Water System: A Matrix

Apr 10, 2012 - The environmentally important interaction products of trimethylamine (TMA) and water molecules have been observed by Matrix Isolation F...
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H-Bonded Clusters in the Trimethylamine/Water System: A Matrix Isolation and Computational Study Mark Rozenberg and Aharon Loewenschuss* Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Claus J. Nielsen Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, 1033 Blindern, N-0315 Oslo, Norway S Supporting Information *

ABSTRACT: The environmentally important interaction products of trimethylamine (TMA) and water molecules have been observed by Matrix Isolation Fourier Transform Infrared Spectroscopy (MIS-FTIR). Infrared spectra of solid argon matrix layers, in which both TMA and H2O molecules were entrapped as impurities, were analyzed for bands in the ν(O−H) region, not seen in matrix layers containing either of the parent molecules alone. Results were interpreted on the basis of the emergence of several spectral band pairs and their red shifts from the position of the matrix isolated H2O monomers as compared to semiempirically scaled frequencies from the B3LYP/aug-cc-pVTZ calculations and empirical correlations with a large body of data on H-bonded complexes. Bands were assigned to a complex cluster of two TMA molecules flanking a closed ring of four H-bonded H2O molecules. The formation of this cluster is argued to be formed in the vapor phase (as opposed to being a result of diffusion of the trapped species) and is related to its large stabilization energy (enthalpy) because of strong cooperative effects in its H-bond system.

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hydrogen-bonded complexes. Gas phase infrared studies4 indicate that in the vapors of these liquids an H-bonded complex formed with a stabilization enthalpy of about 30 kJ mol−1. A later microwave study of the rotational spectrum of the complex suggested it to be bound by an almost linear hydrogen bond of 1.82 A in length.5 The measured enthalpy of adsorption of TMA on a liquid water surface is 36 kJ mol−1.6 The gas phase infrared study of the TMA/H2O complex found the ν(OH) of the H2O moiety to be red-shifted by 277 cm−14 at 3375 cm−1. The infrared spectrum of the complexation product of water and the analogous tertiary amine, triethyl amine, in a CCl4 solution shows a broad (200 cm−1) band at around 3200 cm−1 with a well resolved Fermi resonance between the ν(OH) stretch and the 2ν2(HOH) bending mode. In preliminary experiments for this study, we found an analogous broad weakly structured band at 3150 cm−1 for the water complex product of TMA in a diluted solution of CCl4. The infrared spectrum of pure TMA both as a solid and as isolated in argon matrixes was studied by Goldfarb et al.7 and in

INTRODUCTION Amines are organic bases that may be considered as derivatives of ammonia with one or more hydrogen atoms replaced by alkyl or aryl groups. The electron donation properties of the substituents enhance the basicity of these compounds beyond that of ammonia. It has recently become evident that amines contribute to the atmospheric aerosol mass via a number of mechanisms. Among the atmospherically relevant organic compounds, amines are unique in their acid neutralizing capacity, yet there is limited knowledge of their thermodynamic and kinetic properties. A detailed list of sources of atmospheric amines was published by Ge et al.,1 with the major sources being of both natural and anthropogenic origin. Examples are biological processes in oceans, combustion, agriculture, and waste treatment. In addition, there is an increasing use of amines in carbon capture and storage techniques (CCS). Amines are utilized to trap CO2 in flue gases of combustion plants and emission from absorber towers may then contribute to the concentration of atmospheric amines.2,3 The soluble lowmolecular weight amines may undergo rapid acid−base reactions with atmospheric acids (HNO3, HCl, H2SO4) to form the respective amminium salts. The trimethylamine (TMA)/water system is a primary model for the interactions of atmospheric amines to form © 2012 American Chemical Society

Received: February 29, 2012 Revised: April 4, 2012 Published: April 10, 2012 4089

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the gas phase by Murphy et al.8 In the present study, which continues our studies of hydrogen bonded molecular complexes of atmospheric interest,9,10 we concentrate on the hydrogen bond schemes involving TMA and water vapors. A further study of such complexes also including a sulfuric acid moiety is in preparation. Calculated binding energies for the 1:1 TMA*H2O complex span a range of values. Rablen et al.11 obtained a value of 25.5 kJ mol−1 by density functional theory (DFT) methods and a value of 29.2 kJ mol−1 from their ab initio calculations. Their calculated rN···H value is 2.102 Å. Mmereki et al.12 found a binding enthalpy of 24 kJ mol−1 and a binding energy of 21.5 kJ mol−1. However, in spite of the lower binding energy their calculated rN···H value is lower, 1.87 Å. These results were later13 updated by MP2/6-31+G(d,p), B3LYP/6-31+G(d,p), and B3LYP/6-31+G(2d,p) calculations resulting in binding energies of 21.4, 21.0, and 18.9 kJ mol−1, respectively and rN···H values of 1.868, 1882, and 1.908 Å, respectively. The authors also suggest that the binding to a water surface involves two water molecules for each attached TMA molecule. A more recent quantum chemical calculation by Graton et al.14 finds the binding energy of the 1:1 TMA*H2O complex to be 26.9 kJ mol−1. Despite the obvious interest in them, the gas-phase studies mentioned above4,5 remain the only spectral studies of TMA/H2O hydrogen bonded complexes. One of the more successful attempts to systematize a large amount of spectral data of hydrogen bonded systems was suggested by Iogansen by correlating observed spectral shifts of R-X····H stretching frequencies with the strength of the X···H H-bonding interaction.15 On the basis of this correlation of the calculated binding enthalpies, and the available spectral studies of the TMA/H2O system in the liquid phase, the H-bond shifted ν(OH) band of H2O in the TMA*H2O complex is expected in the 3000−3100 cm−1 range. Because of the low temperature in matrix isolation studies, this band may also be expected to be of lower bandwidth than in the liquid or gas phases16 and to be structured due to a Fermi resonance with the 2ν2(H2O) overtone.17,18 However, the matrix isolation samples described below have a complicated infrared signature requiring the assumption of more than only a single 1:1 TMA*H2O H-bonded system for the assignment of the observed spectral bands.

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Deposited samples were temperature cycled to up to 40 K; however, the observed spectra were only slightly affected by this procedure. Spectra were recorded on a Bruker Equinox 55 FTIR spectrometer, equipped with a DTGS detector at a resolution of 0.5 cm−1 and generally coadding 128 scans.

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COMPUTATIONAL METHODS

MP2 and DFT calculations employing the B3LYP functional19 were carried out using Gaussian 03.20 Geometries were optimized, and the frequencies of vibration including infrared intensities were calculated. Dunning’s correlation consistent aug-cc-pVTZ basis set,21,22 which includes both diffuse and polarization functions, was chosen to obtain a reasonably accurate geometry of the isolated molecules and the complexes bonding. The energy of the complex minus the monomer energies is the directly calculated energy of complex formation, ΔEcomplex = E(A···B) − E(A) − E(B), which is subsequently corrected for the Basis Set Superposition Error (BSSE) by the Counterpoise (CP) correction.23,24 Vibrational wavenumbers were obtained in B3LYP calculations. Additional MP2 calculations were carried out for TMA, H2O, and the 1:1 TMA*H2O complex. Provided an adequate basis set is used in calculations of the normal modes of vibration, the calculated wavenumbers are invariably too high. A common procedure to remedy this discrepancy is to scale the calculated wavenumbers to compensate for, among others, mechanical anharmonicity. In the present study the cubic and quartic force constants were calculated for the 1:1 TMA*H2O complex allowing a prediction of the anharmonic vibrational wavenumbers directly. The force fields were scaled according to the procedure, 1/2 Fscaled = Fcalc. where αi and αj are scaling parameters for i,j i,j ·(αi·αj) the valence coordinates i and j, respectively. The scaling parameters are derived from fitting vibrational data of the monomeric compounds. It should be pointed out that the described frequency scaling has the advantage of being more mode specific than the application of a uniform scaling factor.

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RESULTS As pointed out in the Introduction, we shall concentrate on the spectral region in which the ν(OH) stretching modes may be observed. Figure 1 reproduces this region for water vapors matrix isolated in solid Ar (trace A), for matrix isolated pure TMA (trace B), and for two solid argon layers containing both TMA and H2O vapors. Trace C is a spectrum recorded of a layer produced by the deposition of a jet with an Ar/TMA in the ratio 200:1 and a jet of an Ar/H2O mixture in a ratio of 400:1. For Trace D was recorded of a layer richer in water, produced with a jet with an Ar/H2O ratio of 40:1. It has to be considered that for the weak complex bands to be observed, the layers that need to be produced are more concentrated than those formed for matrix isolation experiments aimed at the spectral features of single isolated species. To emphasize the new bands, not observed in either of the pure, single contaminant matrixes, we also show trace E which is the difference spectrum of layer [D − (A + B)]. Trace F was obtained by an analogous subtraction with a matrix layer significantly richer (2−2.5%) in water than the mixed layer characterized by trace D. In the higher frequency region of Figure 1, to the left of the scale break, four new, relatively sharp bands appear in the

EXPERIMENTAL SECTION

Materials. Anhydrous TMA (Analytical grade) was supplied by Sigma-Aldrich. Argon gas (5.7 purity), supplied by AGA was used to produce the solid matrix layers. Sample Preparation. TMA/Ar and water/Ar mixture in ratios from 1:40 to 1: 400, were prepared by standard manometric techniques. We could obtain matrixes ranging from “dry”, that is, showing no traces of water spectral lines, to “wet”, with prominent water polymeric bands. The water rich matrixes showed water cluster bands. Samples were deposited on a CsI window, with deposition rates ranging from 10 to 1000 mM of Ar/h and deposition window temperatures in the 17−24 K range. Cooling was provided by an Air Product Displex model 202A closed cycle helium refrigerator. Deposition temperatures were monitored by an Au-0.007%Fe/Chromel thermocouple and controlled with an APDE temperature controller. A pure Ar layer was deposited for several minutes before the first sample layer deposition. 4090

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Figure 2. FTIR spectra of the ν(OD) region of Ar/H2O+D2O, Ar/ TMA and Ar/H2O+D2O/TMA layers. (A) Ar/TMA reference spectrum. (B) Ar/D2O reference spectrum. (C) Ar/TMA + (H2O+ 10% D2O) layer; new bands marked in red. (D) Ar/TMA + 1:1 D2O/ H2O layer; new bands marked in red. (E) Similar to D, but thicker matrix layer; new bands marked in red.

Figure 1. FTIR spectra of the ν(OH) region of Ar/H2O, Ar/TMA and Ar/H2O+TMA layers. (A) Ar/H2O reference spectrum. (B) Ar/TMA reference spectrum. (C) Ar/TMA + H2O layer; new bands marked in red. (D) Ar/TMA + H2O layer with greater H2O concentration; new bands marked in red. (E) Difference spectrum obtained from spectra D − (A + B). (F) Difference spectrum of an analogous subtraction from a matrix layer with high H2O content.

Table 1 summarizes the observed complex band positions (cm−1) in both the ν(OH) and ν(OD) regions.

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spectra of the mixed Ar/TMA/H2O matrix layer without having counterparts in the spectra of either the Ar/TMA or the Ar/H2O matrix layers. Of these, the three lower frequency bands at 3356.7, 3265.8, and 3176.4 cm−1 appear even in the spectra of layers with the lowest amount of trapped water vapors. The wider, higher frequency band at 3466.6 cm−1 is only recorded off water rich mixed matrixes. In the lower frequency region, to the right of the scale break, two, somewhat broader and weaker band pairs are observed: the first pair at 2991.5 cm−1 and 2961.1 cm−1 and the second at 2839.6 cm−1 and 2788.8 cm−1. The effect of a rather radical increase in water content of the matrix layer (trace F) has a marked different effect on the high and low frequency bands. While the two band pairs in the low frequency range (2991.5 cm−1, 2961.1 cm−1) and (2839.6 cm−1, 2788.8 cm−1) only gain intensity and clarity and the broad spectral feature centered at 2888 cm−1 clearly emerges, the four high frequency bands at 3466.6, 3356.7, 3265.8, and 3176.4 cm−1 become washed out by this increase of water content. Analogous studies were conducted on D2O enriched matrix layers. In Figure 2 shows spectra obtained from Ar/TMA/ (H2O+D2O) matrixes: trace A and trace B are spectral traces from pure Ar/TMA and Ar/D2O layers. Trace C was obtained from a mixed matrix layer containing TMA and 1:10 mixture of D2O/H2O vapors. Trace D represents an analogous matrix layer with a 1:1 D2O/H2O mixture. To enhance the complex band intensities, trace E shows the lower frequency region of a layer similar in composition to that of trace D, but of a considerably higher thickness. Vapor phase equilibrium dictates that trace C is, in essence, a spectrum of an Ar/TMA/HDO matrix layer. In the ν(OD) range shown, five bands at 2554.5, 2475.7, 2398.0, 2247.9, and 2125.9 cm−1 are isotopically related to the complex bands shown in Figure 1, with an isotopic shift ratio of 1.36−1.30. With a higher D2O content of the matrix layer (traces D, E) additional bands emerge at 2418.0, 2353.0, and 2231.7 cm−1.

BAND ASSIGNMENTS In examining the spectral traces in Figure 1, one cannot fail to observe, in the right-hand, lower frequency region, the emergence of two pairs of bands (2788.8, 2839.6 cm−1 and 2961.1, 2991.5 cm−1). In the higher frequency region, to the left of the wavenumber scale break, a third pair of bands appears even at the lowest H2O/TMA ratios at 3265.8 cm−1 and 3356.7 cm−1; the third band at 3176.4 cm−1 has no counterpart in the ν(OD) range (Figure 2) and is assigned to the bending mode overtone 2ν2(H2O). These band pairs which are highly shifted from the position of the free ν(OH) modes of water monomers and dimers, strongly suggest their origin to be in coupled symmetric and antisymmetric H-bonded ν(OH) water modes. In the following we shall discuss the assignments of these spectral bands in terms of various possible structure models computed for the TMA/H2O system shown in Figure 3 (panels A−G). The striking spectral feature in Figure 1 is the appearance of three closely spaced band pairs with essentially unchanged relative intensities in the various matrix layers. This suggests the existence of pairs of coupled ν(OH) in the complex formed. As each TMA moiety can form only a single H-bond to its central nitrogen atom, it is concluded that the formed complex involves two TMA molecules. This conclusion comes as no surprise given the experimental conditions required for the observation of the low intensity complex ν(OH) modes, which demand the deposition of rather concentrated Ar/TMA ratios. This inevitable excess of TMA favors the formation of complexes in which two TMA molecules, rather than a single one, are involved and both hydrogen protons of each water molecule are forming a hydrogen bond with the polarized nitrogen of a TMA molecule. The lowest wavenumber (highest red-shifted) band pair (2788.8 cm−1, 2839.6 cm−1) is, therefore, assigned to these symmetric and antisymmetric coupled modes. The simplest such complex, schematically designated as TMA*HOH*TMA 4091

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Table 1. ν(OH) and ν(OD) band positions and assignments for the TMA*(H2O)4*TMA cluster

#

The relevant normal modes of this structure, as well as those of other calculated complexes discussed in the text, are shown as “movies” in the Supporting Information. *By the empirical correlations. a−ΔH = 1.3(Δνc)1/2; Δνc − pair center.15 bΔν = 0.011r−6.1.26 c−ΔH = 0.134r−3.05.26

or “t-w-t”, is depicted in Figure 3D and is the result of B3LYP calculation. However, this structure can explain the appearance of only a single pair of coupled ν(OH) bonds involved in a hydrogen bonding scheme. Moreover, the scaled vibrational frequencies computed for this structure indicate the shift to lower wavenumbers due to hydrogen bonding to be lower than the observed red shift by a large, unacceptable, extent: while the observed experimental shift for the band pair center is −885 cm−1, the calculated value is only −382 cm−1, that is, a difference of over 500 cm−1. The splitting observed for this band pair is 51 cm−1, and the calculated splitting amounts to 61 cm−1. The presence of a second band pair at positions higher by slightly over 140 cm−1 indicates the existence of an additional pair of two coupled or of two very similar H-bonded ν(OH) modes. Most probably, these are the O−H bonds of two additional water molecules hydrogen bonded to the free electron pairs of oxygen of the H2O molecule bridging two TMAs. Figure 3F depicts the calculated structure of this cluster. For this structure, the calculated shift for the lowest frequency band pair now increases to 525 cm−1, which is notably closer to the observed value because of the significant cooperative effect between the H--O hydrogen bonds and the H--N hydrogen bonds. In other words, the additional H2O molecules Hbonded to the free electron pairs of the central O-atom, act cooperatively to enhance the two O−H--N bonds of the central H2O molecule to the TMA moieties. This effect is also well demonstrated in our computations of the two species designated as “t-w-w-t” and “t-w(w)-t” and depicted in panels C and E of Figure 3, respectively. Because of the cooperative effect, the second H2O molecule in the “t-w(w)-t” clusters adds to its stabilization enthalpy. The alternative “t-w-w-t” structure is located only on a local energy minimum and relaxes into the more stable “t-w(w)-t” configuration.

Thus, when additional H2O molecules are attached to this 1:1:1 TMA*H2O*TMA complex to form the open or closed complexes shown in panels E, F, and G of Figure 3, the cooperative effect between the H2O H-bonds is evident in the red shift increase to −435, −525, and −565 cm−1, respectively (Table 2). These shifts being larger than the one computed for the 1:1 TMA*H2O complex, indicate that this cooperative effect goes beyond a mere increase between the mutually repulsive amine moieties and also is not a result of mode coupling. We show a visual realization of this in the Supporting Information, where movies of the various modes of the complexes discussed here are shown. The antisymmetric mode ν3(H2O) of the water molecule bridging the two TMA moieties of the “t-w-t” complex shown in Figure 3D, remains essentially isolated from any other H2O vibrations also in all the complexes shown in panels E, F, and G of Figure 3. Therefore the marked increase in red shift cannot be a result of mode coupling but rather is a direct result of a significant static cooperative effect between the hydrogen bonds on the clusters. This large cooperative effect may be the underlying cause in promoting the formation in the vapor phase of the cluster depicted in Figure 3G, rather than a straightforeward 1:1 complex (Figure 3A) or one of the simpler complexes shown in Figure 3. A comparison of calculated complexation energies an red shifts of the various models is given in Table 2. Although the two O−H bonds giving rise to the additional, higher frequency, pair of bands do not belong to the same molecule, they still do interact by being bonded to the same oxygen of the central H2O molecule bonding the two TMA molecules. The calculated red shift for this additional band pair is 254 cm−1, still lower by over a factor of 2 from the observed band positions at 2961.1 cm−1 and 2991.5 cm−1, a shift of −750 cm−1 from the ν(OH) bands of H2O monomers. As for the 4092

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Figure 3. Calculated structures for TMA*H2O complexes. Acronyms refere to files containing movies of relevant modes, included in the Supporting Information. Inset: Simulated spectrum for structure G.

band pair splitting, the calculated value is 38.7 cm−1, somewhat higher than the 30.4 cm−1 observed value. The still underestimated calculated red shift for the structure in Figure 3F, as compared to the experimental shift and the existence of a third, higher wavenumber band pair, strongly indicate the need to consider an additional, fourth H2O molecule for the cluster joining the two TMA moieties. The computed structure reproduced in Figure 3G is significantly closer in its predicted spectral properties. The relevant scaled

band wavenumbers are listed in Table 1, and a simulated spectrum for the ν(OH) frequency range is shown also in Figure 3G . For this structure the band pair centers are redshifted by about −185, −380, and 565 cm−1 from the position of matrix isolated water monomer . We conclude that, although the experimental red shifts significantly exceed the respective calculated values, the structure in Figure 3G represents the dominant species trapped in the matrix layer. We note that the “three band pair” spectral 4093

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Table 2. Stabilization Energies and Red Shifts for TMA*H2O complexes shift/cm−1 complex

−1

ΔEelec/kJ mol

a

1:1 TMA*H2O (“t-w”) 1:2 TMA*H2O*H2O (“t-w-w”) 1:2:1 TMA*H2O*H2O*TMA (“t-w-w-t”) 1:1:1 TMA*H2O*TMA (“t-w-t”) 1:2:1 TMA*H2O(H2O)*TMA (“t-w(w)-t”) 1:3:1 TMA*H2O*(H2O)2*TMA (“t-w(w2)-t”) 1:4:1 TMA*H2O(H2O)3*TMA (“t-w(w3)-t”) a

b

−24.4 −55.7 relaxes to “t-w(w)-t” −42.6 −78.7 −105.3 −146.5

calculated

observed

−420 −636.5

−277b

−283 −435 −525 −565

−885c

c

Structures shown in Figure 1 Ref 4. Pair center.

Figure 4. Comparison calculated stabilization energies, red shifts, and bond lengths of H-bonded complexes with empirical correlations of these entities. A. Comparison of computed H-bond stabilization energies ( enthalpies), and the red shifts with empirical correlation Δν = 0.59(ΔH)2 (solid curve).15 1- (CH3NH2)2;33 2- C2H2-pyridine;34 3- phenol-dimer;35 4- 2fluorPy-methanol;36 5- methanol-acetone;37 6- phenol-water;35 7HCOOH-H2O;38 8- cytosine dimer;39 9- H2O2−NH3;40 10- (HCOOH)2;41 11- (CH2)2O-HF;42 12- HCOOH-DME;43 13- H2SO4−H2O;31 14H2O2-N(CH3)3;40 15- HCl-pyridine;44 16- H2SO4-H2O;9 17- H2SO4-NH310 1. For systems 7, 13, 16, and 17, the calculated stabilization energy relates to two bonds, 2. squares- computed (−ΔH) and Δν for several H-complexes of phenol derivatives R-C6H4OH (R = 1- NH2, 2- CH3, 3- H, 4Cl, 5- CN, 6- NO2) with trimethyl amine.45 Inset: analogous comparison for single acid (methanol) with 23 different bases full circles, experimental; open squares, calculated.46 B. Computed (ab initio MP2 aug-cc-pVTZ) red shifts and bond lengths compared to experimental correlation Δν = 0.011r−6.1 (solid curve).26,32 1- NH3-H+-NH3;10 2- H2SO4-(NH3)2;10 3- H2SO4−NH3;10 4- HCl-pyridine;44 5- HF-NH3;47 6- H2SO4-H2O;31 7H2O2-N(CH3)3;40 8- (CH2)2O-HF;42 9- HCOOH-DME;43 10- (HCOOH)2;41 11- Ice XI;48 12- HCOOH-H2O;38 13- H2O2-NH3;40 14- phenolwater;49 15- phenol-water;35 16- methanol-acetone;37 17- cytosine dimer;39 18- phenol-NH3;49 19- phenol-dimer;36 20- 2fluorPy-methanol;3621(CH3NH2)2;33 22- C2H2-pyridine.34 Full squares (this work): 1−4, computed values for O−H···O bonds; 5,6, computed values for O−H···N bonds of cluster depicted in Table 1G.

shortest ones computed for this cluster and are, therefore, associated with the most shifted band pair peaking at 2839.6 and 2788.8 cm−1. Despite the expectation that the N--H−O− H--N be the strongest H-bond interactions of this cluster, the relevant calculated N--H bond lengths are the second shortest at 1.8855 Å. The spectral band pair associated with the mode involving mainly these O−H stretches is assigned to the 2961.1 and 2991.1 cm−1 peaks. The smaller than expected red shift is probably due to an “anti cooperative” effect27,28 related to the repulsion between the methyl groups of the two TMA moieties. The least red-shifted band pair at 3265.8 and 3356.7 cm−1, on the high frequency side of Figure 1, is associated to the stretching modes of the left H2O molecule H-bonded to the central O-atom. The computation associates it with the longest H-bond distances and, hence, with the smallest red shift (−389 cm−1, experimental and −185 cm−1, calculated for the band pair center). It is expected that these modes be affected and become “washed out”, as observed, when further H2O molecules become attached to this cluster in water richer matrix layers. The highest frequency band in Figure 1 is observed at 3466.6 cm−1. Increasing the water content of the matrix layer causes

signature appears even for layers with the lowest H2O content and that the relative intensities remain essentially unaffected by annealing procedures or by varying the deposition temperature. We therefore infer that the clusters are already formed in the gas phase of the TMA vapors between the TMA vapors and the water molecules inevitably present therein. The predominance of this large cluster in the vapor is probably related to the high electronegativity of the central oxygen atom, amplified by being H-bonded to the two TMA molecules. The interaction may be envisioned as if the cental electronegative oxygen atom preferentially attracts the H2O molecules present in the vapors. This conclusion is well suported by the high stabilization energy of 146.5 kJ mol−1 computed for this complex as well as by our observation that the band pair system described persists in matrix layers of trapped TMA/H2O and H2SO4 vapors.25 Hydrogen bond interaction energies and related red shifts of the relevant X-H bonds correlate well with the H-bond lengths.15,26 We note that in the TMA*(H2O)4*TMA complex suggested above the two H2O molecules H-bonded to the central O atom are very dissimilar in their bond lengths. In fact, the two O···H bonds of the H2O molecule on the right are the 4094

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the bond energy. The calculated complexation energies (Table 2) also illustrate this effect: the calculated stabilization energy the complex 1:1:1 TMA*H2O*TMA (Table 1D) with its two H-bonds, is lower by some 13% than twice the stabilization energy of the 1:1 TMA*H2O complex (Figure 1A). We also considered the effect of the computation method on the calculated value of the ν(O−H···N) frequency and the resulting red shift. To this intent, we calculated the wavenumber postion of this mode in the simplest 1:1 TMA*H2O complex by both harmonic (scaled and unscaled) and anharmonic DFT methods and by harmonic (scaled and unscaled) methods. The comparison is given in Table 3. The

this band to grow markedly, with its intensity increasing relative to the three band pairs discussed above. It also becomes washed out when the matrix layer contains an excess of trapped water vapors (Figure 1F), indicating its source to be an “outer” molecule in the cluster. Its wavenumber value is between that of the matrix isolated water dimer29 at 3573.6 cm−1 and the calculated wavenumber of the O−H--OH2 stretch in the TMA*H2O*H2O complex at 3405.6 cm−1. On the basis of these observations we assign it to be due to the attachment of an additional water molecule to the cluster shown in Figure 3G.

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COMPARING EXPERIMENT, COMPUTATION, AND CORRELATION For all three band pairs discussed in the section above, Table 1 shows significant, even striking differences between the experimental red shifts and the much lower values obtained by the computations. For the ν(O−H···O) shifts the magnitudes obtained by correlation with calculated distances26 are consistent with those calculated directly by theory while for the ν(O−H···N) bonds the experimental red shifts due to Hbonding are significantly larger. Underestimated computed red shift values are not unique for the present system. For the H2SO4*H2O monohydrate, the experimnetal red shift of the ν(O−H) stretch was found to be −911 cm−1.9 The DFT calculations by Natsheh et al.30 using the PW91 method and TZP basis set obtained reasonably close red shift value of −860 cm−1. The shift obtained in the anharmonic calculation of Miller et al.31 was only −655 cm−1. As a second example, for the molecular 1:1 H2SO4*NH3 complex (of highly ionic character),10 the anharmonic computation renders a shift value of approximately 1000 cm−1 lower than the experimental value. An overview of the relation between calculated and experimental red shift values is illustrated in Figure 4A. The solid line represents the well established empirical relationship, suggested by Iogansen,15 between experimental red shift and complexation enthalpy. The individual markers indicate calculated values. It may be seen that for the stronger H-bonded systems, the underestimation of the theoretically obtained shift values is more pronounced, whereas for the weaker interactions the general tendency is that the computed values exceed the experimental ones (see inset of Figure 4A). Another important conclusion from Figure 4A is a consequence of the steepness of the curve relating the two entities: a small variation (increase) of the stabilization energy involves a large change in the extent (gain) of the estimated red shift. Similar to the dependence on the bond enthalpy (Figure 4A), the computed red shift has very sharp dependence on the magnitude of the computed H-bond lengths (Figure 4B). However, unlike the computed Δν(OH--O) shifts, the computed, and even more so, the experimental Δν(OH--N) red shifts, notably deviate from the empirical curve (solid curve in Figure 4B). Further insight into discrepancy between calculated and observed red shift values may be obtaind by considering the calculated red shifts of several model complexes. For the “simple” 1:1 TMA*H2O complex (Figure 3A) we calculated a red shift of −420 cm−1, a value which is still lower than the one observed experimentally in this work, but exceeds the value reported in the vapor phase experiments.4 However, the addition of a second TMA molecule, to form the 1:1:1 TMA*H2O*TMA complex depicted in Figure 3D significantly reduces the calculated shift to −282 cm−1 only. This is a clear example of a anticooperative ef fect27,28 of a second H-bond on

Table 3. Calculated Frequency and Red Shift of the ν(O−H ···N) Mode in the TMA*H2O Complex method DFT DFT DFT MP2 MP2

(harmonic) (harmonic, scaled) (anharmonic) (harmonic) (scaled)

frequency/cm−1

“Red” shift/cm−1

3429.9 3281.3 3188.5 3416.6 3245.3

−270.1 −418.7 −511.5 −283.4 −454.7

indication is that, were it possible, anharmonic MP2 calculations would yield results closesest to the observed values. However, such calculations are at present impracticable for molecular systems as large as the other complexes considered here.

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SUMMARY AND CONCLUSIONS The matrix isolation infrared spectra of trimethyl amine (TMA)/water mixtures show bands in the ν(OH) region not seen in the matrix isolation spectra of either of the parent molecules. The most impressive spectral feature is the appearance of several band pairs, even at low H2O/TMA ratios. Their wavenumber positions show a consecutively increasing red shift from the band positions of matrix isolated H2O monomers and exceed the shift for the 1: 1 TMA*H2O, as previously reported. It is concluded that the predominant species isolated in the matrix is a cluster in which a closed ring of four H-bonded H2O molecules is flanked by two TMA molecules. The extra stabilization of this cluster is due to cooperative effects between the H-bonds which promote its formation over that of simpler complexes. Experiments involving highly deuterated water vapors can produce a myriad of isotopomeric samples, and hence render impossibe full assignments. However, the observed bands in Figure 2C and listed in Table 1 were produced with poorly enriched vapors, where only the HOD deuterated water isotopomer would exist, support the above assignments: The isotopic ratio of the new bands is within the range expected for H-bond frequencies, and they lose the pair pattern observed in the spectral traces of Figure 1, indicating the decoupling of modes because of deuteration. These conclusions are supported by MP2 and DFT computations employing the B3LYP functional with an augcc-pVTZ basis set on the structures and frequencies of several possible TMA/H2O complexes. However, these theoretical calculations fail to replicate the strong cooperative effects observed on the (O−H--N) bonds and underestimate the red shift of their stretching frequency. Similarly, correlation with data from many other H-bonded complexes shows that, contrary to the ν(O−H--O) stretching 4095

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frequencies, the stronger bonded ν(O−H−N) bands deviate from the well established empirical correlations found for these systems.

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ASSOCIATED CONTENT

S Supporting Information *

“Movies” of the relevant normal modes of the TMA*(H2O)4*TMA cluster structure, as well as those of other calculated complexes discussed in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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