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Water molecule interactions. Stability of cyclic polymers
1.H. S. Frank and W. Y. Wen, Discuss. Faraday Soc. 24, 133 (1957).
2.A. T. Hagler, H. A. Scheraga, and G. Nemethy, J. Phys. Chem. 76, 3229 (1972).
3.K. Morokuma and L. Pederson, J. Chem. Phys. 48, 3275 (1968).
4.P. A. Kollman and L. C. Allen, J. Chem. Phys. 51, 3286 (1969).
5.K. Morokuma and J. R. Winick, J. Chem. Phys. 52, 1301 (1970).
6.G. H. F. Diercksen, Theor. Chim. Acta 21, 335 (1971).
7.J. Del Bene and J. A. Pople, J. Chem. Phys. 52, 4858 (1970).
8.D. Hankins, J. W. Moskowitz, and F. H. Stillinger, J. Chem. Phys. 53, 4544 (1970).
9.D. Eisenberg and W. Kauzmann, The Structure and Properties of Water (Oxford, U.P., New York, 1969), p. 139.
10.B. R. Lentz, A. T. Hagler, and H. A. Scheraga (unpublished).
11.D. Neumann and J. W. Moskowitz, J. Chem. Phys. 49, 2056 (1968).
12.There is a misprint in this table. The coefficient of the first Gaussian primitive of the oxygen 2s‐type orbital should be 1.051534 as in Ref. 11.
13.S. Aung, R. M. Pitzer, and S. I. Chan, J. Chem. Phys. 49, 2071 (1968).
14.D. B. Neumann, H. Basch, R. L. Kornegay, L. C. Snyder, J. W. Moskowitz, C. Hornback, and S. P. Liebmann “The POLYATOM (Version 2) System of Programs for Quantitative Theoretical Chemistry,” QCPE, University of Indiana, Bloomington, Indiana.
15.C. C. J. Roothaan, Rev. Mod. Phys. 23, 69 (1951).
16.The stabilization energies from Ref. 8 have been rescaled since HMS subtracted the energies of monomers computed with six d‐type functions from those of dimers and trimers computed with five d‐type functions per oxygen to obtain stabilization energies17 (see Sec. II and Table II). The stabilization energies of the dimers and trimers reported by HMS are therefore all too positive.
17.D. Hankins, J. W. Moskowitz, and F. H. Stillinger (private communication).
18.The dimers considered here do not have exactly the same geometry that exists in ice I since we have used 106° for the H‐O‐H bond angle, whereas the exact value for this angle in ice I is uncertain.19 However, we expect the relative stabilization energies of the various dimer geometries to be unaffected by this uncertainty in the H‐O‐H bond angle.
19.Reference 9, Sec. 3.1, p. 71.
20.Even though the cyclic trimer with symmetry is not the most stable one found by DBP,7 nevertheless it is valid to use it for comparison of our extended basis set results with those of DBP.7 We chose this trimer for illustration, since its symmetry reduces the time required for computations.
21.In Fig. 7 of Ref. 8, it appears that the, of two linear trimers change sign at When these results are rescaled,7 this crossing behavior disappears.
22.The value of corresponds to the minimum‐energy value of the DBP dimer; the minimum‐energy value for the DBP noncyclic trimer is 2.63 Å.
23.A. Ben‐Naim and F. H. Stillinger, in Water and Aqueous Solutions, edited by R. A. Horne (Wiley, New York, 1972), p. 295.
24.P. A. Kollman and L. C. Allen, J. Am. Chem. Soc. 93, 4991 (1971).
25.The results of Morokuma and Winick5 were not included in this trend because they used an STO basis set; similarly, the GTO results of Morokuma and Pedersen3 were not included because they give an anomalously‐high hydrogen bond energy of
26.R. W. Bolander, J. L. Kassner, and J. T. Zung, J. Chem. Phys. 50, 4402 (1969).
27.We have used the estimate given by HMS8 for the effect of correlation terms on the interaction energy of the dimer. These authors relate this to the dispersion attraction between two water molecules and estimate this quantity to be at We have calculated this term at other values of R by using the accepted dependence of the dispersion energy.
28.At large distances, the two‐body energy should be essentially electrostatic in nature. Coulson and Eisenberg29 calculated the electrostatic contribution of third and fourth neighbor unpolarized water molecules to the energy of ice to be We have estimated the third and fourth neighbor dispersion energy contribution as less than using the dispersion energy approximation of HMS.8 Thus, the total third and fourth neighbor contribution should be of the order of Fifth and higher neighbor contributions should be negligible.
29.C. A. Coulson and D. Eisenberg, Proc. R. Soc. A 291, 445 (1966);
29.C. A. Coulson and D. Eisenberg, Proc. R. Soc. A 291, 454 (1966).
30.N. Bjerrum, Science 115, 385 (1952).
31.L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935).
32.It should be noted that there is a third‐nearest neighbor in ice I at a distance (4.60 Å) only slightly larger than the second‐neighbor distance (4.51 Å). This could be considered as a thirteenth second‐neighbor, but we have chosen to treat it as a third‐neighbor as in Ref. 29. The interaction energy for this pair is included in our calculation when we add the third‐ and fourth‐neighbor terms from Ref. 29.
33.The three data available at show a spread in of 0.25 kcal/mole ( for cis‐cis,8 for distorted trans‐trans from our tetramer, and for trans‐cis8 trimers).
34.A. W. Searcy, J. Chem. Phys. 17, 210 (1949).
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