J. PbyS. Cb8m. 1982, 8 6 , 1607-1610
1607
Ab Initio Self-Consistent Fieid Calculations on I,-NH, and HI-NH,. The Classic “Charge-Transfer” Interaction, an Example of Gas-Phase Proton Transfer, and the Duality of Lewis Acid Sites on H I Peter Kollman,’ Andrew Dearlng, Department of Pharmaceutlcal Chemisby, University of California, Sen Francisco, California 94 143
and E. Kochanskl Department of Chemktty, University of Strasbourg, Strasbourg, France (Received: October 9, 198 1)
We present ab initio SCF calculations on NH3-12 and NH3-HI using valence-shell double { basis sets on the complexes. The interaction energy between NH3 and I2 is calculated to be approximately 10 kcal/mol and shows a small amount of charge transfer (-0.le) from NH3 to IF The H3N...HI complex is calculated to be most stable with essentially complete proton transfer, consistent with extrapolation from previous calculations on H3N...HF (no proton transfer) by us and on H3N..-HC1 olalf proton transfer) by Clementi and us. In addition, unlike H3N. .FH, there is an additional attractive well when the molecules approach in an electrostatically unfavorable direction, HI..-NH3, with a well depth of -3 kcal/mol. At long distances, this HI-..NH3 approach is (very slightly) repulsive, providing the first example of a weak, noncovalent intermolecular interaction with an initially repulsive potential surface and then attraction. The perpendicular approach (structure 1) is strongly repulsive, in contrast to both linear approaches; this results allows one to understand the observed dependence of C-I...O distances on C-I...O angle observed in many crystal structures.
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Introduction Iodine is an interesting element for a number of reasons. From a biological point of view, it is the heaviest endogenous element in most life forms. From a physical chemical point of view, iodine compounds have long been of interest for their spectral properties, including the formation of “charge-transfer complexes”.l Theoretical studies on iodine compounds have been difficult because of the number of electrons on the atom, but the recently developed atomic basis set for iodine by Kochanski and co-workers2has allowed the studies of the complexes Iz.. CzH42and Iz- ‘C6H6.3 We have earlier carried out ab initio SCF calculations on amine (NH3, CH3NHz,(CH,),NH, and (CH3)3N)-S02 complexes and have suggested that the behavior of these complexes would be similar to the more extensively studied amine+ complexes, in that the charge-transer component was critical to the interaction, and it was this component which make the amine-SOz complexes stronger as one adds methyl groups to NH3. We thus decided to begin a study of the interaction of Iz with NH3. Previous ab initio calculations on H3N*-.HF“’ and H3N...HCle8 have found rather different proton potential surfaces for these two complexes, in complete agreement with subsequent matrix IR experiment^.^ It was thus of interest to examine the proton potential surface of H3N.**HI.
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(1)R. Mulliken, J. Am. Chem. SOC.,74,811 (1952). (2)J. Prissette, G.Seger, and E. Kochanski, J.Am. Chem. SOC.,100, 6941 (1978). (3)E.Kochanski and J. Prissette, Nouu.J. Chim. 4, 509 (1980). (4)J. E.Douglas and P. A. Kollman, J. Am. Chem. SOC.,100,5226 (1978). (5)P. Kollman and L. C. Allen, Am. Chem. SOC.,93, 4991 (1971). (6)W.Topp and L. C. Allen, J . Am. Chem. SOC.,96, 5291 (1974). (7) P. Kollman, J. McKelvey,A. Johansson and S. Rothenberg, J. Am. Chem. Soc., 97, 965 (1975). (8)E. Clementi, J. Chem. Phys., 46, 3851 (1967);47, 2323 (1967). (9)B. Ault, E. Steinback and G. Pimentel, J. Phys. Chem., 79, 615 (1975). (10)P. Murray-Rust and W. Motherwell, J.Am. Chem. SOC.,101,4374 (1979) (11)R. Ditchfield, W.Hehre, and J. A. Pople, J. Chem. Phys., 54,724 (1971). 0022-3654/82/2086-1607$01.25/0
Finally, the interesting analysis of C-I. -0 intermolecular contacts by Murray-Rust and Motherwell has indicated a rather different distance and strength of 0.-.I interaction, depending on the directionality of approach. We thus attempted to see whether the rationalization for their empirical results could be found in a study of the H-1.. .N intermolecular interaction studied here, so we examined the energy for H3N...I-H (iodine closest to N) and
i
H,N- * *I
(H-I bond perpendicular to N-I axis) for comparison with the corresponding surface for H3N. -HI.
Methods We used the program GAMESS, developed at the VAX 11/780 at the NRCC in Berkeley and adapted to run under UNIX by A.D. in these studies. Standard ab initio closed-shell SCF calculations were carried out on NH,, 12, HI, NH3-I,, and NH3-HI, as a function of geometrical parameters. We used a 4-31G basis for nitrogen and hydrogen and a valence-shell double {basis set for I.2 Results The total energies, interaction energies, and optimized distances are given in Table I. As noted previously by Kochanski,2 the calculated Iz distance is about 0.16 A longer than the experimental value. On the other hand, the calculated H-I distance is 1.60 A, in excellent agreement with the experimental value of 1.61 A.12 The calculated dipole moment is 1.0 D, significantly larger than with the experimental value of 0.4 D,13with the polarity H6+-I”. For NH,, we used the experimental monomer geometry, since it is known that an optimization with a 4-31G basis set flattens the NH3 to near ~1anarity.l~ (12)S.Naude and H. Verleger, Proc. Phys. SOC.,London, Sect. A., 63 470 (1950). (13)D. E. Stogryn and A. P. Stogryn, Mot. Phys., 11, 371 (1966). (14)W.A. Latham, L. A. Curtuss, W. J. Hehre, J. B. Lisle, and J. A. Pople, Prog. Phys. Org. Chem., 10, 175 (1973).
0 1982 American Chemical Society
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The Journal of Physical Chemistry, Vol. 86,No. 9, 1982
TABLE I: Calculated Energies of Monomers and Dimers optimized monomer or dimer ETe distancef -AE' 1-1 -13818.47631 2.286 I-H -6909.80736 1.60 -56.10255 (1.01)' NH 3 -99.88726 (0.917)h F-H H,N.. .HI -6965.9222 3.4 (proton fixed)a (2.3)' H,N. .HI -6965.9345 (proton opt)b 3.2 H,N, .IH -6965.9149 2.67 H,N, . .I2 -13874.5954 (1-1 fixed)c (2.88)j H,N, . .I, -13874.5959 (1-1 0pt)d (3.2)' H,N.. .IH -6965.9003 ( e (NHI) = 90") - 155.9849 (3.4)' H3N. ,FH (2.6)' H,N.. ,FH -155.9757
TABLE 11: Net Charges and Dipole Moments of Molecules and Complexes net charges molecule or complexa p,b D IA(H)" I B ( H ) ~ Ne
HI 7.7 (4.5)M 15.4 3.1 (l.l)m 10.4 (7.1)m 10.7
NH, NH,-I,(fix.) NH,-I,(opt) NH3-IH NH,-HI(fix.) NH,-HI(opt)
1.01 (0.38) 2.30 (1.47) 7.13 7.37 2.25 5.59 12.96
Hf
1.0.02 -0.02
-0.21 -0.23 +0.06 -0.13 -0.71
t0.13 +0.13 -0.08 t0.05 t0.35
-0.90
+0.70
-0.94 -0.94 -0.90 -0.91 -0.90
+0.34 +0.347 t0.31 t0.33 +0.42
Molecule considered; see Table I for geometry. Calculated dipole moment in debyes (experimental values in Net charge of atom farthest from N in parentheses). A-B, . .NH3 complex. Net charge of atom nearest N in A-B, .NH, complex. e Net charge on NH, nitrogen. f Net charge on NH, hydrogen.
-6.0
- 3.1 -8.9
Proton held fixed; only N. . .I distance optimized. Proton position optimized at optimum N. . .I distance found previously. 1-1 bond held fixed and N. . I distance optimized. 1-1 distance optimized at optimum N. . I distance found previously. e Total energy in atomic units. f Optimum distance; for intermolecular distance, refers to I. . .N or F.. . N distance unless otherwise specified. g Held fixed at experimental R(N-H) = 1.01 A , 6 = 106.7". Held fixed at experimental R(F-H) = 0.917 A . I Optimum H-I distance. I Optimum 1-1 distance. Surface completely repulsive, so no minimum found. Interaction energy in kcal/mol. Interaction energy kcal/mol after correcting for counterpoise error at optimized distance. For HI-NH,, we recalculate an optimized distance of 3.4 A and an interaction energy of 1 . 4 kcal/mol after counterpoise correction at different distances. a
The first intermolecular complex that we studied was 1,-NH3. We examined only the linear IA-IB***NH3 approach, and first optimized the 12...NH3 distance, finding an optimum IB- .N distance of 2.67 A and an interaction energy of -10.4 kcal/mol. At this I g . .N distance, we optimized the IA-IB distance and found an optimum distance of 2.88, and about 0.05 A longer than in I2in itself, and an interaction energy of -10.7 kcal/moi. There are no experimental data on the structure of Iz---NH3,but in the crystal structure of (CH3)3N-**12, the N.s.1 distance15is 2.27 A and the 1-1 distance is 2.82, the latter 0.16 A longer than the experimental value for I2 itself. We determined the basis set superposition error16 for Iz. .NH3,R(1-N) = 2.67 A, and found it to be 3.3 kcal/mol. thus, the calculated interaction energy is 7.4 kcal/mol, significantly larger than the experimental value (H3N...12 in n-heptane solution) of 4.8 kcal/mol." The results for H3N. .HI indicate that in the H3N. .HI complex the hydrogen-bonding proton transfers essentially completely from I to N with an N-H6+ distance of 1.1 A, only about 0.1 8, longer than in NH4+,and an N.e.1 distance of 3.4 A. This is consistent with indirect evidence from matrix IR work by Pimentel et aL9that Clementi's prediction of "half proton transfer" in NH3.. .H-Cl is correct8 and the knowledge that the reaction HX H+ + X- is less unfavorable (in the gas phase) for H-I than for HC1. The study of other structures of the NH3-HI complex is important not because they would be expected to compete with the H-bonded structure but because of the in-
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(15)K.Stramme, Acta Chem. Scand., 13, 268 (1959). (16)A. Johansson, P.A. Kollman, and S. Rothenberg, Theor. Chim. Acta, 29, 167 (1973). (17)A. Yada, d. Tanaka, and S. Nagakura, Bull. Chem. SOC.Jpn. 33, 166 (1960).
sight that they give us into the intermolecular packing of 1.. .N in alkyl-I compounds. For the structure H-1. * .NH,, we find a minimum energy at 3.2 A and a well depth of 3.1 kcal/mol. Even at 2.7 A, there is a repulsion of only 0.5 kcal/mol. On the other hand, for the structure H H
H
I \I I*..N I H
with the same N-I distance, but the H-I hydrogen rotated perpendicular to the N.. .I line, the repulsion at 3.2 A is 6 kcal/mol, with the interaction still repulsive by 1.4 kcal/mol at 3.8 A. This very nicely rationalizes the observation of the dependence of C-1.. -0 distance on C-1.. -0 angle,1° in which I-e.0 distances of 2.8-3.8 A were observed for C-I..-O angles near 180°, but most of the distances were -3.8 A for C-I.--O angles near 90°. The structure H-I. .NH3 is also interesting to a theoretician because it has an attractive well, despite the unfavorable dipolar alignment of the two molecules. Thus, at long distances, the AI3 should actually become repulsive, and we found that the maximum repulsion, about 0.06 kcal/mol, occurred at R(N.m.1) = 8 A. At a distance of 9 A, the repulsion was only 0.04 kcal/mol; at 6 A, there was already a weak attraction of 0.02 kcal/mol. On the other hand, the system H-F- .NH3 has a completely repulsive potential curve, as is clear from the data in Table I. The dipole momenta and net charges for the monomers and complexes are presented in Table 11. It is interesting that there is only approximately O.le transferred frm NH3 to I2 in the optimized H3N-..Ipcomplex, not greatly different from that found in typical H-bonded complexes. On the other hand, the dipole moment enhancement for this complex is very large, -5 D. This is because of significant polarization of the 1-1 bond. It is interesting that, although only O.le is transferred from NH3 to 12,it is transferred from the hydrogens to I*, a distance of about 6 A. This charge transfer accounts for about half of the dipole enhancement; the remaining half comes from the obvious intramolecular polarization 16-16+.N6--Ht+ which is evident from the Mulliken populations. For H3N. -IH, we find about 0.02e charge transfer, but significant polarization 16+-H", which is similar to what is found in H3N..-1-1. The dipole moment for this complex is larger by -1.1 D than the s u m of the monomer moments (2.30-1.01). H3N...H-I has a very large dipole moment enhancement, both before and following proton transfer from I N. As one would expect, the polarization of H-I
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Ab Initio SCF Calculations on I,-NH,
and HI-NH,
The Journal of Physical Chemistry, Vol. 86, No. 9, 1982
1609
TABLE 111: Orbital Energiesa and Their Changes upon Complex Formation orbital(s)
I,
HI
NH,
av change of inner-shell orbital energy of Lewis baseb av change of inner-shell orbital energies of Lewis acidC 1-1 lone pair (E symmetry) 1-1 lone pair ( E symmetry) I-H lone pair (E symmetry) 1-1 or I-H u bond 1-1 or I-H U * N-H bonds ( E symmetry) N lone pair N-H U * (A, symmetry)
I,-NH,(fix.)d -0.0686 0.0163 * 0.0014e 0.0597 * 0.0012f -0.40 -0.34
-0.45 -0.37 -0.44 -0.44
-0.39 -0.53 0.11 -0.62 -0.41 0.22
-0.37 0.00 -0.69 -0.52 0.15
H,N. . .HI(fix.)
HI-NH, -0.0119
0.0280 0.005
-0.0519
0.0552 i: 0.0011
i:
- 0.36 -0.50 0.15 -0.63 -0.42 0.22
-0.34 -0.54 0.18 -0.67 -0.41 0.23
H,N. . .HI(opt) -0.1990
0.1443 i: 0.0035 -0.27 -0.29 0.19
-0.80 -0.67 0.11
Average of orbital energy change upon complex formation of two most tightly bound (1s and a , , In atomic units. Average of inner-shell (all of those orbitals not explicitly tabulated below) orbital energy N-H bonding orbital) of NH,. Molecule (or complex) as described in Tables I and 11. Since 1,-NH,(opt) is so similar to 1,changes for I, or IH. NH,(fix.) (Table 11), we tabulate only the former here. e Average orbital energy changes for IA (see Table 11). Average orbital energy changes for IB (see Table 11).
on complexation to form H3N-.H-I is opposite in sign to that of H-I in H3N...I-H Table I11 is a summary of the orbital energies in the molecules and the complexes. Earlier we notedI8 that the orbital energies in Lewis acids are destabilized and those in Lewis bases are stabilized upon complex formation. As expected,l8 the magnitudes of these orbital energies correlate with the AB of complex formation (the stronger complex has larger shifts). In addition the orbital energy changes for all of the inner-shell electrons for HI (or 12) in a given complex are remarkably constant (note the standard deviation in the orbital energy changes). In the valence shells, there is much more mixing, although the orbital energies of the Lewis acids generally increase and those in Lewis bases decrease. In the proton-transfer complex H3N-H+...I, the I-H u bond orbital and N lone-pair orbitals undergo rather large changes from -0.53 and -0.41 to 0.29 and 0.69 atomic units, exactly what one would expect from the protonation of the lone pair and the "breaking" of the I-H bond. This simple interpretation is somewhat flawed by the extensive mixing the these top two orbitals, however. The inner-shell orbital energy changes for I, in IA-IB. .NH3 are interesting because they fall into two categories: those that are destabilized by -0.06 au (mainly on IA) and those that are destabilized by -0.015 au (mainly IBorbitals). This is consistent with what one would expect in view of the net charge of these two atoms. IAhas a net charge of -0.21, is relatively electron rich, and thus has more destabilized orbital energies.
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Discussion Although the theoretical approach used here is simple, using only SCF ab initio theory with a double t valenceshell basis set and no correlation or relativistic effects considered, it appears to give results for the interaction energies and geometies whch are in reasonable qualitative agreement with experiment. The results for the system 12...NH3 appear to contain the largest discrepancy between theory and experiment, with the calculated interaction energy (7.4 kcal/mol) significantly greater than the observed AH of complex formation in n-heptane (4.8 kcal/mol). There is precedent for this, in that the calculated AB for H 2 0 dimerization with the 4-31G basis set is significantly larger than the experimental ~ a l v e . ~On ~ ' the other hand, the experimental AH value is more sensitive to errors than AG. Also, inclusion of dispersion attraction in the theory would be
expected to worsen the correspondence between theory and experiment, as would the solvation correction (n-heptane would stabilize the highly dipolar H3N.-.12relative to H3N and I2 better than would the gas phase). The calculated N...I distance of 2.67 A for H3N..-12is longer than that observed in the crystal for TMA-I2 (2.27 A). This difference between calculation and experiment is due to the effect of methyl substitution, to the differences between the gas phase and the crystal, and to the lack of inclusion of dispersion attraction in the theory. It is interesting how similar our calculated N.. -1distance is to the calculated N.-.S distance in H3N..-SOz (2.63 A).4 In TMA...S02 our calculated N...S distance is 2.36 A, compared to the experimental value of 2.06 A.l9 Thus, we expect that calculations on TMA...12 will show a shorter N. -1 distance than in H3N. .I2 by -0.2 A, or an N. -1 distance of -2.5 Both inclusion of dispersion attraction in the theory and a consideration of crystal compression effects would be expected to improve the agreement between the calculated and experimental (2.27 A) values. The results of the calculations on H3N...HI are much more interesting, in that they provide the first clear calculated example of the amphoteric Lewis acidity of HI and complete proton transfer in a gas-phase hydrogen-bonded complex. For H3N-..HI, only the latter is likely to be important and the reason for this favorable proton transfer is worth emphasizing. The main difference between NH3...HF (no proton transfer, AB 16 kcal/m~l)~,' NH3...HC1 (half proton transfer, AB 12.6 k~al/mol)~J and NH3...HI (full proton transfer, AE 15.4 kcal/mol) is the proton affinity of the halogen, since this is directly related to the stability of an NH4+. species. In these complexes, changes in stability relative to NH3. .HX result from the electrostatic (NH4+.* .X-) attraction, which favors the smaller X due to the shorter N. .Xdistance, and from the proton affinity of X-.The experimental proton affinitiesm of I-, C1-, and F- are 314, 333 and 371 kcal/mol, and those calculated (using a 4-31G basis seet for H, C1, and F and the I basis set used here) are 313, 349, and 401 kcal/mol. Iodine, by
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(18)P. Kollman and S. Rothenberg, J. Am. Chem. Soc., 99, 1333 (1977). (19) D. van der Helm, J. Childs, and S. D. Christian, Chem. Commun., 887 (1968). (20) The experimental proton affinities are reported by J. Bartmess, J. Scott, and R. McIver, J. Am. Chem. Soc., 101, 6046 (1979). The theoretical affinities for P and Cl- are in D. M. Hayes and P. Kollman, "Catalysisin Chemistry and Biochemistry: Theory and Experiment"B. Pullman, Ed., Reidel, Dordrecht, The Netherlands, 1979, p 77.
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that the dispersion attraction at R(N-I) = 3.2 A is 1.4 kcal/mol, which brings the estimated interaction energy back to -3 kcal/mol. The basis set employed here will underestimate the polarizability of iodine and thus the intermolecular polarization energy; thus, the well depth for HI.. .NH3should be close to -3 kcal/mol after all. The difference between the calculated attractive linear N-s.1-H and repulsive perpendicular (structure 1) approaches is nicely consistent with the observations of Murray-Rust and Motherwellloon C-I..-O interactions in crystals and suggest that, unlike the first-row elements N, 0, and F, where a spherical-atom approximation is reasonable in molecular mechanics models, such a model is not appropriate for the significant deviations from “sphericity” present in R-I molecules. The fact that our calculations on H-1.e.N can be so directly related to the crystal analysis of C-I. angular dependent distances suggests further that substituting C-I for H-I does not have a large effect on the electron distribution around I. In addition, our calculations let us suggest that an analysis of the dependence of C-1.. .N distance on C-I. .N angle will give results similar to those foundlo for C-I. -0. The fact that Murray-Rust and Motherwell observe I...O distances as short as 2.8 A and our minimum-energy distance in H3N...IH (after counterpoise correction) is 3.4 A is probably due to the fact that 0 is -0.1-0.2 A “smaller” than N, our lack of inclusion of dispersion attraction in our calculations, and crystal compressive effects. In fact, using the I...N dispersion coefficient22of 1500 noted above we estimate that dispersion attraction will decrease the N.s.1 distance by -0.2 A. All in all, these calculations on HI. .NH3 have given us some insight into the nature of nonbonded interactions involving R-I as a Lewis acid. The net changes and orbital energy changes found here are not surprising and are in line with the changes found in calculations of other donor-acceptor interaction^.^^
being sufficiently polarizable and stable as an anion, can favorably exist as a stable anion in an appropriate anioncation complex even in the gas phase. Since the basis set used here overestimates the proton a f f ~ t of y NH28 by about 15 kcal/mol and gives a correct proton affinity for I-, we cannot be certain about the calcualted tendency of proton transfer in H,N-..H-I NH4+. .I-. Using the approach that we employed earlier21 in which the proton affinity error is scaled by the net charge in the complex, we estimate that our energy for the reaction NH3.. .HI NH4+- .X- (-7.7 kcal/mol) is too favorable by (15 kcal/mol X 0.71), giving a net hE for this reaction of about +4 kcal/mol. On the other hand, such an approach tends to “overcorrect”and correlation energy terms would be expected to favor the proton-transferred structures. Thus, we expect that H3N...HI and H3NH+...X- will be very close in energy and may even be in thermal equilibrium. In view of the large difference between the dipole moments between these species, gasphase electric deflection experiments on this complex are of interest. Our calculations suggest that the molecule might have a very temperature-dependent dipole moment but that the presence of one molecule of “solvent” (e.g., (NH3)2***HI) should suffice to strongly favor the protontransferred structure. A study of the H-I-.NH3 surface is of general qualitative interest, because it shows not only an attractive well but a (very small) activation barrier for complex formation; this is what one would expect from a complex with unfavorable dipole-dipole but favorable charge transfer as well as dipole-quadrupole electrostatic interactions. In fact, our analysis21 of the electrostatic potential around the halogen in HF and HCl is of interest here. The lone-pair directionality of the electrostatic potential in HF and HC1 is quite different. In HF, at 1.1 8, from F, the potential is most negative a t an angle of 4 5 O from the H-F line (0.0691 au) and only slightly less negative along the axis at the same distance from F (-0.060 au). For HC1 at 1.9 A from C1, the potential is most negative at 0 60’ (-0.0282) and more than 3 times less attractive along the axis (-0.0086). In F, and C12,the electrostatic potentials along the axes are positive21and are negative only the the “lone-pair” directions. The elecrostatic potentials reflect the orientational-dependent electron density (or deficiency). Thus, R-I, like R-C1 and R2S, would be expected to behave very differently than RF and R 2 0 toward Lewis bases. In the former cases, we expect an “attractive” L..O and 1.. .N interaction if the Lewis base approaches the acid along the R-I line and a repulsive interaction if the angle of approach is much different from this. Our calculations on H3H.. .IH support this, with an attractive interaction (hE = -3 kcal/mol) for a linear N.m.1-H approach and a significant ( 7 kcal/mol) repulsion at the same N. .I distance when 0(N.-.I-H) = 90°. The counterpoise error for the H3N.. .IH interaction is significant (Table I) in that it reduces the calculated interaction energy from 3.1 to -1.5 kcal/mol. On the other hand, using a typical I. .N dispersion coefficient22of -1500 kcal/mol A6, we calculate
Acknowledgment. We are pleased to acknowledge the NSF (CHE-80-26560)for support of this research. We are grateful for the use of the UNIX VAX 11/780, system manager T. Ferrin, in this research and to G. Wipff for useful comments.
(21) P. Kollman, J.Am. Chem. SOC.,99,4875 (1977). (22) Using the van der Waals parametera in the program MM2, QCPE Program no. 395.
(23) P. A. Kollman in “Modern Theoretical Chemistry: Applications of Electronic Structure Theory”, Vol. 4, H. F. Schaefer, Ed., Plenum Press, New York, 1977, Chapter 3.
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Conclusions We have presented ab initio calculations on H3N...I2and H,N...HI . The calculations lead to the prediction of complete proton transfer in H3N.--HI, i.e., a structure H4N+..-I-. The calculations have been successful in rationalizing the strong directionality of R-1.. .B (where B is a Lewis base) interactions. The agreement with experimental structural data on the N(CH3)3--.12complex is reasonable, but the calculations find a larger hE for H3N. .I2in the gas phase than AH found experimentally in n-heptane solution. A further analysis of this point, a systematic study of the methyl-substituent effect, and Morkuma energy component analyses of Lewis-base.s.1-R interactions will be subjects for future study.
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