ARTICLE pubs.acs.org/JPCA
Partial Proton Transfer in a Molecular Complex: Assessments From Both the Donor and Acceptor Points of View Galen Sedo† and Kenneth R. Leopold* Department of Chemistry, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States
bS Supporting Information ABSTRACT: Microwave spectra have been observed for the gas phase complexes (CH3)314N-H14NO3 and (CH3)315NH14NO3 and rotational and nuclear quadrupole coupling constants are reported. The structure and binding energy have also been calculated at the MP2 level of theory using the 6-311þþG(d,p) and 6-311þþG(2df,2pd) basis sets both with and without corrections for basis set superposition error. The HNO3 forms a nearlinear hydrogen bond to the amine nitrogen with a rather short hydrogen bond distance of about 1.5-1.6 Å (depending on the basis set and method of computation). The C3 axis of the trimethylamine lies in the plane of the nitric acid. For both the H14NO3 and the (CH3)314N moieties of the parent species, the component of the nuclear quadrupole coupling tensor perpendicular to the molecular symmetry plane, χcc, is sensitive to the electronic structure at the corresponding nitrogen but independent of relative orientation within the plane. Its value, therefore, provides a convenient experimental measure of the degree of proton transfer within the complex. For the HNO3, χcc lies 62% of the way between those of free HNO3 and aqueous NO3-, indicating a substantial degree of proton transfer. A similar comparison of the quadrupole coupling constant of (CH3)3N in the (CH3)3N-HNO3 complex with those of free (CH3)3N and (CH3)3NHþ indicates only about 31% proton transfer, about half that determined from the HNO3 coupling constant. Though surprising at first, this disparity is to be expected if the quadrupole coupling constants vary nonlinearly with the position of the proton relative to the donor and acceptor atoms. Calculations of the 14N nuclear quadrupole coupling constants as a function of proton position using density functional theory are reported and confirm that this is the case. We suggest that when proton transfer is assessed according to changes in individual monomer molecular properties, the overall process may be best described in terms of a dual picture involving proton release by the acid and proton acquisition by the base.
’ INTRODUCTION Proton transfer reactions play a pivotal role in chemistry, comprising critical steps in numerous chemical1 and biological2 mechanisms. Indeed, the recognition of their importance dates back many decades and is, perhaps, epitomized by their role in the fundamental definition of acids and bases first proposed by Brønsted3 and Lowry.4 Although proton transfer processes are most common in solution-phase environments, a valuable approach to their understanding has involved the study of small molecular complexes in the gas phase. Detailed studies of the interaction between an acid and a base help to characterize the potential surface on which proton transfer takes place and results from a series of related systems allow the effects of acidity or basicity to be assessed. A disadvantage of the cluster approach is that the systems often lack the stabilizing influence of solvent and are therefore too small to fully accomplish proton transfer. Nevertheless, the sequential addition of solvent molecules to an acidic solute has been explored in a number of cases, and has provided opportunities to observe an acid in the earliest stages of its solvation5-16 The influence of chemical substitution on proton transfer has also been investigated in an extensive series of studies on amine-hydrogen halide complexes.17 Recent work in our own laboratory has involved the application of microwave spectroscopy to the study of the sequential hydration of r 2011 American Chemical Society
nitric acid. Building on an earlier report on HNO3-H2O,18 we examined the complexes HNO3-(H2O)213 and HNO3-(H2O)314 and observed an increasing degree of proton transfer with the addition of each new water molecule to the complex. Initially, we employed a structural approach to quantifying proton transfer, but in the case of HNO3-(H2O)3, the 14N nuclear quadrupole coupling was also used. In particular, by analyzing nuclear quadrupole coupling constants, we determined that in the trihydrate, the proton transfer is about a third complete, at least as viewed from the perspective of the proton donor (HNO3). However, with no quadrupolar nuclei on water, these measurements did not allow for an independent confirmation from the point of view of the proton acceptor. In this work, we use rotational spectroscopy to examine the degree of proton transfer in the complex formed from trimethylamine and nitric acid. With 14N nuclei in both the acid and the base, quadrupole coupling data can be used to assess proton transfer from both the donor and acceptor points of view. While such an approach, in principle, could be applied to the H3NHNO3 complex studied previously in our laboratory,19 the Received: September 16, 2010 Revised: January 6, 2011 Published: February 22, 2011 1787
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Table 1. Spectroscopic Constants of the Nitric AcidTrimethylamine Complexa (CH3)314N 14
H NO3
(CH3)315N H14NO3
A B
3654.80(17) 1048.85105(11)
3653.53(23) 1044.39648(17)
C
979.41064(10)
975.52208(16)
ΔJ
0.0001996(47)
ΔJK
0.001273(24)
χaa [HNO3]
0.0001491(52) 0.001428(39)
-0.3504(11)
-0.3496(13) -0.4142(36)
(χbb - χcc) [HNO3]
-0.4036(28)
χaa [N(CH3)3]
-3.28901(63)
(χbb - χcc) [N(CH3)3] σ (rms)b
-0.5810(16) 0.0025
0.0046
a
Figure 1. The 322 r 221 transition of (CH3)314N-H14NO3 (top) and (CH3)315N-H14NO3 (bottom) showing 14N nuclear hyperfine structure.
(CH3)3N system has two advantages for the present purpose: (1) Because of increased methylation of the amine, the degree of proton transfer is expected to be larger and therefore more easily measured, and (2) the large moments of inertia of the trimethylamine minimize the effects of large amplitude motion on the interpretation of the coupling constants. Ab initio calculations of the structure and binding energy for both complexes, and of the 14N nuclear quadrupole coupling constants for the trimethylamine complex, are also presented. Taken together, the experimental and theoretical results cast an interesting light on the way in which we should view proton transfer in simple acid-base systems.
’ EXPERIMENTAL METHODS AND RESULTS Rotational spectra of (CH3)314N-H14NO3 and (CH3)315N14 H NO3 were recorded using a pulsed-nozzle Fourier transform microwave spectrometer. Instrumental details have been given elsewhere.20 To limit mixing times and reduce the formation of solid (CH3)3NHþNO3-, gaseous complexes were formed in situ using an injection source, similar to that previously employed in our laboratory.18,19 Specifically, a mixture containing 0.35% trimethylamine in argon was pulsed into the instrument through a 0.8 mm diameter nozzle at a stagnation pressure of 1 atm and a repetition rate of 5 Hz. In addition, the vapor from a liquid sample of 90% nitric acid was allowed to flow continuously into the early part of the supersonic expansion via a stainless steel needle with an inner diameter of 0.016 in. The observed signals required the simultaneous presence of both HNO3 and (CH3)3N. For the isotopically enriched (CH3)315N-H14NO3 complex, 15N-trimethylamine was synthesized using literature procedures21 and the appropriate isotopic reagents. All spectra were recorded over 500 gas pulses with the resulting signal averaged over 3000 free induction decay signals. A total of 111 and 37 a-type rotational transitions (counting individual hyperfine components) were observed for the parent and 15N substituted complexes, respectively, and no evidence of internal rotation was observed. Sample spectra showing the 322 r 221 transition of each isotopologue are given in Figure 1 and complete lists of rotational transition frequencies are provided as Supporting Information. The observed spectra were fit using the SPFIT program of Pickett.22 Transition frequencies were analyzed using a Hamiltonian of the form23 H ¼ H Rot þ H Q ð1Þ
All values are in megahertz. Numbers in parentheses are one standard error in the least-squares fit. b Root mean square of the residuals from the least-squares fit.
where HRot is Watson’s A-reduced Hamiltonian including quartic centrifugal distortion terms, viz. ðB þ CÞ ðB þ CÞ - ΔJ J 2 J 2 þ A - ΔJK J 2 H Rot ¼ 2 2 ðB - CÞ 2 2 2 - 2δJ J ðJ 2x - J 2y Þ - ΔK J z J z þ 2 - δK ½J 2z ðJ 2x - J 2y Þ þ ð J 2x - J 2y ÞJ 2z and HQ is given by H Q ¼ H Q ðN1Þ þ H Q ðN2Þ
ð2Þ ð3Þ
Each term in eq 3 represents the usual Hamiltonian describing the nuclear electric quadrupole interaction for a single nucleus.23 For the 15N(CH3)3 complex, I2 = 1/2 and HQ(N2) = 0. A, B, and C in eq 2 are rotational constants, and the deltas are centrifugal distortion constants. Following close examination of the data set and a series of preliminary fits, it was determined that only the ΔJ and ΔJK distortion constants were needed to fit the observed rotational frequencies. Thus, in the final analysis, the remaining quartic distortion constants were omitted, effectively constraining them to zero. The 14N nuclear quadrupole coupling for the parent species was treated according to standard methods23 using a | J, K, F1,F æ basis, viz. ð4Þ J þ I1 ¼ F1 and F1 þ I2 ¼ F
ð5Þ
where I1 refers to the HNO3 nitrogen spin and I2 corresponds to that of the trimethylamine. For (CH3)315N-H14NO3, since I2 = 1/2 and HQ(N2) = 0, a simple | J, K, F æ basis was used. The experimentally determined rotational, centrifugal distortion, and nuclear quadrupole coupling constants, along with their standard errors from the leastsquares fit, are listed in Table 1. Note that the determination of the HNO3 quadrupole coupling constants in the 15N(CH3)3 substituted form allows those of the parent complex to be unambiguously associated with their respective nuclei.
’ COMPUTATIONAL METHODS AND RESULTS Ab initio calculations were performed to determine minimum energy structures and binding energies using second order 1788
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Table 2. Calculated Binding Energies and Selected Bond Lengths in H3N-HNO3 and (CH3)3N-HNO3a MP2/6-311þþG(2df, 2pd) non-CPC
CPC
Table 3. Comparison between Experimental and Computed Rotational Constantsa experiment
MP2/6-311þþG(d,p) non-CPC
13.8
12.3
14.3c
11.6
R(H1-N2) [Å]b R(O1-H1) [Å]
1.668 1.016
1.707 1.011
1.684c 1.013c
1.757 1.006
R(N1-N2) [Å]
3.326
3.364
3.357
3.431
18.3
15.5
18.4
14.1
R(H1-N2) [Å]
1.495
1.571
1.518
R(O1-H1) [Å]
1.070
1.048
1.061
1.033
R(N1-N2) [Å]
3.259
3.319
3.287
3.388
1.634
Atom number is defined in Figure 2. “CPC” refers to counterpoise corrected calculations. b Experimental value from ref 19 is 1.736(63) Å. c These values are in perfect agreement with those previously determined by Tao (ref 30). a
Figure 2. Equilibrium structures of (a) H3N-HNO3 and (b) (CH3)3N-HNO3 calculated at the MP2/6-311þþG(2df,2pd) level/ basis without counterpoise corrections.
Møller-Plesset perturbation theory24,25 and the Gaussian ’03 program package.26 Structural optimizations employed the Pople extended 6-311þþG(d,p) and 6-311þþG(2df,2pd) basis sets27 using the frozen core approximation, and calculations were performed both with and without corrections for basis set superposition error.28 The full series of complexes, (CH3)nH(3-n)NHNO3 [n = 0-3], was investigated but only results for the ammonia and trimethylamine species (for which experimental results also exist) are reported here. Details of the calculations on the mono- and dimethylamine systems may be found elsewhere.29 Structural optimizations were initiated at multiple starting geometries with the amine oriented either in or above the plane of the nitric acid and forming a hydrogen bond with the acidic proton. Table 2 contains the optimized binding energies and selected structural parameters obtained for both complexes. The equilibrium structures are shown in Figure 2. For both systems, the acid forms a near-linear hydrogen bond to the amine nitrogen, and the pseudo-C3 axis of the (slightly distorted) amine lies in the plane of the HNO3. For H3N-HNO3, the calculations properly reproduce MP2/6-311þþG(d,p) results of Tao,30 and the hydrogen bond length is in reasonable agreement with the experimental value of 1.736(63) Å.19 The MP2/6-311þþG(d, p) calculations with counterpoise correction provided the best prediction of the hydrogen bond distance, giving a value only 0.021 Å larger than experiment.31 For (CH3)3N-HNO3,
A
3654.80(17)
3704
-49
B C
1048.85105(11) 979.41064(10)
1045 975
4 4
(CH3)315N-H14NO3
(CH3)3N-HNO3 ΔEbind [kcal/mol]
experiment - theory
(CH3)314N-H14NO3
CPC
H3N-HNO3 ΔEbind [kcal/mol]
theoryb
A
3653.53(23)
3704
-50
B
1044.39648(17)
1040
4
C
975.52208(16)
971
5
a
All values in megahertz. b Calculated from the MP2/6-311þþG(2df, 2pd) optimized structure without the counterpoise correction.
a similar comparison cannot be made, as only two isotopologues were studied and the hydrogen bond length has not been determined. For the rotational constants, most calculations were in reasonable agreement with experiment, though no one calculation was uniformly superior to the rest. A comparison of observed and calculated rotational constants of (CH3)3N-HNO3 from the MP2/ 6-311þþG(2df,2pd) calculations is given in Table 3 and demonstrates quite good agreement. Complete sets of Cartesian coordinates from the MP2/6-311þþG(2df,2pd) calculations are provided as Supporting Information. The interaction of HNO3 with trimethylamine is seen to be stronger than that with ammonia by about 2.5-4.5 kcal/mol (depending on the calculation), consistent with the increase in basicity upon methylation. Correspondingly, the hydrogen bond length in (CH3)3N-HNO3 is about 0.17 Å shorter than that of H3N-HNO3 using either basis set without the counterpoise correction (0.12-0.13 Å with the counterpoise correction). The calculations further indicate an increase in the OH bond length in the nitric acid when ammonia is replaced by trimethylamine. It is interesting to note that this increase is rather small (in the 0.030.05 Å range, depending on the calculation) compared with the shortening of the hydrogen bond. For both H3N-HNO3 and (CH3)3N-HNO3, the 3-fold barrier to internal rotation of the amine about the hydrogen bond axis was determined in a series of calculations in which the amine was rotated in increments of 2 and remaining structural parameters optimized. The barriers obtained using the MP2/ 6-311þþG(d,p) level/basis were 63 and 342 cm-1 for the NH3 and (CH3)3N complexes, respectively. Finally, for reasons discussed below, nuclear quadrupole coupling constants for both nitrogens of the (CH3)3N-HNO3 complex were calculated as a function of OH and NH distances. Since quadrupole coupling constants depend on the electric field gradient at a nucleus resulting from all charges external to that nucleus, the EPR-III basis set32 was used, as it is optimized for properties sensitive to the core electron distributions. Density functional theory was employed due to its computational efficiency. In a series of calculations, the OH bond length was held fixed, and the geometry of the complex optimized with respect to the remaining atomic positions. Quadrupole coupling constants were calculated in the principal axis system of the complex, and the resulting values of χcc are plotted as a function of OH and NH distances in Figure 3 panels a and b, respectively. Note that using the B3LYP/EPR-III method/ basis, the value of χcc for the HNO3 nitrogen at the calculated, 1789
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Figure 3. Calculated values of χcc (MHz) for (a) HNO3 as a function of OH bond length and (b) (CH3)3N as a function of NH bond length. See text for details.
Table 4. Values of χcc, QAPT, and QBPT for Complexes of HNO3 complex H14NO3-H2O H14NO3-(H2O)2 H14NO3-(H2O)3 H14NO3-14NH3 H14NO3-14N(CH3)3
χcc(HNO3)/ χcc(amine)/ MHz MHz 0.0749(45)c 0.1489(45)d 0.2060(70)e 0.1738(60)f 0.3770(15)g
1.9350(9)f 1.6603(43)g
QAPT (%)a
QBPT (%)b
21 ( (1,4) 31 ( (1,5) 39 ( (1,6) 34 ( (1,6) 18.8 ( 0.2 62 ( (1,10) 31.2 ( 0.1
Obtained from eq 11 using χccFreeAcid = -0.0773(51) MHz (ref 38) and χccAnion = 0.656(5) MHz (ref 40). Two uncertainties are given for each value. The first number in parentheses represents a statistical uncertainty, derived using experimental uncertainties in χcc values for HNO3, the complex, and NO3-(aq). The second number in parentheses represents an estimate of the possible systematic error resulting from the use of and aqueous phase value for the coupling constant of NO3-. See text for discussion. The coupling constant for NO3-(aq) was given in the original work without an estimate of the uncertainty and thus a value of (0.005 MHz has been assumed in determining the statistical uncertainty. b Obtained from eq 12 using χ^ = 2.7512 MHz for (CH3)3N (ref 34) and 2.0449 MHz for NH3 (ref 45). c Data of ref 18. d Data of ref 13. e Data of ref 14. f Data of ref 19. g This work. a
lowest energy structure is 0.141 MHz, which is smaller by a factor of 2.7 than the experimental value of 0.3770 MHz reported in Table 4 (i.e., χccobs/χcccalc = 2.7). In general, the B3LYP/EPR-III calculations gave values of χaa, χbb, and χcc for HNO3 that were accurate to within 250 kHz, small on an absolute scale, but relatively large, given the small magnitude of the experimental constants. For the (CH3)3N, the absolute errors were larger, typically between 400-1000 kHz, but since the (CH3)3N constants are also larger, the relative error was in the 20-30% range.33 As discussed below, however, the goal of these calculations was not a systematic study aimed at obtaining the best agreement with experiment, but rather a qualitative representation of the dependence of χcc on R(OH) and R(NH). Further exploration of basis sets and computational methods, therefore, was not pursued.
’ DISCUSSION Although only two isotopic forms of the (CH3)3N-HNO3 complex have been studied, the identity of the observed species is unambiguously established on the basis of several independent pieces of evidence. First, as noted above, the observed signals required both HNO3 and (CH3)3N to be present in the jet. Second, the spectra of the parent species clearly display hyperfine structure resulting from two nuclei with spin equal to one, and substitution of 15N (I = 1/2) on the amine eliminates one of the quadrupolar nuclei. Moreover, the coupling constants for the remaining nucleus are virtually identical to those of the HNO3 in the parent form of the complex, positively establishing the correspondence between the coupling constants and their respective nuclei. A third piece of evidence is the excellent agreement between the experimentally determined rotational constants and those calculated from the structures described in the previous section. Table 3 lists the experimental and calculated rotational constants from the MP2/6-311þþG(2df,2pd) calculations (without counterpoise corrections), and demonstrates the B and C rotational constants are predicted to within 4 MHz (0.4%), while the A rotational constant is accurate to within about 50 MHz (1.4%). Finally, as demonstrated by the bottom half of Table 3, the small isotopic shifts observed upon 15N substitution on the (CH3)3N are fully reproduced by the calculated structure. All in all, the available evidence leaves no doubt that the observed spectra are those of (CH3)3N-HNO3. The main focus of this study is the degree of proton transfer between the nitric acid and the trimethylamine. In previous work,14 we have used two methods of quantifying proton transfer. The first, based on structural data, involves the proton transfer parameter,35 F, defined in general by complex
F ¼ ðrOH
complex 3 3 3N
free - rOH Þ - ðrH
- rHfree
Þ 3 3 3N
ð6Þ
and rfree For (CH3)3N-HNO3, rcomplex OH OH are the O1-H1 bond lengths in the complex and in free nitric acid, respectively. See Figure 2 for atom numbering. rcomplex H 3 3 3 N is the hydrogen bond length in the complex (i.e., the H1 3 3 3 N2 distance) and rfree H 3 3 3 N is the H1-N2 distance in the covalent species that would be formed in the event of complete proton transfer (i.e., the NH bond length in (CH3)3NHþ). When the proton is nearer to the acid than the base (i.e., little proton transfer), the first term is small, giving a negative value of F. On the other hand, when the proton is close to the base (i.e., a large degree of proton transfer), the second term is small and F is positive. Equal proton sharing between the acid and the base is indicated when F = 0. Values of F obtained from the MP2/6-311þþG(2df, 2pd) calculated structures of H3N-HNO3 and (CH3)3N-HNO3 are -0.60 and -0.37 Å, respectively, indicating significantly more advanced proton transfer in the latter complex36 Both values are negative, however, a result interpreted to mean that in both complexes the HNO3 proton is still more closely associated with the acid. The proton transfer parameter is useful for comparing members of a related series of complexes, but since the limiting hydrogen bond length cannot be precisely specified, it does not offer a well-defined “value” for the degree of proton transfer. In our recent study of HNO3-(H2O)3, however, we employed 14N nuclear quadrupole coupling constants as an alternate means of assessing proton transfer. By comparing the coupling constants of the complex with those of free HNO3 and aqueous NO3-, the electronic structure of the nitric acid in the complex could be 1790
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compared with that in these two limiting cases. However, since the measured coupling constants of the complex are referred to its principal axis system, the comparison must be made in such a way that the geometry of the complex is properly taken into account. This is easily done by examining the component of the quadrupole coupling tensor perpendicular to the HNO3 plane. Since this method is also used here to analyze the data for (CH3)3N-HNO3, a brief summary is given below. The eigenvalues of the quadrupole coupling tensor of HNO3 (χXX, χYY, and χZZ) are well-known, as is the orientation of its principal axis system, (X,Y,Z), within the molecule.37,38 For complexes such as HNO3-(H2O)n (n = 1 - 3), which are planar except for some out-of-plane hydrogens, the c-inertial axis of the complex is parallel to the c-axis of HNO3, that is, perpendicular to the HNO3 plane. Thus, to the extent that the nitric acid is unperturbed upon complexation, the observed quadrupole coupling constants for the complex are related to χXX, χYY, and χZZ by a second rank tensor transformation corresponding to rotation about the axis perpendicular to the HNO3 plane, viz. χaa ¼ χXX cos2 θ þ χYY sin2 θ ðχbb - χcc Þ ¼ χXX ð1 þ sin2 θÞ þ χYY ð1 þ cos2 θÞ χcc ¼ χZZ
ð7Þ ð8Þ ð9Þ
Here, θ is the angle formed between the X-axis of free HNO3 and the a-inertial axis of the complex, and χaa and (χbb - χcc) are the coupling constants referred to the principal axis system of the complex, obtained directly from the microwave spectra (Table 1). The value of χcc is readily determined from experimental quantities by exploiting the traceless character of the quadrupole coupling tensor, so that 1 χcc ¼ - ½χaa þ ðχbb - χcc Þ 2
ð10Þ
χXX, χYY, and χZZ depend on the electric field gradient at the 14N nucleus resulting from all charges external to that nucleus, and therefore contain information about the electronic structure of the HNO3. Thus, from eqs 7-9, it is evident that the values of χaa and (χbb - χcc) depend both on the electronic structure of the HNO3 (via their dependence on χXX, χYY, and χZZ) and on the orientation of the HNO3 in the complex (because of their dependence on θ). χcc, however, depends only on electronic structure. Thus, if the HNO3 were unchanged upon complexation, χcc would be invariant across the series of complexes in which the c-inertial axis remains parallel to the HNO3 plane. Observed changes in χcc, on the other hand, reflect changes in the electronic structure of the nitric acid due to complexation and may be interpreted as a measure of progress between the limits of HNO3 and NO3-. Although (CH3)3N-HNO3 is not planar, the pseudo-3-fold symmetry axis of the amine lies in the HNO3 plane and the c-axis of the complex is still parallel to that of HNO3. Thus, the same approach used for water complexes above may be applied to (CH3)3N-HNO3 as well. For all of these systems, it is convenient to define a “proton transfer quotient”,39 QAPT, such that A QPT ¼
χcomplex - χFreeAcid cc cc 100% Anion χcc - χFreeAcid cc
ð11Þ
where the superscript “A” is used to indicate that the parameter is and χAnion are the based on the coupling of the acid. χFreeAcid cc cc coupling constants for free HNO3 and NO3 , respectively, and
define limiting values in which there is no proton transfer and complete proton transfer, respectively. QAPT provides a measure of where the complex lies between these two limits. Using values of χcc = -0.0773(51) MHz for free HNO338 and 0.656(5) MHz for aqueous nitrate ion,40,41 QAPT can be computed for (CH3)3NHNO3, as well as the aqueous complexes HNO3-(H2O)n (n = 1 - 3). These values are given in Table 4. See below for a discussion of the uncertainties listed. Also included in the table is the value for HNO3-NH3 obtained from previously reported quadrupole coupling constants.19 Note that the value of χcc = 0.656 MHz used above for the nitrate ion is that measured in aqueous solution. This seems most appropriate for use with the water complexes and it is, in turn, sensible to use this value with the amine complexes as well to provide the most direct comparison. Since the coupling constant depends on the electric field gradient at the nitrogen nucleus,42 it is primarily sensitive to chemical bonding within the moiety and is expected to be much more sensitive to proton transfer than to intermolecular interactions. Thus, while it is certainly possible that proton transfer could be complete before the anion is fully solvated, any further changes in χcc following the proton’s release are expected to be small. In short, QAPT, in the strictest sense, is a measure of where the complex lies between the limits of HNO3(g) and NO3-(aq), but to the extent that the coupling constant stops changing once the proton is released, it is also a reasonable measure of proton transfer. To obtain some measure of the effect of solvation on the value and hence assess any systematic error arising from the of χAnion cc use of an aqueous phase value, we note that the 14N coupling constant in crystalline NaNO3 is 0.745 MHz, about 14% higher than that for NO3-(aq). This provides a crude measure of how much the “true value” may be altered by environmental effects. With this in mind, uncertainties in QAPT were calculated in two ways. The first employs only the experimental uncertainties in the quadrupole coupling constants used in the calculation and thus reflects a “statistical” uncertainty. These values are given as the first number in parentheses in Table 4. The second method includes the range in which are 14% above and values obtained using values of χAnion cc below that from aqueous solution and reflects the effect of a . These values are given as systematic error in the choice of χAnion cc the second number in parentheses in Table 4. The statistical uncertainties are useful for comparing trends among values of QAPT since each computed value is subject to the same systematic . The systematic errors are important to consider when error in χAnion cc comparing values of QAPT with QBPT (defined below), since the latter does not employ any value for the quadrupole coupling constant of the NO3- anion. The value of 62% obtained for the degree of proton transfer in (CH3)3N-HNO3 is large and undoubtedly reflects the higher basicity of trimethylamine compared with NH3 or H2O. It is interesting to note that on the basis of the nitric acid coupling constants, one trimethylamine molecule does more to promote release of the proton than do three water molecules and one ammonia produces an effect similar to that of two to three water molecules. As noted in the Introduction, observation of the (CH3)314N14 H NO3 complex allows the degree of proton transfer to be independently assessed from the point of view of the trimethylamine. The ab initio calculations above confirm that the pseudoC3 axis of the (CH3)3N also lies in the HNO3 plane, and thus the perpendicular component of its quadrupole coupling tensor is also parallel to the c-inertial axis of the complex. Hence, we define 1791
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a second proton transfer quotient, QBPT, such that B ¼ QPT
χcomplex - χTMA cc ^ 100% þ TMAH χcc - χTMA ^
ð12Þ
where the superscript “B” refers to the base in general and “TMA” refers specifically to trimethylamine. Using the literature value34 of χo = -5.5024(25) MHz for (CH3)3N (which is the = 2.7512(13) value along the (CH3)3N axis), a value of χTMA ^ MHz is obtained43 for free (CH3)314N. The quadrupole coupling constant of (CH3)3NHþ has not been determined experimentally, but B3LYP/6-311þþG(2df,2p) calculations give a value of -0.2644 MHz,44 corresponding to a perpendicular component equal to þ0.1322 MHz. Since this is a computed value, the error is not known. However, at the same level of theory, the coupling constant for (CH3)3N was in agreement with experiment to within 8%,44 and thus we have assumed a ( 8% error in when calculating the uncertainty in QBPT. Fortunately, χTMAHþ cc = 2.7512(13) MHz, it is much larger in magnitude since χTMA ^ , whose value is indeed expected to be small since than χTMAHþ cc the ion is nearly spherically symmetric. Thus QBPT is only weakly dependent on the value chosen. Using the values of χaa and (χbb - χcc) given in Table 1 for the (CH3)314N in (CH3)314N= 1.9350(9) MHz and hence a value of H14NO3 gives χComplex cc QBPT = (31.2 ( 0.1)%. A similar calculation for H3N-HNO3 using previously determined hyperfine constants19 and known quadrupole coupling constant for NH3 (-4.08983 MHz)45 gives a value of QBPT= (18.8 ( 0.2)%. Here, we note that the coupling constant for NH4þ is identically zero by symmetry. Values for both the (CH3)3N and NH3 complexes are included in Table 4. The proton transfer quotients for the HNO3 and (CH3)3N moieties of (CH3)3N-HNO3 differ by a factor of 2 and a similar disparity is observed for the complex with NH3. This raises the obvious questions: (i) Should these quotients necessarily agree and (ii) what does the disagreement between them mean? Regarding the first question, if proton transfer involved the direct movement of increasing fractions of a proton from the acid to the base, then any meaningful measures of proton transfer should agree. But of course, the notion of splitting a proton in this way is nonsensical. Moreover, since there is no sharp boundary between the acid and base, the “degree of proton transfer” is somewhat ill defined, indeed defined only by the method used to measure it.46 The quadrupole coupling constants used in this work are physical properties of the individual moieties which depend on molecular electric field gradients, and hence on the existence or nonexistence of chemical bonds. It is through this dependence that each moiety reports its view of where the complex lies in the continuum between hydrogen bonding and ion pair formation. However, the rate of change of the quadrupole coupling constants is likely to be very nonlinear between these limits. In the HNO3, for example, rapid change is expected when the O-H bond is only slightly longer than that in free HNO3 (i.e., when the bond is “beginning to break”), but these changes are expected to slow as the proton gets far from the oxygen. Conversely, in the early phases of the proton release from the acid, new bond formation to the amine is negligible, as the proton is still far from the nitrogen. The concomitant changes in the amine coupling constants should therefore be small. Only when the N-H bond distances approaches that in (CH3)3NHþ will there be a significant amount of new bond formation, and hence rapid changes in the 14N quadrupole coupling constants. Thus, it is entirely reasonable that as the O-H bond is broken, the HNO3 quadrupole coupling constants will undergo
much of the full change they would experience between the hydrogen bonded and ion paired limits, while the N(CH3)3 will show much smaller changes. The DFT calculations reported above support this point of view at least qualitatively. Indeed, from Figure 3 it is clear that the most rapid change in χcc of the nitric acid occur at short OH distances, while the most rapid changes for the trimethylamine occur at short NH distances. This result is similar to that previously obtained for (CH3)3N-F2 and (CH3)3N-ClF.44 The above line of reasoning suggests that from a practical standpoint it may be appropriate to regard the proton transfer process as arising from component processes of “proton release from the acid” and “proton acquisition by the base”. Each can be quantified experimentally and each reflects the extent to which individual moieties have been impacted by the degree of proton transfer. However, “equity” is not a requirement, that is, proton release by the acid does not necessarily imply equal proton acquisition by the base, at least in the intermediate regime between hydrogen bonding and complete proton transfer. Indeed, we might fully expect that evidence of proton acquisition by the base should lag that of proton release from the acid. This dual description may turn out to be more useful than simply discussing “proton transfer”, as it directly relates to the experimentally observable properties of the individual acid and base.
’ CONCLUSIONS The complex (CH3)3N-HNO3 has been studied by spectroscopic and computational methods. As expected, the system forms a near-linear hydrogen bond involving the HNO3 proton and the nitrogen of the trimethylamine, with the pseudo-C3 axis of the (slightly distorted) amine in the HNO3 plane. The calculated binding energy is 18.3 kcal/mol, and the computed hydrogen bond length is 1.495 Å using the MP2/6-311þþG(2df, 2pd) level/basis (15.5 kcal/ mol and 1.571 Å with counterpoise corrections). This system was chosen because it is a strongly hydrogen-bonded complex with nitrogen atoms on both the acid and base. This feature allows changes in the electronic structure of the interacting moieties to be assessed through nuclear electric hyperfine interactions, and we have argued that χcc, the component of the nuclear quadrupole coupling tensor along the c-inertial axis of the complex, is most useful for this purpose. The changes in electronic structure upon complexation reflected in these coupling constants are interpreted as measures of the degree of proton transfer. For the HNO3 moiety, the value of χcc for the complex lies 62% of the way between that of free HNO3 and that of aqueous NO3-. For the trimethylamine moiety, χcc lies only 31% of the way between that of free N(CH3)3 and HN(CH3)3þ. Thus, the degree of proton transfer reported by the acid and the base differ substantially, with the base lagging by a factor of 2. This seemingly surprising result arises because χcc for the HNO3 varies more rapidly than that of the N(CH3)3 as the OH bond is just beginning to break and suggests that the position of the proton may, in some cases, be less important than the effect its position has on the physical properties of the interacting moieties. Thus, it might be useful to conceptually divide the proton transfer process into an early (proton release) phase and a later (proton acquisition) phase. In the former, the properties of the acid change most rapidly, while in the latter, the properties of the base change most rapidly. ’ ASSOCIATED CONTENT
bS
Supporting Information. Tables of observed microwave frequencies, assignments, and residuals from the least-squares fits for (CH3)314N-H14NO3 and (CH3)315N-H14NO3 and Cartesian
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The Journal of Physical Chemistry A coordinates from MP2/6-311þþG(2dp, 2df) calculations for (CH3)3N-HNO3, H3N-HNO3, and constituent monomers. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
Department of Chemistry, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.
’ ACKNOWLEDGMENT This work was supported by the National Science Foundation (Grants CHE 0514256 and CHE 0845290), the donors of the Petroleum Research Fund, administered by the American Chemical Society, and the Minnesota Supercomputer Institute. ’ REFERENCES (1) Bell, R. P. The Proton in Chemistry, 2nd ed.; Cornell University Press: Ithaca, NY, 1973. (2) Berg, J. M.; Tymoczko, J. L.; Stryer, L. Biochemistry, 6th ed.; W.H. Freeman and Co.: New York, 2007. (3) Br€onsted, J. N. Recl. Trav. Chim. Pays-Bas 1923, 42, 718. (4) Lowry, T. M. Trans. Faraday Soc. 1923, 18, 285. (5) Leopold, K. R. Annu. Rev. Phys. Chem. 2011, in press, and references therein. Web release date: January 3, 2011. (6) Priem, D.; Ha, T.-K.; Bauder, A. J. Chem. Phys. 2000, 113, 169. (7) Kisiel, Z.; Biazkowska-Jaworska, E.; Pszczozkowski, L.; Milet, A; Struniewicz, C.; Moszynski, R.; Sadlej, J. J. Chem. Phys. 2000, 112, 5767. (8) Kisiel, Z.; Pietrewicz, B. A.; Desyatnyk, O.; Pszczozkowski, L.; Struniewicz, I; Sadlej, J. J. Chem. Phys. 2003, 119, 5907. (9) Hurley, S. M.; Dermota, T. E.; Hydutsky, D. P.; Castleman, A. W., Jr. J. Chem. Phys. 2003, 118, 9272. (10) Huneycutt, A. J.; Stickland, R. J.; Hellberg, F.; Saykally, R. J. J. Chem. Phys. 2003, 118, 1221. (11) (a) Weimann, M.; Farník, M.; Suhm, M. A. Phys. Chem. Chem. Phys. 2002, 4, 3933. (b) Farník, M.; Weimann, M.; Suhm, M. A. J. Chem. Phys. 2003, 118, 10120. (12) Hunt, S. W.; Higgins, K. J.; Craddock, M. B.; Brauer, C. S.; Leopold, K. R. J. Am . Chem. Soc. 2003, 125, 13850. (13) Craddock, M. B.; Brauer, C. S.; Leopold, K. R. J. Phys. Chem. A 2008, 112, 488. (14) Sedo, G.; Doran, J. L.; Leopold, K. R. J. Phys. Chem. A 2009, 113, 11301. (15) Ouyang, B.; Starkey, T. G.; Howard, B. J. J. Phys. Chem. A 2007, 111, 6165. (16) Ouyang, B.; Howard, B. J. Phys. Chem. Chem. Phys. 2009, 11, 366. (17) Legon, A. C. Chem. Soc. Rev. 1993, 153 and references therein. (18) Canagaratna, M.; Phillips, J. A.; Ott, M. E.; Leopold, K. R. J. Phys. Chem. A 1998, 102, 1489. (19) Ott, M. E.; Leopold, K. R. J. Phys. Chem. A 1999, 103, 1322. (20) (a) Phillips, J. A.; Canagaratna, M.; Goodfriend, H.; Grushow, A.; Alml€of, A.; Leopold, K. R. J. Am. Chem. Soc. 1995, 117, 12549. (b)Phillips, J. A. Ph.D. Thesis, University of Minnesota, Minneapolis, MN, 1996. (21) (a) Adams, R.; Brown, B. K. Organic Synthesis, 2nd ed.; Gilman, H., Blatt, A. H., Eds.; Wiley: New York, 1941. (b) Clippard, P. H. Ph.D. Thesis, The University of Michigan, Ann Arbor, MI, 1969. (22) Pickett, H. M. J. Mol. Spectrosc. 1991, 148, 371. (23) Gordy, W.; Cook., R. L. Microwave Molecular Spectra, 3rd ed.; John Wiley & Sons: New York, 1984.
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(24) Møller, C; Plesset, M. S. Phys. Rev. 1934, 46, 618. (25) Krishnan, R.; Frisch, M. J.; Pople, J. A. J. Chem. Phys. 1980, 72, 4244. (26) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; , Jr., Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; M. A. Al-Laham, Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (27) Frisch, M. J.; Pople, J. A. J. Chem. Phys. 1984, 80, 3265. (28) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (29) Sedo, G. Ph.D Thesis, University of Minnesota, Minneapolis, MN, 2008. (30) Tao, F.-M. J. Chem. Phys. 1998, 108, 193. (31) In making these comparisons, of course it should be noted that the calculations produce equilibrium structures while the experimental values are averaged over the zero point vibrations of the complex. (32) Barone, V. In Recent Advances in Density Functional Methods, Part I; Chong, D. P., Ed.; World Scientific: Singapore, 1995; p 287. (33) Not surprisingly, the MP2/6-311þþG(d,p) performed worse for the HNO3, even getting the wrong sign for χaa (0.2945 MHz vs an experimental value of -0.3502 MHz from Table 1). On the other hand, for the (CH3)3N moiety, the calculated values of χaa, χbb, and χcc were all within 15% of the experimental values obtained from ref 34. (34) Rego, C.; Batton, R. C.; Legon, A. C. J. Chem. Phys. 1988, 89, 696. (35) Kurnig, I. J.; Scheiner, S. Int. J. Quantum Chem. Quantum Biol. Symp. 1987, 14, 47. (36) The value of F for H3N-HNO3 using the experimental hydrogen bond length is -0.67 Å. (37) Albinus, L.; Spieckermann, J.; Sutter, D. H. J. Mol. Spectrosc. 1989, 133, 128. (38) Ott, M. E.; Craddock, M. B.; Leopold, K. R. J. Mol. Spectrosc. 2005, 229, 286. (39) This is similar in spirit to the method used by Legon and coworkers (ref 17) for amine-hydrogen halide complexes, but differs somewhat in details. Here, the free acid and its conjugate base are used to define the limiting values for the hydrogen bonded and ion-paired systems. Moreover, the approach is modified to employ χcc since the nitric acid complexes lack 3-fold symmetry. (40) Adachi, A.; Kiyoyama, H.; Nakahara, M.; Masuda, Y.; Yamatera, H.; Shimizu, A.; Taniguchi, Y. J. Chem. Phys. 1988, 90, 392. (41) This value is slightly smaller than the 0.745 MHz value obtained in crystalline NaNO3 by Gourdji, M.; Guibe, L. C. R. Acad. Sci. Paris 1965, 260, 1131. However, the 0.656 MHz value is from aqueous solution and therefore seems more appropriate for comparison with small microsolvated complexes. (42) Lucken, E.A.C. Nuclear Quadrupole Coupling Constants; Academic Press: New York, 1969. (43) Note that (CH3)3N is an oblate top so that the c-inertial axis is the symmetry axis. The desired component perpendicular to the C3 axis is χaa or χbb. (44) Domene, C.; Fowler, P. W.; Legon, A. C. Chem. Phys. Lett. 1999, 309, 463. (45) Marshall, M. D.; Muenter, J. S. J. Mol. Spectrosc. 1981, 85, 322. Note that the quadrupole coupling constant for NH4þ, also needed for this calculation, is zero by symmetry. 1793
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(46) In this light, one should not be misled by the apparent accuracy of QAPT and QBPT indicated in Table 4. The uncertainties are those obtained for these quantities, as defined by eqs 11 and 12, but their values provide only one possible measure of the degree of proton transfer. Since the degree of proton transfer itself is only loosely defined, these parameters should be regarded only as a guide to picturing the physical state of the system.
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