ARTICLE pubs.acs.org/JPCA
Fourier Transform Infrared Spectroscopy and Theoretical Study of Dimethylamine Dimer in the Gas Phase Lin Du and Henrik G. Kjaergaard* Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark
bS Supporting Information ABSTRACT: Dimethylamine (DMA) has been studied by gas-phase Fourier transform infrared (FTIR) spectroscopy. We have identified a spectral transition that is assigned to the DMA dimer. The IR spectra of the dimer in the gas phase are obtained by spectral subtraction of spectra recorded at different pressures. The enthalpy of hydrogen bond formation was obtained for the DMA dimer by temperature-dependence measurements. We complement the experimental results with ab initio and anharmonic local mode model calculations of monomer and dimer. Compared to the monomer, our calculations show that in the dimer the NH bond is elongated, and the NHstretching fundamental shifts to a lower wavenumber. More importantly, the weak NH-stretching fundamental transition has a pronounced intensity increase upon complexation. However, the first NH-stretching overtone transition is not favored by the same intensity enhancement, and we do not observe the first NH-stretching overtone of the dimer. On the basis of the measured and calculated intensity of the NH-stretching transition of the dimer, the equilibrium constant for dimerization at room temperature was determined.
’ INTRODUCTION Dimethylamine [(CH3)2NH, DMA] has been studied both experimentally and theoretically. Fang et al. reported the gasphase overtone absorption spectra of DMA by intracavity laser photoacoustic and FTIR spectroscopy in an attempt to detect aggregates.1 They measured the temperature and pressure dependence of the NH-stretching overtone intensities of DMA. No relative intensity changes of the various NH-stretching overtone bands were observed when the vapor pressure of DMA changed from 3 to 100 Torr or when the temperature was increased from 0 to 80 C. On the basis of these results, they concluded that formation of aggregates is unlikely in their experiments. In 2007, Marinov et al. reported high-resolution absorption spectrum for gas-phase DMA in the region of the first NH-stretching overtone by cavity-ringdown spectroscopy.2 They measured the spectra at room temperature and at pressures in the range from 29.4 to 204.4 mbar. Very recently, Miller et al. measured absolute intensities of the fundamental to third NH-stretching overtone transitions in DMA.3 Several studies have been aimed at understanding the structure and bonding of molecular complexes involving NH3 and methylamines.417 However, the DMA dimer [(DMA)2] has been the subject of only a few studies. Early in 1950, Lambert and Strong studied the dimerization of ammonia and amines and pointed out that the dimerization is attributed to hydrogen bonding.18 The energy of the NH 3 3 3 N bond in the DMA dimer was determined to be 10.5 kJ mol1 by measuring the compressibility of the vapor. Wolff and Gamer investigated the infrared spectra of DMA in the fundamental and in the first r 2011 American Chemical Society
overtone range of the NH-stretching vibration as a function of concentration and temperature in different solutions (CCl4, n-hexane) and identified a characteristic band from DMA associates.19 The self-association of DMA was also examined in Bernard-Houplan and Sandorfy’s low temperature infrared study of dissolved DMA.20 The solvents were 1:1 mixtures of CCl3F and CF2Br-CF2Br and of CCl3F and methylcyclohexane, which can form rigid glasses near liquid nitrogen temperature. Odutola et al. performed an electric deflection study of (DMA)2 and found that the dipole moment of (DMA)2 is greater than 0.3 D.21 It is more favorable for the dimer to exhibit a linear hydrogenbonded conformation, compared with a cyclic structure with two hydrogen bonds between N and H atoms, which would have a dipole moment of only a few tenths of a Debye. Bohn and Andrews identified bands of (DMA)2 in their measured FTIR spectra of NH3DMA complexes in solid argon.22 On the basis of the spectrum, they proposed that the two submolecules are inequivalent in (DMA)2 like in (NH3)2.13 Several years later, Tubergen and Kuczkowski measured the rotational spectra for six isotopmers of (DMA)2 using a Fourier-transform microwave spectrometer and determined the most stable structure of the DMA dimer.23 In addition, the ultraviolet photoelectron spectrum of (DMA)2 was obtained in the vapor phase by spectrum stripping and assigned with the help of ab initio molecular orbital (MO) calculations.24 The calculated orbital energies based on a Received: July 15, 2011 Revised: September 23, 2011 Published: September 27, 2011 12097
dx.doi.org/10.1021/jp206762j | J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A
ARTICLE
nearly linear hydrogen bonded dimer structure show reasonably good agreement with the experimental values. Recently, Cabaleiro-Lago and Ríos studied the interaction in the DMA dimer and trimer with the HF, DFT/B3LYP, and MP2 ab initio methods in conjunction with the 6-31+G* and aug-cc-pVDZ/ cc-pVDZ (i.e., the aug-cc-pVDZ set for carbon and nitrogen atoms and the cc-pVDZ set for hydrogen atoms) basis sets.25 They found the most stable conformer for DMA dimer to have Cs symmetry and a close to linear hydrogen bond. Vibrational spectroscopy is extensively applied to the study of hydrogen bonded complexes; however, measurements in solution and in matrices are affected by solvent effects. Gas-phase spectroscopy can be used to quantify the complexes and the equilibrium constant of their formation. On the basis of previous experience with FTIR and quantum chemical calculations of weakly bound methanol clusters in the gas phase,26,27 we have recorded the FTIR spectra of the DMA dimer and supported these experiments with ab initio calculations of the monomer and dimer. The NH-stretching wavenumbers and oscillator strengths for DMA and its dimer were calculated with an anharmonic oscillator local mode model.2831 Furthermore, by measuring the dimer spectra over a range of temperatures, the dimerization enthalpy ΔH was obtained and compared with the theoretical results. The equilibrium constant of the DMA dimerization reaction was also estimated based on experimental and calculated NH-stretching intensities.
step size = 1 105 au., and energy = 1 107 au., and the global thresholds for single-point calculations were set to energy = 1 108 au. The harmonic frequencies were calculated with the B3LYP/aug-cc-pVTZ and QCISD/aug-cc-pVDZ methods with MOLPRO. The integration grid-size used for the B3LYP density functional calculations was set with an overall target accuracy of 1 108 au. Unless otherwise stated, QCISD calculations were performed with MOLPRO and B3LYP calculations were carried out with Gaussian 03. We have used the Boys and Bernardi counterpoise correction procedure (CP) to reduce the basis set superposition error (BSSE) in the dimer calculations.34 We apply the CP correction only to the energy of the non-CP optimized geometry. The CP-correction method has been shown to improve interaction energies of weakly bound complexes with some methods.810,3537 Furthermore, the behavior of the NH-stretching vibration is a very sensitive probe for the local environment. An anharmonic oscillator local mode model was used to calculate the NHstretching frequencies and intensities.30,31 Previously, the NHstretching modes in a range of molecules have been shown to be isolated from other vibrational modes, and hence are well described by the local mode model of vibration.3840 We assume that the NH-stretching vibrations can be described by a Morse oscillator, with the vibrational energy levels given by 1 1 2 ω ~x ð1Þ EðvÞ=ðhcÞ ¼ v þ ω ~ v þ 2 2
’ EXPERIMENTAL AND THEORETICAL METHODS The IR spectra were recorded at 1.0 cm1 resolution with a VERTEX 70 (Bruker) FTIR spectrometer fitted with a CaF2 beam splitter and an MCT detector. During the experiments, the FTIR spectrometer was purged with dry nitrogen gas to minimize the interference by water and CO2. Several gas cells with different path lengths were used, including a 10-cm cell equipped with KBr windows and a 2.4 m and a 4.8 m path length multireflection gas cell (Infrared Analysis, Inc.) fitted with Infrasil quartz windows. The 2.4 m cell was equipped with a heating jacket, and the temperature was controlled by a Digi-Sense electronic temperature controller (Eutech Instruments Pte Ltd., Model 6890003). The gas samples were prepared on a glass vacuum line (base pressure less than 1 104 Torr) equipped with a Varian cold cathode vacuum gauge (1 107 to 1 102 Torr, Model 860A). Sample pressures were measured with a Varian diaphragm pressure gauge (11500 Torr, DV100). In the variable temperature experiment, the DMA spectra were measured with the 2.4 m cell in the temperature range from 296 to 368 K. The pressure was measured at room temperature, and the ideal gas law used to calculate the pressure at the elevated temperature. Before each measurement, we waited for at least 20 min to let the temperature of the gas in the cell stabilize. The adsorption of DMA to the cell walls was observed, however the rate of adsorption was slow and did not affect our measurement significantly. DMA (anhydrous, 99+%) was purchased from Aldrich and used without any further purification. Gaussian 03 (revision E.01)32 and MOLPRO (version 2009.1)33 were used to perform the calculations. The geometries of DMA and (DMA)2 were optimized using B3LYP hybrid density functional theory and QCISD ab initio theory with the aug-cc-pVDZ and aug-cc-pVTZ basis sets, and using CCSD theory with the cc-pVDZ basis set. The optimization threshold criteria of the MOLPRO calculations were set to: gradient = 1 105 au.,
The Morse oscillator frequency ω~ and anharmonicity ω ~x are found from the second, third, and fourth-order derivatives of the potential energy curve.31 These derivatives are found by fitting an eighth-order polynomial to a symmetric 9-point ab initio calculated potential-energy curve, obtained by displacing the NH bond from 0.20 to 0.20 Å in 0.05 Å steps around equilibrium bond length. This range and step size of the potential-energy curve ensure converged energy derivatives.41 The dimensionless oscillator strength f of a transition from the ground vibrational state 0 to an excited vibrational state v is given by42 fv, 0 ¼ 4:702 107 ½cmD2 ~vv, 0 jμ ~v, 0 j2
ð2Þ 1
where ~vv,0 is the transition frequency in cm and μBv,0 = Æv|μB|0æ is the transition dipole moment in Debye (D). The transition dipole moment matrix element can be expanded as a Taylor series in the NH-stretching displacement coordinate q, and we limit the expansion to fifth-order terms. The dipole moment coefficients are found by fitting an eighth-order polynomial to a 9-point dipole moment curve calculated at the same points as the potential. The integrals Æv|qn|0æ needed for the transition dipole moment were evaluated numerically.
’ RESULTS AND DISCUSSION Geometries. The optimized geometries of DMA and two different DMA dimer conformers are shown in Figure 1. DMA has Cs symmetry, and the QCISD/aug-cc-pVTZ calculated NH bond length is 1.011 Å, which agrees well with the 1.022 Å bond length derived from the microwave spectrum.43 Compared with the monomer, much less structural information is available on the dimer. Motivated by the potential similarity between the DMA dimer and the ammonia dimer, Tubergen and Kuczkowski obtained sufficient experimental information to rule out many possible dimer conformers and 12098
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A
ARTICLE
concluded that the two most likely structures have nonlinear hydrogen bonds.23 With the help of ab initio calculations and a distributed multipole analysis to estimate the electrostatic energy, they concluded that one particular structure is most likely. Wales et al. studied the potential energy surface of the DMA dimer by using a semiempirical potential function and identified two minima on the potential surface.17 One of them corresponded to the structure proposed by Tubergen and Kuczkowski;23 however, the other minimum that previously had not been reported agreed very well with experimental values. Mayer et al. performed an ab initio study on the DMA dimer at the MP2/6-31G* level and found only one minimum, which was similar to the structure derived from microwave spectrum.44 They claimed that no other stable orientation of the two monomers could be found on the MP2/6-31G* surface. To eliminate these discrepancies, Cabaleiro-Lago and Ríos studied the DMA dimer using DFT and MP2 methods in conjunction with different basis sets.25 They identified minima for three different dimer conformers, which they called 2A, 2B, and 2C. Among them, structure 2B is a minimum on the potential surface with all the methods and basis sets used and has the lowest energy compared with the other two structures. The properties of structure 2C depend largely on the particular method used and introducing dispersion with the MP2 method substantially alters the structure of this minimum. Structure 2A is similar to 2B except that the H-donor DMA molecule is rotated about the N 3 3 3 N axis.25 The region of the potential surface near structures 2A and 2B is very flat, and the molecules can rotate relatively freely about the N 3 3 3 N axis. They concluded that the most stable minimum corresponds to structure 2B, which is similar to that derived from the microwave spectrum for the dimer.25 On the basis of previous studies, we include only the two conformers A and B (Figure 1), which correspond to structure 2A and 2B in ref 25. After preliminary examination, the geometry
Figure 1. Optimized structures of DMA and two conformers of its dimer.
changes of DMA upon dimerization is very similar for conformers A and B. The QCISD/aug-cc-pVDZ energy of conformer B is 1.6 kJ mol1 lower than that of conformer A, and for simplicity only conformer B was optimized at higher levels and used in our discussion. We also calculated the NH-stretching frequencies and intensities for conformer A with a few methods and found the results to be close to those of conformer B. The comparison between conformer A and B results is given in the Supporting Information. As shown in Figure 1, conformer B is a hydrogen-bonded complex of Cs symmetry. To discuss more clearly, geometric parameters are defined: RNH is the NH bond length in DMA, and R(NHb) and R(NHf) are the bonded and free NH bond length in the dimer, respectively, d is the length of the hydrogen bond (the H 3 3 3 N distance), ψ is the angle between the CNC plane of the acceptor DMA molecule and the donor H, and θ is the NH 3 3 3 N angle or H-bond angle. The R(NHb), R(NHf), and change in NH bond length upon complexation (Δr), together with the d, ψ, and θ angels obtained at different computational levels, are listed in Table 1. The z-matrix of DMA and (DMA)2 at the QCISD/aug-cc-pVTZ level are given in Supporting Information. Generally, due to the lack of dispersion forces, DFT methods predict complexes too loosely bound. As seen in Table 1, the B3LYP method predicts larger d value compared to the other methods. At the QCISD/aug-cc-pVTZ level, the change in the NH bond length upon complexation is 0.0036 Å, while this change was reported to be 0.005 Å in the previous MP2 study.25 The geometry change with dimerization is small, which suggests that the hydrogen bond in the dimer is weak. The NHf bond length of the dimer is roughly the same as in the isolated molecule. The length of the hydrogen bond (the H 3 3 3 N distance) is calculated to be 2.1810 Å (QCISD/aug-cc-pVTZ), which is shorter than the hydrogen bond in the ammonia dimer (2.38 Å) as expected, but it is close to the hydrogen bond length in the CHCl3NH3 complex (2.25 Å).9 The angle between the CNC plane of the acceptor and Hb is calculated to be 99 at the QCISD/aug-cc-pVTZ level. This is smaller than the comparable angle in DME-MeOH but larger than in DMS-MeOH.27 In an ideal hydrogen bond, the NH 3 3 3 N angle θ is close to 180.45 In DMA dimer there is a 25 deviation from linearity of the hydrogen bond, which again suggests that the hydrogen bond is not strong in this complex. As in the ammonia dimer, this deviation can be rationalized by electrostatic interactions.9 Besides the primary hydrogen bond, there is a secondary interaction between the positive region on the NH bond in the hydrogen bond acceptor DMA with the negative region around the partially negatively charged N of the donor which makes the deviation from linearity energetically favorable.9
Table 1. Selected Optimized Geometric Parameters (Ångstroms and Degrees) in the DMA Dimer conformer A
B
a
method
R(NHb)
R(NHf)
Δra
d
ψ
θ
B3LYP/aug-cc-pVTZ
1.0160
1.0120
0.0048
2.2912
133.1
171.5
CCSD/cc-pVDZ
1.0256
1.0240
0.0023
2.2059
143.6
152.9
QCISD/aug-cc-pVDZ
1.0235
1.0199
0.0033
2.1888
111.6
165.4
B3LYP/aug-cc-pVTZ
1.0161
1.0117
0.0049
2.2698
114.1
167.5
CCSD/cc-pVDZ QCISD/aug-cc-pVDZ
1.0256 1.0234
1.0231 1.0198
0.0023 0.0031
2.1932 2.1655
100.3 99.6
147.8 155.0
QCISD/aug-cc-pVTZ
1.0149
1.0115
0.0036
2.1810
99.3
154.6
Change in the NH bond length upon complexation, R(NHb) RNH. 12099
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A
ARTICLE
Table 2. Calculated BEs of the DMA Dimer (Conformer B) method B3LYP/aug-cc-pVTZ a
BE/kJ mol1 BE (CP corrected)/ kJ mol1 7.65
7.35
CCSD/cc-pVDZ a
23.60
7.49
QCISD/aug-cc-pVDZ a
21.41
13.37
QCISD/aug-cc-pVTZ a
18.34
14.93
a
BE includes zero-point vibrational energy (ZPVE) correction (ZPVEtot = ZPVEdimer 2ZPVEmonomer), obtained from unscaled B3LYP/aug-ccpVTZ harmonic frequencies and amount to 2.79 kJ mol1.
Figure 3. The DMA dimer spectra in the fundamental NH-stretching region as a result of spectral subtraction of DMA spectrum from the spectra measured at different vapor pressures. The spectra were measured with a 10 cm cell at 296 K. The higher pressure spectra are offset to avoid overlapping between the spectra. The absorbance is obtained by log(I0/I).
Figure 2. DMA spectra in the fundamental NH-stretching region measured at 700 and 2 Torr vapor pressures with a path length of 10 cm and 4.8 m, respectively, at 296 K. The left-hand side ordinate corresponds to the spectrum at 700 Torr. The absorbance is obtained by log(I0/I).
The binding energy (BE) defined as the energy difference between the dimer (ED) and the two monomers (EM), i.e., BE = ED 2EM, was calculated at various levels and are given in Table 2. Zero-point vibrational energy corrections (ZPVE) were included in the BE and obtained from the unscaled B3LYP/augcc-pVTZ harmonic frequencies. The B3LYP/aug-cc-pVTZ harmonic frequencies are given in Table S1 of the Supporting Information. The binding energy of the QCISD/aug-cc-pVTZ optimized dimer is calculated to be 18.3 kJ mol1, which the CP correction on the energy changes to 14.9 kJ mol1. The magnitude of the CP correction decreases with increase in basis set size, as expected. Very recently, optimization of the DMA dimer with the explicitly correlated coupled cluster method CCSD(T)-F12/VDZ-F12 found the binding energy of conformer B to be 18.6 kJ mol1.46 The CCSD(T)-F12/VDZ-F12 method have been found to give binding energies for small complexes that are in good agreement with CCSD(T) results at the complete basis set limit.10 FTIR Spectra of the DMA Dimer. Fang et al. measured the temperature and pressure dependence of the NH-stretching overtone intensities of DMA and no relative intensity changes of the various NH-stretching overtone bands were observed with a DMA vapor pressure range from 3 to 100 Torr and a temperature from 0 to 80 C.1 However, when we focused on the fundamental NH-stretching region and changed the vapor pressure from 2 to 700 Torr, a new feature appears in the spectra to the low energy side of the DMA NH-stretching band (Figure 2). The relative intensity of the low energy shoulder
increases with pressure. To confirm that the difference between the two spectra arises from DMA dimer, a series of spectra at different pressures were measured. We measured DMA spectra at pressures of 2, 70, 204, 315, 445, and 700 Torr. The spectrum at 2 Torr was measured with a path length of 4.8 m and the other spectra with a path length of 10 cm. The spectrum at 2 Torr is subtracted with appropriate weights taking into account the pressure and path length difference of the FTIR spectra recorded at the five higher pressures. All spectra were measured at 1.0 cm1 resolution. We also measured a few spectra at 0.2 cm1 resolution. These higher resolution spectra were almost identical to the spectra recorded with 1.0 cm1 resolution, and no fine structure was observed at higher resolution. We assign the residual to be the fundamental NH-stretching band of DMA dimer located at 3339 cm1. This position is found by fitting a Lorentzian function to the observed band. In the region from 2400 to 7000 cm1, we did not observe any other transitions that we could assign to the DMA dimer. The spectra obtained after subtraction are shown in Figure 3. According to the chemical equilibrium for DMA dimerization, 2DMA / ðDMAÞ2
ð3Þ
Kp ¼ pD =pM 2
ð4Þ
where Kp is the equilibrium constant and pD and pM are the vapor pressures of the dimer and monomer, respectively. At a given temperature, Kp is a constant, and therefore, pD is proportional to pM2. In the IR absorption spectrum, the integrated intensity of the DMA dimer band is proportional to pD, providing the same path length is used. We integrated the band areas shown in Figure 3, and plot the band area vs pM2 in Figure 4. The results fit well with a linear fit (Figure 4), which suggests that the complex formed at higher pressures is (DMA)2 and not large aggregates and also support our assignment of the measured band to the DMA dimer. We have calculated IR frequencies and intensities of DMA and DMA dimer both with a harmonic oscillator linear dipole (HO) 12100
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A
ARTICLE
Figure 4. The linear fitting between integrated area of the DMA dimer absorption band and pM2. These integrated areas are obtained from room temperature spectra at 296 K.
Table 3. Observed and Calculated NH-Stretching Fundamental Frequency (cm1) and Relative Intensities for the DMA Dimer method harmonic anharmonic
observed
υNH
Δυa
fD/fMb
B3LYP/aug-cc-pVTZ
3445
82
363
QCISD/aug-cc-pVDZ
3477
45
952
B3LYP/aug-cc-pVTZ
3277
103
835
QCISD/aug-cc-pVDZ
3313
57
144
QCISD/aug-cc-pVTZ Bohn and Andrewsc
3348 3304,3313
61 73
571
this work
3339
35
Δv = vmonomer vdimer b fD/fM is the oscillator strength of dimer vs monomer. c Taken from ref 22. a
approximation and with an anharmonic oscillator local mode (AO) model. The calculated DMA dimer NH-stretching fundamental frequency and intensity relative to that of the monomer are listed in Table 3. Additional results of the calculated frequencies and absolute intensities are given in Tables S1S3 of Supporting Information. The calculations at all levels predict an H-bonded dimer with a characteristic redshift and a very pronounced intensity increase of the NHb-stretching vibration. The measured peak of the dimer band at 3339 cm1 is in reasonable agreement with our QCISD/aug-cc-pVTZ anharmonic oscillator (AO) calculated NHb-stretching vibration frequency of 3348 cm1. It is also in good agreement with peaks at 3312.8 and 3304.3 cm1 observed in the Ar-matrix and assigned to (DMA)2.22 In an argon matrix, one typically observes a redshift of transitions by around 25 cm1.47 It is clear from Tables 2 and 3 that there is a large variation in the calculated binding energies and the calculated frequency shift and intensity enhancement with the range of theoretical methods used. The large CP correction in the calculated binding suggests that the cc-pVDZ and aug-cc-pVDZ basis sets are too small to describe well the weak interactions in the dimer. The calculated IR intensities also vary significantly between the HO and AO vibrational models when the aug-cc-pVDZ basis set is used.
We believe that a VTZ quality basis set is necessary to describe the dimer well. In the spectrum of DMA, two transitions at 3374 and 3359 cm1 are observed in the NH-stretching region, due to splitting by tunneling in the inversion mode. The higher frequency transition arise from the ground state and is observed to be slightly more intense.3 In our measurements, the DMA dimer transition observed at 3339 cm1 leads to an observed gas-phase frequency redshift of 35 cm1. Our QCISD/aug-cc-pVTZ AO calculated red shift of the NHb-stretching vibration is 61 cm1. However, it has been observed that the coupling to lower frequency modes ignored in the AO model can change the stretching frequencies.48 If we compare the HO and AO calculated redshift with the B3LYP/aug-cc-pVTZ method we find that the shift is about 20 cm1 larger with the AO model. A 20 cm1 decrease of the QCISD/aug-cc-pVTZ calculated shift would bring it in very good agreement with the observed shift. In the Ar matrix experiment, the NH-stretching fundamental transition in DMA is assigned to a peak at 3377 cm1, and only one transition is assigned. However, this transition is higher than both transitions observed in the gas phase, and with the usual redshift caused by the Ar matrix we believe that this assignment is perhaps incorrect. It should also be noted that the NH-stretching transition in DMA is about 100 times weaker than normal NH-stretching transitions, and perhaps difficult to assign in the matrix experiment.3 Thus, the reported redshift of 73 cm1 from the solid Argon matrix FTIR experiment is likely too high.22 One should also take into consideration that we measure at room temperature but calculate at 0 K. Previously, a difference between room temperature redshift and low temperature redshift has been found for the CHCl3NH3 complex.9 The redshift of the CH-stretching vibration in the jet-cooled spectrum (38 cm1) is somewhat larger than the observed redshift at room temperature (17.5 cm1). The reason for this discrepancy is a temperature effect. At room temperature, the low-frequency intermolecular vibrational modes are expected to be populated, which lead to a broadening of the band and an overall redshift of the band maximum.9 The fundamental NH-stretching transition in DMA is very weak is due to a very small dipole moment derivative.3 Thus, deviations from a harmonic oscillator and a linear dipole become important, and intensity ratio between dimer and monomer NH-stretching transitions (fD/fM) is likely more reliable with the AO model. We believe that fD/fM ≈ 600 is a reasonable value for the intensity enhancement based on our QCISD/aug-cc-pVTZ calculations. In comparison, the recent CCSD(T)-F12/VDZF12 value for fD/fM is 611.46 This is significantly higher than the predicted values for trimethylamine-methanol (TMA-MeOH), dimethylsulfide-methanol (DMS-MeOH), and dimethylethermethanol (DME-MeOH) dimers,26,27 which all lie in the range of fD/fM ≈ 1368. An IR intensity increase is often observed for the hydrogen stretching vibration of a hydrogen bond donor and is often considered as a defining feature of a typical hydrogen bond.45 In the ammonia dimer, the NH-stretching vibration is increased by up to a factor of 9 compared to the monomer.49 However, the NH-stretching fundamental transition in (DMA)2 is calculated to be ∼600 times stronger than that of the monomer. The IR intensity is determined mainly by the derivative of the electronic dipole moment of the molecule, which changes significantly between the monomer and the dimer. Furthermore, 12101
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A
ARTICLE
the NH-stretching fundamental vibration of DMA is very weak due to a very small first derivative of dipole moment function.3,50 Comparison of the experimental integrated band intensity and the QCISD/aug-cc-pVTZ calculated oscillator strength of the NHb-stretching band indicates that there is only about 0.1% dimer present at room temperature with a total DMA pressure of 700 Torr. The large intensity enhancement of the NH-stretching fundamental in the DMA dimer makes it possible to observe the dimer in the gas phase, even at room temperature where only a very small fraction of DMA undergoes dimerization. The intensity of the NHf-stretching transition is calculated to be 2.6 times stronger than the NH-stretching transition in DMA monomer; however this small enhancement is not sufficient for us to observe the NHf-stretching transition. For comparison, we also calculated the intensity of the first NH-stretching overtone transition of (DMA)2 at the QCISD/ aug-cc-pVTZ level with our AO local mode model, to see if we could record NH-stretching overtone transitions of the DMA dimer. For the DMA monomer, it was found that the first NH-stretching overtone was stronger than the fundamental transition.3 However, we predict the first NHb-stretching overtone of (DMA)2 to have only 0.01% of the intensity of the fundamental vibration of the dimer and only 1% of the intensity of the first overtone transition of DMA. This intensity decrease of the first NHb-stretching overtone transition is also typical for NH or OH bonds involved in hydrogen bonding.47,50 This is part of the reason why overtones of complexes are difficult to measure at room temperature.1,51,52 Enthalpy of Hydrogen Bond Formation. If we assume that the enthalpy of a chemical equilibrium is independent of temperature, we can use the van’t Hoff equation to write53 ln Kp ¼ ΔH=RT þ C
ð5Þ
where Kp is the equilibrium constant, ΔH the enthalpy of a chemical equilibrium, R the gas constant, T the absolute temperature, and C an integration constant. The enthalpy ΔH can be determined if we can obtain Kp at different temperatures. In our case, Kp is the equilibrium constant of DMA dimerization and ΔH is the enthalpy of hydrogen bond formation for the DMA dimer. As seen in eq 4, Kp is proportional to pD on the condition of keeping pM a constant. The dimer pressure pD is proportional to the measured integrated absorbance of the dimer band. Therefore, we have lnðAÞ ¼ ΔH=RT þ C
0
Figure 5. The temperature dependence of the NH-stretching band in the DMA dimer. A path length of 2.4 m was used. At a given temperature, the spectrum was measured with a total pressure of 200 Torr.
ð6Þ
where A is the integrated absorbance of the dimer band and C0 is a new constant. We recorded the IR spectra of (DMA)2 in the temperature range from 296 to 368 K to determine the enthalpy of hydrogen bond formation for the DMA dimer. In general, to get the dimer spectrum at a certain temperature, two absorption spectra are needed: a high-pressure spectrum of DMA and its dimer and a low pressure spectrum where dimer contribution is minimal. The latter is a pure DMA monomer spectrum necessary for subtraction. The vapor pressure of DMA should be kept constant for all the high pressure measurements. The pressure of the dimer in the mixture is less than 0.2% of the total pressure and can therefore be neglected in the total pressure. We select the constant pressure such that the DMA dimer spectrum after subtraction should be measurable and the absorbance of the NH-stretching band in the spectrum should not saturate the detector. After several test measurements, we decided to use
Figure 6. Linear least-squares fitting of the van’t Hoff equation plot for the DMA dimer.
200 Torr for the high pressure spectra. Similarly, since we will use appropriate weights on the low pressure spectrum used in the spectral subtraction, the pressure cannot be too low, otherwise the uncertainties would be amplified. Finally, we decided to use 20 Torr in the low pressure spectrum, which will need a weighting of around 10 in the subtraction. We used the ideal gas law to determine the filling pressure necessary to obtain 200 Torr pressure at each of the elevated temperatures. Representative IR spectra in the NH-stretching region of DMA dimer after spectral subtraction are shown in Figure 5 and the van’t Hoff equation plot for DMA dimer is shown in Figure 6. Because of the weighting of the low pressure spectra, the quality of the spectra in Figure 5 is not as good as the spectra in Figure 3. We used intergrated band areas as the measure of the absorbance in each of the different temperature spectra. After linear least-squares fitting, the dimerization enthalpy ΔH in the temperature range 296368 K is determined to be 23.8 ( 2.2 kJ mol1 from the slope in Figure 6. We calculated the enthalpy of dimerization to be 23.1 kJ mol1 with the QCISD/aug-cc-pVDZ method and for the higher level 12102
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A QCISD/aug-cc-pVTZ method with a B3LYP/aug-cc-pVTZ thermodynamic correction we obtain 20.4 kJ mol1, both in good agreement with our experimental determination. The enthalpy ΔH of H-bond formation is directly related to the stabilization energy of a complex.54 In a stronger H-bonded complex like methanol-trimethylamine (MeOH-TMA), the observed enthalpy is approximately 29 kJ mol1.55,56 The enthalpies of H-bond formation in weaker complexes have been determined to be 14.8 and 19.1 kJ mol1 for DMS-MeOH and DME-MeOH, respectively.27 However, in ref 27, no correction for change in total pressures was considered in the measurements at different temperatures; therefore, at temperatures higher than room temperature, the pressure of the monomers are slightly higher than the pressure read when the cell was filled with sample gas and the determined ΔH values are likely a few kJ mol1 too small. For comparison, we also measured ΔH without corrections for pressure changes and obtain a value of 16.9 ( 3.0 kJ mol1. The linear least-squares fitting of van’t Hoff equation plot of DMA dimer for the experiment without pressure correction is given in Supporting Information (Figure S1). Thermodynamic Dimerization Equilibrium Constant. As seen from eq 4, at a certain temperature, the thermodynamic dimerization equilibrium constant Kp can be determined provided that the partial pressure of DMA (pM) and DMA dimer (pD) could be measured. This has been used to determine Kp for dimers with large Kp values.57 However, due to the small changes in pD for different total pressure, this is impossible for DMA. Instead, we estimate the partial pressure of the dimer pD from the measured and anharmonically calculated NH-stretching intensities. At the QCISD/aug-cc-pVTZ level, the NH-stretching fundamental transition in (DMA)2 is calculated to be 571 times stronger than that of the monomer. The ratio of the experimental integrated band intensity and the theoretical oscillator strength gives the partial pressure of the dimer.36 A plot of pD against p2M for each of the experiments is shown in Figure S2 of Supporting Information. The slope of the least-squares fitting of these data is the thermodynamic dimerization equilibrium constant, Kp, which we determined to be 1.4 103 atm1 at a temperature of 296 K. The Kp determination method depends on the calculated intensity enhancement, which varies with theoretical method used. We have used our highest level value obtained with the QCISD/ aug-cc-pVTZ AO method, with a fD/fM ≈ 571. Uncertainty in the calculated intensity will be reflected in uncertainty in the determined Kp value. However, at the aug-cc-pVTZ basis set level, the intensity ratio of our different approaches is in the range (363 to 835), and thus our Kp value is accurate to within a factor of 2. The decrease in band absorbance with increasing temperature, as shown in Figure 5, clearly illustrate the decrease in the equilibrium constant with increasing temperature. We have estimated Kp theoretically with a statistical thermodynamics procedure and find it to be 3.8 105 atm1 at the B3LYP/aug-cc-pVTZ level and 2.6 103 atm1 at the QCISD/aug-cc-pVTZ level with B3LYP/ aug-cc-pVTZ thermodynamic values.58 The loose binding of complexes with the B3LYP method is in agreement with the smaller Kp value obtained with this method. The better calculation agrees reasonably well with our combined experimental and theoretical determined value.
’ CONCLUSIONS The dimethylamine dimer in the gas phase has been investigated by FTIR and ab initio calculations. The geometry of the
ARTICLE
most stable conformer of the dimer is characterized by a nonlinear hydrogen bond NH 3 3 3 N between the two DMA molecules. The IR spectrum of the dimer shows a characteristic small redshift of the NH-stretching vibrational band and a pronounced intensity increase. The large increase in IR intensity makes it possible to obtain the IR spectrum of the dimer in the gas phase at room temperature. The detected fundamental NHstretching band of the dimer is obtained by subtracting monomer spectra and shows the expected pressure square dependence. This provided evidence of the DMA dimer in the gas phase. On the basis of the measurements of the temperature dependence of the dimer spectra, the enthalpy of hydrogen bond formation in DMA dimer in the temperature range of 296368 K was determined to be 23.8 ( 2.2 kJ mol1 in agreement with theoretical predictions. We combine the experimental integrated intensity of the NH-stretching dimer band with anharmonic local mode intensity calculations to obtain an estimate of the thermodynamic dimerization equilibrium constant of 1.4 103 atm1 at room temperature.
’ ASSOCIATED CONTENT
bS
Supporting Information. The linear least-squares fitting of van’t Hoff equation plot of DMA dimer without pressure correction; a plot of pD against pM2 to determine the thermodynamic dimerization equilibrium constant; calculated frequencies and intensities for DMA and DMA dimer with normal mode method; calculated NH-stretching fundamental and overtone frequencies and oscillator strengths for DMA dimer with an AO local mode model; calculated NH-stretching fundamental frequency and relative intensities for the two conformers A and B of DMA dimer; z-matrices of DMA and DMA dimer (conformer B) at QCISD/aug-cc-pVTZ level. This material is available free of charge via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Fax: 45-35320322. Phone: 45-35320334.
’ ACKNOWLEDGMENT We thank Lauri Halonen, Benjamin J. Miller, and Joseph R. Lane for helpful discussions and Rene W. Larsen for help with the FTIR measurements. We are grateful for support from The Danish Council for Independent Research—Natural Sciences and the Danish Center for Scientific Computing. ’ REFERENCES (1) Fang, H. L.; Swofford, R. L.; Compton, D. A. C. Chem. Phys. Lett. 1984, 108, 539. (2) Marinov, D.; Rey, J. M.; Muller, M. G.; Sigrist, M. W. Appl. Opt. 2007, 46, 3981. (3) Miller, B. J.; Du, L.; Steel, T. J.; Paul, A. J.; Sodergren, A. H.; Lane, J. R.; Henry, B. R.; Kjaergaard, H. G. J. Phys. Chem. A 2011submitted. (4) Bako, I.; Palinkas, G. THEOCHEM 2002, 594, 179. (5) Boese, A. D.; Chandra, A.; Martin, J. M. L.; Marx, D. J. Chem. Phys. 2003, 119, 5965. (6) Bricknell, B. C.; Ford, T. A. J. Mol. Struct. 2010, 972, 99. (7) Buck, U.; Gu, X. J.; Krohne, R.; Lauenstein, C.; Linnartz, H.; Rudolph, A. J. Chem. Phys. 1991, 94, 23. (8) Hippler, M. J. Chem. Phys. 2007, 127, 084306. 12103
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
The Journal of Physical Chemistry A (9) Hippler, M.; Hesse, S.; Suhm, M. A. Phys. Chem. Chem. Phys. 2010, 12, 13555. (10) Lane, J. R.; Kjaergaard, H. G. J. Chem. Phys. 2009, 131, 034307. (11) Lane, J. R.; Vaida, V.; Kjaergaard, H. G. J. Chem. Phys. 2008, 128, 034302. (12) Mmereki, B. T.; Donaldson, D. J. J. Phys. Chem. A 2002, 106, 3185. (13) Nelson, D. D.; Fraser, G. T.; Klemperer, W. J. Chem. Phys. 1985, 83, 6201. (14) Nelson, D. D.; Fraser, G. T.; Klemperer, W. Science 1987, 238, 1670. (15) Rodham, D. A.; Suzuki, S.; Suenram, R. D.; Lovas, F. J.; Dasgupta, S.; Goddard, W. A.; Blake, G. A. Nature 1993, 362, 735. (16) Tubergen, M. J.; Kuczkowski, R. L. J. Mol. Struct. 1995, 352, 335. (17) Wales, D. J.; Stone, A. J.; Popelier, P. L. A. Chem. Phys. Lett. 1995, 240, 89. (18) Lambert, J. D.; Strong, E. D. T. Proc. R. Soc. London, Ser. A 1950, 200, 566. (19) Wolff, H.; Gamer, G. J. Phys. Chem. 1972, 76, 871. (20) Bernardh, M. C.; Sandorfy, C. J. Chem. Phys. 1972, 56, 3412. (21) Odutola, J. A.; Viswanathan, R.; Dyke, T. R. J. Am. Chem. Soc. 1979, 101, 4787. (22) Bohn, R. B.; Andrews, L. J. Phys. Chem. 1991, 95, 9707. (23) Tubergen, M. J.; Kuczkowski, R. L. J. Chem. Phys. 1994, 100, 3377. (24) Pradeep, T.; Hegde, M. S.; Rao, C. N. R. J. Mol. Spectrosc. 1991, 150, 289. (25) Cabaleiro-Lago, E. M.; Rios, M. A. J. Chem. Phys. 2000, 113, 9523. (26) Howard, D. L.; Kjaergaard, H. G. J. Phys. Chem. A 2006, 110, 9597. (27) Howard, D. L.; Kjaergaard, H. G. Phys. Chem. Chem. Phys. 2008, 10, 4113. (28) Henry, B. R. Acc. Chem. Res. 1977, 10, 207. (29) Henry, B. R. Acc. Chem. Res. 1987, 20, 429. (30) Henry, B. R.; Kjaergaard, H. G. Can. J. Chem. 2002, 80, 1635. (31) Howard, D. L.; Jorgensen, P.; Kjaergaard, H. G. J. Am. Chem. Soc. 2005, 127, 17096. (32) 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.; Al-Laham, M. A.; 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 E.01; Gaussian, Inc.: Wallingford, CT, 2004. (33) Werner, H.-J.; Knowles, P. J.; Manby, F. R.; Sch€utz, M.; Celani, P.; Knizia, G.; Korona, T.; Lindh, R.; Mitrushenkov, A.; Rauhut, G.; Adler, T. B.; Amos, R. D.; Bernhardsson, A.; Berning, A.; Cooper, D. L.; Deegan, M. J. O.; Dobbyn, A. J.; Eckert, F.; Goll, E.; Hampel, C.; Hesselmann, A.; Hetzer, G.; Hrenar, T.; Jansen, G.; K€oppl, C.; Liu, Y.; Lloyd, A. W.; Mata, R. A.; May, A. J.; McNicholas, S. J.; Meyer, W.; Mura, M. E.; Nicklass, A.; Palmieri, P.; Pfl€uger, K.; Pitzer, R.; Reiher, M.; Shiozaki, T.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, version 2009.1. (34) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (35) Hippler, M. J. Chem. Phys. 2005, 123, 204311. (36) Chung, S.; Hippler, M. J. Chem. Phys. 2006, 124, 214316.
ARTICLE
(37) Simon, S.; Duran, M.; Dannenberg, J. J. J. Phys. Chem. A 1999, 103, 1640. (38) Howard, D. L.; Robinson, T. W.; Fraser, A. E.; Kjaergaard, H. G. Phys. Chem. Chem. Phys. 2004, 6, 719. (39) Niefer, B. I.; Kjaergaard, H. G.; Henry, B. R. J. Chem. Phys. 1993, 99, 5682. (40) Robinson, T. W.; Kjaergaard, H. G.; Ishiuchi, S. I.; Shinozaki, M.; Fujii, M. J. Phys. Chem. A 2004, 108, 4420. (41) Rong, Z. M.; Kjaergaard, H. G. J. Phys. Chem. A 2002, 106, 6242. (42) Kjaergaard, H. G.; Yu, H. T.; Schattka, B. J.; Henry, B. R.; Tarr, A. W. J. Chem. Phys. 1990, 93, 6239. (43) Wollrab, J. E.; Laurie, V. W. J. Chem. Phys. 1968, 48, 5058. (44) Mayer, P. M.; Keister, J. W.; Baer, T.; Evans, M.; Ng, C. Y.; Hsu, C. W. J. Phys. Chem. A 1997, 101, 1270. (45) Arunan, E.; Desiraju, G. R.; Klein, R. A.; Sadlej, J.; Scheiner, S.; Alkorta, I.; Clary, D. C.; Crabtree, R. H.; Dannenberg, J. J.; Hobza, P.; Kjaergaard, H. G.; Legon, A. C.; Mennucci, B.; Nesbitt, D. J. Pure Appl. Chem. 2011, 83, 1619. (46) Du, L.; Lane, J. R.; Kjaergaard, H. G. Unpublished, 2011. (47) Schofield, D. P.; Kjaergaard, H. G. Phys. Chem. Chem. Phys. 2003, 5, 3100. (48) Kjaergaard, H. G.; Garden, A. L.; Chaban, G. M.; Gerber, R. B.; Matthews, D. A.; Stanton, J. F. J. Phys. Chem. A 2008, 112, 4324. (49) Slipchenko, M. N.; Sartakov, B. G.; Vilesov, A. F.; Xantheas, S. S. J. Phys. Chem. A 2007, 111, 7460. (50) Kjaergaard, H. G.; Low, G. R.; Robinson, T. W.; Howard, D. L. J. Phys. Chem. A 2002, 106, 8955. (51) Garden, A. L.; Halonen, L.; Kjaergaard, H. G. J. Phys. Chem. A 2008, 112, 7439. (52) Shillings, A. J. L.; Ball, S. M.; Barber, M. J.; Tennyson, J.; Jones, R. L. Atmos. Chem. Phys. 2011, 11, 4273. (53) Paiva, J. C. M.; Gil, V. M. S.; Correia, A. F. J. Chem. Educ. 2002, 79, 583. (54) Curtiss, L. A.; Blander, M. Chem. Rev. 1988, 88, 827. (55) Fild, M.; Swiniars., Mf; Holmes, R. R. Inorg. Chem. 1970, 9, 839. (56) Millen, D. J.; Mines, G. W. J. Chem. Soc., Faraday Trans. 1974, 70, 693. (57) Crawford, M. A.; Wallington, T. J.; Szente, J. J.; Maricq, M. M.; Francisco, J. S. J. Phys. Chem. A 1999, 103, 365. (58) Vaida, V.; Headrick, J. E. J. Phys. Chem. A 2000, 104, 5401.
12104
dx.doi.org/10.1021/jp206762j |J. Phys. Chem. A 2011, 115, 12097–12104
