1744
C. K. R. RAO,A. GOEL,I 20". It appears as though that with carbonyl donors, a 0 of -20" can be (16) A. Geol, A . S. K. Murthy, and C. N. R. Rao, J . Chem. Soc A , 190 (1971). (17) J. Del Bene and J. A. Pople, J . Chem. Phys., 52, 4858 (1970). (18) P. A . Kollman and L. C. A411en,ibid.,51, 3286 (1970).
DISTORTED HYDROGEN BONDS
1747
Table I11 : CN1)0/2 Calculations of the Effect, of Bending Hydrogen Bonds 7$
9,
,
De, kcal mol-'
ET, eV
A
dea
Charges&
_ _ _ _
Cb
HC
XAd
~r(D)
2.966 (2.955) 0.811 (0.835) 2.965 0.810 2.965 0.810 2.962 0.821
0.831 (0.865)
4.50
0.0 (0.0) 0.829 0.0 0,828 0.0 0.849 0.0
4.314 (4.270) 2.00 (2.00) 4,315 2.00 4.315 2.00 4.295 2.00
0.835 (0.880) 0.0 (0.0) 0.834 0.0 0,842 0.0 0.854 0.0
3.445 (3.402) 1.853 (1.859) 3.446 1.853 3.435 1.854 3.420 1.855
OD
Formaldehyde-Water (+ = 0')
0
- 1271. ,74
'2.6
7.5
20
2.6
- 1271.71
6.9
30
2.7
- 1271.69
6.3
60
2.8
- 1271.57
3.4
a4.997 (5.027) n l , 190 (1.165) u4.998 nl.190 u4.999 nl,190 a5.014 irl, 179
4.40 4.30 3.90
Formamide Open Dimer (6 = 0')
0
2.6
- 2138.92
5.0
20
2.6
-2138.88
4.4
30
2.7
- 2138.86
3.8
60
2.9
- 2138.75
1.3
u4.944 (4.964) n l .371 (1.343) a4.945 n l .370 a4.951 ?rl ,364 a4.960 nl .355
2.863 (2.857) 0.779 (0.798) 2.863 0.779 2.861 0.783 2.858 0,790
a Charges on the atoms in the parent electron donors (D) and acceptors (A) are shown in the parent>heses. carbonyl group. Hydrogen taking part in hydrogen bonding. d X is the acceptor atom.
I
215
I
D c8
\I/
I
I
I
3.0
3.5
4.0
-
R,#
?
Figure 2. Variation of AE (kcal/mol) with e in formaldehyde-water ( I ) and formamide trans dimer (11). Angle of bending, 8, is 60', 30", 20', and 0" in curves A, B, C, and D, respectively. The AE values were obtained from CNDO/2 calculations.
7.30
6.85 6.40
5.07
Carbon of the donor
accommodated without much gain in the energy of the system (Figure 2). I n the case of the water dimer, Rao and find that the decrease in De beThese comes marked when 8 is greater than -20". results of molecular orbital calculations on bent hydrogen bonds are consistent with experimental observations. 1 , 3 , 4 From the CKD0/2 results (Tables I and 111),we see that hydrogen bonding in formamide dimer causes u gain and a small a loss in both nitrogen and carbon, u loss and a gain in oxygen, and CT loss in hydrogen; the direction of transfer of negative charge is from the C=O group to the H-N group. The changes in the charges of the formaldehyde-water system are very similar. Variation of d, does not significantly alter the charges or the dipole moments of the hydrogen bonded systems; increase in 8, however, markedly affects both the charges and the dipole moments, particularly beyond a 8 of 20". As 8 increases, we see that charges approach those in the isolated monomers as expected. As mentioned earlier, the E H T method exaggerates charge separation particularly in the case of the C=O bond. We see that the changes in the E H T charges are essentially due to CT contributions (Table I1 and IV). Although the CNDO charges are likely t o be more reasonable, we see that the Mulliken overlap populations as well as the E H T charges listed in Table IV show the expected variations with 8. The Journal of Physical Chemistry, Vol. 75, N o . 11, 1071
S.G. CHRISTOV AND 2.I,. GEOIZGIEV
1748
~
~
~~~
Table I V : EHT Calciilatioris on the Effects of Bending the Hydrogen Bond in Formaldehyde-Water System (+
=
0')
De, 8, deg
R," A
eV
koa1 mol-'
ET,
I
0
2.6
-436.95
3.2
20
2.6
-436.94
3.0
30
2.7
-436.93
2.8
60
3.2
-436.83
0.5
CtlargoSa 00
cr5.438 (5.519) ? r l ,821 (1.821) cr5.438 ~1,821 ~5.456 ?rl,821 ~5.506 ~l ,821
C*
HC
Sad
2.695 (2.690) 0.179 (0.179) 2.694 0.179 2.692 0.179 2.692 0.179
0,380 (0.372) 0.0 (0.0) 0.380 0.0 0.379 0.0 0.373 0.0
5.326 (5.257) 2.0 (2.0) 5.326 2.0 5,311 2.0 5.268 2.0
-----Overlap 0-H
0.3959 (0.4527)
0.1017 (0.0)
0.7609 (0.7573)
0.3963
0,1016
0.7626
0.4089
0,0790
0.7623
0.4408
0.0151
0.7568
* Carbon of
the donor
Charges on the atoms in the parent electron donors ( D ) and acceptors (A) are shown in the parentheses. carbonyl group. Hydrogen taking part in hydrogen bonding. d X is t,he acceptor oxygen atom. Q
Acknowledgment. The authors are thankful to the Council of Scientific and Industrial Research, India, for
populations-----O.'.H cF=o
the support of this research and the staff of the I I T K Computer Centre for the facilities.
On Tunneling Corrections in Chemical Kinetics by S. G. Christov* Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia, Bulgaria
and Z. L. Georgiev Department of Physical Chemistry, Higher Chemico-Technological Institute, Sofia, Bulgaria
(Receited August 6 , 1970)
Publication costs borne completely by T h e Journal of Physical Chemistry
A comparison is made between the results of one-dimensional and two-dimensional procedures of calculating tunneling corrections for reactions of the type AH B -+ A HB (via a linear activated complex A-H-E), where A and B are heavy atoms. An improvement of the method of Johnston and Rapp for estimation of two-dimensional tunneling corrections for these reactions is proposed. Computations show that the onedimensional treatment of the (extended) reaction path overestimates tunneling, but not too much, but underestimates it, if the mass transferred is taken to be equal to the proton mass.
+
I. Introduction The role of the tunnel effect in the kinetics of themical reactions of hydrogen and its isotopes has been discussed many times in recent years.'-1° There exist both theoretical reasons and experimental facts which clearly show that it is necessary to introduce a correcting factor t o the classical reaction rate in order t o account for the tunneling of protons or hydrogen atoms through the potential energy barrier. An exact solution of the tunneling problem is possible in the usual one-dimensional approximation. Johnston5 has posed the question whether this approximation is justified if one wishes t o connect it with an apT h e Journal of Physical Chemistry, Vol. 7 6 , S o . 11, 1971
+
plication of the activated complex method for a complete evaluation of the reaction rate. He has stressed (1) R.P. Bell, T r a n s . Faraday Soc., 5 5 , 1 (1959). (2) R . E. Weston, J . Chem. P h y s . , 31, 892 (1959). (3) S. G . Chrlstov, 2. Elektrochem., 62, 567 (1958). (4) S. G. Christov, Dokl. A k a d . S a u k S S S R , 136,663 (1960). (5) H. S. Johnston, A d z a n . Chem. P h y s . , 3, 131 (1960). (6) T. E. Sharp and H. S.Johnston, J . Chem. Piiys., 37, 1541 (1960). (7) H. S.Johnston and D. Rapp, J . Amer. Chem. Soc., 83, 1 (1961). (8) E. I?. Caldin, Discussions Faraday Soc., 39, 2 (1965). (9) S. G. Christov, J . Res. Inst. Catalysis, Hokkaido Unin., 16, 169 (1968). (10) E. M . Mortensen, J . Chem. P h y s . , 48, 4029 (1968); 49, 3526 (1968).
