2176
J. Am. Chem. SOC.1981, 103, 2176-2179
A Theoretical Study of the Structure and Stability of H + ( C O ) n , H s ( N 2 ) n , and H ' ( O 2 ) n Clusters ( n = 1-6) Shinichi Yamabe*l* and Kimihiko Hiraolb Contributionfrom the Department of Chemistry, Nara University of Education, Takabatake-cho, Nara 630, Japan, and Department of Chemistry, College of General Education, Nagoya University, Chikusa-ku, Nagoya 464, Japan. Received August 18, 1980 Abstract: An ab initio MO calculation is made for H+(CO),, H+(N2), (n = 1-6), and H+(02)n(n = 1-4) clusters by using
the 4-31G basis set. H+(C0)2and H+(N2)*,for which linear structures are stable, form shells for clustering reactions. Then, CO and N2 attack successively the r*-type MO's of these shells to form clusters up to n = 6. The correlation effect on the stabilization energy of H+(C0)2and H+(N2)2is examined with CI of single and double excitations. A general picture of the gas-phase clustering process is discussed on the basis of various theoretical results.
The stability of gas-phase complexes between a proton and a variety of bases (B's) has been examined extensively with the pulsed electron-beam mass spectrometer.2 Recent experiments revealed the existence of H+(B), complexes (B = Nz, CO, and 0,) and provided their thermochemical data (AGon.l,n,AHon.l,n and ASon.l,n)in the clustering pr0cess.j It was shown that the stability of H+B2 toward the dissociation H+B B increases in the order CO < N 2 < 02,whereas the proton affinity is of the order 0, < N 2 < CO. For Nz and CO, the stability of H+(B), decreases very slowly for n = 3-6, but it becomes sharply small at n = 7. For 02,the observed largest cluster is H+(O2)4. These experimental results may be related to the structure and the electronic distribution of the cluster and it is tempting to compare AHon.l,nwith the theoretical data (AEn-,J to elucidate the clustering mechanism. In this work, an ab initio MO-CI calculation is made for H+(CO),, H+(N2), (n = 1-6), and H+(O2), ( n = 1-4), and their structures are determined. Also, a general picture of the clustering is discussed on the basis of various theoretical studies. Method of Calculation The electronic distribution of H+(CO), and H+(NZ), is calculated by the Hartree-Fock (HF)-SCF method with the 4-31G basis set. The STO-3G basis set was reported to have failed in reproducing the experimental datae3 Although the 4-31G basis set employed here is small in the sense of accurate energetics, we are obligated to use it owing to the large size of the system. For instance, H+(CO)6has 110 functions in this basis set. GAUSSIAN 127 program package4 which was developed by the Institute for Molecular Science (IMS) is used for the M O calculation. The geometries of H+(CO), and H+(N2), (n = 1-6) are optimized to minimize the total energies (EGs), and the stabilization energies (AEn-l,n) are evaluated for these series of clusters. To estimate the correlation effect on the stabilization energy, we make C I calculations for H+(CO), and H+(N2)> The CI includes the singly and doubly excited configurations except those from inner (K) shells on the basis of the H F MO. The optimal geometries of H+(O), (n = 1-4) with the nonsinglet spin states are predicted by the unrestricted H F calculations. For the singlet state of H+Oz and H+(02)2,the restricted closed-shell wave function is adopted. HF Results and Discussion of H+(CO), H+(N2)mand H+( 0 2 ) n Figure 1, a and b, depicts the optimized structures of H+(CO), and H+(N2),,. Table IA gives the energetics of H+(CO), clusters and Table IB is for H+(N2),. Since the trend of the structural changes in both clustering reactions is similar, the reaction of
+
(1) (a) Nara University of Education; (b) College of General Education, Nagoya University. (2) P. Kebarle, Annu. Reo. Phys. Chem., 28, 445 (1977). (3) K. Hiraoka, P. P. S. Saluja, and P. Kebarle, Can. J . Chem., 57, 2159 (1979). (4) W. J. Hehre, W. A. Lathan, R. Ditchfield, M. D. Newton, and J. A. Pople, QCPE,No. 236,(1973) (GAUSSIAN 70). It is extended to GAUSSIAN 127 by K. Kitaura and K. Morokuma of IMS.
0002-7863/81/1503-2176$01.25/0
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H+(CO),.l + CO H+(CO), is examined. When CO is protonated, the length of the new C-H bond of H+CO is found to be similar to that in the standard hydrocarbons. The proton attacks the CT lone-pair electrons on C to form a strong bond. However, when the second C-O approaches H'CO, its H-C bond becomes elongated (1.08 1.38 A) in H+(CO),. That is, the proton is shared by two C O S in the collinear form, and the H. .C bond is weakened. While the structures of H+CO and H+(C0)2 are predictable even before the MO calculation and indeed were already investigated with the STO-3G basis set3 those of larger clusters (n > 2 ) are hard to predict and are of theoretical interest. The most likely and the highest symmetry structure of H+(CO)3 is of the equilateral form (D3h). However, its optimized geometry is found to give a positive AEZ3(18.8 kcal/mol, unstable) relative to the infinite separation between H+(CO), and CO (Table IA). Now, we have to seek another geometry of H+(CO)3with negative A E 2 , 3 . As a result of optimization, a T-shaped structure is most stable. It is regarded as a weakly interacting system of H+(CO),. C O , where the geometry of H+(CO), is almost maintained for n = 2 3. Figure 2, the dominant charge-transfer interactions which determine the shape of the clusters are schematically sketched. Thus we may expect that the further clustering of CO is merely a perturbative coordination to H+(CO),I ( n 1 4) with the fixed structure of H+(CO)z. In fact, the fourth C O attacks the T-shaped H+(C0)3to form H+(C0)4with DZhsymmetry. The fifth and sixth C O S attack the plane of H+(C0)4 perpendicularly. In these clustering processes, the cation center of H+(CO), is attacked successively by CT lone-pair electrons of four CO's. In this respect, H+(CO), is a shell undeformed by the approach of COS. Once H+(CO)6 is completed, further attack of CO is expected to be blocked by the coordinated CO's. This means that H+(CO), is much less stable than H+(C0)6, and indeed H+(N2), was not detected experimentally even at very low t e m p e r a t ~ r e .Another ~ noticeable point of H+(CO), geometries is that the highest symmetry structures (D3hfor n = 3, D4hor Td for n = 4, D j h for n = 5 , and Oh for n = 6) are found to be extremely less stable than those in Figure la. This is because during n - 1 n, the geometrical deformation of H+(C0)2 brings about significant destabilization. Concerning energetics of H+(CO), (Table IA), we have found These dissome disagreement between AEpl,n and crepancies are explicable in terms of other factors given in the next section. For H+(N2),, surprisingly AEwl,, and AHo,,+ are almost the same (Table IB). This coincidence is rather fortuitous, and the former is regarded as overestimated on the HF level. AE,l,n of both clusters reproduces the trend of AHo,l,n, Le., it decreases very slowly with n (13). Usually, there is a gradual decrease of AHoWl,,with charge dispersal through the addition of the neutral specie^.^.^ For H+(CO), (n 2 3), however, the cationic character of H+(CO), is maintained, and its attractive
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-
-
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( 5 ) K. Hiraoka and P. Kebarle, J . Chem. Phys., 62,2267 (1975). (6) K. Hiraoka and P. Kebarle, J . Am. Chem. SOC.,97, 4179 (1975).
0 1981 American Chemical Society
J. Am. Chem. SOC.,Vol. 103, No. 9, 1981 2111
Structure and Stability of H+(CO),, H+(N2),,and H+(02),, a
n 0
b ~'.09~
c""0
_ _ - c--
0
1.08
N-N
11.09
C
N
0 18.329)
N (6.9261
0
N
____ H _---N-N 1.26
(0.5241 15.4611 18.2781
10.2261
(7.049)
(6.838)
N
O\
N
11.12
. ? . 3 7 6 ) ( 7 . 0 1 3 1 (6.6111
(5.3641 (8.1521
o 1- .C1-1- - H1.36
2
0
4
N 1.08 -N
H1.os 1.lo 0 (0.484)
b
a
(7.000)
(5.604) (8.3961
1
n
\
c,
N\
I 1
I
I cF
3
I 12.92 12.92
I.
f
/c
0-
2.92
I
C ---- H'T--C-o
N
0
N i / N ,*I
,c _,
I _,'
N-N
1.37
I'
,'
1.26
N
0 /c"2'92
N
0
I
c (5.648)
____
! ,' H/---N-N
I
6
11.12
0 (8.3271
I
(J
N
Figure 1. Geometries of H+(CO), and H+(N2), optimized with the 4-31G RHF MO. Bond distances are in 8,and numbers in parentheses are Mulliken atom populations. For n = 5 and 6, C-0 and N-N bond lengths are fixed to those of H+(C0)4and H+(N2)4. Table I. Total Energies (ET'S)and Stabilization Energies ( I S , , - ~ , ~ ' S ) n
number of basis functions (4-31G)
0 1 2 3
18 20 38 56
4 5 6
14 92 110
0
1 2 3
18 20 38 56
4 5 6
14 92 110
point group cluster of the cluster E T , au A. H+(CO), Clusters for Optimized Geometries in Figure l a
co
H+CO H+(Coli H+(CO),
c-h C-h
D-h Dsh c 2u
H+N2 H+(Nl)i H+(N,)J
D-h C-h D-h
Dsh c 2U
H+(N2I4 H+") 5 H+(N 16
Dih C2U
Dzh
kcaymol
Aff"n-l,n, kcal/moP
- 112.55231 -112.17933 -225.34450 -337.86688 -337.90272 -45 0.46094 -563.01822 -615.57486
-142.4 -8.0 18.8 - 3.7 -3.7 -3.1 -2.7
-139.0 - 12.8
-108.75424 -108.95026 -211.72951 -326.46086 -326.48914 -435.24963 -544.00898 -652.76832
-123.0 -15.7 14.4 -3.7 - 3.6 -3.2 -3.2
-113.7 -16.0
H+(CO), Dih H+(CO), C2" H+(CO), Dih B. H+(N,), Clusters for Optimized Geometries in Figure l b N2
4 - 1 , n 9
-6.6 -6.3 -6.2 -5.8
-4.0 - 3.8 -3.5 -3.2
* Taken from ref 3. power is not weakened by the addition of CO. This results in the nearly constant value of AHo,,+, ( n = 3-6). In particular, the Mulliken population of H+(N2), ( n = 0-4) exhibited in Figure l b demonstrates clearly that H+(N2)2polarizes N2's and its cationic character is rather increased so as to welcome more N2)s. In Figure 3, the optimized structures of H+(Oz), (n = 0-4)are shown and Table I1 gives the energetics of the clusters. In Figure 3, H + 0 2is bent because H+ attacks favorably the sp2 lone-pair electrons on the oxygen atom. For H+(02)2,two oxygen molecules share a proton in that direction. The difference of the spin multiplicities [Le., (2s + l ) , s = spin quantum number] gives a
negligible difference in the bond lengths, whereas the angle A00 of H+(02)2is somewhat affected. The third and the fourth 02)s attack the proton of H + ( 0 2 ) 2along t h e y axis very weakly, resulting in the polarization of the attacking species. For H+(02)3, the coordination of O2along the z axis is slightly less stable than that along t h e y axis. However, this energy difference is meaningless, because the CZhH+(O& can rotate around the x axis almost freely, with T > 0 K. The feature of H+(Oz),, clustering obtained by this M O calculation is that the third and the fourth 02)s are located linearly far from the proton of H+(02)*to avoid the exchange repulsion and get the induction stability. In Table
2118 J . Am. Chem. SOC.,Vol. 103, No. 9, 1981 Table 11. ET's and AE,-,SI,.
of H+(O,), Clusters for Optimized Geometries
spin quantum number, s, in
cluster
n 0
(2s
H+O,
2
H+(O,),
+ 1)
point group of the cluster
ET,au
D-h
- 149.39299
1 1 0 2 1 0 3 4
0 2
1
Yamabe and Hirao
H+(O,), H+(O,), Taken from ref 3. 3 4
cs
cz h
c, cz h
9
B
Figure 2.
n
S
0
1
kcal/mola
-102.9
- 101.0
n
-20.0
-3.1 -3.2
-6.6 -3.2
s
O X 6 O
0
127.0
3
3
10.388) (7.6161 117.1
(7.628)
(0.317h//1. 21
18.2281
H
-12.0
11, the H+02and H+(02)2results show that the state with the higher multiplicity gives the lower energy. For H'O2, ET(triplet) is better than ET(singlet), which indicates that the Hund's rule for the high-spin state is still effective, overcoming the orbital gap in the C, symmetry. In view of E> 0 K), this bond would be easily broken and not observed. When the parent molecule is polar (e.& H,O), clustering is not constrained to the shell and the surroundings on account of the Coulombic attraction. Acknowledgment We thank IMS for allotment of CPU time on the HITAC M-200Hcomputer. This research is supported in part by the Ministry of Education, Japan. We thank Drs.0. Nomura and S. Ikuta for their advice on the asymmetric structure of H*(CO), and H*(N,), during the revision of this manuscript.
_ _
( 9 ) M. D. Newtan and S. Ehrcnson, 1.Am. Chrm. Soe., 93,4971 (1971); M. D. Newton, 1.Chem. Phyl.. 67,5535 (1977). (IO) S. Yamabe, K. Hiraa, and K. Kitaura, Chem. Phys. Lcll.. 56, 546
,.,,",. ,IP.)*\
(7) R. Ahlrichs, Thror. Chim. Acta, 39, 149 (1975) (8) H. H u h , Chem. Phys. Lm., 70,353 (1980).
(11) S.Yamabc, Y. Osamura, and T. Mimto, 1.Am. Chem. Soe., 102, 2268 (1980).
