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J. Phys. Chem. A 2010, 114, 10842–10849
Hydrogen Bonding in Hydrates with one Acetic Acid Molecule Liang Pu,†,‡ Yueming Sun,§ and Zhibing Zhang*,† Separation Engineering Research Center of Nanjing UniVersity, Key Laboratory in Meso- & Microscopic Chemistry of Ministry of Education of China, School of Chemistry and Chemical Engineering, Nanjing UniVersity, Nanjing, 210093, China, College of Science, Northwest A&F UniVersity, Shaanxi 712100, China, and School of Chemistry and Chemical Engineering, Southeast UniVersity, Nanjing, 211189, China ReceiVed: December 1, 2009; ReVised Manuscript ReceiVed: August 10, 2010
Hydrogen bonding (H-bond) interaction significantly influences the separation of acetic acid (HAc) from the HAc/H2O mixtures, especially the dilute solution, in distillation processes. It has been examined from the HAc mono-, di-, tri-, and tetrahydrates by analyzing the structures, binding energies, and infrared vibrational frequencies from quantum chemical calculations. For the first coordinate shell the 6-membered head-on ring is surely the most favorable structure because it has (1) the most favorable H-bonding parameters, (2) almost the largest binding energy per H-bond, (3) the biggest wavenumber shifts, and (4) the highest ring distribution (the AIMD simulations). Moreover, the comparison of the calculations with the experiments (the X-ray scattering data and IR frequencies) suggests that the possible structures in dilute aqueous solution are those involving two or more coordinate shells. The H-bonding in these water-surrounded HAc hydrates are the origin of the low-efficiency problem of isolating HAc from the dilute HAc/H2O mixtures. It is apparently a tougher work to break the H-bonds among HAc and the surrounded H2O molecules with respect to the case of more concentrated solutions, where the dominant structures are HAc or H2O aggregates. 1. Introduction To obtain the high-purity product of acetic acid (HAc) by separating HAc from the HAc/H2O mixtures, distillation is the most widely used method in the modern chemical industry. However, this process is always accompanied by a low efficiency, especially for very dilute solutions. This problem leads to frustrations and failures in tower design or revamping of the separation system. As a matter of fact, the crucial reason causing these problems is the hydrogen bonding (H-bonding) in the mixtures. Hydrogen bonds (H-bond), which establish relatively strong interactions between molecules, are known to strongly influence the properties of vapor-liquid equilibrium of a system, such as the temperature and the heat of evaporation.1 For acetic acid, the HC-H · · · OW interaction involving the methyl group is very weak2 and is enhanced under high pressure.3 The carbonyl CdO and hydroxyl O-H are active hydrogen acceptor and donor groups, respectively. They tend to form double OCdO · · · HO-H H-bonds, resulting in the known cyclic dimer in gas4,5 and some nonpolar solvents6-8 as well as chain structures in pure liquid.9,10 As to aqueous solution, early works suggested the single HAc molecule and its cyclic dimer coexisted.11-15 Recently, the vibrational sum frequency spectra of the HAc/H2O solutions were assigned to several species including the HAc cyclic dimer, especially for those with high acid concentrations.16,17 Moreover, Nishi et al.18 supported that the HAc or H2O molecules form large HAc or H2O aggregates, resulting in microphases. In these cases the interactions between HAc molecules are more favorable than those between HAc and H2O molecules. * To whom correspondence should be addressed. Phone: +86 25 83593772/83596665; E-mail:
[email protected]. † Nanjing University. ‡ Northwest A&F University. § Southeast University.
In contrast, some studies supported that the dominant structures in HAc aqueous solutions are the HAc hydrates.19-21 The interactions between HAc and H2O molecules become more competitive when the concentration decreases.13,14 Using largeangle X-ray scattering (LAXS) and NMR techniques, Takamuku et al. investigated the structure of the pure liquid of HAc and its aqueous mixture.10 The results indicated that the favorable structures transformed from HAc chains to HAc hydrates when the HAc mole fraction xA decreased, and the hydrates finally predominated when xA e ∼0.18. The attenuated total reflectioninfrared and Raman spectra inferred that hydrates of a single HAc molecule are the only species in 0.1-1 mol · L-1 solutions.22 Recently, the presence of the monohydrates and dihydrates of acetic acid, trifluoroacetic acid, and propionic acid was determined by the high-resolution microwave spectroscopic.23-25 Gao et al.26 investigated the H-bonding in the mono- and dihydrates of a single HAc molecule from a density functional theory with three large basis sets. Pu et al.27-29 reported more hydrates combined quantum chemical calculations (QCC) and ab initio molecular dynamics simulations (AIMD). These works suggested that the structure of the favorable hydrates involves head-on rings (see Section 2 for the definition). To date, it is acceptable that the structure in HAc aqueous solution changes with the concentrations and the HAc hydrates dominate the dilute solution. However, the specific structures and H-bonding were limited to small hydrates (mono- and dihydrates),23,26 and a thorough study, for finding out the origin of the low-efficiency problem of distillation, was not presented.27 So this work is intended to present a detailed investigation to the H-bonding interactions in HAc hydrates, from mono- to tetra-, using a high level QCC method and comparing to experimental data. Three parts are included: (1) the H-bonded structures, (2) the binding energies, and (3) the infrared spectroscopy (IR) due to its particular sensitivity to the presence of H-bonds.1,30
10.1021/jp103331a 2010 American Chemical Society Published on Web 09/20/2010
J. Phys. Chem. A, Vol. 114, No. 40, 2010 10843 2. Computational Methods All hydrates in current work involve one HAc and some water molecules (from one to four). These hydrates are classified into four groups, the mono-, di-, tri-, and tetrahydrate, according to the number of water molecules. The geometries, binding energies, and vibrational IR frequencies were determined by using Gaussian 98 and 03 programs.31,32 Hartree-Fock calculation (HF) does not include electron correlation that should be considered for a more reliable and accurate description of weak interactions.33 Beginning with a HF calculation, the second-order Møller-Plesset theory (MP2) offers a correction for electron correlation and has been chosen for all calculations in this work. The basis set cannot be too large because more than 10 conformers were considered for every group except for the monohydrates in this series of works. Then, 6-311++G(d,p), a large triple-ζ basis set including polarization and diffuse functions on all hydrogen atoms, was used throughout, considering H-bonding is the relevant interaction in HAc/H2O complexes. So all calculations were carried out at MP2/6-311++G(d,p) level. For a hydrate that has one HAc and n water molecules, the binding energy (∆E) is derived by eq 1, where Ehydrate, EHAc, and Ewater stand for the total energies of the hydrate, the HAc molecule, and the water, respectively, and n refers to the number of water molecules in the hydrate. Furthermore, the binding energy is corrected for both basis set superposition error (BSSE), using the counterpoise (CP) method34,35 (EBSSE), and vibrational zero-point energies (ZPE, ∆EZPE) according to eqs 2-4.
∆E ) Ehydrate - (EHAc + nEwater)
(1)
∆ECP ) ∆E + EBSSE
(2)
ZPE
∆E
) ∆E + ∆EZPE
∆ECP,ZPE ) ∆E + EBSSE + ∆EZPE
(3) (4)
The vibrations in H-bonded structures are very anharmonic. Gaussian 03 program32 supplies a second-order perturbation approach36 to directly calculate anharmonic frequencies. However, this approach is extremely time-and-memory consuming37 and is not applicable for current work because the number of hydrates involved is up to ∼50. Another approach is uniform scaling of the harmonic vibrational frequencies that are derived by most frequency calculations. However, the scaling factors are usually derived from the calculated and experimental data of free molecules. It is not appropriate to use the same scaling factor for H-bonded complexes because of the wavenumber shift resulting from H-bonding with respect to the free molecules. On the other hand, using a high level of theory with a large basis set can supply very accurate results for the HAc hydrates.26 So in this work the harmonic frequency calculations were performed at MP2/6-311++G(d,p) level without further corrections. A H-bond is denoted as OA · · · HW or HA · · · OW. The left item, OA or HA, stands for the oxygen or hydrogen atom in HAc and the right one, HW or OW, refers to that in H2O. The subscript indicates the functional group to which the atom O or H belongs, where A denotes that in HAc including O-H, CdO, C-O, and C-H, and W refers to that in H2O.
Figure 1. Schematic structures of the head-on, hydroxyl side-on, and carbonyl side-on rings.
Figure 2. Schematic structures of six relative positions, H, A, B, C, D, and E, of the water molecules with respect to the HAc.
Ring structures always appear in favorable hydrates. Figure 2 shows six rings labeled as H, A, B, C, D, and E. Ring H is a head-on ring (short for HO). Rings A and B are side-on rings (SO), where the former is a hydroxyl side-on ring (HSO), and the latter is a carbonyl side-on one (CSO). Rings C, D, and E are the second coordinate shells. The size of a ring is derived by counting the number of heavy atoms. An n-membered HO, SO, HSO, or CSO ring is abbreviated to n-HO, n-SO, n-HSO, or n-CSO, respectively. Examples are given in Figure 1, including three different 4-membered rings. A hydrate is labeled as HhAiBjCkDlEm, composed of different items with an uppercase letter following a lowercase, where the uppercase shows the corresponding ring in Figure 2 and the following lowercase refers to the number of water molecules in that ring. Note that for a water molecule that is coshared in two rings, once it is counted in the former ring, it will not be included in the latter (following the order H, A, B, C, D, and E). 3. Results and Discussion A. Structures. The schematic structures of the top three mono-, three di-, three tri-, and four tetrahydrates are displayed in Figure 3. One group is shown in a single column and the hydrates with similar rings are given in the same row. Arranged according to the binding energies (see subsection B), the structures are less stable from the top to the bottom row for all groups except for the tetrahydrates, where the order is H2D2 > H2C2 > H2E2 > H4. Since the syn-conformer of HAc and its hydrates are more favorable than those with the anti-conformer,26 the hydrates in Figure 3 all possess the syn-conformer of HAc.
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Figure 3. Schematic structures of the top mono-, di-, tri-, and tetrahydrates.
It can be found that the H2O molecules are inclined to attach to the HAc molecule through H-bonds, forming ring structures. Generally, these rings include three types: (1) the HO ring, the first coordinate shell, containing OCdO · · · HW and HO-H · · · OW H-bonds; (2) the HSO and CSO rings with one OCdO · · · HW or OO-H · · · HW H-bond and one HC-H · · · OW; (3) the second coordinate shell around the HO ring. For the mono-, di-, and trihydrates the most stable structures are H1, H2, and H3, respectively. All of them only have one ring, a HO ring. However, for the tetrahydrates, H4 that only involves a 7-HO ring is not the most favorable structure, but H2D2 that has a second coordinate shell (a 4-membered ring) besides the first one (a 5-HO ring) is. The optimized H-bonding parameters, the X · · · H length, the X · · · Y distance, and the X · · · H-Y angle, are given in Tables 1 (the H-bonds between HAc and H2O molecules) and 2 (the H-bonds between water molecules). It can be found that the H-bond length generally increases in this order: HO-H · · · OW (HO) < OCdO · · · HW (HO) < OCdO · · · HW (CSO) < OO-H · · · HW (HSO) < HC-H · · · OW, where HO, CSO or HSO in the parentheses indicates which ring the H-bond is in. The HO-H · · · OW H-bond is shorter and more collinear than others, showing the strong hydrogen donor ability of the hydroxyl group. From the H-bonding parameters, the rings are less favorable following this order: the HO ring > the ring in the second coordinate shell > the SO ring. The HO ring is the most important structure for the first coordinate shell. In hydrate H1 the HO-H · · · OW H-bond is shorter and more collinear than OCdO · · · HW, indicating that for the hydrogen donor ability the hydroxyl is stronger than water.
Going from H1 to H2, significantly shortening is found for both the HO-H · · · OW and the OCdO · · · HW H-bonds, showing that the geometry of H2 is much favorable than that of H1. When one more water molecule is added in H2, the length of the H-bonds keeps on decreasing, however, with a small magnitude. Growing from H3 to H4, the slight shortening of HO-H · · · OW continues, but an elongation of OCdO · · · HW happens. As to the OW · · · HW H-bond (Table 2), a minor decrease always occurs going from H2 to H3 and H4. These trends suggest that the HO ring becomes more favorable from H1 to H2, H3, and H4. Hydrate H3 might possess the most stable HO ring. Hydrates H2C2, H2D2, and H2E2 have two coordinate shells. In these structures the first shell is a 5-HO ring, similar to that in H2, and the second is a 4-membered ring. H2D2 possesses the most favorable parameters. Of all hydrates H2D2 has the shortest OCdO · · · HW and the second shortest HO-H · · · OW Hbonds. These H-bonds in H2D2 are more favorable than those in H2, suggesting that the ring is more stable in the hydrate with two coordinate shells than with one. Note that H2E2 possesses the shortest OO-H · · · HW H-bond. This is because the hydroxyl is inclined to be deprotonated in structures like H2E2, which has a HO-H · · · OW H-bond in the HO ring and a OO-H · · · HW in the HSO ring27 [The O-H length is 1.0206 Å in H2E2 and 0.9917 Å in H2.]. In H2E2 and H2C2 the OO-H · · · HW and OCdO · · · HW H-bonds in the second coordinate shell are more favorable than those in the SO rings (A1, H1A1 or H2A1 and B1, H1B1 or H2B1). The SO rings involve the HC-H · · · OW H-bond, which plays an important role in determining molecular conformation, supramolecular architecture, and the structure of biological
J. Phys. Chem. A, Vol. 114, No. 40, 2010 10845 TABLE 1: Hydrogen Bond Lengths (Å) and Corresponding Angles (°) Involving the HAc Molecule in Various Hydrates Derived at the MP2/6-311++G(d,p) Level of Theory HO ring
SO ring or the second coordinate shell
hydrates
OCdO · · · HWa
HO-H · · · OW
H1 A1 B1 H2 H1A1 H1B1 H3 H2A1 H2B1 H4 H2C2 H2D2 H2E2 exp.
2.0411, 2.7906, 132.74
1.8065, 2.7429, 158.35
1.8554, 2.7993, 162.84 2.0925, 2.8092, 129.50 2.1172, 2.8161, 127.86 1.8200, 2.7913, 176.98 1.8730, 2.8085, 160.72 1.8676, 2.8108, 169.97 1.8792, 2.8079, 158.88 2.0453, 2.9413, 153.46 1.7374, 2.7162, 175.32 1.8986, 2.8386, 162.30 2.822c
OCdO · · · HW (OO-H · · · HW)b
HC-H · · · OW
2.0430, 2.9361, 153.35 1.9630, 2.8882, 159.46*
2.5370, 3.3635, 131.67 2.4993, 3.3732, 136.51
1.9944, 2.9130, 158.39 1.9342, 2.8759, 163.84*
2.5943, 3.4154, 131.33 2.5404, 3.4245, 137.67
1.9938, 2.9159, 159.14 1.9237, 2.8765, 167.83*
2.5685, 3.3515, 127.83 2.5889, 3.4677, 137.23
1.6954, 2.6863, 177.03 1.7725, 2.7201, 160.43 1.7834, 2.7307, 160.66 1.6717, 2.6547, 169.17 1.6722, 2.6651, 175.73 1.6730, 2.6660, 176.04 1.6536, 2.6446, 174.04 1.6281, 2.6279, 175.63 1.6096, 2.6126, 176.32 1.5405, 2.5549, 171.84 2.684,d 2.635-2.656e
1.8581, 2.8025, 163.40* 1.9006, 2.8358, 161.17
a The data order is the O · · · H length, the O · · · O or C · · · O distance, and the O · · · H-O or C-H · · · O angle. b The data with an asterisk refer to OCdO · · · HW, the one without is OO-H · · · HW. c The O · · · O distance of water-water and HAc-water in HAc aqueous solution from ref 10. d The O · · · O distance in the HAc cyclic dimer from ref 38. e The O · · · O distance of linear H-bonds of HAc-HAc in ref 10.
TABLE 2: Hydrogen Bond Lengths (Å) and Corresponding Angles (°) Only Involving the H2O Molecules in Various Hydrates Derived at the MP2/6-311++G(d,p) Level of Theory hydrates H2 H3 H2A1 H2B1 H4 H2C2 H2D2
H2E2 water dimer trimer tetramer pentamer
H-bonda 1 2 1 2 3 1 2 3 1 2 3 4 1 2 3
OW · · · HWb 1.7832, 1.7587, 1.7405, 1.7729, 1.7830, 1.7544, 1.7395, 1.7263, 1.7054, 1.8422, 1.8807, 2.0340, 1.8268, 1.8108, 1.8097, 1.8476, 1.8495, 1.8539, 2.976c 2.90d 2.78e 2.76f
2.7146, 2.7195, 2.7183, 2.7073, 2.7119, 2.7313, 2.7089, 2.7038, 2.6607, 2.7970, 2.8190, 2.8827, 2.7871, 2.7622, 2.7656, 2.7555, 2.7820, 2.8037,
158.30 166.75 175.17 158.78 157.69 175.34 169.50 173.98 162.16 166.23 161.18 145.49 168.13 164.39 165.45 154.13 159.33 164.60
a The number refers to the numbered OW · · · HW H-bond in Figure 3. b The data order is the O · · · H length, the O · · · O distance, and the O · · · H-O angle. c Reference 43. d Reference 44. e Reference 45. f Reference 46.
systems.39 However, the length of HC-H · · · OW is ∼2.55 Å, showing the weak donor ability of the methyl group. Because of this, the OCdO · · · HW H-bond in a CSO ring (B1) shows more favorable parameters than that in a HO ring (A1). The OO-H · · · HW H-bond in a HSO ring is longer and less collinear than OCdO · · · HW in a CSO ring, indicating that for the hydrogen acceptor ability the hydroxyl is weaker than the carbonyl even though its donor ability is pretty strong. The LAXS experiments showed that the O · · · O distance between HAc and water molecules was ∼2.82 Å.10 In this work the H-bond whose length is close to this value is OCdO · · · HW, especially in the complexes of a HO and a SO rings or those having two coordinate shells. This result indicates that the complexes of rings might be the basic structures in HAc aqueous
TABLE 3: Binding Energies (∆E, in kJ · mol-1) of Various Hydrates of HAc Derived at the MP2/6-311++G(d,p) Level ∆E (kJ · mol-1) hydrates
∆E
∆E
CP
∆EZPE
∆ECP,ZPE
reference -38.041a, -39.941b -12.726b -22.745b -79.887a, -86.166b -54.846b -61.801b
H1
-45.948
-35.378
-35.661
-25.091
A1 B1 H2
-20.683 -26.836 -101.377
-14.279 -21.084 -78.723
-13.710 -19.374 -80.609
-7.306 -13.622 -57.955
H1A1 H1B1 H3 H2A1 H2B1 H4 H2C2 H2D2 H2E2
-67.904 -73.741 -145.909 -124.300 -130.220 -185.221 -189.047 -197.014 -187.476
-50.430 -56.849 -111.979 -94.417 -99.927 -140.288 -143.555 -150.545 -141.910
-50.754 -56.428 -114.668 -96.436 -101.382 -144.389 -146.493 -153.861 -146.873
-33.280 -39.536 -80.738 -66.553 -71.089 -99.456 -101.001 -107.392 -101.307
a Reference 23, calculated at MP2/6-311++G(2df,2pd) level with counterpoise correction. b Reference 26, calculated at B3LYP/ 6-311++G(3df, 3pd) level without any corrections.
solution. The O · · · O distance of most HO-H · · · OW H-bonds is close to 2.68 Å38 that appears in the HAc cyclic dimer and 2.635-2.656 Å10 that is assigned to the linear H-bonds of HAc-HAc in the LAXS. The OW · · · OW distance of the experimental results of water clusters is presented in Table 2. It is rapidly converging to the ordered bulk value (2.85 Å,40 2.76 Å41) going from water dimer, trimer, tetramer, to pentamer.42 The calculated OW · · · OW distances in the hydrates only possessing the first coordinate shell are shorter than any experimental data. Those in the hydrates possessing two coordinate shells, especially H2D2, are close to that of the water tetramer45 and pentamer46 because they have similar structures. These results indicate that the hydrates with two coordinate shells are the possible structures. The 5-membered ring similar to the water pentamer might be more stable than the 4-membered one in H2C2, H2D2, and H2E2. B. Binding Energies. Table 3 lists the binding energies of various hydrates, including the uncorrected (∆E), CP-corrected (∆ECP), ZPE-corrected (∆EZPE), and CP, ZPE-corrected data (∆ECP,ZPE), along with references.23,26 It can be found that the uncorrected values are all too large with respect to the corrected ones and the references. Both the CP and ZPE corrections reduce
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TABLE 4: Wavenumbers (cm-1) of Fundamental Vibrations of the Free HAc and H2O Molecules, the Mono- and Dihydrates with One Acetic Acid Molecule Obtained at the MP2/6-311++G(d,p) Level and the Available Experimental Dataa assignmentb
gasc
ν(O-H) νs′(CH3) νas(CH3) νs(CH3) ν(CdO) δas(CH3) δs′(CH3) δs(CH3) δ(COH) ν(C-O) F⊥(CH3) F|(CH3) ν(C-C)
3583 3051 2996 2944 1788 1430 1430 1382 1264 1182 1048 989 847
νas(O-H)
MWd
HAc/H2O
H1
A1
B1
H2
H1A1
H1B1
3808 (73) 3226 (3) 3187 (3) 3101 (2) 1824 (303) 1494 (10) 1494 (14) 1427 (62) 1348 (44) 1221 (220) 1071 (5) 1015 (72) 878 (7)
3529 (577) 3224 (4) 3185 (3) 3100 (2) 1793 (286) 1496 (10) 1494 (21) 1406 (22) 1458 (57) 1305 (264) 1076 (5) 1033 (36) 903 (15)
HAc 3800 (87) 3227 (2) 3185 (3) 3099 (2) 1836 (296) 1499 (15) 1494 (14) 1430 (48) 1334 (29) 1219 (249) 1078 (5) 1015 (86) 865 (19)
3803 (57) 3227 (1) 3186 (2) 3100 (3) 1806 (342) 1502 (11) 1495 (11) 1435 (69) 1363 (67) 1234 (209) 1078 (6) 1030 (65) 885 (3)
3325 (1084) 3223 (8) 3185 (3) 3099 (2) 1781 (344) 1496 (10) 1495 (16) 1411 (67) 1476 (30) 1326 (292) 1075 (5) 1040 (29) 914 (18)
3477 (731) 3225 (4) 3183 (2) 3097 (2) 1806 (286) 1500 (16) 1494 (18) 1417 (37) 1458 (27) 1293 (289) 1080 (6) 1037 (44) 892 (18)
3499 (696) 3226 (0) 3184 (2) 3099 (3) 1775 (323) 1503 (10) 1497 (16) 1414 (19) 1469 (77) 1326 (263) 1081 (6) 1047 (34) 912 (56)
3734
4003 (63)
3960 (112)
H 2O 3978 (130)
3968 (115)
νs(O-H)
3638
3885 (13)
3767 (196)
3837 (103)
3783 (283)
δ(HOH)
1589
1629 (57)
1625 (130)
1640 (52)
1651 (74)
3959 (118) 3951 (98) 3701 (673) 3601 (493) 1652 (72) 1682 (83)
3958 (116) 3973 (131) 3784 (141) 3820 (165) 1626 (132) 1648 (38)
3961 (131) 3968 (101) 3797 (98) 3768 (346) 1621 (123) 1654 (75)
1711 1431 1386 1065 1319 1055 1005 848
a The relative infrared intensities of the vibrational modes are given in the parentheses. b ν ) stretch, δ ) scissors, F ) rock, s ) symmetric, as ) asymmetric. c Reference 49. d Reference 22.
the energies with a large magnitude. The ∆ECP,ZPE values appear to be too small. For example, hydrate B1 has a OCdO · · · HW H-bond, where the O · · · O distance (2.8882 Å) is slightly shorter than that in water dimer (2.976 Å),43 and a weak HC-H · · · OW. So the binding energy of B1 should be similar to that of the water dimer (-20.9 kJ · mol-1).47 Apparently, the ∆ECP,ZPE value of hydrate B1 is too small and the ∆ECP is close (slightly larger). On the other hand, the ∆ECP values are close to those in refs 23 and 26, derived by using very large basis sets. In this case the CP corrected values, ∆ECP, are employed in the following discussion. In general, the binding energy of a HO ring is larger than that of a SO ring [H1 with respect to A1 or B1]; that of a CSO ring (B1) is about 6-7 kJ · mol-1 more negative than that of a HSO ring (A1), which shows the strength difference of the OCdO · · · HW H-bond with respect to OO-H · · · HW. For the SO rings the main contribution to the binding energy is from the H-bond between HAc and water molecules because the Hbonding energy of HO-H · · · O was estimated as 5-10 times of that of HC-H · · · O.48 Hydrates H1, H2, H3, and H4 have similar structures and H-bonding interactions. So the binding energy per H-bond (∆ECP/nH-bond) can reflect the changing trend of the H-bonding interactions. The ∆ECP/nH-bond increases from 17.689 to 26.241, 27.995, and 28.058 kJ · mol-1, going from H1 to H2, H3, and H4. The H-bonding interaction is significantly enhanced by adding one H2O molecule to hydrate H1. It undergoes a small increase growing from H2 to H3. Further incorporation of the H2O molecule (H3, H4) results in a minor increase. The H-bonding interactions are similarly strong in H3 and H4. For tetrahydrates, H4 has the smallest binding energy in the four conformers though it possesses only a 7-HO ring similar to the most stable structures in mono-, di-, and trihydrates (H1, H2, and H3). The ∆ECP of others involving the second coordinate shell is about 7-10 kJ · mol-1 more negative than that of H4. In particular, H2D2 has the largest binding energy and is the most favorable structure in tetrahydrates. The result of the binding energies is consistent with that of the structures. For the structures only involving the first
coordinate shell, hydrate H3, with a 6-HO ring, is the most favorable one. Although H4 shows similar H-bonding parameters and binding energies per H-bond to H3, it is inclined to turn into more stable tetrahydrates with two coordinate shells where the first one is a 5-HO ring. Such structures with two or more coordinate shells are more favorable while more water molecules are invovled. C. Vibrational Frequencies. The calculated IR frequencies and intensities of various hydrates are shown in Tables 4 and 5, along with the experimental data in gas phase49 and those assigned to a possible hydrate, MW (The HAc molecule for this hydrate is CH3COOD).22 The data of the free HAc and H2O molecules, three mono- and three dihydrates are presented in Table 4, and those of three tri- and four tetrahydrates are listed in Table 5. The frequencies include 13 normal modes of acetic acid and three of water. As to the free HAc and H2O molecules, the calculated wave numbers are larger than the experimental data49 about 2.0-7.2% [HAc: ν(O-H), 6.3%; ν(CdO), 2.0%; δ(COH), 6.6%; ν(C-O), 3.3%. H2O: νas(O-H), 7.2%; νs(O-H), 6.8%; δ(HOH), 2.5%]. Wavenumber shift ∆ν always appears in a hydrate, where the H-bond leads to the change of the force constant of the covalent bond.30 It reflects the strength of the regarding H-bonding interaction. In this work, if it is not specified, the wavenumber shift implicitly refers to the frequency difference of a hydrate with respect to the single HAc or water molecule. For acetic acid, the hydroxyl stretching mode ν(O-H) shows a red shift with a broad and intense band (200-1000 cm-1), which is the typical characteristic for the hydrogen donor group of a HX-H · · · Y H-bond. When the HO-H · · · OW H-bond is established, the electron density is transferred from the hydrogen acceptor, the O atom of H2O, to the σ*-antibonding orbital of the O-H bond (the hydroxyl), which causes a weakening and elongation of the O-H bond and a decrease of ν(O-H).50,51 The changes of the ν(CdO), ν(C-O), and δ(COH) modes are induced by the OCdO · · · HW and HO-H · · · OW H-bonds.50 The CdO group accepts a H-bond, the C-O bond is in the vicinity of the two H-bonds, and the COH implies the H atom that establishes the HO-H · · · OW H-bond. For the OCdO · · · HW H-bond,
J. Phys. Chem. A, Vol. 114, No. 40, 2010 10847 TABLE 5: Wavenumbers (cm-1) of Fundamental Vibrations of the Tri- and Tetrahydrates with One Acetic Acid Molecule Obtained Computationally at the MP2/6-311++G(d,p) Level and the Available Experimental Dataa assignmentb
MWc
H3
H2A1
H2B1
H4
H2C2
H2D2
H2E2
3284 (1323) 3222 (13) 3184 (4) 3099 (2) 1779 (388) 1498 (11) 1494 (17) 1403 (46) 1467 (49) 1324 (320) 1077 (3) 1033 (54) 913 (2)
3270 (1239) 3224 (17) 3182 (2) 3098 (2) 1793 (337) 1501 (16) 1494 (17) 1419 (72) 1471 (16) 1314 (307) 1078 (8) 1044 (34) 908 (18)
HAc 3275 (1242) 3224 (3) 3184 (2) 3098 (2) 1758 (390) 1504 (15) 1500 (12) 1418 (64) 1485 (49) 1349 (282) 1081 (4) 1054 (26) 921 (21)
3275 (1514) 3221 (17) 3184 (4) 3099 (3) 1780 (407) 1496 (9) 1495 (14) 1407 (64) 1473 (38) 1325 (308) 1074 (8) 1036 (68) 912 (7)
3136 (1465) 3220 (5) 3186 (2) 3098 (1) 1760 (361) 1499 (13) 1485 (29) 1420 (125) 1515 (14) 1354 (232) 1084 (62) 1042 (29) 919 (3)
3081 (1654) 3223 (3) 3184 (3) 3099 (6) 1761 (279) 1496 (10) 1488 (32) 1418 (118) 1508 (11) 1350 (240) 1075 (4) 1044 (24) 922 (16)
2792 (1938) 3221 (4) 3180 (3) 3095 (2) 1787 (331) 1499 (11) 1492 (18) 1421 (139) 1553 (24) 1330 (331) 1075 (4) 1039 (28) 917 (16)
νas(O-H)
3957 (127) 3952 (81) 3949 (92)
3971 (119) 3958 (131) 3946 (97)
H 2O 3966 (117) 3955 (123) 3948 (104)
νs(O-H)
3710 (670) 3596 (762) 3520 (748)
3816 (168) 3716 (620) 3588 (516)
3768 (322) 3717 (602) 3602 (506)
δ(HOH)
1714 (85) 1689 (47) 1670 (66)
1685 (88) 1659 (40) 1649 (72)
1678 (101) 1657 (39) 1649 (80)
3953 (45) 3952 (117) 3949 (94) 3946 (101) 3720 (528) 3584 (553) 3546 (1302) 3481 (595) 1719 (3) 1701 (92) 1686 (85) 1674 (73)
3957 (89) 3953 (132) 3945 (84) 3844 (396) 3721 (267) 3706 (659) 3653 (389) 3431 (942) 1745 (143) 1685 (100) 1673 (49) 1659 (61)
3956 (81) 3954 (100) 3941 (104) 3831 (305) 3677 (290) 3648 (830) 3598 (373) 3519 (1170) 1740 (190) 1692 (11) 1669 (77) 1658 (106)
3961 (120) 3957 (88) 3953 (153) 3748 (134) 3742 (1003) 3713 (742) 3671 (267) 3637 (169) 1695 (55) 1676 (41) 1659 (71) 1651 (67)
ν(O-H) νs′(CH3) νas(CH3) νs(CH3) ν(CdO) δas(CH3) δs′(CH3) δs(CH3) δ(COH) ν(C-O) F⊥(CH3) F|(CH3) ν(C-C)
1711 1431 1386 1065 1319 1055 1005 848
The relative infrared intensities of the vibrational modes are given in the parentheses. b ν ) stretch, δ ) scissors, F ) rock, s ) symmetric, as ) asymmetric. c Reference 22. a
the hydrogen donor, O-H, shows a red shift. The hydrogen acceptor group, CdO, also weakens and ν(CdO) moves to lower frequency (40-60 cm-1),52 with the magnitude much less than the case of the donor group. Both ν(C-O) and δ(COH) anticorrelate with ν(O-H) and ν(CdO),26 showing blue shifts. Those modes involving the methyl group display minor shifts because the HC-H · · · O H-bond is weak. As to water, the asymmetrical and symmetrical stretching modes, νas(O-H) and νs(O-H), both show red shifts and considerably enhanced intensities in all hydrates. The bending mode δ(HOH) exhibits blue shifts. The nature of these shifts is similar to that of acetic acid. Wavenumber Shifts and the Strength of H-Bonding. The ∆ν(CdO), ∆ν(O-H), ∆ν(C-O), and ∆δ(COH) for HAc in various hydrates are displayed in Figure 4a-d, respectively. With the solid line, the square, circle, and triangle refer to the hydrates in the first (only with a HO ring), third (with a CSO ring), and fourth rows (with a HSO ring) in Figure 3, respectively. The single square shows the shifts of H2D2. The dashed line presents the ∆ν of the hydrate involving a HO ring and a SO ring from the one only with the same-sized HO ring [For example, H1A1 and H1B1 with respect to H1.], for estimating the H-bonding of the SO ring. The straight dashed line presents the experimental result that is the wavenumber difference of the MW,22 a hydrate, from the gas,49 the free HAc molecule, in Table 4. The ∆ν value of the hydrates only with a HO ring (the solid line with the square) generally increases in this trend: H1 < H2 < H3 ≈ H4. It reflects the relative strength of the H-bonding interactions and the stability of the hydrates, which is consistent with the results of the structures and energies. For the hydrates with a SO ring (the solid line with the circle or triangle) the ∆ν value always increases going from mono-, di-, tri-, to tetrahy-
drate. Comparing the circles or triangles with the squares, the ∆ν value is generally smaller for the mono- and dihydrate, similar for the trihydrate and larger for the tetrahydrate. The dashed lines show that the mono-, di-, and trihydrates have similar values. They are much smaller than the solid line with the square, indicating that the H-bonding interaction in the 4-SO ring is much weaker than that in the HO ring. The dashed line shows an increase for the tetrahydrates, especially for ∆ν(O-H) and ∆δ(COH). These structures possess two coordinate shells, and the second shell is more favorable than the 4-SO ring. It can be found that the structures whose ∆ν values are closer to the experimental results22,49 (the straight dashed line) are the tetrahydrates possessing two coordinate shells, especially for ∆ν(CdO) and ∆ν(C-O) of H2C2 and H2D2, and ∆δ(COH) of H2E2. The possible hydrate in the reference work22 was also assigned to the structure possessing a 4-HO ring and one H2O molecule H-bonded to the CdO group at the side-on position. These results indicated that those complexes of rings might be the possible structures in HAc aqueous solution. The ∆νas(O-H), ∆νs(O-H), and ∆δ(HOH) for H2O in various hydrates are displayed in Figure 5a-c, respectively. The open and solid squares show two water molecules in a HO ring, where one accepts the hydroxyl group and one is H-bonded to carbonyl groups. The solid circle and triangle refer to those H-bonded to the CdO group in a CSO ring and the O-H group in a HSO ring, respectively. The lines refer to four H2O molecules that are H-bonded to different groups in different positions. According to the magnitudes of ∆ν, the group that forms one H-bond with a water molecule is generally less favorable in this trend: the hydroxyl (the HO ring, the open square) > carbonyl (HO, the solid square) > carbonyl (CSO, the circle) > hydroxyl (HSO, the triangle). This trend shows that the strength of the corresponding H-bond
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Pu et al.
Figure 4. The wavenumber shifts for acetic acid in various hydrates. The solid lines show the shifts with respect to that of the free acetic acid molecule. The dashed line with the symbol denotes the ∆ν difference of the hydrate that involves a head-on ring and a side-on ring from the hydrate containing only the same-sized head-on ring. The straight dashed line presents the experimental results.22,49
in the following order: H3 > H4 > H2 > H1, similar to that reflected by the ∆ν of HAc. This result indicates that the H-bonding interaction is more favorable in the 6-HO ring (in H3) than in others. In summary, the results of the wavenumber shifts are consistent with the analysis of the structures and binding energies. Comparing the calculations with the experiments (the X-ray scattering and the IR frequencies), the possible structures in dilute aqueous solution might be the HO rings with more coordinate shells, the H-bonded network. For the first coordinate shell the 6-HO ring (hydrate H3) is the most favorable structure. This result is also in good accord with those of two AIMD simulations in previous works,27,28 which were performed on two systems possessing one and two HAc molecules, respectively, and many water molecules. The statistics of the results for both systems, the ring distributions, clearly indicated that the 6-HO ring had the largest population (see Supporting Information).
Figure 5. The wavenumber shifts of the three vibrational modes of H2O in various hydrates. The open and solid squares, solid circle, and triangle show the ∆ν for the water molecules H-bonded to the following respective group: the hydroxyl (the HO ring), carbonyl (HO), carbonyl (CSO), and hydroxyl (HSO).
decreases in this order: HO-H · · · OW (HO) > OCdO · · · HW (HO) > OCdO · · · HW (CSO) > OO-H · · · HW (HSO). The squares show that the hydrates only with a HO ring are generally less stable
4. Conclusions The H-bonding interactions in HAc mono-, di-, tri-, and tetrahydrates have been examined from the structures, the binding energies, and the IR frequencies. For the first coordinate shell the stable structures appear to be three ringssthe HO, CSO, and HSO. The 6-HO ring (hydrate H3), with the binding energy per H-bond of 28.0 kJ · mol-1, is the most favorable structure. By comparing the calculated results to the X-ray scattering data and experimental IR frequencies, the possible structures in dilute HAc aqueous solution appear to involve two or more coordinate shells. In more concentrated solutions the main structures are the HAc or H2O aggregates, which are relatively easy to separate. So it is definitely more difficult to break the H-bonds between HAc and the surrounded H2O molecules in dilute aqueous solutions than those in more concentrated solutions. The understanding of those favorable structures in this work is very helpful to the further research of the low-efficiency of isolating HAc from its aqueous solutions. Acknowledgment. We are grateful to the High Performance Computing Center of Nanjing University for awarding CPU
J. Phys. Chem. A, Vol. 114, No. 40, 2010 10849 hours to accomplish this work. This work is supported by the Natural Science Foundation of Jiangsu Province of China (No. BK2008023). Supporting Information Available: Three distributions of the H-bonded head-on ring involving a single HAc molecule from two AIMD simulations in the previous work.27,28 This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Mare´chal, Y. The Hydrogen Bond and the Water Molecule: The Physics and Chemistry of Water, Aqueous and Bio-Media; Elsevier Science: 2007. (2) Hobza, P.; Havlas, Z. Chem. ReV. 2000, 100, 4253–4264. (3) Chang, H.-C.; Jiang, J.-C.; Lin, M.-S.; Kao, H.-E.; Feng, C.-M.; Huang, Y.-C.; Lin, S. H. J. Chem. Phys. 2002, 117, 3799–3803. (4) Karle, J.; Brockway, L. O. J. Am. Chem. Soc. 1944, 66, 574. (5) Frurip, D. J.; Curtiss, L. A.; Blander, M. J. Am. Chem. Soc. 1980, 102, 2610–2616. (6) Davis, J. C., Jr.; Pitzer, K. S. J. Phys. Chem. 1960, 64, 886–892. (7) Waldstein, P.; Blatz, L. A. J. Phys. Chem. 1967, 71, 2271–2276. (8) Tjahjono, M.; Allian, A. D.; Garland, M. J. Phys. Chem. B 2008, 112, 6448–6459. (9) Nakabayashi, T.; Kosugi, K.; Nishi, N. J. Phys. Chem. A 1999, 103, 8595–8603. (10) Takamuku, T.; Kyoshoin, Y.; Noguchi, H.; Kusano, S.; Yamaguchi, T. J. Phys. Chem. B 2007, 111, 9270–9280. (11) Freedman, E. J. Chem. Phys. 1952, 21, 1784. (12) Cartwright, D. R.; Monk, C. B. J. Chem. Soc. 1955, 2500–2503. (13) Ng, J. B.; Shurvell, H. F. Can. J. Spectrosc. 1985, 30, 149–153. (14) Ng, J. B.; Shurvell, H. F. J. Phys. Chem. 1987, 91, 496–500. (15) Tanaka, N.; Kitano, H.; Ise, N. J. Phys. Chem. 1990, 94, 6290– 6292. (16) Johnson, C. M.; Tyrode, E.; Baldelli, S.; Rutland, M. W.; Leygraf, C. J. Phys. Chem. B 2005, 109, 321–328. (17) Tyrode, E.; Johnson, C. M.; Baldelli, S.; Leygraf, C.; Rutland, M. W. J. Phys. Chem. B 2005, 109, 329–341. (18) Nishi, N.; Nakabayashi, T.; Kosugi, K. J. Phys. Chem. A 1999, 103, 10851–10858. (19) Colominas, C.; Teixido, J.; Cemeli, J.; Luque, F. J.; Orozco, M. J. Phys. Chem. B 1998, 102, 2269–2276. (20) Aquino, A. J. A.; Tunega, D.; Haberhauer, G.; Gerzabek, M. H.; Lischka, H. J. Phys. Chem. A 2002, 106, 1862–1871. (21) Chocholousova, J.; Vacek, J.; Hobza, P. J. Phys. Chem. A 2003, 107, 3086–3092. (22) Ge´nin, F.; Quile`s, F.; Burneau, A. Phys. Chem. Chem. Phys. 2001, 3, 932–942. (23) Ouyang, B.; Howard, B. J. Phys. Chem. Chem. Phys. 2009, 11, 366–373. (24) Ouyang, B.; Starkey, T. G.; Howard, B. J. J. Phys. Chem. A 2007, 111, 6165–6175. (25) Ouyang, B.; Howard, B. J. J. Phys. Chem. A 2008, 112, 8208– 8214. (26) Gao, Q.; Leung, K. T. J. Chem. Phys. 2005, 123, 074325. (27) Pu, L.; Wang, Q.; Zhang, Y.; Miao, Q.; Kim, Y.-s.; Zhang, Z. AdV. Quantum Chem. 2008, 54, 271–295. (28) Pu, L.; Sun, Y.; Zhang, Z. J. Phys. Chem. A 2009, 113, 6841– 6848. (29) Pu, L.; Sun, Y.; Zhang, Z. Sci. Chin. Ser. B: Chem. 2009, 52, 22192225. (30) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological Structures; Springer: 1991.
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