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The Secret of Dimethyl Sulfoxide-Water Mixtures. A Quantum Chemical Study of 1DMSO-n Water Water Cluste Clusters rs Barbara Kirchner*,† and Markus Reiher*,‡ Contribution from the Physikalisch-Chemisches Institut, Uni V ersita ersita¨ t Zu¨ rich, Winterth Winterthurerstrasse urerstrasse 190, CH-8057 Zu¨ rich, Switzerland, and Theoretische Chemie, Uni V ersita ersita¨ t Erlangen-Nu¨ rnberg, Egerlandstrasse Egerland strasse 3, D-91058 Erlangen Erlangen,, Germany Received December 7, 2001
Abstract: DMSO DMSO-water mixtures exhibit a marked freezing point depression, reaching close to 60 K at n DMSO DMSO ) 0.33. The phase diagram indicates that stable DMSO-water clusters may be responsible for this phenomenon. Using time-independent quantum chemical methods, we investigate possible candidates for stable supermolecules at mole fractions n DMSO DMSO ) 0.25 and 0.33. The model clusters are built by adding various numbers of water molecules to a single DMSO molecule. Structures and interaction energetics are discussed in the light of experimental and theoretical results from the literature. A comparison with results from molecular dynamics simulations is of particular interest. Our optimized structures are spatially very different diffe rent from those previ previousl ously y ident identified ified through MD simu simulatio lations. ns. To ident identify ify the stru structur ctural al patt patterns erns characterizing the clusters, we classify them on the basis of hydrogen acceptor interactions. These are well separated on an interaction energy scale. For the hydrophobic interactions of the methyl groups with water, attractive interactions of up to 8 kJ/mol are found. In forming clusters corresponding to a range of different mole fractions, up to four water molecules are added to each DMSO molecule. This corresponds to a rough local model of solvation. Examination of the trends in the interactions indicates that the methyl water interaction becomes more important upon solvation. Finally, we investigate how the clusters interact and attempt to explain which role is played by the various structures structures and their intercluster interaction interaction modes in the freezing freezing behav behavior ior of DMSO-water.
1. Introduction Many mixtures of water with organic solvents show properties deviating from ideality. For the system consisting of water and dimethyl sulfoxide (DMSO), extreme deviations from additivity are observed for a wide range of properties, such as density, viscosity, viscos ity, and adiaba adiabatic tic and isothe isothermal rmal compr compressibil essibility. ity.1 At the mole fraction nDMSO of ∼0.33, a very low freezing point ( 140 °C) was measured.2 The author suggested that a stable
the computer experiments. To solve the puzzle pr thiss int thi intere eresti sting ng mix mixtur ture, e, we tak takee one ste step p bac simulations and focus on the interactions, i.e., the inte potential. Thisup is to thevote hearton of this the MD Sign titlesimulation, as it the forces acting on all molecules and therefore the Useful Not useful the system. It is also the point at which quantum che MD simulations meet. Specifically, in this work, we examine closely the
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Table 1. Correspondence of Mole Fractions and Cluster
Compositions n DMSO
NoH2O
NoDMSO
0.5 0.33 0.25 0.2
1 2 3 4
1 1 1 1
All interaction energies (IE) were counterpoise-cor procedure of Boys and Bernardi.21,22 For the correction energy (IEpair), two possibilities arise, namely
IEpair(φ2) )
∑[ E
(AB)i(φ2i)
- E Ai(φ2i) - E B
i
and
a 1DMSO-3H2O cluster and also why they are not able to explain the unusual behavior of the mixture at mole fraction nDMSO ) 0.33-0.25. The article is organized as follows: The quantum chemical methodology used is described in detail in the next section. We then present the structures of the 1DMSO -nH2O clusters found to be minimums on the electronic potential energy surface (section 3) and classify the different types of hydrogen-acceptor interactions (section 4). The following section 5 gives a detailed evaluation of the interaction energetics in these clusters, including (section 5.2) an analysis of the contribution of the nuclei in addition to the purely electronic effects discussed so far. The assumption of pairwise additivity of these interactions is examined in section 6. Finally, section 7 gives a discussion of solvation effects.
IEpair(φn+1) )
∑[ E
(AB)i(φn+1)
- E Ai(φn+1) - E
i
These formulations differ in the size of the basis sets calculation of dimer and monomer energies. While φ 2i den functions of the molecule pair i constituting a dimer, basis of the entire 1DMSO-nH2O cluster. Obviously, in case of the 1DMSO-1H2O configurations. For neon tr been shown that the difference between the two negligible.23 We therefore chose the latter way of calculatin energies for practical reasons. Note that the definition of pair interaction energies excludes the energy contribut conformational relaxation of the fragments when the com formed. This is in line with current definitions of comple energy (ref 24, p 1377) (structural relaxation would interaction energies only by ∼1 kJ/mol per molecule in th ecule). 2. Methodology Whereas the counterpoise correction has been interaction energies, it has not been applied during the For this work, we used both density functional theory (DFT) and procedure. Test optimizations with larger basis sets confirm second-order Møller-Plesset (MP2) perturbation theory, to gain a deviations to our minimum structures. consistent picture independent of quantum chemical method. The You're Reading a To Preview visualize a potential electron-pair interaction, we application of MP2 is particular important in this case, as the DFT electron localization function (ELF). ELF is a me results lack a correct description of dispersion interactions. For all Unlock full access with a free trial. spherically averaged Fermi hole around a reference quantum chemical structure optimizations, we used the density funcdescribed by Becke and Edgecombe,25 the function can be tional and ab initio programs provided by the TURBOMOLE 5.1 suite.9 an interval 0 < ELF < 1. ELF ≈ 1 indicates areas of We employ the hybrid Hartree-Fock/DFT functional B3LYP10,11 as Download With Free Trial exchange potential. Such areas are occupied by electron p implemented in TURBOMOLE. The B3LYP results were obtained from plots were generated with the Car-Parrinello MD all-electron restricted Kohn-Sham calculations. For the MP2 calculaParrinello group.26 tions, we applied the resolution of identity (RI) technique.12-16 The For the vibrational analysis, the second derivative molecular orbitals, which are mainly of the character of 1s atomic electronic energy were computed as numerical first deriv orbitals of the DMSO sulfur atoms, are kept frozen in the MP2/RI TUR the analytic energy gradients obtained from calculations. Ahlrichs’ TZVP basis set was used throughout, featuring Sign up to vote onthethis title vibrational e vibrational frequencies and zero-point a valence triple- basis set with polarization functions on all atoms.17 obtained the harmonic For the c Useful useful within Notapproximation. To analyze the electron density of the compounds, we made use of ∆ D0 values, the zero-point energy differences were the 18 the concept of shared-electron numbers (SEN) as implemented in total electronic energy differences. TURBOMOLE. In this approach, interaction energies are evaluated The program MOLDEN29 was used to visualize the st
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Figure 1. Configurations of the smaller clusters. An additional view from the top of the cluster has been added for clarity. All structures are ful minimums on the potential energy surface, except structure 0.5-V, which was optimized in C s symmetry and turned out to be a first-order sadd With are Free structures depicted were obtained from B3LYP calculations.Download The MP2/RI structures veryTrial similar and could not be distinguished from the B3L in these representations.
treating the component molecules as units without ingoring the intramolecular energetics. We refer to a particular structure at a given mole fraction as a configuration. Figure 1 and Figure 2 depict all optimized minimum-energy configurations at the different mole fractions. As it is also part of this study to test how well the assumption
0.33-VI, in which the oxygen atom of the water m further away from the sulfur atom than its hyd Sign up to1).vote on this title (compare Figure useful0.33-I, 0.25-II, a We refer to configurations Useful Not 0.5-I, ‘Ru¨ssel’ configurations (from the German: Ru¨ss because all water molecules are arranged in a trunkli
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Figure 2. Configurations of the larger clusters with additional view from the top. The structures depicted were obtained from B3LYP calcu Unlock full with structures a free trial. MP2/RI structures are very similar and could not be distinguished fromaccess the B3LYP in these representations.
4. Classification of Hydrogen-Acceptor Interactions as dimer, in agreement with refs 32 and 33. The increase Download Withbond Freeenergy Trial may be understood in terms of a Key Structural Feature of Different Configurations attraction. We calculated partial charges obtai In view of the variety of different configurations occurring different population analyses, namely, the one by A at each mole fraction (Figures 1 and 2), the need to identify the co-workers and the one by Cioslowski (for detai key structural characteristics of each arises. Elements charactermethods see section 2). We used both analyses since izing the differences between the configurations are given by Sign up to vote on this title charge of an atom is not a well-defined quantum m dividing the different intermolecular bonds into categories. The quantity is thus affected a certain arbitrarin Useful useful and Not by following four types of intermolecular-bonding modes, which case, both population analyses show a clear distincti are well separated according to their different interaction the partial charges of oxygen atoms in water and D energies, may be distinguished (Note that the structural parampartial charge is 0.7 for DMSO oxygen atoms an
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Table 2. B3LYP/TZVP Interaction Energies Obtained with the
SEN Method (in kJ/mol)a configuration
pair
0.33-IV
H(W1)‚‚‚O(D) O(W1)‚‚‚H1(D) O(W1)‚‚‚H1b(D) H(W2)‚‚‚O(D) O(W2)‚‚‚H2(D) O(W2)‚‚‚H1(D) H(W2)‚‚‚O(W1)
0.33-II
H(W1) ‚‚‚O(D) H(W2)‚‚‚O(W1) O(W2)‚‚‚H(D)
σ HA
0.0545
<0.0050 <0.0050
0.0322
<0.0050 <0.0050
0.0138 0.0704 0.0634 0.0148
IE SEN
r B3LYP
r MP2/RI
-28.0 <-2.6 <-2.6 -16.6 <-2.6 <-2.6 -7.1 -36.2 -32.6 -7.6
186.4 321.5 301.9 204.7 267.8 261.6 227.7
182.5 310.3 296.3 201.6 251.3 255.8 235.7
176.1 180.4 222.3
174.1 179.1 222.6
a Only an upper bound is given for SENs less than the threshold of 0.005. Water molecules are abbreviated as W and DMSO as D. Donor -acceptor distances are given for B3LYP and MP2/RI (in pm).
Figure 3. ELF isosurface (ELF ) 0.85) for the lowest-energ 1DMSO-1H2O. The lone pair at the sulfur atom, the doughnu pairs at the DMSO oxygen atom, and the lone pairs at the atom are visualized. Note the interaction of the water oxyge with the methyl group hydrogen atoms, resulting in a reduce of finding a localized electron pair in between.
bond network, because rings involving only the hydrogenacceptor oxygen atom of DMSO lack a hydrogen donor atom from DMSO. (see also section 5). In this case, the optimum distance and angle of H2a cannot be achieved. This intermolecular bond energy cannot be estimated from the decomposition of a cluster; i.e, it is not possible to attribute the decomposition energy solely to the broken hydrogen bond. An alternative way to obtain the energy of this bond is given by the SEN method19 (see Table 2 and section 2 for details on the method). We chose configuration 0.33-IV with a total B3LYP interaction energy of -67.8 kJ/mol (cf. Table 4) and distributed this energy between the three different contacts of the water molecule under consideration. The hydrogen bond energy for You're the strained Reading a Preview H‚‚‚O bond with HsO distance 225 pm and O ‚‚‚OsH angle 35.2° is less than 10 kJ/mol. Unlock full access with a free trial. Note that strained hydrogen bonds also occur in those Figure 4. Rotation curve of a methyl group in 0.33-II (plus points; dotted line, spline) and in DMSO alone (stars, calcu configurations where attraction by the methyl groups of DMSO solid line, spline) calculated with B3LYP/TZVP. Download With Free Trial are important, as in the case of 0.25-IV. 4.3. Water-Oxygen-Methyl-Hydrogen Contacts (Type H3). As we observed many configurations featuring the oxygen shall denote the situation where certain coordinatio atom of a water molecule in close proximity to a hydrogen atom along the ring around the DMSO oxygen atom are fa of the DMSO methyl group, we were curious to see whether others.) This is in agreement with previous MD si Sign up to vote on this title there is a pronounced attraction between the two. We call this However, in this structure, the water molecule is c interaction a contact , because its interaction energy may range place by methyl groups, useful interaction wit theUseful Notwhose from very weak to strong intermolecular bonding. Table 2 gives oxygen atom is expressed by the deformed ELF is estimates for the H3-type contacts in 0.33-IV and 0.33-II the participating C-H moiety. We thus note that p calculated by the SEN method. Indeed, it is found that the energy
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Table 3. Order of Stable Configurations for Different Mole
Fractionsa structural features n DMSO no.
rings
H1 H2a H2b H3
B3LYP ∆IE
MP2/RI ∆IE
B3LYP ∆D 0
0.5
I II III IV V
2×6 1×6
1002 1001 1000 1000 0000
0.0 6.1 10.4 15.0 19.6
0.0 5.2 9.4 13.7 16.5
0.0 5.5 8.6 13.5 16.6
0.33
I II III IV V VI
2×8 1×8 2×6 3×6 2×6 2×6
1102 1101 2002 2012 2002 1002
0.0 7.2 16.2 16.5 17.2 32.3
0.0 6.7 12.8 11.5 13.1 25.3
0.0 6.8 13.4 16.3 15.4 27.4
0.25
I II III IV V VI VII
2×8 2×6 2 × 10 2×8 1×6 1×8 2×6 1×8 2×6 1×8 1×6 4×6
2112 1203 1122 2112 2102 2111 3003
0.0 0.1 1.8 2.3 3.6 8.9 18.2
0.0 1.4 2.1 1.9 2.6 8.9 13.3
0.0
-1.4 2.3 3.1 1.4 8.7 16.5
To characterize the structures alternatively to the cl in section 4, we give in the third column the num structures present in the particular configuration. F “1 × 6” means one ring consisting of six ato the rings include four atoms from the DMSO sometimes only the oxygen atom. If other atoms are involved, there is always one large methyl water-oxygen separation distance. If this distance is 290 pm, the structure is not counted as a ring. In ad number of different types of intermolecular inte classified in the previous section is given for each In the next three columns, the difference between the energy of the lowest-energy configuration and the co considered in a particular row is given. The energie for B3LYP, MP2/RI, and B3LYP corrected vibrational energy.
Within the configurations considered, the structures at mole fractions n DMSO ) 0.5, 0.33, and global minimum structures as the next lowest stru 0.2 I 2 × 12 1303 0.0 0.0 0.0 approximately 5-7 kJ/mol higher in energy. This is II 1 × 10 2 × 6 2212 4.7 6.2 5.6 the error of the methods we used, which we expec III 3 × 10 2203 5.2 4.7 9.6 IV 3×8 2203 5.3 4.5 4.4 than 5 kJ/mol. For mole fraction nDMSO ) 0.25, the id V 2×8 2202 14.4 13.8 12.8 of the lowest-energy configuration is impossib VI 2×8 2×6 3103 16.7 12.9 15.6 structures are energetically too close to be clearly d VII 2×8 2×6 2104 18.7 14.5 26.5 able, although they are spatially very different. In ad a The interaction energies ∆IE are given relative to the minimum found that the average number of unsaturated configuration of the particular mole fraction obtained with B3LYP and MP2/ contacts that have not been used for intracluster bo RI calculations. The last column gives the B3LYP interaction energies particular mole fraction. The energetics at mo corrected for the zero-point vibrational energy, ∆ D0. TheYou're third to sixth Reading ata this Preview columns contain characteristic structural features of the particular configuranDMSO ) 0.2 seem to be already dominated by the tions. All energies in kJ/mol. hydrogen bond network. At every mole fraction, Unlock full access with a free trial. configurations in which an additional methyl gro The rotation of a methyl group in DMSO yields a rotation leads to more stable configurations. (Compare fo curve profile with 9.5 kJ/mol amplitude (FigureDownload 4). This is With Free Trial 0.5-II and 0.5-I, 0.33-II and 0.33-I, 0.25-VI and 0. ∼3 kJ/mol more than calculated in ref 37. Subtracting this 0.2-V and 0.2-IV). contribution from the total above leaves an energy for the By closer inspection, rules of thumb can be given attractive methyl group contact of 5.5 kJ/mol. On building the complementary to the classification of hydrog hydrogen contact, the C-H distance of the methyl group interactions in section 4. These can makeit possibl hydrogen atom, which is closest to the oxygen atom of the water Sign up structures to vote on of this title that have no how minimum clusters molecule, is elongated very little (by at most 0.4 pm). This is studied may look, similar to the rules for hydrogen Useful useful Not expected, as the strong covalent C-H bond is disturbed only 34 Ring structures are more favorable th pure water: by the weak intermolecular attraction of the water oxygen atom. structures (compare 0.5-III (no ring) versus 0.5-II (o These effects are so small that a detailed analysis of C -H bond 0.33-II (one ring) with 0.33-I (two rings)). This is r
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Figure 5. Rotation curve to distinguish between configurations of [35] and of [32]. The water molecule rotates along the DMSO sulfur -oxygen axis under partial relaxation (B3LYP/TZVP).
Figure 6. Rotation curve calculated with B3LYP/TZVP investigate preferential coordination. One water molecule is kep the second rotates along the DMSO sulfur-oxygen axis relaxation.
sion so far applies also for MP2/RI. The only differences are that configuration 0.33-III is higher in energy than configuration curve, configuration 0.5-I is indeed the global min 0.33-IV and 0.25-III is higher in energy than 0.25-IV, but these looking at the sequence of this rotation, 0.5-III, differences lie within the range of error of the methods. 0.5-I, it can be realized that in each step a methyl gro 5.2. Contributions from the Nuclei. So far, we have is gained. Looking now closely at the energy, the f discussed the purely electronic effects on the stabilization of contact leads to a gain in energy of 4.3 kJ/mol, w different DMSO-H2O clusters. Since the potential energy wells next step yields another 6.3 kJ/mol. From a steric You're Reading view, a Preview of the total electronic energy may be shallow for weak one would expect exactly the opposite hydrogen-acceptor interactions, we should investigate the effect molecule looks as if it would be exposed to so mu Unlock fullfor access with free trial. of the nuclei at 0 K and at standard temperature. Values thata one would anticipate a decreasing energy for ∆ D0 for all configurations are given in Table 3. The energetic methyl group contact. However, the difference be order of configurations given in Table 3 is unchanged. However, in the minimum configuration and the Download Withangles Free Trial there are two exceptions of minor importance. First there is the 0.5-II is ∼5° more favorable for the minimum stru Ru¨ssel structure 0.25-II, which is electronically a little more is also in accordance with, and maybe due to, the f unstable than the lowest-energy structure, 0.25-I. The zero-point second hydrogen bond yields more energy for the energy correction favors this Ru¨ssel structure by 1.4 kJ/mol. molecule than the first.34 Configuration 0.2-III is much less stable when accounting for Our lowest-energy configuration at mole fractio Sign up to vote on this title zero-point effects, which changes the order of structures 0.2-II, 0.33 does not match the findings of MD sim Not useful 0.2-III, and 0.2-IV (compare Table 3). However, these changes Almost all Useful simulation studies observe configuration are within the range of uncertainty of the quantum chemical 0.33-IV or 0.33-V at this concentration. In ref 36, methods we used. The results for the corresponding enthalpies which two water molecules might be distributed
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Table 4. Pairwise Additivity of the Interaction Energies looks like our configuration 0.25-VIII, but because of its short appearance, it was not considered to be stable by the authors. B3LYP As in ref 36, a stable 1DMSO-3H2O configuration also failed n DMSO no. IE IEpair IE ∆IE to appear, the authors used a very sophisticated spatial distribu0.5 I 0.0 -40.0 -40.0 -37.5 tion function to predict the structure of this cluster. The authors II 0.0 -33.9 -33.9 -32.3 III 0.0 -29.6 -29.6 -28.1 propose that if two water molecules are already donating protons IV 25.0 25.0 0.0 -23.8 to the oxygen in the SdO group, there would be a possibility -20.4 -20.4 -21.0 V 0.0 for a third water molecule from the second hydration shell to -84.3 -68.2 16.1 -77.2 0.33 I form hydrogen bonds to the first two water molecules, similar -77.1 -64.0 13.1 -70.5 II to configuration 0.25-IV or 0.25-VI. -68.1 -67.5 -64.4 III 0.6 IV 1.0 -67.8 -66.8 -65.7 While there has been no consensus among the MD simulation V 0.6 -67.1 -66.5 -64.1 work on whether the methyl groups could be involved in the VI 0.8 -52.1 -51.3 -51.9 interaction with water, our work points toward minimum 0.25 I -118.0 -99.0 19.0 -109.3 configurations where a water molecule does interact with the II -117.9 -89.5 28.4 -107.9 methyl groups. In ref 36, no preferential coordination of two III -116.2 -96.0 20.2 -107.2 IV -115.7 -102.4 13.3 -107.4 water molecules to one DMSO molecule is found. Nevertheless V -114.4 -101.8 12.6 -106.7 it is admitted that the united-atom ansatz could blur this VI -109.1 -94.0 15.1 -100.4 interaction with the methyl groups. VII 1.5 -99.8 -98.3 -96.0 In ref 4, the radial pair distribution function is given, which 0.2 I -162.2 -119.7 42.5 -149.5 provides knowledge about the structure of a liquid. The peak II -157.5 -129.5 28.0 -143.3 III -157.0 -132.8 24.2 -144.8 of the water-oxygen-DMSO-carbon function is found at IV -156.9 -130.0 26.9 -145.0 shorter distance than that of the water -hydrogen-DMSOV -147.8 -122.9 24.9 -135.7 carbon function; i.e., on average, the MD simulations show the VI -145.5 -127.3 18.2 -136.6 VII -143.5 -124.2 19.0 -135.0 methyl groups closer to the oxygen atoms of the water molecules 33 than to the hydrogen atoms. Luzar et al. criticized the authors a The total interaction energy obtained with B3LYP of ref 4 for interpreting their results as indicating the presence denoted as IE, and the pairwise-sum interaction energy is give of a weak O-methyl group hydrogen bond. Luzar et al. attributed columns. Their difference is ∆IE. All energies in kJ/mol. their own observations and those of Vaisman and co-workers You're Reading a At Preview mole fraction n DMSO ) 0.25, there are larger to packing effects. effects than at the higher mole fractions. The large 6. Pairwise Additivity Unlock full access with a free trial. observed for Ru¨ssel configuration II. According In the previous section, we identified the minimum configuraenergy, it is the most unfavorable configuration w tions for each cluster. We found the structures to deviate from lowest-energy configuration of 13 kJ/mol. Sim Download Withthe Free Trial those discussed in MD simulation work; therefore, we test in are observed for MP2/RI. Many-body effects this section the extent to which the pairwise additivity assumpnounced for the methyl-group-free configurations. tion is valid. We calculated for every cluster all energies given The largest many-body effect is shown for by the different possible pairs of molecules in exactly the same configuration at mole fraction n DMSO ) 0.2 with 42 geometrical arrangement as in the cluster and added them up This time of the configur Signthe upenergetic to vote onorder this title to give a total pair energy for the configuration. Note that this disturbed by counting for pairs only, except for Notthe useful pair energy is slightly different from that used in MD simula Useful again configuration, which is most unfavorable co tions, as the simulation potentials are at best site-site potentials. with a gap to the lowest-energy configuration of 1 All energies are counterpoise-corrected. In summary, we find that at every mole fraction m
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Table 5. Stepwise Solvation by Adding One Water Molecule after
the Othera sequence 1
0.5-I
0.33-I
0.25-II
0.2-I
182.4 15.5 253.4 50.4
172.7 5.1 233.1 17.2
170.6 3.3 226.5 12.0
167.8 3.6 238.7 30.5
sequence 2
0.5-I
0.33-III
0.25-VII
r O(D)-H(W) aO‚‚‚O-H r O(W)-H(D) aO‚‚‚C-H
182.4 15.5 253.4 50.4
185.7 17.3 244.2 32.5
190.5 18.0 247.3 32.8
sequence 3
0.33-I
0.25-I
0.2-VI
r O(D)-H(W) aO‚‚‚O-H r O(W)-H(D) aO‚‚‚C-H
172.7 5.1 233.1 17.2
195.2 18.1 229.4 16.6
192.2 14.1 227.0 15.6
r O(D)-H(W) aO‚‚‚O-H r O(W)-H(D) aO‚‚‚C-H
Figure 7. Optimized structure of two clusters. Numbers gi of distances from “bond” lengths in the isolated clusters in p
the trend has its optimum at 0.25-Ru¨ssel and is a from the 0.25-Ru¨ssel to the 0.2-Ru¨ssel for three of th parameters. a Distances r are given in picometers and angles a in degrees. The second The branching sequences 2 and 3 show two oppo and third row describe the distance and angle corresponding to the H1the H1 hydrogen bond becomes a little weaker upo type hydrogen bond. The last two rows correspond to the H3 contact. with a maximum at the 0.25 cluster for sequence the H3 becomes continuously stronger, again with aggregates. This would be appealing from the point of view of at 0.25 for sequence 2. These trends are what one wo the classical paradigm that stable systems can be identified as as we add here the water molecules to the oxygen ato entities in a supermolecule. For instance, we should be able to to a weakening of the existing hydrogen bond. answer the question, whether our 1DMSO-2H2O clusters can For all three sequences, the adding of water mole be found in larger clusters, e.g., 2DMSO-4H2O. to a reinforcement of the H3 contact. We are well aware that the conclusions for “real” solvation 7.2. Optimized Cluster Dimers. In condensed from such an analysis must be drawn with great care and are clusters would interact with each other. This affected by a certain degree of inherent speculation. Despite by the not yet saturated bonding sites of e You're Reading mediated a Preview this speculative character, we shall explore the results from timeleading to “intercluster” contacts. We studied sev independent quantum chemical calculations to the fullest extent, Unlock full access with a freeand trial.found that the structure of each clust dimers which might finally guide findings from Car -Parrinello MD compact in the dimer than in the isolated clust simulations. hydrogen bond lengths are shortened, while the Free Trial 7.1. Adding Water Molecules. A way to treatDownload solvation is Withcontacts act as a glue (Figure 7 gives one typical to add more and more solvent molecules and to track the Significantly, we observed that the spatial arrang changes. As we have calculated clusters of one DMSO molecule given configuration of the isolated supermolecule with up to four water molecules, it is possible to compare a destroyed in the cluster dimer; i.e., there is sequence of clusters with an increasing amount of water, rearrangement of the intracluster hydrogen bonds modeling solvation. up to vote on this title pared toSign an isolated cluster or supermolecule with In Table 5, we list three sequences. Sequence 1 consists of sponding cluster Usefulin a Not dimer. useful cluster all Ru¨ssel configurations; in sequence 2, more and more water Particularly for the 0.25 clusters, we expect that molecules are added to the DMSO oxygen atom (there is no tively rigid, but nevertheless loosely and struc possibility for a fourth water molecule), and in sequence 3, we diverse intercluster network evolves at low tempera
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contacts. The other is the “glasslike” structure of the condensed phase at low temperatures, built up by stable clusters of different shapes. For the relatively loose connection of the clusters, we find indications if we look at the number of unsaturated contacts left in the clusters. We find their contribution to be low (in percentage) for the possible configurations at n DMSO ) 0.25. A stronger argument for the “glasslike” structure is that these clusters are energetically in the same range, they are minimum configurations, but differ significantly in spatial arrangement.
The only exception is again the branching structur where all water molecules are coordinated via the ox and indeed, this structure has also appeared in MD si although too briefly to be considered as a stable con Thus, it appears to be conclusive that most MD simu not able to account for all other 1DMSO-3H because pairwise additivity is assumed. It is important the minimum structures are for a conde study, as already mentioned. Nevertheless, our resu that thorough investigations of the effect of neglec body effects and of using the united-atom ansatz in 8. General Discussion and Conclusion could be enlightening. The first assumption could i Overall, the quantum chemical treatment of the clusters be circumvented by the use of polarizable pair pote showed many structures deviating from what has previously the second could be circumvented by using an all-a been suggested in the literature (or what comes to mind when Note that in the Car-Parrinello type of sim one thinks only in terms of Lewis formulas and partial charges). assumptions are avoided implicitly. This type of si From the frequency analyses of all clusters, we conclude that now in progress in our group. the minimum structures described are dominated by the For the explanation of the complicated pha electronic structure, while the vibrations of the nuclei appear respectively, of the low melting point, Havemeyer to have little effect on the interaction energies and thus the lattice theories. She claimed that “a structure could stabilization energies of the clusters. The agreement of the MP2/ of subunits of (two) water tightly bound to one DMSO RI and the B3LYP results is very good. At almost every mole with each such subunit more loosely bound to the ne fraction, the Ru¨ssel configuration was clearly the lowest-energy Hence, the over-all structure would be held togethe structure, with the exception of n DMSO ) 0.25. of varying strength or force.” This mixture would c The aim of this paper was twofold. The first aspect was to variety of such configurations arranged in chains see what pure quantum chemistry could teach us in preparation Because of the lack of regularities, no standard cry for future MD simulations. In this study, the focus was on testing would be observed. In other words, at low temp the quality of the intermolecular forces. We note that a becomes more and more unlikely that the hyd You're a Preview combination of both “understanding intermolecular forces”Reading and network undergoes gross rearrangements. Thus, a co “treating the system dynamically” is necessary to provide final rigid and structurally highly diverse network evo Unlock full access with a free trial. answers to a bulk problem of this kind. Second, we were temperatures, prohibiting the generation of a crystal-l interested in whether the unusual behavior at the mole fraction structure. Particularly for the 1DMSO -3H2O clus nDMSO ) 0.25-0.33 already emerges at the Download level of the Withdifferent configurations lie in the same interaction en Free Trial intermolecular forces in small clusters. This would, for instance, Considering also the amount of unsaturated contacts lead to an explanation for the low melting points of this mixture in configurations 0.25-I, 0.25-II, 0.25-III, and 0.25at mole fractions of about n DMSO ) 0.25-0.33. A step toward indications that the usual crystallization process c finding a possible cause for the low melting point might be place. For the 1DMSO-2H2O clusters, some con found by investigating small supermolecules. (0.33-III, 0.33-IV, 0.33-V) alsotitle exhibit only few u Sign up to vote on this As suggestions for MD simulations, we can give the following contacts and lie in the same energy range. In oppos Useful -3H Not useful resume´. The minimum energy or optimized structures are 1DMSO 2O clusters (i) these are not the lowes certainly biased by the methyl groups of the DMSO. This is a configurations and (ii) these configurations are secondary effect, but it is of the order of ∼5 kJ/mol and thus changeable through simple rotation, leaving
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