r e s . ~The ~-~~ development of N-N three-electron bonds (see below) via resonance between structures 2,3, 7, and 8 (and also between 12, 13, 17, and 18) can produce antibonding N-N destabilizations when (hzlh3)is large.
w
Cis 0-0Overlap and the Rotation Barrier As has been discussed p r e v i o ~ s l y ,the ~ ~ cis ~ ' 0-0 ~ ~ ~ overlap ~ stabilization of the planar conformer could arise from various sets of VB structures. They include the following: (a) the existence of the long cis 0-0 bond, as in structure 4. However, this bond has insufficient strength to stabilize the planar conformer; we have calculated Eiot = -3.1 and -14.2 kJ mol-' for k = 0 and k = 0.45 (cf. Table I ) . (b) Electron-pair covalent-ionic resonance, as in 4 9 10. (c) Three-electron bond covalent-ionic reso(A. :B) 6 (AT -B+) = (A B), as in 2 7 3 nance,'0*16,23,24 CJ 8. E,ach of b and c involves the transfer of an electron between the iio AOs on a pair of cis oxygen atoms and therefore the magnitudes of the Hamiltonian and overlap matrix elements for a pair of covalent and ionic structures are cis 0-0 overlap dependent. Of these, the resonance of c is calculated to be primarily responsible for the cis 0-0 overlap contribution to the rotation barrier. The (three-electron bond) covalent-ionic resonances of d and e, which involve the covalent trans structures 12-14, are also cis Q
(4 (e)
.
Q
12
Q
14
21
Q
13
Q
23
Q
24
22
Q
Q
The'Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7011
Origin of the Rotation Barrier for N 2 0 4
0-0overlap dependent. The barriers for d and e are reported in Table VII; those for resonance between the ten structures 11-16 + 21-24 are reported in Table 111. When k = 0.45, the latter barrier (1 1.8 kJ mol-') is similar to the 16.3 kJ mol-' for resonance between structures 1-10, but as for resonance between 11-20, resonance between 11-16 + 21-24 generates a higher planar energy than does resonance between the ten cis structures (cf. Tables 11 and 111). Therefore the latter sets of structures are those from which the primary understanding of the origin of the barrier must be sought. One other type of resonance also requires consideration, namely, that which occurs between the covalent structures 2 and 3. It generates a substantial value for the rotation barrier, namely, 20.1 kJ mol-' when k = 0 and 29.0 kJ mol-' when k = 0.45 (Table I). Structure 2 may be converted into structure 3 via either h2 ii, and ii4 h3 or h2 h3 and ii4 iil electron transfers. The latter type of electron transfer indicates that the rotation barrier is cis 0-0overlap dependent, and this is exemplified by the leading term in the overlap matrix element S23 = (\kzl\k3) for either conformer, namely, (iil(h2)-(h3(ii4) + (iillii4)-(h21h3). However because structures 2 and 3 make quite small contributions when only the covalent structures 1-4are included in the resonance schemes (cf. the weights of Table IV), it is not surprising that the resulting barriers are calculated to be very small, namely, 2.7 and 1.1 kJ mol-' (Table VI) when k = 0 and k = 0.45. It is therefore necessary to include the ionic structures in order to obtain a substantial barrier, unless the weights for structures 2 and 3 are somewhat larger than those of Table IV, Le., the extent of iio electron delocalization is smaller. It should be noted that due to the presence of formal negative charges on pairs of cis or trans oxygen atoms, there is also a Coulombic contribution to the rotation barrier. This may be either planar stabilizing or destabilizing, according to the nature of the signs of these charges. When k = 0.45, all O1and O4atoms of Figure 2 and all 0,and O5atoms of Figure 3 carry fractional formal charges. Quite obviously, differences in the magnitudes of the barriers for the k = 0 and k = 0.45 calculations must to some extent be associated with the changes in the formal charges. However the calculations with k = 0 make clear that the cis 0-0 overlap effect, primarily via the 2 e 3 e 7 8 covalent-ionic resonance, is mainly responsible for the existence of a substantial rotation barrier. When k = 0, no Coulombic contribution to the barrier arises from resonance between these structures.
-
- -
-
-
N-N r Bonding and the Rotation Barrier To study aspects of the contribution to the rotation barrier that arises from N-N A bonding in the planar conformer, we have performed some VB calculations for the four A electrons whose A 0 occupancies differ in the Lewis structures 1, 11, 26,and 27, ........ .........'.. "..
TABLE VIII:
r Electron Enemies (nu) TO
localized' delocalized
= 1.0,F N = 2.0
trans cis 4.3054 4.3058 2.7823 2.7826
perp 4.3053 2.7798
FO
=FN
1.0
trans cis perp 3.6236 3.6309 3.6124 1.3232 1.3507 1.3045
'Resonance between structures with the *-electron distributions of either 1 26 or 11 27, together with two ionic structures that arise from polarization of the N-N T bond of 26 or 27.
+
+
structures. The results of these calculations (Table VIII) again indicate no stabilization of the planar conformer. These sets of results are in accord with the conclusion obtained by Whitehead et al.,9 namely, that no N-N A bonding occurs in N2O4 and therefore this type of bonding cannot be responsible for the rotation barrier. Recent experimental and theoretical studiesu of the geometries for (Me2N)2C=C(NMe2)2 and [(Me2N)2CC(NMe2)2]2+ also support the conclusion that the rotation barrier for NzO4 does not arise from any N-N A bonding in the planar conformer. The N2CCN2components of the neutral ethylenic molecule and the dication are found to be respectively nearly planar and almost perpendicularly twisted." For the dication, the standard Lewis structures are of types 1 and 11 of Figures 2 and 3, with -NMe2 and =N+Me2 replacing the -0-and =O in these structures. In the planar conformer for the dication, the lone-pair electrons are A electrons and therefore no iielectrons are present. Consequently, the cis N-N analogue of the cis 0-0 overlap effect for N 2 0 4 is absent in these species and coulombic repulsions between the N + stabilize the nonplanar conformer (cf. resonance between 1, l', 11, and 11' for N2O4, as in Table I).
NZO3 The barrier to rotation around the N-N bond for N2O3 has been estimated to be 4 kJ m01-I.'~ Bibart and E ~ i n have g ~ ~ suggested that the cis 0-0 overlap hypothesis of planarity could also be relevant for N20!. In terms of Lewis VB structures, the cis 0-0overlap stabilization would arise primarily from resonance between the covalent and ionic structures 28 and 29, which corresponds to the 12 21 resonance for N204. For the latter molecule, the covalent-ionic resonance of 2 3 7 8 generates a substantially larger barrier than does 12 13 e 21 e 22 cf. Table VII. The equivalent of the 2 3 IJ 7 e 8 resonance does not exist for N2O3. Therefore the magnitude of the cis 0-0 overlap stabilization for N 2 0 3would be expected to be smaller than it is for NzO4. The ab initio M O studies of N203 by Doonan and M a ~ l a g a nhave ~ ~ indicated the presence of a cis 0-0overlap interaction in the planar conformer. However Doonan and Maclagan were unsure if this interaction would be large enough to account for most of the barrier.
-
Q
-
Q
.^
(26)
(27)
together with the two sets of ionic structures that arise through polarization of the N-N A bonds of 26 and 27. (In each of these structures 1, 11,26,and 27,four singly occupied 2ps AOs arise. The S = 0 VB structure functions for the A electrons of these structures then involve four Slater determinants, cf. ref 32.) In these structures, the oxygen and nitrogen core charges for the A electrons are + 1 and +2, respectively. In other calculations, the electron delocalization effect on the nitrogen core charges of iio from the 0-was simulated by changing these core charges from +2 to +1 (as in structures 4 and 14). For each set of core charges, the N-N *-electron contribution to the rotation barrier is reported in Table V111. No stabilization of the planar conformer is calculated to occur. In some additional A-electron calculations, all (S = 0 spin) Lewis structures that differ in the A 0 occupancies for the four K electrons were included, i.e., delocalization of these electrons amongst four AOs was permitted to occur. There are 20 such
It may be noted that the results of some STO-5G VB calculations for N202," with all electrons included in the calculations, indicate the following. (a) The long N-N bond of N 2 0 2involves a fractional IJ bond, which is almost entirely 2p in character. The nature of the hybridization of the nitrogen lone-pair AOs, rather than the fractionality of the N-N IJ bond, is calculated to be primarily responsible for the existence of a very long N-N bond (2.24 in this molecule. (b) For N-N distances near 2.24 A, the AOs that form the fractional N-N IJ bond are preferentially oriented perpendicular (38) Bibart, C. H.; Ewing, G. E. J. Chem. Phys. 1974, 61, 1293. (39) Doonan, I. J.; Maclagan, R. G.A. R.Ausr. J . Chem. 1977,30,2613. (40) Harcourt, R.D. J. Mol. Srrucr. (Theochem) 1990,206,253. See also refs 24 and 41. (41) Harcourt, R. D. J. Mol. Srrucr. (Theochem) 1989, 186, 131. (42) Kukolich, S. G. J . Am. Chem. SOC.1982, 104, 4715.
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The Journal of Physical Chemistry, Vol. 94, No. 18, 1990
TABLE IX: Variation of Rotation Barrier (W mol-') with Core Charges for Resonance between Either the 9 Covalent Structures or the 21 Covalent Ionic Structures with the Average r-Electron Distribution of Structure 25
+
core changes ZN 20 0.5 3.25 1 .0 3.0 2.0 2.5 3.0 2.0 4.0 1.5 4.5 1.25
PO' covalent -22.9 -8.5 +5.5 +7.2 +5.8 -9.5
covalent + ionic -19.8 -4.9 +11.9 +24.4 +70.6 +76.3
TABLE X Energies (E(planar), E(perp), au; Ed, kJ mol-') as a Function of N-N Internuclear Separation (r(NN), A) for the ZN= 2.0 and ZN= 2.5 Calculations of Table IX. r(NN) !?(planar) E(perp) IF' 1.782 1.722 1.662
48.8963 48.8926 48.8979
48.9008 48.8965 48.9013
11.9 10.4 8.9
to the axes of the N - 0 bonds (cf. Figure l), rather than along the N-N bond axis, Le., the N-N u bond is a bent bond. These results have relevance for the nitrogen AOs that form the (fractional) N-N u bond of N203. A VB treatment for N 2 0 3 should therefore require the N,02-type properties of a and b for the nitrogen AOs of the N O moiety,40 as is indicated in Figure I . Whitehead et al.9 have calculated that, in contrast to what occurs for these orbitals in the NO2 moieties of N 2 0 3and N204, the corresponding N O orbitals of N 2 0 3 and N 2 0 2are almost entirely p in character. However, due to the nature of the MO localization procedure that was used, these AOs are oriented along the N-N bond axis, rather than perpendicular to the N-0 bond axis. Conclusions
The results of the nonempirical VB calculations reported here provide further support for the theory that cis 0-0 overlap in the planar conformer of N2O4 contributes substantially to the stabilization of this conformer relative to the perpendicular conformer. The stabilization manifests itself via covalent-ionic resonance when oxygen lone-pair electrons delocalize into the AOs that form the N-N u bond. Due to electronegativity considerations, these types of delocalizations are much less extensive in B2X4 with X = F, CI and Br and C2042-'8and therefore it is not surprising to find that these species have much smaller barriers
Harcourt and Skrezenek to rotationI4 and that the perpendicular conformers for B2CI4and B2Br4 have the greater stability in the gas phase.43 Acknowledgment. We thank Dr. W . Roso for putting his valence bond program at our disposal. F.L.S. thanks the University of Melbourne for the award of a Post-graduate Scholarship. Appendix: Calculations with Averaged ?r-Electron Distributions for the N-O Bonds As indicated earlier, we were unable to include all of the 84
cis and trans Lewis structures simultaneously in the calculations with 34 valence shell electrons. However, with an average selectron distribution, as in structure 25,for example, and fewer electrons explicitly considered, the 21 structures that differ in the locations of the ten electrons amongst the mobile s-electron AOs of Figure 1, may be included simultaneously. This has been done in calculations for ten mobile u + four IsN electrons, in which the nitrogen and oxygen core charges for these electrons (ZN and Zo) have been varied. Inspection of the rotation barriers reported in Table IX indicate that when ZNand Zo are close to 2.0 and 2.5, respectively, the calculated barrier of 11.9 kJ mol-' is close to the experimental value of 8- 12 kJ mol-'. Omission of the eight structures with the mobile u-electron distributions of types 2, 3, 7,and 8 (or 12, 13,17,and 18), reduces the barrier from 11.9 kJ mol-' to 4.9 kJ mol-', thereby showing that covalent-ionic resonance of the general type 30 31 32 33 is primarily responsible for the calculated rotation barrier.
---
With ZN= 2.0 and Zo = 2.5, we have also calculated (Table X) the total energy for the mobile u and IsN electrons for different values of the N-N bond length, r(NN). For either conformer, an energy minimum is obtained when r(NN) z 1.722 A. This length is close to the experimental estimate^^^^^* of 1.782 A and 1.756 A for r(NN) in the planar conformer. When r(NN) = 1.722 A in both conformers, the resulting rotation barrier is 10.4 kJ mol-' (cf. 8-12 kJ The similarity that exists between the calculated and experimental values for r(NN) and E" provides some justification for our association of the rotation barrier primarily with the properties of the mobile u-electrons. (43) Danielson, D. D.; Hedberg, K. J. Am. Chem. SOC.1979, 101, 3199. (44) Bock, H.; Ruppert, K.; Merzweiler, K.; Fenske, D.; Goesmann, H. Angew. Chem., Int. Ed. Engl. 1989, 28, 1684.
