Effects of Alkylation upon the Proton Affinities of Nitrogen and Oxygen Bases

Paul Redfern and Steve Scheiner*+ Department of Chemistry and Biochemistry, Southern Illinois University, Carbondale, Illinois 62901

Received 16 September 1984; 15 November 1984

The protonation energies of alkylated derivatives of NH, and OHz are calculated at the Hartree-Fock level with the split-valence 4-31G basis set. The methyl, dimethyl, and ethyl amines are studied; oxygen bases include methanol, dimethylether, and ethanol. The geometries of each molecule and its protonated analog are fully optimized. It is found that protonation leads to significant changes in the molecular structures. In particular, the bonds to the N and 0 atoms are substantially elongated, especially when the other atom involved is C rather than H. The calculated absolute proton affinities are somewhat larger than the experimental values. However, the differences in protonation energies of the various molecules relative to one another agree quantitatively with experiment. Replacement of one H atom of the base by a methyl group induces an increase in proton affinity of some 10 kcal/mol. If a second methyl group is added to the N or 0 atom, a further increment of about 70% this amount is noted. On the other hand, placement of the second C atom on the first methyl group (to form an ethyl substituent) leads to a smaller increase (-30%). The magnitudes of these alkyl substituent effects are somewhat larger for the oxygen bases than for the amines.

INTRODUCTION

Advances in a number of experimental techniques have facilitated the determina- tion of the intrinsic basicities of a large num- ber of molecules by allowing evaluation of their proton affinities in the gas phase.1-8 Quantum chemical calculations have helped to shed light on some of the factors re- sponsible for the relative proton affinities of related compounds. Hehre and Popleg first showed that ab initio calculations were ca- pable of reproducing experimentally observed trends in proton affinity. This point was con- firmed several years later by Kollman and coworkers1o using a larger basis set. An en- ergy decomposition analysis by Umeyama and Morokuma" demonstrated that it is the polarizability of alkyl groups that is pri- marily responsible for the increase observed in proton affinity as amines or alcohols are progressively methylated. More recently, Eades et aZ. examined the question of the importance of basis set choice in calculating methylation effects upon proton affinities of amines.12 Their results indicated that where-

*Author to whom correspondence should be addressed. tReci ient of NIH Research Career Development

Award 8982-1987).

as most basis sets can correctly predict the relative ordering of proton affinity, double-f sets provide nearly quantitative agreement with experiment.

Perhaps the greatest source of error in the above calculations is the use of either assumed or experimental geometries. For example, Umeyama and Morokuma" had assumed no change in geometry upon pro- tonation; Eades et uZ.12 had subtracted the energies of the experimental geometries of the bases from optimized geometries (using a semiempirical method) of the protonated spe- cies. Recent full geometry optimizations of both species by Smith et aZ.13 and by Huber and Vogt'" have rectified this situation with- in the framework of two different double-f basis sets. Their results demonstrate sub- stantial changes in the geometry of each base as a result of protonation (e.g., C-0 bond elongation of 0.1 A in methanol). From the previous calculations, we may therefore an- ticipate that application of a double-f basis set, in conjunction with geometry opti- mizations of both the base and protonated species, leads to quite satisfactory re- production of the experimentally observed ef- fect of alkylation upon proton affinities. While basis set superposition errors, cor-

Journal of Computational Chemistry, Vol. 6, No. 3, 168-172 (1985) 0 1985 by John Wiley & Sons, Inc. CCC 0192-8651/85/030168-05$04.00

Effects of Alkylation 169

relation effects, and zero-point energies must be included for accurate elucidation of abso- lute proton affinities, the influence of these factors upon the relative values within a re- lated series is quite minor.12-14

We address ourselves in the present work to a quantitative evaluation of the effects of al- kyl groups upon the proton affinity of both oxygen and nitrogen bases. Replacement of one hydrogen of either water or ammonia by a single methyl group leads unambiguously to methanol and methylamine, respectively. Addition of a second group may be accom- plished in one of two ways; replacement of a second hydroxyl H yields dimethyl ether while addition onto the already existing alkyl chain leads to ethanol. Similarly, two “methyl” groups on NH, lead to either di- methylamine or ethylamine. The differing ef- fects of these two types of disubstitution are considered explicitly below.

A number of these points have been ad- dressed previously by calculations including full geometry optimizations. The addition of one or two methyl groups to water and am- monia was treated by Smith et al. using a 3-21G basis set.13 However, the relative effects of an ethyl group were not considered. Huber and V0gt14 studied ethanol with their FOG0 double-6 calculations but did not consid- er dimethyl ether; in addition, no alkyl sub- stituent effects were examined for nitrogen bases.

The calculations are carried out here using the 4-31G basis for the following rea- sons. A future aim of this research is an inves- tigation of proton transfers between various pairs of alkylated bases. The theoretical pro- cedures to be used in these calculations must satisfy two primary criteria. First of all, the relative proton affinities of the two species involved in the interaction must be re- produced with some accuracy. The 4-31G basis set is of double-6 type and may hence be expected to produce reliable treatment of the alkylation effects for reasons stated above. The second requirement is that the procedure be capable of accurately describing the proton transfer itself. Recent calculations in this laboratory16-18 have pointed to SCF calcu- lations with the 4-31G basis set as providing proton transfer energetics in good agreement with more rigorous treatments including polarization functions and correlation con-

tributions (despite the poor treatment by this basis set of inversion barriers). While the seemingly similar 3-21G basis set has been shown previously to satisfy the first criterion of accurate proton affinity difference^,'^ it fails in the second regard as it can lead to qualitatively incorrect and potentially mis- leading description of proton transfer in some cases.19 For these reasons, the capability of the 4-31G basis set to accurately reflect alkylation effects on proton affinity is thor- oughly tested here.

METHODS AND RESULTS

All calculations were carried out at the SCF level within the framework of the 4-31G basis set.15 Geometries of all species were fully opti- mized using the gradient procedures con- tained within the G A U S S I A N - 8 0 package of programs.20 No assumptions were made concerning the symmetries of the mole- cules or their protonated ions. In cases where a number of different, approximately stag- gered conformations were possible (e.g., ethylamine), the geometry of each was opti- mized separately and the converged energies compared.

The fully optimized geometries of each spe- cies are reported in Tables I and I1 along with their SCF energies. Bond angles are denoted by 8 while 4 is used to represent dihedral angles. All configurations are fully staggered with the exception of protonated oxygen bases where the planar arrangement about the oxy- gen atom leads to some eclipsed arrange- ments as described below. In cases where the three hydrogens bonded to a single atom are not symmetrically identical, H, refers to the hydrogen lying in the symmetry plane and H, to the two others which are above and below this plane. For the ethyl substituents, C ” represents the C atom connected to the 0 or N and C p the next carbon.

With regard to specific molecules, the low- est energy conformation of ethylamine was that in which both amine hydrogens are gauche to the terminal methyl group. All three methyl hydrogens of dimethylamine are nonequivalent; H, refers to the hydrogen trans to the other methyl group, H,, is gauche to the methyl group and trans to the amine H, and H, is gauche to both of these. (Hgt and H, are of course identical in the protonated

170 Redfern and Scheiner

Table I. Geometries of nitrogen bases and corre- sponding protonated species. All distances in A and angles in degrees. 0 represents bond angles and 4 di- hedral angles.

~~

Parameter Base Base-H+

NH3 (Csv) 0.991

112.1 -56.45889

CHsNHz (C.1 1.450 0.994 1.089 1.081

116.4 114.5 109.4 68.8 52.5

-95.07166 CHaCHzNHz (CA

1.453 1.531

0.995 1.083 1.084 1.084

-

114.9

116.2 108.0 111.2 110.8 68.6 54.1 58.2 59.9

-

-134.05290 (CHdzNH (CJ

1.449 0.995 1.081 1.083 1.091

116.6 114.1 109.7 109.5 113.7 44.7 59.7 60.9

-134.04019

NHI' (Td 1.012

109.5 -56.10669

1.526 1.010 1.076 1.076

CH3NHs+ (CaV)

111.0 108.2 108.2 60.0 60.0

-95.44076 CH&HzNH3+ (C.1

1.541 1.517 1.010 1.010 1.078 1.081 1.082

110.1 111.2 110.6 106.0 108.8 111.9 59.8 62.2 62.0 61.4

-134.42695 (CH3)zNHz' (Czv)

1.514 1.009 1.076 1.077 1.077

113.6 109.2 109.0 108.4 108.4 58.0 59.9 59.9

-134.42069

molecule.) The H, and H, designations are used for the hydrogens bonded to oxygen. H, is trans to a hydrogen (H,) of the adjacent methyl group in CH,OH; the additional pro- ton is added as H,, cis to the same methyl hydrogen. Similarly, H, and H, are respec- tively trans and cis to the terminal methyl group in ethanol and its protonated species.

Table 11. Geometries of oxygen bases; distances in A and angles in degrees.

Parameter Base Base-H+

OH, (Czv) 0.951

111.2 -75.90864

CH30H (C.1 1.430 0.951

1.076 1.083

-

113.2

106.2 111.6 61.3

-

-114.87045 CH3CHZOH (C,)

1.435 1.513 0.951

1.084 1.083 1.081

-

107.1 113.5

110.2 110.8 110.1 59.6 59.9 59.6

-

- 153.85564 (C&)z0 (CPV)

1.422

1.077 1.085

-

116.0 106.8 111.1 60.8

- 153.83835

OH3+ (D3d 0.964

120.0 -76.20061

CH30Hz' (C.1 1.544 0.959 0.959 1.073 1.072

121.5 122.1 104.3 105.2 60.6

-115.18919 CH&HzOHz+ ((2.1

1.589 1.501 0.958 0.958 1.073 1.084 1.081

106.7 122.2 121.4 102.1 107.7 112.0 54.3 67.3 61.9

-154.18216 (CHdzOH' (Czv)

1.503 0.956 1.074 1.074

122.6 106.1 106.5 60.3

-154.17241

The geometries in Tables I and I1 exhibit a number of interesting features. The r(NH) bond lengths of the amines undergo a uniform increase from 0.99 A to 1.01 A as a result of protonation. The corresponding increase of r(OH) in the oxygen analogs is not quite as uniform, being 0.013 A for OH, and about 0.007 for the two alcohols. Protonation pro- duces a more pronounced stretch of the bonds to N and 0 involving carbon. r(NC) increases by 0.076 A in methylamine, by 0.088 in ethylamhe, and by the somewhat smaller amount of 0.065 A in dimethylamine. A simi-

Effects of Alkylation 171

lar trend of even greater magnitude is noted in the oxygen bases. The CO bond length is stretched by 0.114 A in methanol and by the larger amount of 0.154 A in ethanol, but the stretch in the disubstituted dimethyl ether is only 0.081 A. At the same time, smaller con- tractions occur in the bonds which are one removed from the site of protonation (i.e., CH bonds in methyl derivatives as well as CC bonds in the ethyl groups).

Protonation of each amine leads to a reduc- tion in the O(CNH) angle as a result of the greater separation needed between the amine hydrogens. On the other hand, the opposite trend of increased NCOH) and NCOC) angles are observed when the alcohols and ether are protonated, resulting in part from the planar arrangement about the oxygen center. (This planarity is probably an artifact of the un- polarized double-b basis 14) A secondary effect of the protonation is a decrease in the OCH and OCC bond angles.

The first column of Table I11 contains the proton affinities calculated here with the 4-31G basis set. These values are computed simply as the difference in total energy between each molecule and its protonated analog. The next column lists, for purposes of comparison, the protonation energies com- puted previously by Smith et al. using the similar 3-21G basis set. Experimentally mea- sured proton affinities are provided in the last column. However, a number of adjustments must be made to the theoretical values before comparisons are drawn with experiment. First, the theoretical quantities have not been corrected for vibrational energies. Pre- vious work by Del Bene et al. 21 has indicated that zero-point vibrations can lower the theo- retical proton affinities by up to 10 kcal/mol. Thermal corrections to vibrational and to ro- tational and translational energies have been neglected as well.

The theoretical proton affinit ies in Table I11 are clearly substantially greater than the experimental quantities. Although 4-31G values are somewhat lower than 3-21G data, both follow similar trends which are not unlike the experimentally observed al- kylation effects. These trends are more read- ily apparent in Table IV, in which the first row indicates the increase in proton affinity brought about by replacement of one hydro- gen of NH, by a methyl group. Addition of a

Table 111. Proton affinities (kcal/mol) of N and 0 bases.

4-31G 3-21G" expb

221.0 231.6 234.7 238.8 183.2 200.0 204.9 209.6

226.9 205.0 237.0 214.1 - 217.1

243.5 220.5 191.6 173.0 205.1 184.9 - 190.3

213.1 193.1

"From Ref. 13. 'From Ref. 8.

Table IV. Alkylation effects on proton affinities (kcal/mol) of N and 0 bases.

4-31G 3-21G" expb ~~ ~~ ~

10.6 10.1 9.1 3.1 - 3.0

[::H3) - CH3 7.2 6.5 6.4 16.8 13.5 11.9

0 C2H5-CH3 4.9 - 5.4 [:zH3) - CH3 9.6 8.0 8.2

N CzHs-CH3

"From Ref. 13. 'From Ref. 8.

second carbon to the methyl group is repre- sented by the second row (i.e., this row con- tains the difference in proton affinity between methylamine and ethylamine). Replacement of a second amine hydrogen by methyl is con- sidered in the third row (i.e., dimethylamine vs. methylamine). Analogous data for the oxygen bases are contained in the second half of the table.

As may be seen from the first row of Table IV, substitution of a single H of NH, by a methyl group raises the proton affinity by 10.6 kcal/mol with 4-31G, as compared to an experimental increment of 9.1. Elongation of the alkyl chain to an ethyl group further en- larges the proton affinity by the smaller in- crement of 3.1 kcal/mol which agrees nicely with the experimental value of 3.0. On the other hand, placement of a second methyl group on the N atom rather than on the methyl group (yielding dimethylamine) in- creases the proton affinity of methylamine by 7.2 kcal/mol (6.4 experimental). The trends observed in the oxygen bases are quali- tatively quite similar but are magnified somewhat. Replacement of the first H atom

172

by a methyl group raises the proton a f h i t y of OH, by 16.8 kcal/mol, as compared to 10.6 for the amines. As before, a greater increase is noted when the second methyl group is placed directly on the oxygen than on the already existing alkyl group.

It therefore appears that calculations at the SCF level with a 4-31G basis set are capable of providing estimates of the increases in proton affinity caused by alkyl substituents in quite reasonable accord with experiment. One pos- sible source of disagreement noted above is the neglect of zero-point vibrational energies. However, while these terms do contribute sig- nificantly to the absolute proton affinities, it is unlikely that there would be much varia- tion from one molecule to the next in a given series. We therefore expect the alkylation effects in Table IV to be little affected by vibrational energies. Similar arguments apply to the effects of correlation upon the relative proton affinities which we expect to be quite sma11.12-14 As a final point, Eades et al. have provided evidence that basis set superposition introduces only very small errors into the computed proton affinities.”

In conclusion, our calculations indicate that the 4-31G basis set is capable of re- producing the experimental trends of al- kylation effects upon proton affinities of both oxygen and nitrogen bases. Introduction of a methyl group increases the protonation en- ergy by a large amount (-10 kcal/mol). A smaller increment results from addition of a second methyl group. This effect is greater if the second group is bonded directly to the 0 or N atom than if to the first methyl group.

This work was supported by grants from the Na- tional Institutes of Health (GM29391 and AM01059) and the Research Corporation. Allocations of com- puter time were made available by the SIU Computing Center.

Redfern and Scheiner

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