J. Phys. Chem. 1882, 86, 1529-1535
1528
Molecular Orbital Study of Some Protonated Bases Janet E. Del Bene; Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555
Mlchael J. Frlsch, Krlshnan Raghavacharl, and John A. Pople Department of Chemistry. Carnegie-Mellon University, Pittsburgh, Pennsylvankr 152 13 (Received: July 30, I981)
Hartree-Fock and fourth-order Maller-Plesset calculations with the 6-31G** basis set have been performed on the protonated hydrides NH3,HzO,and HF and the protonated closed-shell bases H,ABH,, where the two nonhydrogen atoms may be C, N, 0, or F. Inclusion of correlation generally leads to relatively small changes in computed protonation energies and does not necessarily yield better agreement between computed and experimental data. However, both Hartree-Fock and Maller-Plesset protonation energies are reasonable, and trends in protonation energies for related bases are the same at both levels of theory. The Hartree-Fock and Maller-Plesset relative stabilities of the isomers which result when protonation occurs at nonbonded electron pairs on A and B are similar, except for the C- and 0-protonated forms of C-. However, the Hartree-Fock barrier to proton transfer which separates the isomers is significantlylowered by electron correlation. Correlation also lowers the barrier to proton transfer for ions H,AAH,+,+ except for NzH+. Zero-point vibrational energy corrections have also been evaluated and found to lead to significant decreases in computed protonation energies. Protonation may result in an increase or decrease of the A-B bond distance depending on the nature of the A-B bond and the nature of the protonation site.
Introduction The set of molecules AH, and H,ABH,, containing one or two heavy (nonhydrogen) atoms (A, B = C, N, 0, or F), includes the parents of many important organic functional groups. In this paper, we present a systematic study of the structures and energies of the protonated forms of these molecules, treated as bases. This parallels a study of the corresponding closed-shell neutral species.’ Many of the closed-shell ions H,ABH,+ have been examined previously. Minimal basis (STO-3G) structures for the complete set were obtained some years ago by Lathan et al.2 Since that time, many of the ions have been reexamined with larger basis sets and with electron correlation included in some ~ a s e s . ~ -These l~ studies have shown significant changes in geometries and energies of protonation as the theoretical technique has improved. Since it is important to analyze trends by using a uniform theoretical method, we believe it is now opportune to reexamine the full set at a higher level of theory, including polarized basis sets, electron correlation, and corrections for zero-point vibrational energies. The five principal objectives of the investigation are (1)to deter(1)K. Raghavachari, M.J. Frisch, H. B. Schlegel, J. A. Pople, and P. v. R. Schleyer, to be submitted for publication. (2)W. A. Lathan, L. A. Curtiss, W. J. Hehre, J. B. Lisle, and J. A. Pople, h o g . Phys. Org. Chem., 11, 175 (1974). (3)J.-J.Delpuech, G.Serratrice, A. Strich, and A. Veillard, Mol. Phys., 29,849 (1975).(4)(a) G.H.F. Diercksen and W. P. Kraemer, Theor. Chim.Acta, 36, 249 11975): 1b) . , W. R. Rodwell and L. Radom. J. Am. Chem. SOC.. , 103. , 2865 (igsi). (5)(a) H. Lischka, Theor. Chim.Acta, 31,39(1973);(b) P. C. Hariharan and J. A. Pople, Mol. Phys., 27,209 (1974). (6)H. Lischka and H.-J. Kohler, J.Am. Chem. Soc., 100,5297(1978). (7)K. Raghavachari, R. A. Whiteeide, J. A. Pople, and P. v. R. Schleyer, J. Am. Chem. SOC.,in press. (8)N. L. Summers and J. Tyrell, J.Am. Chem. Soc., 99,3960(1977). (9)L. Radom. Awt. J. Chem.. 28. 1 11975). (10)R. A. Eades, D. A. Weil, D.’ A. Dixon, A d C. H. Douglass,J.Phys. Chem., 85, 981 (1981). (11)P. J. Bruna, S. D. Peyerimhoff, and R. J. Buenker, Chem. Phys., 10,323 (1975). (12)N. L. Summers and J. Tyrell. Theor. Chim.Acta, 47,223(1978). (13)R. H. N o h , L. Radom, and W. R. Rodwell, Chem. Phys., 74,269 (1980). (14)W. L. Jorgensen and M. E. Cournoyer, J. Am. Chem. Soc., 100, 5278 (1978). 0022-3654/82/2086-1529$01.25/0
mine the structures of the protonated bases and to assess the change in the A-B bond length upon protonation, (2) to analyze trends in the protonation energies of the bases H,ABH,, (3) to evaluate the zero-point vibrational corrections to computed protonation energies, (4) to compare the stabilities of isomers H,ABH,+ in systems where protonation may occur at nonbonded electron pairs on A and B, and ( 5 ) to evaluate the barriers to proton transfer in ions having two lone-pair protonation sites.
Method of Calculation Gradient optimization techniques15J6 have been employed to optimize the geometries of the bases AH, and H,ABH, and the corresponding protonated species at the single determinant Hartree-Fock level, using the splitvalence 6-31G* basis set with polarization functions on A and B.I7 This is the HF/6-31G* model. Since polarization functions on hydrogen are necessary to describe the relative stabilities of neutral and protonated bases,lsJ9 the 6-31G* basis set was augmented by the addition of polarization functions on hydrogen to form the 6-31G** basis set,20and this basis has been employed to evaluate Hartree-Fock and correlated energies at the 6-31G* geometries. The correlation energies were calculated by Maller-Plesset perturbation theory21s22 at second (MP2), third (MP3), and fourth order, including all single, double, and quadruple substitutions (MP4SDQ). Owing to the computational expense of evaluating the contribution of triple substitutions at fourth order with the 6-31G** basis set, this contribution was determined only with the 6-31G* basis. Throughout this paper, MP4 will refer to this (15)J. S.Binkley, J. Chem. Phys., 64,5142 (1976). (16)R. Fletcher and M. J. D. Powell, Comput. J., 6,163 (1973). (17)P. C. Hariharan and J. A. Pople, Theor. Chim. Acta, 28, 213 (1973). (18)R. Kari and I. G.Csizmadia, Znt. J. Quantum Chem., 11, 441 (1977). (19)The Hartree-Fock protonation energies of NH,, HzO, and HF calculated with the 6-31G*basis set are increased by 2.2,5.0,and 5.1 kcal/mol, respectivley, when computed with the 6-31G**basis set. (20)P.C. Hariharan and J. A. Pople, Mol. Phys., 27, 209 (1974). (21)J. A.Pople, J. S. Binkley, and R. Seeger, Int. J.Quantum Chem., Symp., 10, l(1976). (22)R. Krishnan and J. A. Pople, Znt. J. Quantum Chem., 14, 91 (1976).
0 1982 American Chemical Society
1530
Del Bene et at.
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982
TABLE I:
Energies (hartree) of Protonated Bases
base
proton- ion ation s y m site metry
F-2 Hk
N
HC=CH H,C= CH HC-N H,C=NH H3C-NH , (20
n
H,C= 0 H3C-OH H3C-F N= N HN=NH H ,N-NH HN= 0 H,N-OH H,N-F HO-OH HO--F
0 F 71
N N N C 0 0
0 F N N N N 0 N 0 N
F 0 0
Hartree-Fock
-56.545 52 -0.187 -0.195 -76.310 05 -100.214 54 -0.187 -0.251 -77.084 42 -0.270 -78.320 94 -0.279 -93.165 30 -0.296 -94.394 71 -0.327 -95.588 86 -0.291 -112.96809 -112.921 40 -0.270 -0.301 -114.167 1 3 -115.357 32 -0.331 -139.289 89 -0.313 -0.309 -109.136 22 -0.324 -110.317 44 -0.351 -111.536 32 -0.339 -130.071 89 -0.331 -130.050 1 2 -0.359 -131.324 08 -0.358 -131.281 60 -0.347 -155.274 81 -0.338 -155.20684 -0.369 -151.052 22 -0.362 -174.968 20 -0.353 -174.943 86 -0.335 -198.826 96 e(3) = E(MP3) - E(MP2).
F F a E ( ' ) = E(MP2) - E(HF). E(MP4SDQ) with the 6-31G* basis set. F-F
4QC
b
a
88 78 52 51 04 73 15 21 59 10 37 46 56 07 61 28 19 97 88 80 81 66 86 18 80 28
particular computational scheme. Only valence-shell correlation energies have been evaluated. Analytical second derivatives of the electronic energy with respect to the nuclear coordinates were calculated at the Hartree-Fock 6-31G* optimized geometries using the 6-31G* basis set. The force constants obtained were used to determine harmonic vibrational frequencies and associated zero-point energies. The computational details of the second derivative calculations and estimates of the accuracy of Hartree-Fock frequencies have been presented p r e v i o u ~ l y .All ~ ~calculations ~~ were performed by using the Gaussian 80 system of programs on a VAX 11/780 computer.
Results The Hartree-Fock 6-31G** energies of the optimized ions AH,+ and H,ABH,+, the correlation energy contributions to the total energies at the various levels of Maller-Plesset theory, and the zero-point vibrational energies are reported in Table I. A significant correlation energy contribution to the electronic energy of these ions arises at second-order Maller-Plesset theory. This contribution, @, which is the difference between the MP2 and Hartree-Fock energies, is larger by 1 order of magnitude than the third-order = [E(MP3) - E(MP2)I) and fourth-order = [E(MP4) - E(MP3)I) contributions. The relationships among d2), &&, and €6' for the protonated bases are similar to those noted previously for neutral molecules.25~26The HF/6-31G* structures will be published in full in the Carnegie-Mellon Quantum Chemistry Archive (CMQCA).27 However, the A-B bond (23) J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S. Binkley, Int. J . Quantum Chem., Symp., 13,325 (1979). (24) J. A. Pople, H. B. Schlegel, R. Krishnan, D. J. DeFrees, J. S. Binkley, M. J. Frisch, R. A. Whiteside, R. J. Hout, and W. J. Hehre, Proceedings of the Sanibel Symposium, March 1981. (25) J. A. Pople, R. Krishnan, H. B. Schlegel, and J. S . Binkley, Znt. J. Quantum Chem., 14,545 (1978). (26)M. J. Frisch, R. Krishnan, and J. A. Pople, Chem. Phys. Lett., 75, 66 (1980).
e Q) d
zero point
-0.014 -0.008 -0.002 -0.016 -0.026 -0.006 -0.019 -0.026 +0.004 -0.007 -0.012 -0.020 -0.015
50 -0.001 99 -0.002 04 0.053 28 0.036 73 11 -0.002 28 -0.001 75 23 -0.003 1 6 -0.002 1 3 0.020 03 -0.003 48 53 -0.009 75 0.036 64 -0.003 55 12 -0.007 06 0.065 04 -0.005 98 52 -0.011 30 0.030 50 53 0.058 44 -0.007 66 -0.004 59 13 -0.005 81 -0.003 70 0.085 1 3 09 -0.012 65 -0.011 14 0.018 10 03 -0.010 33 -0.009 55 0.013 93 25 -0.007 92 0.043 82 -0.007 00 11 -0.005 45 0.068 59 -0.004 85 60 -0.005 44 0.051 32 -0.007 11 +o.ooo 77 -0.013 31 0.018 06 -0.008 24 0.046 1 5 -0.015 16 -0.005 59 -0.009 38 -0.006 27 0.073 70 -0.021 47 -0.003 51 0.031 57 -0.006 53 -0.007 53 -0.010 22 -0.010 54 0.031 12 -0.008 24 -0.009 36 -0.015 60 -0.00647 0.059 50 -0.004 29 -0.006 76 0.056 69 -0.01600 -0.005 42 -0.011 19 -0.006 77 0.046 30 -0.005 62 -0.012 58 -0.007 36 0.039 84 -0.009 45 -0.010 1 5 -0.007 21 0.042 90 -0.005 87 -0.007 49 -0.005 75 0.029 36 -0.006 40 -0.006 22 -0.009 1 2 0.024 87 -0.011 04 -0.000 93 -0.009 23 0.013 05 -0.009 90 e$') = E(MP4SDTQ) = E(MP4SDQ) - E(MP3).
TABLE 11: Effect of Protonation o n A-B Bond Lengths ( A ) A-B distance in base
protonation site
HC=CH H,C=CH, HC= N H,C= NH H,C-NH, c=0
1.185 1.317 1.133 1.250 1.453 1.114
n
H,C= 0 H,C-OH
0 0 F
N=N HN= NH H N-N H , HN= 0
1.184 1.400 1.365 1.078 1.216 1.413 1.175
H,N-OH
1.403
H,N-F
1.386
HO-OH HO-F
1.397 1.376
F-F
1.345
base
H,C-F
II
N N N C 0
N N N N
0 N 0 N F 0
0 F F
G(A-BP +0.022 +0.055 -0.016 +0.013 +0.054 - 0.027 t 0.027 t 0.048 to.lll
t0.317 -0.007 -0.012 + 0.015 -0.026 + 0.024 -0.029 t 0.087 -0.053 + 0.237 t 0.013 -0.022 +0.128 t 0.043
A positive value indicates an increase in the A-B bond length in the ion.
lengths in the neutral base and the changes in going to the protonated species are listed in Table 11. The total and zero-point vibrational energies of the ions are combined with the corresponding energies of the neutral bases to compute the protonation energies, the energies of the reaction B + H+ BH+, listed in Table 111. For those ions for which two lone-pair sites are
-
(27) R.A. Whiteside, M. J. Frisch, D. J. DeFrees, K. Raghavachari, J. S. Binkley, H. B. Schlegel, and J. A. Pople, The Carnegie-Mellon Univ-
ersity Quantum Chemistry Archive, Pittsburgh, PA 15213.
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982 1531
Molecular Orbital Study of Some Protonated Bases
TABLE 111: Energies (kcallmol) for the Reaction B base
d;:
protonation site
zero-point contribution
N
10.2 8.6 6.3 4.5 6.4 7.9 9.5 10.2 7.9 5.3 9.2 8.3 5.6 7.4 9.2 9.8 9.7 9.4 9.6 7.8 10.0 5.9 8.5 8.6 5.8 6.4
0
FH HC=CH H,C=CH, HC=N H,C=NH H,C-NH, c=0 H,C= 0 H,C- OH H,C-F N=N HN=NH H, N-NH, HN= 0
F R R
N N N C 0
0 0
F N N N N 0 N 0 N F 0 0 F F
H,N-OH H,N-F HO-OH HO-F
F-F
+ H+ + BH+ protonation energy AE(HF + Z P E p AE(MP4 t ZPE)b -209.4 -171.2 -121.1 -160.3 -170.6 -172.9 -215.8 -220.1 -136.6 -109.9 -177.4 -186.6 -151.4 -113.2 -189.2 -211.6 -167.8 -154.4 -199.0 -174.2 -185.7 -147.2 -164.2 -137.2 -124.7 -87.2
AH(exptl)C -205.0 -173.0 -112
-210.6 -172.2 -124.7 -158.3 -166.4 -171.3 -211.9 -220.6 -142.8 -107.2 -172.6 -185.8 -149.0 -117.8 -188.3 -212.5 -168.9 -153.4 -199.5 -175.2 -186.7 -146.1 -164.9 -139.3 -125.8 -92.0
-163.5 -178.9 -214.1 -139.0 -177.2 -184.9 -113.7
" The computed Hartree-Fock protonation energy including the Hartree-Fock zero-point energy correction. puted fourth-order Mdller-Plesset protonation energy including the Hartree-Fock zero-point energy correction. mental data from ref 30.
The comExperi-
TABLE IV: Energies (hartree) of Transition Structures" base
symmetry
c=0
c, c,
HN= 0 H,N-OH H,N-F HO- F N=N HN= NHC H,N-NH, HO-OH
Cl
c,
Cl C,, C,, C,, C,
F-F
Czu
Hartree-Fock -112.834 -129.937 -131.216 -155.154 -174.878 -109.059 -110.185 -111.443 -150.973 -198.755
88 72 42 57 86 35 19 74 09 58
E (2)
-0.297 -0.364 -0.379 -0.367 -0.387 -0.304 -0.348 -0.366 -0.396 -0.384
4iiQ
E (3)
80 43 17 83 30 50 97 38 05 68
+0.00179 t 0 . 0 0 4 62 -0.009 68 -0.004 1 7 t0.003 46 -0.001 49 -0.006 62 -0.017 19 -0.001 55 t0.00848
-0.011 -0.012 -0.006 -0.010 -0.012 -0.007 -0.007 -0.004 -0.008 -0.012
e$)
41 72 49 85 30 69 59 06 79 44
-0.013 2 1 -0.014 56 -0.009 48 -0.010 99 -0.012 49 -0.013 62 -0.012 62 -0.00844 -0.010 96 -0.012 72
zero pointb
+0.01029 +0.02245 t0.05136 +0.036 82 t0.02167 +0.01128 +0.035 79 t 0 . 0 6 5 70 +0.036 64 +0.007 24
" See footnotes a-d
in Table I. In computing the zero-point energy of the transition structure, we ignored the imaginary frequency. At the Hartree-Fock level, the predicted transition state has C, symmetry. However, the C,, structure is favored a t MP4. TABLE V: Barriers to Proton Transfer (kcal/mol) for Bases Having Two Lone-Pair Protonation Sites base
E(HF t ZPE)" E(MP4
+ ZPE)b
base
52.0 37.2 N'N CE oc HN= Oc 65.1 48.2 HN=NH H,N-OHC 37.6 26.4 H,N-NH, H,N-FC 30.9 14.7 HO-OH HO-FC 38.8 20.9 F-F a Hartree-Fock barrier including the zero-point vibrational energy correction. correction. Measured from the less stable form of the protonated base.
available for protonation, the reaction path for proton transfer was also explored to find HF/6-31G* transition structures for the rearrangement. The energies of these structures a t the same level as used for the equilibrium structures are given in Table IV. Geometrical parameters will be available in CMQCA. Finally, rearrangement barriers derived from these total energies are listed in Table V. Discussion We begin with a discussion of the individual structures and follow with a comparative study of trends in proton-
E(HF
+ ZPE)= E(MP4 t
44.0 76.5 53.1 45.7 41.1
ZPE)b
45.6 63.3 44.6 30.5 24.8
Barrier at MP4 including the zero-point
ation energies and bond length changes. NH4+,OH3+,and FH,+.These ions have been studied exhaustively at high levels of t h e ~ r y . ~The - ~ HF/6-31G* calculations give C3, and CZusymmetries for OH3+ and FH2+with bond angles of 113.1' and 113.9', respectively. The pyramidal structure of OH3+ is in agreement with recent experimental data.28v29 (28)M.C.R. Symons, J . Am. Chem. SOC.,102,3982 (1980). (29)J. 0.Lundgren and J. M. Williams, J. Chem. Phys., 58, 788 (1973);J. 0.Lundgren and I. Olovsson in "The Hydrogen Bond", Vol. 11, P. Schuster, G. Zundel, and C. Sandorfy, ME., North-Holland Publishing Co.,Amsterdam, 1976.
1532
The Journal of Fhysical Chemistry, Vol. 86, No. 9, 1982
C a 3 + and C a s + . Protonated acetylene (vinyl cation) and protonated ethylene (ethyl cation) have been discussed in detail Both are found to be bridged with Czusymmetry when correlation is included. Only bridged structures (corresponding to a protonation) are listed in Table I. HCNH+. The most stable form of protonated hydrogen cyanide is the linear structure HCNH', with the additional proton attached to the u lone pair on nitrogen. The C=N triple bond is shortened by 0.016 A, a result previously noted by Summers and Tyrell.s H&NH2+. Methylenimine is protonated on the nitrogen u lone pair to give a C,, planar structure, 1, which is comH\
H
+ /H
N-C
/
1
\H
z
parable to the isoelectronic molecule ethylene. In contrast to HCN, protonation of H2CNHleads to an increase in the C-N distance by 0.013 A. H3CNH3+. The methylammonium ion is found to have a staggered CBustructure, 2, comparable to ethane. The
Del Bene et al.
polarized basis seta but show similar results. H3COH2'. Protonated methanol has a staggered structure of the type 5, comparable to the isoelectronic
5
molecule methylamine. In this case there is a remarkably large increase in the C-O length on protonation, going from 1.400 to 1.511 A. This effect was noted previously by Jorgenson and Cournoyer14at the HF/4-31G level. They ascribed it to incipient dissociation into a methyl cation and a water molecule. H3CFH+. Protonated methyl fluoride is isoelectronic with methanol and has a similar staggered structure, 6. H\
+
,c-
F,
H Y H'
\H
6
z
-
H-
H '
2
HF/6-31G* C-N bond length is increased substantially from 1.453 A in methylamine to 1.507 A in 2. HCO+ and C O P . Carbon monoxide may be protonated a t either end to give the isomers HCO+ and HOC+. Our computations show HCO+ to be the more stable by 35.6 kcal/mol. It is noteworthy that this separation is considerably larger than the energy gap between the isoelectronic pair HCN and HNC, which is 15.9 kcal/mol at the same level of the0ry.l Also, electron correlation increases the energy gap, the HF/6-31G* value being only 26.7 kcal/mol. I t is also interesting to note that protonation on carbon shortens the C-0 bond length by 0.027 A, whereas protonation on oxygen causes a lengthening by the same amount. These results are consistent with others in the recent literature.aJ1J2 The transition structure for proton exchange between the sites has the bridged form 3 and is predicted to lie 37.2 H
c-0
+
The increase in the C-F length is now as high as 0.317 A, again as found previously at the HF/4-31G 1 e ~ e l . l ~ N&+. Nitrogen protonates a t one of the u lone pairs to give a linear structure of C,, symmetry. A slight decrease (0.007 A) of the N-N distance is found on protonation. Protonation at the center of the a bond, giving a symmetrical C2, structure, is higher in energy by 45.6 kcal/mol. However, this is not a minimum, but rather corresponds to the transition structure for the degenerate rearrangement in which the hydrogen changes ends in the ion. It is noteworthy that, in this structure, electron correlation unusually increases the barrier slightly. HJVNH'. Diazine protonates on one of the u lone pairs to give a planar structure, 7. This may be also considered H
\+ N-N H/
7
as an aminonitrenium ion. Protonation leads to a small decrease in the N-N distance. The transition structure for the 1,2 shift in the degenerate rearrangement is found to have the C2,structure 8. The barrier is high (63.3 kcal/mol).
3
H
5
kcal/mol above the less stable HOC+ isomer. It may be noted that this barrier, like all of those listed in Table V which separate isomers, is substantially reduced by electron correlation. H,COH+. Protonated formaldehyde is found to have a planar C, structure 4. This is similar to the isoelectronic
"\ c=o
\H
+
+ H /N-N
H' 8
*
HflNH2+. Protonation of hydrazine occurs on one of the nitrogen lone pairs, leading to a structure, 9, similar H
H 4
\ NN+ -
5
molecule methylenimine. Protonation has led to some increase in the C-O bond length (from 1.184 to 1.232 A). Previous studies of this structure2J3have been with un-
H-
?
The Journal of phvsical Chemistry, Vol. 86, No. 9, 1982 1533
Molecular Orbital Study of Some Protonated Bases
to the isoelectronic methylamine. A slight N-N bond lengthening (by 0.015 A) accompanies the process. The transition structure found for the 1,2 shift is the symme, structure 10, the corresponding activation barrier trical C being 44.6 kcal/mol. ..H..
at either end are separated by a transition structure, 18, with C2symmetry. This is approximately trans-hydrogen peroxide, protonated on top of the ?r system. The corresDondina barrier is 30.5 kcal/mol. H20$ and HOFH’. These two species have C, structures 19 and 20. The 0-protonated form, 19, is more
+ n
H
’,o
H
\;=0
/
H
12 z
1’
electronic neutral molecule formaldehyde. Oxygen protonation leads to a trans structure, 12. The N-protonated form is more stable by 15.5 kcal/mol. The barrier for the rearrangement 12 11 is high (48.2 kcal/mol), the transition structure being planar C,. HJVOH+ and H a O H , + . Hydroxylamine can also be protonated on nitrogen or oxygen. Theory predicts a staggered structure, 13, for the N-protonated form, which
-
-
14
’2
is 24.3 kcal/mol more stable than the 0-protonated form 14, which has an anti structure. The barrier for the rearrangement 14 13 is 26.4 kcal/mol, the transition structure being a nonsymmetrical C1 structure with a bridging hydrogen. H J V F and H a F H ’ . Protonation at nitrogen is the more stable form of this species, giving a C% structure, 15,
-
+
H,j-F
/H
+
H,q-F
H
H 15
16
5
*
which is comparable to methyl fluoride. The other isomer, 16, has an anti structure. However, the energy difference is large at 40.6 kcal/mol. The connecting transition structure has C, symmetry as 16 with the hydrogen in the bridging position. H,OOH+. Protonated hydrogen peroxide has the anti classical structure 17, analogous to the neutral species
+
/
I
-
19
H a O + and HNOH+. Protonation of HNO at nitrogen gives a CZ0planar structure, 11, comparable to the iso-
H\
0-F
.. + ..’..
:
H-O’-O
---H
H-
’2 H2NOH. The equivalent species obtained by protonation
-
/H
0-F
20 *
stable by 13.5 kcal/mol. The barrier for the rearrangement 20 19 is 20.9 kcal/mol, the transition structure having C1symmetry. F a + . Protonation of F2occurs nonlinearly at one end to give a C,structure. The two equivalent structures are separated by a bridged Czutransition structure, the activation barrier being 24.8 kcal/mol. Protonation Energies. The zero-point vibrational energy corrections to the protonation energies of the bases AH, and H,ABH, are reported in Table III. It is apparent that the zero-point vibrational corrections have a significant effect on computed protonation energies. The zero-point correction is always positive, owing to the three additional degrees of vibrational freedom in the ions arising from the presence of the additional hydrogen, thereby lowering the computed protonation energies. The zero-point vibrational correction ranges from 4.5 kcal/mol for ?r protonation of HC=CH to 10.2 kcal/mol for protonation of NH3 and H3CNH2. When protonation of a molecule can occur at lone pairs of electrons on A and B, the zero-point vibrational correction is greater in the more stable isomer as a result of the stronger binding of the proton. The computed protonation energies at the Hartree-Fock and MP4 levels of theory, including the zero-point vibrational corrections, are also reported in Table I11 along with the available gas-phase experimental protonation energies as compiled by Aue and Bowers.30 The experimental values are estimated to have errors of several kilocalories per mole. It is evident from the data of Table I11 that the change in the computed HartreeFock protonation energy due to electron correlation is generally small and does not exceed 5 kcal/mol except for C-protonated C=O. Recently, it has been demonstrated that the sign of this correction cannot be consistently predicted unless a basis set larger than 6-31G** is employed.31 Therefore, no attempt will be made in this study to analyze the nature of the correlation correction to the Hartree-Fock protonation energy. However, it is apparent from Table I11 that both HartreeFock and MP4 protonation energies are in reasonable agreement with experimental data and that inclusion of correlation with this basis set does not necessarily lead to better agreement with experiment. For example, the dependence of the protonation energy on bond type (hybridization) is in better agreement with experiment at Hartree-Fock than MP4, as seen from the relative protonation energies of H C r N and H3C-NH,, and of H&=O and H3C-OH. However, the methylsubstituent effect on the protonation energy is in better agreement with experiment at Mp4 than at HartreeFock, as evident from the relative protonation energies of NH3 and H3C-NH2, and of HzO and H3C-OH. (30) D. H. Aue and M. T. Bowers in “Gas Phase Ion Chemistry”,Vol. 2, M. T. Bowers, Ed.,Academic Press, New York, 1979, pp 1-51. (31) M. J. Frisch, J. E. Del Bene, K. Raghavachari, and J. A. Pople, Chem. Phys. Lett., 83, 240 (1981).
1534
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982
Substituent effects on protonation energies of related bases have been evaluated. For lone-pair protonation in systems X-BH, H+ X-BH,+,+
+
-+
the order of decreasing protonation energy with respect to X is CH3 > NH2 > H > OH > F for N-, 0-,and F-protonation except for a reversal of H and OH for F-protonation. This order is the same at Hartree-Fock and MP4, and is related to the change in the A-B distance on protonation. Similarly, for X=BH, H+ X-BH,+l+
+
-+
the order of decreasing protonation energy is CH2 > NH > 0 when B is N, and CH2 > NH when B is 0. Again, the order at Hartree-Fock is not changed by the inclusion of correlation and is once more related to the change in the A-B distance on protonation. The bases CEO, HN=O, H2N-OH, H2N-F, and HO-F have two lone-pair protonated forms which are found at local minima on the potential surface. Inclusion of correlation has only a small effect on the relative stabilities of each pair of isomers except for protonated C=V, in which case electron correlation further stabilizes by 8.9 kcal/mol the C-protonated relative to the 0-protonated form. The larger effect in this case may be associated with the change in the direction of the dipole moment vector of CEO when electron correlation is included.32 Both Hartree-Fock and MP4 data indicate that the preferred site of protonation of these bases is the more electropositive atom and that there is a significant barrier to proton transfer between the two sites, as evident from the data of Table V. A comparison of the computed Hartree-Fock and MP4 barriers shows that inclusion of correlation leads to a significant lowering of the barrier to proton transfer, ranging from 11.2 kcal/mol in H2N-OH to 17.9 kcal/mol in HO-F. This indicates that the transition state is not as well described as the local minima at the Hartree-Fock level and is consistent with the results of previous studies.33-36 The bases N s N , HN=NH, H2N-NH2, HO-OH, and F-F also have two lone-pair protonation sites which are equivalent. The barriers to proton transfer between the two sites are also reported in Table V. The large HartreeFock barriers are significantly lowered by correlation except for N2H". Effect of Protonation on A-B Bond Lengths. The A-B bond lengths in the bases and the changes which occur upon protonation are reported in Table 11. When A and B are singly bonded and protonation occurs at a lone pair on the more electronegative atom B, the A-B bond distance increases. The lengthening of the A-B bond is in the order zero < 6(0-0) < 6(N-N) < 6(F-F) < 6(C-N) < 6(N-0) < 6(C-O) < 6(0-F) < 6(N-F) < 6(C-F) (32)R. Krishnan and J. A. Pople, Int. J. Quantum Chem., in press. (33)C. E.Dykstra and H. F. Schaeffer, J.Am. Chem. SOC.,100,1378 (1978). (34)J. D.Goddard and H. F. Schaeffer, J. Chem. Phys., 70, 5117 (1979). (35)M.J. Frisch, R. Krishnan, and J. A. Pople, J . Phys. Chem., in press. (36)R. Krishnan, M.J. Frisch, J. A. Pople, and P. v. R. Schleyer, Chem. Phys. Lett., in press.
Del Bene et al.
indicating that heteronuclear A-B bonds lengthen more than homonuclear and that the lengthening of heteronuclear bonds is greatest for F-protonation, less for 0protonation, and least for N-protonation. Moreover, for protonation at a given atom, the greater the difference in the electronegativities of the bonded atoms, the greater the lengthening of the A-B bond. When protonation occurs at a lone pair of electrons on the more electropositive atom A, the A-B single-bond distance contracts. The A-B bond length changes are in the order 6(N-F) < 6(N-0) < 6(0-F) < zero indicating that the contraction is larger for N- than 0protonation. For N-protonation, the contraction of the bond distance is greater when the electronegativity difference between the bonded atoms is larger. Protonation of a lone pair of electrons on B when A and B are doubly or triply bonded leads to a lengthening of the A-B bond except in HCGN. Protonation at the more electropositive atom A (N in H N = O and C in C=V) leads to contraction of N-0 and C-0 bond lengths. Similarly, the N-N distance in HN=NH and N=N also contracts in the ion relative to the base. I t is also possible to examine changes in A-B bond distances for protonation at a specific lone-pair site, so that substituent effects on bond length changes may be evaluated. For protonation at B in the reaction X-BH,
+ H+
+
X-BH,+,+
the increase in the A-B bond length is greatest when X is CH, and decreases in the order with respect to X CH3 > NH2 > OH > F The A-B distance contracts when B is OH and X is F, and when B is NH2 and X is either OH or F. Similarly, for the reaction X=NH H+ X--NH2+
+
+
the bond length change is in the order 6(C-N) > zero > 6(N-N) > 6(N-0) and for X=O
+ H+
+
X-OH+
the order is 6(C-O) > 6(N-0) > zero Protonation of the a system in H2C=CH2and H C 4 H also leads to a lengthening of the C-C bond. The increase is greater for protonation of H2C=CH2 than H C e H .
Conclusions The calculations performed in this study of the protonated hydrides NH3, H20, and HF and the protonated closed-shell bases H,ABH, where the two nonhydrogen atoms may be C, N, 0, or F support the following statements. (1) Inclusion of correlation generally leads to relatively small changes in the computed protonation energies of bases. The correlation energy correction to the HartreeFock protonation energy computed with the 6-31G** basis set does not necessarily lead to better agreement between computed and experimental data. However, both Hartree-Fock and M~lller-Plesset protonation energies are reasonable, and trends in protonation energies of related bases are the same at both levels of theory. (2) For molecules H,ABH, which have two lone-pair protonation sites, protonation at the more electropositive
1535
J. Phys. Chem. 1082, 86, 1535-1539
atom results in the more stable ion. The relative stabilities of pairs of isomers are similar a t Hartree-Fock and fourth-order Mraller-Plesset theory, except for the C- and 0-protonated forms of C 4 . However, the Hartree-Fock barrier to proton transfer which separates the isomers is lowered by 11-18 kcal/mol by electron correlation. The Hartree-Fock barriers to proton transfer between lone-pair protonation sites in ions H,AAH,+,+ are also significantly lowered by correlation except for N2H+. (3) Zero-point vibrational energy corrections are sig-
nificant, leading to decreases of 5-10 kcal/mol in protonation energies. (4) Protonation may lead to an increase or decrease of the A-B bond distance depending on the nature of the A-B bond and the nature of the protonation site. A-B single bonds lengthen upon protonation in homonuclear molecules and in heteronuclear molecules when protonation occurs a t the more electronegative atom. The A-B single bond distance decreases when protonation occurs at the preferred more electropositive atom.
Polyelectrolyte Effect on Fast Interionic Reactions. Quenching of Cationic Phosphorescence Probes wlth CO(NH,):' in the Presence of Anionic Polyelectrolytes Nicholas J. Turro and Tsuneo Okubo' Chemlstry Department, Columbia University, New Yo& New York 10027 (Received: Septemhr 30, 1981; I n Final F m : November IO, W8l)
The bimolecular rate constants of quenching of cationic phosphorescence probes with CO(NH&~+ (107-10'0 M-I s-') were determined from phosphorescence decay measurements in the presence and in the absence of simple polyelectrolytes. The probes used were n-(4-bromo-l-naphthoyl)alkyltrimethyla"onium bromide, alkyl = methyl (n = I, BNK-19, pentyl (n = 5, BNK-59, and decyl (n = 10, BNK-lo+). Simple electrolytes (NaC1, CaCl,, and LaC13)enhanced the quenching rates. These results may be explained quantitatively in terms of the Bronsted-Bjerrum-Debye-Huckel theory. Polyelectrolyteg such as sodium polystyrenesulfonate, sodium polyethylenesulfonate, and sodium polyacrylate greatly accelerated the quenching. For the slower quenching processes the polyelectrolyte effect suggests that the electrostaticand hydrophobicinteractions between reactants (probes) and macroions, and further dehydration of the activated complex with macroions, are very important. However, the specific polymer concentration dependenceof the quenching rates suggeats that the faster quenching processes are mainly influenced by the diffusional motion of macroions.
Introduction Very fast bimolecular chemical reactions, particularly reactions in aqueous media, are crucial in determining kinetic aspects of biological reactions and of biomolecules and other molecular assemblies. Recent studies of polyelectrolyte catalyses of interionic reactions have revealed some important general features of this important class of reactions.' First, as a result of electrostatic interactions, cationic (or anionic) macroions greatly accelerate the reactions between anionic (or cationic) species, whereas macroions decelerate the interionic reactions between oppositely charged species. These effects of polyelectrolyte are qualitatively interpreted in terms of a local distribution of reactant ions around macroions and more quantitatively interpreted in terms of the change in the thermodynamical activities of reactants and the activated complex via activated-complex theory. Second, in addition to electrostatic interactions, hydrophobic interactions between reactants and macroions are often very important in determining the magnitude of bimolecular reaction rates between charged species. In some cases, even reactions between oppositely charged species are accelerated in the presence of hydrophobic polyelectrolytes. Third, a significant contribution of en(1) For reviews, see (a) Sakurada, 1. J. Pure Appl. Chem. 1968,16,236; (b) Overberger, C. G. Acc. Chem. Res. 1969,2,217; (c) Morawetz, H.Adu. Catal. 1969,20,341; (d) be,N. "Polyelectrolytes and the Applications", Rembaum, A.; Selegny, E. Ed.; D. Reidel: Dordrecht, Holland, 1975; p 71; (e) be, N.; Okubo, T. Macromolecules, 1978, 11, 439. 0022-365418212086-1535$01.25/0
Scheme I BI
c=o
;z I
H3C - N CH3 I CHI Bra
BNK
-
1@
Scheme I1
BI
Br
c=o
I (CH, 1' HIC-N-CH,
)5
c=o
I (CHP'IO 1' H3C -N- C H 3
h H 3 B'I
BNK
-
5@
"o("
L H 3 Br'
BNK
-
IO'
w COf
No'
O y No' NaPES
NoPSS
NoPAA
tropic gain associated with the dehydration of reactants and macroions appears to be important in the course of activation.2 In general it appears that the overall steps of a reaction mechanism are not altered by the polyelectrolyte catalysis in most cases. Interestingly, micellar aggregates of ionic surfactants show similar rate enhancement effects on interionic reaction^.^ (2) (a) Ise, N.; Maruno, T.; Okubo, T. R o c . R. SOC.London, Ser. A , 1980,370,485; (b) Okubo, T.; Maruno, T.;Ise, N. Ibid. 1980,370,501.
0 1982 American Chemical Society
