J. Phys. Chem. 1995,99, 14323-14333
14323
Interaction of HCl with Water Clusters: (HzO)~HCI,n = 1-3 Martin J. Packert and David C. Clary* Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1 EW, England Received: April 7, 1995; In Final Form: June 30, 1995@
A b initio MP2 equilibrium geometries of the clusters (H20),HC1, m = 1-3, and (H20),, n = 1-4, are reported. It is found that the clusters form hydrogen-bonded rings, with HCl acting as a proton donor. There is a significant increase in the HC1 bond length as the cluster size increases, as well as a large red-shift in the HCl stretching frequency. The dissociation energy of HCl from (HzO),HCl is appreciably larger for the trimer and tetramer than for the dimer, which is a consequence of cooperativity effects in the hydrogen bonds. We discuss the relevance of our findings to the understanding of the adsorption of HC1 on ice.
1. Introduction The heterogeneous reaction between HC1 and HOCl,
+
H 2 0 ClONO, HCl
-
+ HOCl
HOCl
+ HNO,
C1, -I-H,O
(1) (2)
is an important source of polar stratospheric chlorine atoms.'-5 The reaction proceeds in the antarctic vortex during the polar winter, with Cl2 being rapidly photolyzed in the polar spring. The resultant chlorine atoms then induce ozone-destroying chain reactions, the details of which have been widely reported.6 Reactions 1 and 2 are very slow in the gas phase, but are catalyzed by ice surfaces.' Polar stratospheric clouds (PSCs), which are composed of nitric acid trihydrate (type 1) or of pure ice (type 2), therefore provide a heterogeneous surface at which reactions 1 and 2 can proceed.8 This reaction requires the HC1 to adsorb onto ice particles. An experimental study of HCl sticking to an ice surface9 has determined the infrared stretching frequencies for the HClwater complex. This experiment is in agreement with solid matrix studies of the dimer H20-HC1, but the authors suggest that the stretch of HCl adsorbed at the ice surface is coincident with that from the H3O+C1- complex. It is therefore difficult to distinguish between physisorbed and dissociated HCl species. Kroes and Clary'O have modeled the sticking of HC1 to ice using a classical trajectory approach but considered only nondissociative physisorption mechanisms. Robertson et al." have reported a molecular dynamics simulation of the solvation of HCl on an ice surface at 190 K. They found that the HCl ionization process was feasible energetically, but a potential energy surface was not available to enable the kinetic aspects of ionic solvation to be studied. A particular question which their molecular dynamics study raised concerned the number of water molecules which are needed to cause ionic solvation of the HC1 molecule. Our aim is to use a correlated ab initio method to study the interaction of HCI with progressively larger water clusters. As the cluster size increases, there will be changes in the HC1 bond length, partial atomic charges, and stretching frequency. By studying the trends in these properties, we hope to be able to aid in the assignment of spectra of HC1 adsorbed onto ice or in small water clusters. We also wish to study the influence of ~~
' Present address:
Department of Chemistry, University of Sheffield, Brook Hill, Sheffield S3 7HF, England. Abstract published in Advance ACS Absrracrs, August 15, 1995. @
0022-365419512099- 14323$09.00/0
hydrogen bond cooperativity on the energy of dissociation of HC1 from the clusters. This has relevance for the study of HCl on ice surfaces, particularly for the design of potentials which will describe this interaction.
2. Ab Initio Calculations The cluster geometries were optimized using second-order Moller-Plesset perturbation theory (MP2). We used three basis sets: a doub1e-S; plus polarization basis (DZP),I2 a 6-31g(2dp) basis,I3 and the Sadlej Poll basis set.14 The Cambridge Analytic Derivatives Package (CADPAC)', was used to obtain the analytic first and second derivatives of the electronic energy, which were required in an eigenvector-following algorithmI5 for the DZP basis set. However, for the water clusters and for the two larger basis sets, we used the gradient-based optimization routines in CADPAC. It was possible to identify the global minima by comparison with previous workI6-l8 or with the MP2DZP results. In addition, we have characterized several local minima on the potential energy surfaces of the (H20),HCl complexes. Guesses of the initial geometries to be used in the ab initio optimization were generated using the ORIENT program. l 9 A distributed multipole analysis (DMA)20.21 up to fourth order was performed for each molecule of the cluster, and the geometry of the cluster was optimized with respect to the electrostatic interaction energy. The geometries of the constituent molecules were fixed. Two ORIENT optimizations were necessary. A Lennard-Jones interatomic potential was used to obtain an initial guess. This guess was then refined by reoptimizing with a hardsphere potential, in which the van der Waals radius of the hydrogen atoms was set to zero. This latter approximation is similar to that used by Fowler and B ~ c k i n g h a m . ~ *It, ~is~a reasonable approach, since, in a hydrogen bond of the type X-H-Y, the distance between X and Y is usually less than the sum of their van der Waals radii. This implies that the hydrogen atom has a van der Waals radius of zero. It is likely that the Lennard-Jones potentials could be refined, so that they would better describe the hydrogen bond potentials. However, the extra cost of the hard-sphere optimization is negligible in relation to that of the ab initio step which follows it. The cluster geometries from ORIENT provided very good initial guesses. In (H20)3HC1, for example, the ORIENT structure gave MP2DZP gradients of less than 0.0025 au. The convergence on the ab initio gradients was set to au. This usually meant that the six unprojected zero normal modes had energies of less than 1 cm-'. 0 1995 American Chemical Society
Packer and Clary
14324 J. Phys. Chem., Vol. 99,No. 39, 1995
TABLE 1: Optimized Geometries of H20 and HCl with Bond Lengths in A and Bond Angles in deg MP2/DZP MP2/6-3lg(2dp) MP2Pol1 exot
0.962 LHOH 104.5 ETOT' -76.258 598 Pb 2.168 a, 7.41 a,, 3.03 a:: 5.64 r(0H)
H20
0.961 104.8 -76.268 631 2.044 7.29 7.51 8.11
0.968 103.5 -76.283 940 1.88
9.64 9.91 10.24
0.958 104.5 1.847 9.62 10.01 9.26
HC1 r(HC1) ETOT P
a, a;: a
1.269 -460.274 610 1.390 5.30 12.42
7.677
1.271 -460.248 058 1.335 11.63 13.95 12.40
1.281 1.275 -460.296 628 1.163 1.093 16.16
17.77 17.44
17.39
a Energy in hartrees. Dipole moment, p, given in D; static polarizability, a,given in au. 1 au of a = eZa$E,' = 1.648778 x C2
m2 .I-'.
TABLE 2: Harmonic, o,and Fundamental, Y , Frequencies (cm-I) of HCl and HzO and Their Deuterated Analogues MP2/ MP2/ MP2/ expt' DZP 6-31g(2dp) Poll 0 11 HC1 31 14 3068 2982 2991 2885 DCl 2233 2201 2139 2145 2091 3856 3812 3832 3657 HzO VI 3912 1658 1647 1648 1595 1665 V? 3944 3942 3756 4058 3993 ~3 2779 2748 2784 2671 D20 VI 2820 1213 1206 1178 1205 ~2 1218 2926 2889 2889 2788 113 2973 "Experimental frequencies for H20 and D20 taken from ref 60. Experimental frequencies for HCl and DC1 taken from ref 61.
possible to predict the shift in the HCl bond stretch on formation of a hydrogen bond.
3. Results
A. HzO and HCl. The optimized geometries of HC1 and H20 are given in Table 1, and the vibrational frequencies, in The DZP and 6-31g(2dp) basis sets would not be the ideal Table 2. All calculations reported in this section are for the choices for this problem but were necessary to enable us to study MP2 level. The MP2/DZP and MP2/6-31g(2dp) optimized all the clusters at a consistent level of theory. Their lack of geometries are in good agreement with experiment; indeed, they polarization functions means that the calculated dipole moments are better than the MP2Pol1 one. The deficiencies of these and polarizabilities can be significantly different from those in basis sets are exposed in the electric properties and vibrational more extended basis sets. This is demonstrated in Table 1, frequencies; the dipole moments are overestimated by more than where the polarizabilities of H20 and HCl are listed. The MP2/ 0.3 D, while the static polarizabilities are considerably underPoll values are much closer to experiment than either MP2/ estimated. The vibrational frequencies are within 80 cm-' of DZP or MP2/6-31g(2dp) values, with the Poll basis having been experiment for MP2/6-31g(2dp), whereas for MP2/Poll they are specifically optimized for the calculation of electric properties. accurate to within 10 cm-I. B. (HzO)~, (H2O)3, and (HzO)~.In order to understand the This will have a bearing on the calculated interaction energies, since these depend on the electric moments and polarizabilitie~.~~ energetics and structures of the (HzO),HCl clusters, it is important first of all to have information on the water clusters, However, given that both H20 and HCl have appreciable dipole at the same level of theory. Water clusters up to the hexamer moments and interact via a hydrogen bond, we would expect have been studied a number of times p r e v i o ~ s l y . ' ~ -We '~~~~~~~ the electrostatic interaction energy to be dominant. If the take the results of Xantheas and Dunning" as benchmarks. permanent electric moments are predicted with reasonable These authors studied cyclic water clusters up to the tetramer accuracy, it should be possible to account accurately for this at the MP2 level and the pentamer and hexamer at the RHF electrostatic contribution. Using an MP2 wave function ensures level. They used a correlation-consistent basis set, which is that the dispersion contribution is also included. It is the based on the DZP basis, extended with basis functions of f-type dispersion and induction contributions which will be most and with diffuse functions. affected by any deficiencies in the molecular polarizabilities. The optimized parameters obtained in our calculations on the The main restriction on the basis set size was disk space. water dimer are given in Table 3 and Figure lb. ExperiOver 4 Gb of storage was required for the MP2 analytic m e r ~ t a l ~and ~ - ~t h' e ~ r e t i c a lstudies ~ ~ . ~ ~have agreed that the water derivatives of (H20)3HCl. In order to assess the performance dimer has a C,ground state, with a single hydrogen bond. The of the DZP and 6-31g(2dp) basis sets, we have compared them 0-0 separation in the water dimer is given accurately in all to the larger Poll basisI4 for (H20)2, Hz0-HCl, and (H20)2three basis sets, as is the angle q5 between the 0-0 axis and HCl. The Poll basis set was designed for the accurate the C:! axis of the acceptor water. The bond angle of the calculation of electric properties. It should therefore give a acceptor water opens out by 0.3", which probably arises from better description of the induction and dispersion components the interaction of the oxygen lone pair with the donor hydrogen. of the interaction energy. The DZP(6-31g(2dp)) basis sets are The 6-31g(2dp) and Poll basis sets predict the dipole moment 4s2pld(4s3p2d) on the oxygen atoms, 2slp(2slp) on the of the dimer very accurately. hydrogen atoms, and 6s4pld(Ss4p2d) on the chlorine atoms. The acceptor and donor OH stretching modes of the dimer The Poll basis is 5s3p2d, 3s2p, and 7sSp2d, respectively. have been measured in both gas phase30-31 and solid matrix29,34-36 We have reported only harmonic vibrational frequencies, environments. These experimental values are listed in Table since as the cluster size increases, calculation of the anharmonic 4, along with our theoretical results. The calculated harmonic correction becomes increasingly complicated. The use of MP2 frequencies are generally quite different from the observed analytic third and fourth derivatives is not feasible for these fundamental frequencies, although the dimerization shifts are systems at present. Hydrogen-bonded interactions can be reproduced quite well. There is only one set of harmonic appreciably anharmonic,2s with the hydrogen atom in X-H-Y experimental values, derived by Fredin et al.29 from Nz matrix remaining bound to the X atom and interacting electrostatically measurements. These seem to be the most appropriate results with Y. It has frequently been suggested that the very broad with which to compare our calculations, given the large band which is observed for the hydrogen bond stretch is due to difference between the fundamental and harmonic frequencies. Fermi resonance with its anharmonic components.26 Despite However, it must be borne in mind that the matrix will have this restriction to harmonic frequencies, however, it is still some effect on the measured frequencies, relative to the gas
J. Phys. Chem., Vol. 99, No. 39, 1995 14325
Interaction of HCl with Water Clusters
TABLE 3: Optimized Geometry and Interaction Energy of (H20)2 with Bond Lengths in di and Bond Angles in deg MP2/DZP
MP2/6-3 1g(2dp)
2.906 1.94 1 0.963 0.968 0.96 1 126.4 1.749 104.8 104.6 - 152.527 273 -21.08 3.06
2.930 1.968 0.962 0.968 0.960 125.3 2.6 12 105.0 105.1 - 152.545 948 -19.16 2.59
MP2Poll 2.863 1.893 0.969 0.975 0.967 124.9
- 152.579 160 -18.08 2.55
expt 2.976 f 0.03b
123 f loh 1 f lob
-23.01 f 2.1' 2.60"
a Labels refer to Figure lb. Reference 62. Angle between 0-0 bond and C2 axis of acceptor water molecule. Interaction energy calculated with full counterpoise correction. Units are kJ mol-'. e Experimental result from ref 55. f Dipole moment in D. H3(0 32)
a)
-----_____
H2(032)
(-061)
b)
'. '.
'. '.
'.
H6(071)
H4f0 1
----______
'.
Figure 1. HzO-HCI, (H20)2, and (H20)2HCI with the DMA atomic charges in parentheses.
phase values. The dimerization shifts in the gas phase differ from the matrix environment, most notably for the V I donor mode, which has a shift of 57 cm-' in the gas phase, while it is less than 10 cm-' for all the matrix experiments. The other modes show less discrepancy. Ventura et ~ 1have . recently ~ ~ compared experimental results for the dimer frequencies with various levels of calculation. They found that although MP4 generally gives the best agreement with experiment, the shifts are given reasonably well at the MP2 level. Comparison between the MP2/DZP and MPUPoll results in Table 4 is revealing. The MP2/Pol1 harmonic frequencies are very close to the harmonic values derived from the N2 matrix experiment of Fredin et aZ.F9 the worst agreement being with the v3 mode, which is around 30 cm-' in error. The MP2/DZP results, on the other hand, are only within 100 cm-l of experiment for v1 and v3, although v2 is significantly better. The dimerization shifts are very similar, however, reinforcing our point that we can have confidence in these shifts, even though the absolute frequencies may be quite poor. The optimized geometries of (H2O)3 and (H20)4 are cyclic, with each water acting as both a hydrogen bond donor and acceptor; the geometry of (H2O)3 is given in Table 5, and that
of (H20)4, in Table 6. The structures are shown in Figure 2a and c. The trimer has no symmetry, while the tetramer has S4 symmetry (although no symmetry restraints were imposed during the optimization). The intramolecular harmonic frequencies are given in Table 7. The MP2/6-31g(2dp) average bond distance for the free OH (OHkJ bond is 0.96 8, in each cluster, while the donor OH bond distance (OI&onor) is 0.97 8, in the dimer and trimer and 0.98 A in the tetramer. The increase in the Ofionor bond distance indicates that the hydrogen bond strength is increasing with the cluster size. The average 0-0 bond distance shows more variation with cluster size, decreasing from 2.93 8, in the dimer to 2.77 A in the tetramer. The hydrogen bond lengths also decrease, from 1.97 8, in the dimer to 1.80 A in the tetramer. This also indicates that the hydrogen bonds are becoming stronger as the cluster size increases, which is in accord with the increase in OHdonor. There is good agreement between our results and those of Xantheas and Dunning;17 in the trimer and tetramer, the optimized OH bond lengths agree to within 0.005 A, the 0-0 separations to within 0.03 A, and the 0-H hydrogen bond lengths to within 0.04 A. Comparing the harmonic frequencies of the trimer, we see a difference of around 100 cm-' in V I and v3. The complexation shifts are in good agreement, however. In the trimer, the red-shifts in the v1 mode, from Xantheas and Dunning, are 234, 175, and 166 cm-I, while we find 227, 169, and 157 cm-' for MP2/6-31g(2dp). Due to computational restrictions, it was not possible to obtain the MP2/6-3 lg(2dp) frequencies for (H2O)4; the difference between the MP2/63 lg(2dp) and MP2/DZP frequencies will presumably be similar to that seen for (H2O)3. The shifts in the MP2/DZP V I modes of (H2O)4 are very close to those of Xantheas and Dunning. It appears from our calculations that a shift in V I of greater than 150 cm-I is indicative of a water molecule which is acting as both a proton donor and acceptor. All such modes of the trimer and tetramer are therefore above 150 cm-I, since these are cyclic clusters. In the dimer, the MP2/6-31g(2dp) V I red-shift is only 98 cm-I for the donor molecule and 12 cm-' for the acceptor. This distinction between the shifts for donor and acceptor modes was used experimentally by Bentwood et aL3' to distinguish between linear and cyclic water trimers. Experimental vibrational frequencies have been reported for the trimer. These results, from Engdahl and Nelander38 and Bentwood et u Z . , ~ are ~ listed in Table 7. Our results differ from experiment by around 100 cm-'. The experimental complexation shifts are given with reference to the monomer in an Ar matrix37 (see footnote a of Table 7). The calculated shifts in the v2 and v3 modes are quite accurate. The predicted shift in the v1 stretch is less good. The experimental frequency, v1 = 3516 cm-l, has a red-shift of 122 cm-I; our MP2/6-31g(2dp)
Packer and Clary
14326 J. Phys. Chem., Vol. 99, No. 39, 1995 TABLE 4: Experimental and Calculated Frequencies (cm-') for the Water DimeP H2O(acceptor) method
VIb
gas phasec gas phased N2 matrixe Ar matrixg D2 matrixh MP2/DZPi MP2/6-3 lg(2dp) MP2Poll
v3
VI
3730(-26) 3722(-34) 37 15.0(- 1 1.9) 3899.5(-13)
2545(- 1 12) 3532(- 125) 3550.0( -84.5) 3717.4(-90.9) 3 5 7 4 3 -63.5) 3561.8(-80.2) 3833(-79) 37S8( -98) 3706(- 106)
v2
36OO(-57) 36OO(-57) 3627.2( -7.3) 38OO.3( -8.0) 3634.1 (-3.9) 3637.0( -5.0) 3904(-8) 3844(-12) 3799(- 13)
f
H20( donor)
1601.1(+3.5) 1653.0(+4.6) 1593.6(+4.5) 1599.4(+1.8) 1667(+2) 1662(+4) 1648(+1)
3728.6(-4.9) 404 1(- 17) 3975(- 18) 3925(- 19)
v2
v3
1618.6(+2 1.O) 1671.3(+22.9) 161 1.2(+22.1) I 6 17.2( 19.6) 1699(+34) 1686(+28) 1679(+32)
3714(-42) 3730(-26) 3698.8(-28.1) 3880.3 -32) 3709.5(-28.8) 3707.9( -24.4) 4024(-34) 3958(-35) 3909(-35)
+
a Numbers in parentheses are the shifts from the monomer frequencies, Av = vdimer - Vmonomer. V I , symmetric stretch; v2, bend; v3, asymmetric stretch. Reference 30. Reference 31. e Reference 29. fThese are the harmonic experimental frequencies in an N2 matrix.29g Reference 34. Reference 36. Calculated values are harmonic frequencies.
TABLE 5: Optimized Geometry of (H20)3 with Bond Lengths in A and Bond Angles in deg ~
~~~
bond lengths atomsa
MP2/ DZPb
bond angles
MP2/ 6-3 lg(2dp)'
atoms ~~~
01H2 01H3 03H7 04H5 01H6 04H6 07H8 04H9 07H9 0104 0107 0407
0.961 0.975 1.884 0.961 1.908 0.974 0.962 1.880 0.975 2.789 2.779 2.773
0.960 0.974 1.927 0.960 1.957 0.973 0.961 1.926 0.973 2.830 2.819 2.819
~~~~
H201H3 H807H9 H604H5 0107H3 0704H9 0401H6
MP2/ DZP
MP2/ 6-3 lg(2dp)
~~~~
105.6 105.8 105.4 9.687 9.855 10.41
105.8 105.6 105.9 9.56 1 9.515 10.47
H7(0.32:
H
a Labels refer to Figure 2a. Total energy, EM^ = -228.807 187 au. Dipole moment, ,u = 1.248 D. Total energy, E m = -228.83 1 972 au. Dipole moment, ,u = 1.180 D.
TABLE 6: Optimized Geometry of (H2O)s with Bond Lengths in A and Bond Angles in deg bond lengths
bond angles
atomsa
MP2/ DZPb
MP2/ 6-3 1g(2dp)C
01H2 01H3 04H2 0104
0.982 0.962 1.760 2.726
0.980 0.961 1.802 2.768
atoms
MP2/ DZP
MP2/ 6-3 1g(2dp)
H201H3 0304H2
105.4 4.713
105.6 4.194
a Labels refer to Figure 2c. All other bond lengths and angles are related by symmetry to those given. Total energy, EME = -305.089 1 15 au. Total energy, EME = -305.120 461 au.
calculation has V I = 3629 cm-I, a red-shift of 227 cm-'. The experimental frequencies point to an open chain structure, since there is a V I stretch with a red-shift of only 26 cm-', which can be assigned to an acceptor water. The stretch at 3516 cm-' is due to a donor-acceptor water molecule, therefore, but the redshift is not as large as that predicted by theory due to the open chain structure. In Figure 3 we have drawn an idealized spectrum for the intermolecular modes of the water clusters. The peaks have been given a Lorentzian line shape,l6 assuming an excited state lifetime of 5 x s. The development of a very intense hydrogen bonded V I band can be seen. C. HzO-HCl, (H2OkHC1, and (H20)3HCI. The (H20),,HCl complexes have similar structures to the water clusters. HCl acts as a proton donor in all cases, as would be expected. The optimized geometry of the H20-HCl dimer is given in Table 8 and is illustrated in Figure la. Our MP2/6-3 1g(2dp) values agree quite well with those of htajka and S~heiner?~ who found the angle between the O-cl axis and the C2 axis of water to be
H l(O.3 I )
Figure 2. (H20)3, (H20)3HCl, and (H20)4 with DMA atomic charges in parentheses. @ M P ~=
133.3', compared with our MP2/6-31g(2dp) value of 130.3'. The three basis sets we have used show quite different values for this angle. Chipot et aL4' have @MP2 = 145.7'. A restricted Hartree-Fock (RHF) pseudopotential calculation by Hannachi and Silvi4' also predicts a C, structure, with @ = 140.1'. The general conclusion is that the correct structure is C,, rather than planar. This is also in agreement with the empirical rules of Legon and Millen42and the electrostatic model of hydrogen bonding given by Buckingham and F o ~ l e r .This ~~.~~ is in conflict with the available experimental geometry, however, which is planar.43 Legon and Millen42 argue that the C, symmetry is correct for the equilibrium geometry, since the experimental value is a ground state vibrational average. The C.,geometry is rationalized by Latajka and S~heiner"~ in terms of a balance between the dipole-dipole interaction, giving @ = 180°, and the quadrupole-dipole interaction, giving @ = 90". They calculated a barrier to inversion (C., C2v C.J of 1.8 kJ mol-'. The experimental O - c l separation is 3.2149 A; our results are 0.03 less than this. This is in contrast to the results
- -
Interaction of HC1 with Water Clusters
J. Phys. Chem., Vol. 99, No. 39, 1995 14327
TABLE 7: Intramolecular Vibrational Frequencies (cm-') of (I32013 and (H20)J
TABLE 8: Optimized Geometry of HzO-HCI with Bond Lengths in A and Bond Angles in deg MP2/ DZP
(H20)3
MP2DZP
MP2/6-3 lg(2dp)
expt
MP2/DZP
VI
3672(-240) 3744(-167) 3752(-160)
3629(-227) 3687(-169) 3699(- 157)
3516(- 122)',' 3528(-110)' 3612(-26)'
~2
1686(+21) 1693(+28) 1714(+49)
1673(+ 15) 1677(+ 19) 1699(+41)
1602(+12)'~' 1620(+30)' 1632(+42)'
~3
3997(-61) 4004(-54) 4006(-52)
3937(-56) 3945(-48) 3946(-47)
3707(-26)' 3700(-33)' 3695(-38)'
3489(-423) 3596(-316) 3597(-3 15) 3645(-267) 1701(+36) 1710(+45) 1711(+46) 1742(+77) 3990(-68) 3991(-67) 3994(-64) 3995(-62)
a Figures in parentheses are the shifts from the monomer frequencies, Av = vclus,er - v,,,,,,,. Experimental result in the Ar matrix.38 Shifts are given relative to the monomer in the Ar matrix (VI = 3638; Y Z = 1590; v3 = 3733). Experimental results in the Ar matrix.37
'
VI
- 100
100
-
80
- 80
60
- 60
.-> v)
C
Q)
"2
I-'
C
-
40
VI
20
0 1
Frequency (cm-') Figure 3. Spectra of the water clusters, assuming a Lorentzian line shape: a, HzO;b, (H20)~;c, (H20)3; d, (H20)d. Harmonic frequencies calculated at the MP2DZP level. of Latajka and Scheiner and Hannachi and Silvi, who both overestimate the bond length, compared to experiment. The optimized geometry of (H20)2HCl is listed in Table 10, and that of (H20)3HCl, in Table 11; the clusters are illustrated in Figures IC and 2b. The HCl bond length increases with the cluster size. This is accompanied by a decrease in the O-HCl hydrogen bond distance and in the O-cl separation, as listed in Table 14. The decrease in the hydrogen bond length implies that the bond strength is increasing with the number of water molecules. This results from the cooperative effect of the water-water hydrogen bonds. The O-cl separation is significantly less than the van der Waals separation of these two atoms, which is 3.2 A; it is not dependent on the hydrogen bond angle, however, There is some evidence for a bonding interaction between the C1 atom and its nearest aqueous proton (H&ls in
ME/ 6-3 lg(2dp)
MP2/ Pol 1
expta
r(01H4)b r(OlC15) r(01H2) LH30H2
1.907 1.910 1.818 3.189 3.196 3.120 3.2149 0.963 0.962 0.970 105.2 105.2 104.0 130.3 128.3 180.0 @ 140.6 LC1501H4 1.225 1.317 0.544 r(H4C15) 1.283 1.287 1.302 ETOT -536.543 348 -536.526 331 -536.593 009 a Reference 43. Labels refer to Figure la. Angle between the O - c l axis and the C2 axis of water.
Figure IC and H2Cl11 in Figure 2b). The MP2/6-3lg(2dp) distance between the atoms is 2.66 8, in the trimer and 2.40 8, in the tetramer; the van der Waals separation would be 3.0 A, assuming a van der Waals radius of 1.2 8, for the hydrogen atom4 (which is not involved in a hydrogen-bonded interaction). Chipot et a1.@ optimized the MP2/6-31+G** geometry of (H20)2HCl using a self-consistent reaction field model. Their results are summarized in footnote b of Table 10. The optimized bond lengths are similar to those calculated here. The dipole moment is 5.46 D, compared with our MP2/6-3lg(2dp) value of 2.32 D. The reason for this large discrepancy is not clear, although it may be due to the fact that they appear to have found a minimum geometry with C, symmetry, while we have a minimum with no symmetry elements. Altematively, it is possible that the high dipole moment structure is stabilized in the reaction field model, while our low dipole moment structure is more appropriate to the gas phase. We are confident that we have found the global minimum for this basis set (see section 3.E). The primary sources of experimental spectra for H20-HC1 are from Ault and Pimentel,45 Schriver et ~ 1 . : ~Ayers and P ~ l l i nAmirand ,~~ and Mailk~d:~and Delzeit et ~ 1 Ault . ~and Pimentel studied the dimer in a nitrogen matrix, Schriver et al. studied it in both argon and nitrogen matrices, and Ayers and Pullin and Amirand and Maillard studied it in an argon matrix. The matrix environment will perturb the molecules to an extent, altering the frequencies from their gas phase values. This should be borne in mind when comparing to our theoretical values. Delzeit et al. studied the interaction of HCl with an ice surface, between temperatures of 15 and 60 K. We have listed the experimental fundamental frequencies of H20-HCl in Table 9. Ayers and P ~ l l i and n ~ ~SchriveF agree on an HCl stretch of 2664 cm-' in an AI matrix, giving a red shift of 222 cm-' from the free HCl stretch. Amirand and Maillard position the HCl stretch at 2659 cm-' in an Ar matrix, giving a shift of 224 cm-I. Ault and Pimente145assigned two peaks to the dimer HC1 stretch in a nitrogen matrix, at 2638 and 2540 cm-I. However, Ayers and Pullin interpreted the higher value to be due to a complex with N2, since they were able to produce a similar peak by doping an argon matrix with nitrogen. Altematively, Shriver et al. assigned the peak at 2638 cm-' to the H20(HC1)2 trimer. The later work of Delzeit et aL9 confirms the presence of the dimer HC1 stretch at around 2540 cm-I, although they consider it to be coincident with peaks from the complex of with C1-. The HC1 stretch therefore seems to be red shifted by around 200-300 cm-' from its monomer value. It is clearly dependent on the matrix environment. The frequency shifts for the fully deuterated system (D20-DCl) vary between 162 cm-I (ref 34) and 271 cm-' (ref 9). Our MP2DZP and MP2/6-31g(2dp) values for the HCl stretch in H20-HC1, in Table 9, are 2929 and 2841 cm-I,
Packer and Clary
14328 J. Phys. Chem., Vol. 99, No. 39, 1995
TABLE 9: Intramolecular Vibrational Frequencies (cm-') of the H2O-HCI Dimer, from Experiment and Theow H20-HCI
VI
H20'
VI v3
HCl
DzO-DCl
expt
MP2DZP
MP216-3 lg(2dp)
MP2Poll
expt
MP2DZP
MP2/6-31g(2dp)
MP2Poll
3638(-7) 1589(+1) 3734 2664(-222)c 2659(-229)d 2540(-314)' 2545( -309y 2550( -336)g
3901(-11) 1666(+1) 4041(-17) 2929(- 185)
3839(-17) 1660(+2) 3971(-22) 2841(-227)
3791(-21) 1645(-2) 3918(-26) 2709( -273) 1929(-224)d
2658(-5) 1175(+1) 2711 1929"(- 162) 1929(-224)d 1849'(-213)
2812(-8) 1220(+2) 2962(-11) 2102(- 131)
2767(-12) 1215(+2) 2910(-16) 2039(- 162)
2734(-14) 1204(-1) 2870(-19) 1944(- 195)
1820(-27 1)'
a Theoretical values are harmonic frequencies. Figures in parentheses are the shifts from the monomer frequencies, Av = vdlmer - vmonomer. results in the Ar matrix.47e Experimental Experimental results in the Ar matrix.34 Experimental results in the Ar m a t r i ~ . ~Experimental ~.~~ '"Experimental results in the N2 matrix.46g Experimental results on the ice ~urface.~ results in the N2
TABLE 10: Optimized Geometry of (H20)2HCI with Bond Lengths in A and Bond Angles in deg MP2/ MP2/ MP2/ atomsa DZPb 6-3lg(2dp)' Polld 0.962 0.975 0.967 0.962 1.874 1.792 2.776 3.055 1.298
0.962 0.974 0.966 0.962 1.902 1.787 2.813 3.059 1.303
theory
bond angles
bond lengths
01H2 01H3 05H4 C5H6 05H3 01H7 05H1 01C18 H7C18
0.969 0.984 0.974 0.969 1.820 1.688 2.750 2.993 1.326
atoms H605H4 H301H2 C1801H7 0105H3
MP2/ MP21 MP2/ DZP 6-31g(2dp) Poll 105.2 105.9 7.440 9.333
105.3 105.9 7.012 8.556
104.2 104.9 5.955 8.287
TABLE 11: Optimized Geometry of (H2O),HCI with Bond Lengths in A and Bond Angles in deg bond lengths
a
+
0.969 0.961 0.977 0.961 0.962 0.983 1.822 1.766 1.657 2.788 2.740 2.976 1.323
MP2/6-31g(2dp)
MP2Poll
exptb
3658(-198) 3805(-51) 1665(+7) 1680(+22) 3926(-67) 3950(-43) 2615(-453)
3565(-247) 3743(-69) 1654(+7) 1670(+23) 3873(-71) 3895(-49) 2394(-588)
3485(-172) 3605(-52)
2390(-498)
TABLE 13: Intermolecular Vibrational Frequencies of (H20)3HCI0 vi(H20) v2
bond angles
MP2/ MP2/ DZPb 6-3 lg(2dp)'
01H2 0.970 01H3 0.962 04H5 0.979 04H6 0.962 08H7 0.963 08H9 0.984 01H5 1.790 04H9 1.741 08H10 1.667 0104 2.753 0408 2.713 08Clll 2.976 HlOClll 1.315
MP2DZP V I ( H ~ O 3729(-183) ) 3865(-47) v2 1675( 10) 1688(+23) v3 3993(-65) 4017(-41) v(HC1) 27 13(-401)
ci Theoretical values are harmonic frequencies. Figures in parentheses are the shifts from the monomer frequencies, Av = vtrlmer- vmonomer. Reference 47.
Labels refer to Figure IC. Total energy, EMp2 = -612.818 236 au. Dipole moment, p = 2.365 D. MP2/6-31+Gf* results of Chipot et ~ 1 . E~ ~~p z= : -612.714 91 au; H701 = 1.809 A; H305 = 1.86 A; HCl = 1.291 A; p = 5.46 D. Total energy, EMR = -612.808 726 au. Dipole moment, p = 2.318 D. Total energy, E m = -612.894 769 au. Dipole moment, p = 2.258 D.
atomso
TABLE 12: Intramolecular Vibrational Frequencies (cm-') of the (H20)2-HCI Trimer, from Experiment and Theow
atoms
MP2/ DZP
H201H3 105.1 H708H9 105.9 H604H5 105.5 0401H5 4.513 0804H9 4.036 C11108H10 3.081
MP2/ 6-31g(2dp) 105.2 105.9 105.7 3.813 3.412 2.367
Labels refer to Figure 2b. Total energy, EMP2 = -689.097 054
au. Dipole moment, p = 2.534 D. Total energy, EMR= -689.094 858 au. Dipole moment, p = 2.506 D.
several hundred wavenumbers short of the available experimental values, although we might expect such a difference, given that we have calculated only the harmonic frequency. The MP2Poll value is 2709 cm-I, which is close to the fundamental frequency in the Ar matrix. The calculated red-shifts of the HC1 stretch are 185 cm-' (MP2/DZP), 227 cm-' (MP2/631g(2dp)), and 273 cm-' (MP2Poll). In the absence of harmonic experimental values (such as those for the water dimer given in Table 4), it is difficult to compare our values with experiment. The MP2Poll dimerization shift lies between those found in the Ar and N2 matrix experiments. The calculated values of the DC1 stretch in the deuterated dimer are 2102 cm-'
v3
v(HC1)
MP2DZP
MP2/6-3 lg(2dp)
3537(-375) 3660(-252) 3823(-89) 1684(+ 19) 1698(+33) 1723(+58) 3982(-76) 3992(-66) 4002( -56) 2482(-632)
3477(-379) 3612(-244) 3770(-86) 1675(+17) 1696(+38) 1717(+59) 3922(-71) 3928(-65) 3937(-56) 2341(-727)
Figures in parentheses are the shifts from the monomer frequencies, Av = vcluster - vmonamer.
TABLE 14: Bond Lengths and Bond Angles for (H20),HCI with Bond Lengths in di and Bond Angles in deg H2O-HCl
MP2DZP MP2/6-3 lg(2dp) MP2Poll (H20)2HC1 MP2DZP MP216-3 lg(2dp) MP2Poll (H20)jHCI MPZ/DZP MP2/6-3 lg(2dp)
177.0 176.7 178.7 162.3 163.3 166.5 173.0 174.7
3.189 3.196 3.120 3.055 3.059 2.993 2.976 2.976
3.370 3.420 3.351 3.302 3.334
1.283 1.287 1.302 1.298 1.303 1.326 1.315 1.323
1.907 1.910 1.818 1.792 1.787 1.688 1.667 1.657
a Hydrogen bond angle. O-Cl separation in the 0-HC1 hydrogen bond, in which HC1 is the proton donor. O-Cl separation in the OH-Cl 'hydrogen bond', in which H20 is the proton donor. HC1 bond length. e Hydrogen bond distance in the 0-HCI hydrogen bond, in which HCl is the proton donor.
(MP2/DZP), 2039 cm-' (MP2/6-3 1G(2dp)), and 1944 cm-' (MP2Poll). In this case, the MP2Poll result is closer to the Ar matrix value. The harmonic frequencies for (H20)2HC1are given in Table 12, and those for (H20)3HCl, in Table 13. Spectra for the (H20),HCl clusters have been plotted in Figure 4, assuming a
Interaction of HC1 with Water Clusters
J. Phys. Chem., Vol. 99, No. 39, 1995 14329
120 1
t ,
1500
1120
.
,
2000
.
,
2500
.
l
'
3000
,
3500
.
,
I -
4000
Frequency (cm-I) Figure 4. Spectra of the (HzO),HCI clusters, assuming a Lorentzian line shape: a, H2O and HCI; b, H2O-HCl; c, (H20)2HCl; d, (H20)3HCI. Harmonic frequencies calculated at the MP2/6-3 lg(2dp) level.
Lorentzian line shape. The most notable difference between the spectrum of (H20)2HCl and that of the water dimer is that V I is red-shifted by 210 cm-' in (H20)2HCl, compared with 98 cm-' in (H20)2. We have mentioned that shifts of greater than 150 cm-I indicate the presence of a water molecule acting as both a proton donor and a proton acceptor, which is indeed the case in (H20)2HC1. The red-shift of 86 cm-' in (H20)3HCl is reminiscent of the water dimer, since the cyclic structure of the water trimer is opened up by the HC1. The water molecule labeled 1-2-3 (Figure 2b) is therefore acting as an acceptor only, as indicated by this red-shift. This means that interaction between the proton and the C1 atom is very weak and cannot be classified as a hydrogen bond. The HCl stretching frequency is significantly smaller in the trimer and tetramer than in the dimer. In (H20)2HCl and (H2O)sHC1 it is red-shifted by 453 and 727 cm-I, respectively. The large red-shift in the HCl stretch implies that this bond is weakening considerably, which means that proton transfer is becoming more favored in the larger clusters. The change in the HCl stretch also correlates with the bond length, which increases by 0.036 8, from the dimer to the tetramer. There are, however, large differences in the red-shifts predicted by the three basis sets we have used for (H20)2HCl, as can be seen in Table 12. The red-shift in the HC1 stretch is 401, 453, and 588 cm-' for MP2/DZP, MP2/6-31g(2dp), and MP2/Poll, respectively. The absolute frequencies also differ by over 300 cm-l. The only experimental frequencies which might be comparable to our theoretical results for the trimer and tetramer are those of Amirand and They recorded the spectra of (H20)m(HCl)ncomplexes in an Ar matrix. They identified a cyclic structure for (H20)2HCl in which the HC1 stretch was red-shifted by 498 cm-I. This is somewhat larger than our MP2/ 6-31g(2dp) shift of 453 cm-I, although it does suggest that they
are observing a complex of similar structure to our global minimum. The good agreement between the MP2Pol1 frequency and the experimental value is coincidental. The MP2/ Poll red-shift, by contrast, is much larger than the experimental value. Amirand and M a i l k ~ dalso ~ ~find red-shifts in the water V I modes of 172 cm-' (for the OH stretch in the OH-O hydrogen bond) and 52 cm-' (for the OH stretch in the OH-Cl interaction). These are again in very good agreement with our MP2/6-3lg(2dp) values of 210 and 48 cm-I. Their assignment of the (H30)3HCl spectrum does not agree with our results, since they are unable to find a four-membered ring of the type we have found (Figure 2b). The red-shift in the HC1 stretch is 388 cm-I, and in V I it is 227, 103, and 74 cm-'. This evidence points to an (H20)2HC1 cyclic structure, with a further water acting as a proton donor outside this ring. We have not been able to identify any minimum geometries of this form, however. The extent of charge transfer in the clusters can be estimated using the atomic charges. These have been obtained using the distributed multipole While care must be exercised in their interpretation, we have compared values for the 6-3lg(2dp) basis only. The charges in HC1 are H(0.13) and C1(-0.13). Figures 1 and 2 show the atomic charges for the (H2O),HCl clusters. The charge on the hydrogen atom becomes more positive as the cluster size increases, while that on the chlorine becomes more negative. This is consistent with the formation of a hydrogen bond. The charge on the acceptor oxygen atom also becomes more negative. Charge transfer would be complete once an H3O+C1- complex was formed. The total charge on the H3O moiety involved in hydrogen bonding with HC1 is 0.22 in H20-HC1, 0.27 in (H20)2HCl, and 0.33 in (H20)sHCl. This would be in the region of 1.0 if charge transfer were complete. It is clear that although the ionic structure is not as stable as the molecular complex for these clusters, there is increasing charge transfer as the cluster size increases. Notice that in (H20)3HC1 the charge on the proton closest to the C1 atom is 0.34. This again indicates that there is not a hydrogenbonded interaction between these two atoms. The atomic charges in H20 are H(-0.60) and 0(-0.30). The charges on the protons not involved in hydrogen bonding show little change in the water clusters. The hydrogen-bonded protons have charges up to 0.41. The charge on the H30 moiety is 0.34 in (H20)2, 0.38 in (H2O)3, and 0.41 in (H20)4. There is more charge transfer in these clusters than in those with HC1. D. Interaction Energies. The interaction energy of a cluster, hE, can be calculated directly from the absolute energies of its constituent molecules,
AE = G u s t e r -
C
~i
(3)
i=I,N
where Gus,, is the fully optimized energy of the cluster (consisting of N molecules) and the summation is over the optimized energies of the monomers. In the case of the water dimer, for example, AE corresponds to the energy of the dissociation reaction,
at a temperature of 0 K. The harmonic frequencies can be used to calculate the zero point energy c o r r e ~ t i o n to ~ ~this , ~ ~dissociation energy. When the energy of the cluster is obtained from a supermolecular calculation, however, it should be corrected for the basis set superposition (BSSE). This error manifests itself as an artifical lowering of the energy of the cluster, which results from the monomers using other basis functions of the
Packer and Clary
14330 J. Phys. Chem., Vol. 99, No. 39, 1995
TABLE 15: Dissociation Energies of (HzO),, and cluster to improve their zeroth-order energies. This is a (H*O).HCl Clusters, Evaluated Using the Full Counterpoise nonphysical effect, which results in overestimation of the Correctiona interaction energy. De/ Dd D,(HCl)/ Do(HC1)I The usual method for eliminating BSSE in dimers is to use kT mol-' kT mol-' kT mol-' kT mol-' the Boys-Bemardi counterpoise (CP) c o r r e ~ t i o n .The ~ ~ mono13.16 21.31 HZO-HCl MP2/DZP 21.31 13.16 mer energies of eq 3 are calculated in the full dimer basis, rather MP2/6-31g(2dp) 21.97 13.74 21.97 13.74 than in the monomer basis. The lowering of the monomer 20.57 10.93 MP2Poll 20.57 10.93 energy due to these 'ghost' functions is the BSSE for that (H20)2 MP2DZP 21.08 11.35 monomer. This correction was originally proposed for dimers MP2/6-3lg(2dp) 19.16 7.91 in which the monomer geometries were unrelaxed. GeneralizaMP2Poll 18.08 9.55 30.62 19.53 (H20)zHCl MP2DZP 51.70 30.88 tions for fully optimized N-mers have been discussed by van MP2/6-31g(2dp) 51.27 30.53 32.1 1 20.98 Lenthe et ~ l . , Wells ~' and Wilson,53and Turi and Da~menberg.~~ 29.59 21.67 50.95 32.86 MP2Poll The counterpoise correction to the energy of an N-mer, 6P*N, (&0)3 MP2DZP 64.08 39.14 is calculated as MP2/6-31g(2dp) 59.50 36.42 (H2O)jHCl MP2DZP 95.36 MP2/6-3lg(2dp) 89.07 (H20)4 MP2DZP 114.96 MP2/6-3 lg(2dp) 102.88
where Eikixj ...) is the energy of monomer i, in the presence of the full N-mer ghost basis set and in the cluster geometry, and Ei(yi) is the energy of monomer i with only its own basis set but at the geometry it has within the cluster. This approach ensures that the relaxation of the monomers is included in the CP correction. In the case of a reaction such as
both the n-mer and the (n - 1)-mer should be corrected using the formula above. This then ensures that the interaction energies are thermodynamically consistent. This method of correcting for BSSE is equivalent to the site-site function counterpoise method suggested by Wells and Wilson.53 We made no attempt to optimize the complexes including the CP correction,**although methods for doing this have been suggested.52 The CP correction was applied to the optimum geometry for the full supermolecular basis. This means, for instance, that no account has been taken of BSSE in the harmonic frequencies or the optimized geometries. The neglect of BSSE in the geometry optimization means that the intermolecular separation will be smaller than it should be, due to the extra BSSE binding energy. This fact would have to be bome in mind in fitting empirical potentials to our calculated geometries. The CP correction is still of relevance to the interaction energies, however. The CP corrected dissociation energies of the water clusters are reported in Table 15; the zero point energy corrections, evaluated using the MP2 harmonic frequencies, are included in the DOvalues. The MP2/6-3 lg(2dp) dissociation energies, De, of the dimer, trimer, and tetramer are 19.16, 59.50, and 102.88 kJ mol-', respectively. The result for the dimer agrees well with previous theoretical results (Xantheas and Dunning, for example, report a value of 23.3 kJ mol-') but is not within the error bars of the experimental result of Curtiss et ~ 1 We . can ~ ~ clearly see the effect of cooperativity in the hydrogen bonds. The average interaction energy per hydrogen bond increases with the number of such interactions. If we assume that the dissociation energy is dependent on these bonds only, then the average hydrogen bond strength shows a large increase in passing from the dimer to the tetramer. The fact that the dimer and trimer have similar hydrogen bond strengths is due to the cyclic nature of the trimer. This results in the hydrogen bonds being nonlinear, in order to accommodate the cyclic structure. This has the effect of lowering the interaction energy. There will, however, be three-body effects contributing to the dissociation energy,27 which cannot be attributed to hydrogen bonding.j6 Lee et u1.I8 have observed that the hydrogen-bonded
62.96 54.70 76.96 6 1.79'
31.28 29.58
23.80 18.29
DOvalues include the zero point energy correction, evaluated from the MP2 harmonic frequencies. De corresponds to the reactions (HZO),HCl- nH20 HC1 and (HzO), nH2O. D,(HCI) corresponds to the reaction (H20),HCl- (H20), HCI. Calculated from the MP2/ DZP harmonic frequencies.
+
+
-
ring in (H20)4 is the most stable conformation in water clusters up to (H20120. Two dissociation energies for the (H*O),HCl clusters are reported in Table 15, corresponding to the reactions D,(HCl): (H,O),HCl
-
(H,O),
+ HC1
and
De: (H,O),HCl-
nH,O
+ HC1
The (H2O),HCl clusters are less stable than the corresponding (H*O)(,+l)clusters, with the exception of the dimers, which have very similar dissociation energies. In (H20)2HCl, for example, D,is 51.27 kJ mol-', compared with 59.50 kJ mol-' in (H20)3. This implies that the HCl forms only one hydrogen bond in the cluster (as a proton donor), since the value of De corresponds to only two hydrogen bond energies. In (HzO)~,by contrast, there are three hydrogen bonds. A similar observation applies to the tetramer. Although HC1 forms only one hydrogen bond in the cluster, this does not mean that the value of D,(HCl) will be a constant; it can be seen in Table 15 that De(HC1) is up to 10 kJ mol-' greater in the trimer and tetramer than in the dimer. This is again the result of cooperative effects in the cluster. This observation has important implications for the modeling of HC1 on ice surfaces,I0 where such cooperativity effects will be significant (see section 4). The MP2DZP and MP2/6-31g(2dp) D,(HCl) values show opposite trends. In the 6-31g(2dp) basis, for example, the HC1 is more strongly bound in the trimer than in the tetramer, which is a surprising result, even though the difference is only 2.53 kJ mol-'. E. Potential Energy Surfaces. The potential energy surfaces (PES's) of these clusters have shallow minima, since the hydrogen bonds have energies of less than 25 kJ mol-'. This means that searching for the global minimum can be quite demanding, requiring tight convergence criteria, along with good starting guesses provided by a program such as ORIENT.I9 The PES's are also characterized by having a number of local minima, in addition to the global minima which we have reported in the preceding section. In the case of the water clusters, we can be reasonably confident of having obtained the global minimum by comparing with previous work. This option
Interaction of HCl with Water Clusters
J. Phys. Chem., Vol. 99, No. 39, 1995 14331
w CIY
C
AE = 1.95 kJ/mol
A
B
C
D
E
F
B
A
D AE = 15.73 kJ/mol
Figure 5. Optimized structures for (H20)2HCl at the RHF/DZP level. AE is the energy difference from the global minimum structure A.
is not available for the (H20),HCl clusters however. We have therefore tied to characterize all the minima which lie close in energy to the global minimum. When using to obtain initial geometries for the ab initio optimization, the procedure we adopted was to take a large number of random starting geometries and to optimize each within ORIENT; this yielded a set of minimum geometries. The global minimum from ORIENT was then used as the starting guess in the MP2 optimization. In order to confirm that this does indeed lead to the MP2 global minimum, we optimized each of the ORIENT minima at the RHFDZP level. In hydrogen-bonded systems, the electrostatic contribution is usually dominant. Buckingham and for example, were able to obtain geometries for hydrogen-bonded dimers which agreed with experiment, by using an electrostatic (DMA) potential only. In addition, Mitchell and Price5' found that for the formamide-formaldehyde dimer the electrostatic term was by far the largest attractive component of the interaction energy; also, although the other attractive contributions were by no means negligible, they showed much less variation with the geometry than the electrostatic term. This means that the RHF and MP2 structures should differ only in the intramolecular parameters and hydrogen bond lengths, rather than in the orientations of the constituent molecules with respect to one another. We have made no attempt to identify the transition states which lie between these local minima. 1. (H20)2HCl. Four minimum geometries were obtained from ORIENT. When these were used as starting guesses for the RHFDZP optimization, they resulted in four geometrically distinct minima. The relative stabilities of these clusters, labeled A-D, are noted in Figure 5. Structure A corresponds to the global minimum, for which the MP2 results are given in Section 3.C (see also Figure IC). Structure B is an enantiomer of A. In structures C and D, the HCl interacts with one of the water molecules but is much further from the other than in either A or B. The distance between C18 and H4 is 5.1 A in C, compared with 2.9 A in A. This is further evidence that there is a stabilizing interaction between the C1 atom and H4, although it is a very weak interaction, since the difference in energy between structures A and C is only 1.95 kJ mol-'. 2. (H20)jHCl. Six distinct minima were found by ORIENT, which are illustrated in Figure 6. Two of these correspond to the MP2DZP global minimum depicted in Figure 2b; structure A has the same conformation as in Figure 2b, and B is an
Figure 6. Optimized structures for (H20)3HCl from ORIENT. Only A and B are minima at the RHF/DZP level and are enantiomers.
enantiomer of A. Structures C and D have an (H2O)3 ring similar to that in Figure 2b, with HCl interacting with one of the water molecules. Finally, structures E and F contain a water molecule acting as a two-proton donor. When these ORIENT structures were optimized at the RHF/ DZP level, only A and B were found to be minima. The other structures all optimized to either A or B. The eight-membered ring of Figure 2b is therefore a very robust minimum, presumably because of the stabilization provided by the hydrogen bonds. 4. Discussion
In addition to characterizing the (H20),HCl clusters, the aim of this work is to provide information about the influence of cooperativity and many-body effects on the H2O-HC1 potential. This is of particular interest in the study of HCl on ice surfaces,IO where such effects may be significant. Kroes and Clary,I0 for instance, used a classical trajectory approach to study the physical adsorption of HCl and HOC1 on ice. The pairpotentials for H20 interacting with HCl were constructed using experimental and theoretical parameters. This ensured that the properties of the dimer were accurately represented. The dissociation energy De, for example, was found to be 17.95 kJ mol-', which compares with our MP2Pol1 value of 20.57 kJ mol-'. The O-cl separation was 3.34 A, compared with our value of 3.12 A. They also determined the minimum geometry for HCl interacting with an ideal (0001) ice surface, at a temperature of 0 K. The geometry of the ice surface is shown in Figure 7. Details of the potentials used to construct the surface are provided by Kroes and Clary. The water molecules in the ice can have six possible orientations, labeled class 1 and class 2.1° In class 1 molecules (protons H1 and H2 of Figure 7) the protons point out from the surface, while for class 2 the protons point into the bulk (molecule containing 0 1 of Figure 7). The minimum geometry has HCl hydrogen bonding with 01, which is of class 2, with interactions between the C1 atom and the
14332 J. Phys. Chem., Vol. 99, No. 39, 1995
Packer and Clary
5. Conclusions
64.-
Figure 7. Hexagonal arrangement of water molecules at an ideal ice surface. An HCl molecule can interact with oxygen 0 1 and protons H1 and H2 (see Discussion). H1 and H2 point away from the surface; H3, H4, and H5 point into the bulk.
two protons H1 and H2, which are of class 1. The energy minimum lies in the range 22-29 kJ mol-'. The trajectory calculation, on the other hand, gave an interaction energy of 19 kJ mol-'. This is to be compared with an experimental enthalpy at 200 K, derived by Elliot et a1.:8 of 46 kJ mol-'. Allowing for zero point and temperature corrections, there is still an appreciable discrepancy between the trajectory calculation and experiment. The interaction of HCl with the ideal ice surface can be compared with our results for the (H20)3HCl cluster. The separation of 0 1 and H2, between which the HCl is located, is 4.6 A on the ice surface (see Fi ure 7). In the (H20)3HC1 cluster, this separation is 3.6 . This suggests that the conformation of the ice surface is not ideal for complexing the HCl molecule, so that the interaction energy will be less than the value which we have calculated for the cluster (Table 15). However, our interaction energy for HCl on ice is larger than that calculated by Kroes and Clary.'O This suggests that the cooperativity effects introduced in the cluster, although relatively small, should be included in the H20-HCl potential. Experimental studies of HCl on pure ice and nitric acid trihydrate-ice mixtures have attempted to determine the extent of molecular absorption'of HCL5 McCoustra and Horn5 observed only a dissociative interaction of HCl with ice at 100 K, while Delzeit et aL9 found that the molecular H20-HCl complex was present at the ice surface, for temperatures below 50 K. Graham and R o b e d 9 also found evidence for HCl adsorbed on an ice-HC1 phase, which appears to be a hexahydrate of HCl. They estimated that the activation energy for desorption of HCl from this hexahydrate surface was 33 f 5 kl mol-', at a temperature of 140 K. By comparison, our MFW6-3 lg(2dp) values for D,(HCl) in (H20)2HCl and (H20)3HCl corrected to 140 K, including zero point effects, are 24.40 and 20.72 kJ mol-'. The MP2DZP values are 23.1 1 and 25.91 kl mol-'. Notice the different trends in the two basis sets, which may be caused by superposition errors. Using a different experimental approach, Amirand and found that for (H20)m(HCl)naggregates below 50 K a cluster of four water molecules was required in order to dissociate the HCl. The calculations which we have performed suggest that, in the gas-phase, HCl will not dissociate to form ions when complexed with up to three water molecules. The increase in the HCl bond length, the large red-shift in the HCl stretching frequency, and the increasing positive charge on the H atom as the cluster size increases, however, show that the nature of HCl in (H20)3HCl is significantly different from that in H20-HCl.
K
We have used ab initio methods to identify optimum structures for the (H20),HCl clusters up to n = 3, as well as for the corresponding water clusters. The most stable conformations involve a ring of hydrogen bonds. HCl acts as a proton donor in all cases, with a weak interaction between the C1 atom and a proton. This interaction is not a hydrogen bond, although it does stabilize the ring structure of the clusters. In the water clusters, the tetramer (H2O)4 is significantly more stable than the trimer, an effect which has also been observed by Lee et al. We find very large red-shifts in the stretching frequency of HCl, as well as for the V I mode of water, as the size of the (H20),HCl cluster increases. These shifts are associated with hydrogen-bonded interactions and might be identifiable in experimental spectra. The red-shift in the V I mode of water is more pronounced if the water molecule is acting as both a proton donor and acceptor. There is also an increase in the HCl bond length, as the cluster size increases, as well as an increase in the charge transfer within the 0-HCl hydrogen bond. Although these trends in the HCl bond length and stretching frequency indicate that the bond strength is decreasing, we have not found any structures in which the HCl has dissociated. This is in agreement with the available experimental results.47 Acknowledgment.. We would like to thank Dr. David Wales for providing us with a copy of the ORIENT program and for much helpful advice. This work was supported by the EC, the NERC (Grant No. GWJ22082), and the EPSRC (Grant No. GW 567 154). References and Notes (1) Abbatt, J. P.; Molina, M. J. J . Phys. Chem. 1992, 96, 7674. (2) Abbatt, J. P.; Molina, M. J. Geophys. Res. Lett. 1992, 19, 461. (3) Hanson, D. R.; Ravishankara, A. R. J . Phys. Chem. 1992,96,2682. (4) Chu, L. T.;Leu, M. T.;Keyser, L. F. J . Phys. Chem. 1993, 97,
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