J. Phys. Chem. 1992, 96, 6494-6500
6494
Calculatlons of the Structures, Stabilities, Raman Spectra, and NMR Spectra of CdCi, (OH,):-" , CdBr, (OH,):-", and ZnCI, (OH,):-" Species in Aqueous Solution P. Butterworth? 1. H. Hillier,*?+N. A. Burton,+.$D. J. Vaughan,s Department of Chemistry and Department of Geology, University of Manchester, Manchester MI 3 9PL, U.K.
M. F. Guest, SERC Daresbury Laboratory, Daresbury, Warrington WA4 4AD, U.K. and J. A. Tossell Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742-2021 (Received: March 9, 1992)
Ab initio self-consistent-field MO methods have been used to calculate minimum-energy geometries, Raman stretching frequencies, and Cd NMR shieldings for Cd complexeswhich may exist in chloridecontaining aqueous solutions, e.g., CdCI+, CdCI2,CdCI,, CdCI,Z-, CdCIs3, CdCl(OH2)5+,CdCI2(OH2),,CdC12(0H2)4,CdC13(OH2)-,CdCI3(0H2)1,and CdC13(OH2);. The optimum geometries calculated using effective core potentials and double-{-quality bases show Cd-O bond distances which are in good agreement with experiment and Cd-CI distances which are somewhat too long. Cd NMR shieldings have been calculated for all these species using coupled Hartree-Fock theory and including all electrons. An analogous set of geometry and Raman spectra calculations were performed for the Cd bromides but the NMR shieldings have been evaluated only for the unhydrated species. Comparisons between theory and experiment are consistent with the following: (i) for the CdC14" species, hydration is very weak or nonexistent, (ii) CdCP and CdC12are strongly hydrated as pseudooctahedral complexes, and (iii) CdC13- is weakly hydrated, probably as a pseudotetrahedral complex CdC13(OH2)-. Results for the bromides are similar to those for the chlorides, suggesting that CdBr42-is unhydrated and CdBr3- only weakly hydrated. Results for some additional structures for the previously studied ZnCLn(OH2)~-n series show that Zn and Cd exhibit essentially the same trends in NMR shielding as a function of the number of halide and water ligands.
Introduction Cadmium is a transition metal concentrated in nature in certain types of hydrothermal ore dep0sits.I Although the cadmium is normally present as CdS or as Cd substituting within both simple (e.g., sphalerite (Zn,Cd)S) and complex (e.g., tetrahedrite (Cu,Zn,Cd),,Sb4SI3) sulfide minerals, the transport of cadmium in hydrothermal solutions is likely to have involved chloride complexes (the Cd2+cation complexes strongly with C1-). Furthermore, the transport and distribution of Cd at the Earth's surface (whether derived from natural or industrial sources) is also likely to involve such complexes. Equilibrium equations of the general type Cd2+
CdCP
s .-CdC12
CdCIq
s
CdCld2-
can be written for the CdCl:" system, and equilibrium constants for the various reactions can be determined experimentally from solubility data.2 However, in such systems different equilibrium constant values have been obtained by different researchers using different media and different assumptions about ~peciation.~ The nature of the first coordination sphere about Cd2+ has been partially characterized by solution X-ray diffraction for the CdZ+, CdCl,, and CdCI3- species, but the other CdC1,2" species, which occur at lower concentration or in the presence of several species, cannot easily be studied using this techniq~e.~Raman spectroscopy has yielded useful information about some of the CdCI:" complexes, but questions remain about many of the Raman spectral assignments and the inferences regarding the symmetries of the various ~pecies.~ Cd NMR spectra have been studied as a function of C1- concentration in CdC12,HCI and other solutions and changes in average Cd NMR shielding with C1- concentration have been used, along with literature values for equilibrium 'Department of Chemistry, University of Manchester. Permanent address: Manchester Computing Centre, University of Manchester, Manchester MI3 9PL, U.K. 5 Department of Geology, University of Manchester.
constants, to evaluate Cd NMR shieldings for the various CdCl,Z-" The basic question to ask about any CdC1,2-" species is: what is the nature of the first coordination sphere about CdZ+? For example, can the species CdCl, be approximately represented as a triatomic molecule or must we consider the waters of hydration around it? If the waters of hydration are important to the properties of this complex, how many waters are there, how are they arranged (on the average), and what degree of flexibfity exists in their arrangement? If a single first coordination sphere complex exists, such as CdC12(0HJ4, in a roughly octahedral geometry, and is of substantially lower energy than alternative structures, then it can be adequately studied using a quantum mechanical approach. If many structures of nearly equal energy exist then the methods of statistical mechanics must be employed. Cadmium-113 NMR chemical shift data indicate that a larger shielding of the Cd nucleus occurs for octahedral aquo complexes than for the halocomplexes. Furthermore, the values obtained suggest that there is a change of coordination from an overall octahedral to a tetrahedral geometry somewhere along the seriesU6 Such a change of geometry is characterized by the liberation of a large number of water molecules which leads to unusually high values of ASo. The reported chemical shift values, however, depend heavily on assumed equilibrium constants which may be in error. Experimental values for Cd shielding in solidss constrain the shielding values for CdX4,-, but not for the cases n = 1-3. Raman spectra for the cadmium halide complexes are difficult to interpret5 and very little evidence has been found to support or refute the changes of coordination suggested from NMR chemical shift data. Very little structural data are available for the monohalide complexes, but it has been suggested that their formation involves the replacement of one water molecule from the hexahydrated metal cation by a single halide ion, resulting in an overall octahedral geometry. The tetracoordinated species CdX42- in each case has been assigned a tetrahedral geometry with no bound water molecules. Because the cadmium cation is softer than the zinc cation one would expect a greater degree of
0022-365419212096-6494$03.00/00 1992 American Chemical Society
Spectra of Cd Complexes covalency for the same ligand. Therefore, charge neutralization of the Cd metal cation isgreater for the same number of coordinating ligands. This suggests that the change of geometry might occur at an earlier ligand step for the Cd complexes relative to the zinc complexes previously studied? In this paper, we present ab initio HartreeFock MO calculations for a number of "bare" and hydrated Cdx,2" species, where X = C1- or Br-. Some additional results are also presented for the ZnC1,Z" series, studied in previous work? Our object here is not to carry out "state-of-the-art" calculations, but to employ a relatively modest basis, and to explore the correlation between theory and experiment, in order to aid the interpretation of experimental data. Indeed, since we are including the interaction of only the first hydration sphere, the use of more sophisticated and timeconsuming quantum chemistry calculations is probably not justified. Previous calculations have included ab initio calculationsI0 on Cd(OH2)a2+and CdC12,and calculations of Il3Cd NMR shieldings using ab initio finite perturbation theory," although no halides were included within the set of molecules studied.
ComputationalDetails Ab initio MO calculations for the species MLn(OH2),2-"[M = Cd, Zn; L = Br, Cl] were carried out using effective core potentials (ECP) to replace the core electrons and double-c or split valence basis sets to describe the valence orbitals.12 The replacement of the atomic core potentials by pseudopotentials has been carried out in view of the large number of basis functions required for all electron calculations. For comparison purposes, some calculations were also performed with the all-electron split valence MIDI bases of Huzinaga,I3 augmented by polarization functions as described in ref 9. Geometry optimizations were performed either with no constraints or with such constraints as identified within the tables. Thus, calculations on the aquated monohalide complexes were performed with an overall octahedral geometry. There is no experimental evidence for the existence of monohalide complexes with overall tetrahedral geometry and so these were not included in the calculations. Aquated dihalide complexes were calculated at overall tetrahedral and octahedral geometries and aquated trihalide complexes at tetrahedral and bipyrimidal geometries. All bond angles and bond lengths were then optimized to give the minimum-energy configuration. Calculations on the aquated trihalide complexes were also undertaken constraining the symmetry to Td and D3hsuggested by full optimizations that give different metal-ligand bond lengths for chemically equivalent ligands. All calculations were done using the program GAMESS'~ at either Manchester or Maryland. Hydration energies were estimated from the total energy of the hydrated species and those of the unhydrated species and appropriate number of water molecules. Although we might expect the inclusion of electron correlation to increase the hydration energies, this may be partly offset at this level by the basis-set superposition error implicit in our use of a limited basis set. Similarly, with the inclusion of correlation effects we may expect a shortening of the M-X bond lengths. As far as comparison with experiment is concerned, we have not attempted to calculatefree energies of hydration, which would necessitate the usual mections to the gas-phase energy differences and the realistic modeling of the rest of the solvent, probably by some continuum approximation. Stretching frequencies were calculated using finite differences and plots of the reciprocal of the bond length versus the frequency of the totally symmetric vibration were made. Such an empirical relationship has previously been used to estimate totally symmetric Cd-X stretching frequencies of the aquated species to compare with experimental Raman freq~encies.'~ Atomic coordinates of the optimized structures can be found in ref 16. We have used HartretFock perturbation theory (CHFFT) as described by Lipscomb" and more recently by Tossell and Lazzeretti18 to calculate the Cd NMR shieldings, ucd, where the effective magnetic field experienced at the Cd nucleus, HeR,and the macroscopic applied field, Ham,are related by
The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 6495 Hcff
= (1 - ~ ) ~ a .. tlLl
All electrons (not just the valence shell) are included in the calculations. The NMR shielding constant, u, consists of a sum of two terms: a diamagnetic part, ad, involving the quantum mechanical average of the reciprocal of the electron-nuclear distance in the ground state, and the paramagnetic part, up, involving the mixing of occupied and unoccupied molecular orbitals under the influence of the magnetic field. The value of o" is around 4800 X 10" or 4800 ppm for a free Cd atom and ranges up to 5100 ppm in the complexes. This quantity can be calculated very accurately from the ground-state wave function and can be estimated reasonably accurately from a free atom superposition model. The paramagnetic term, up, ranges from zero for the free Cd atom (or any other spherically symmetric system) to almost -1300 ppm for the most paramagnetic, or "deshielded" of the species studied. This term is very difficult to calculate accurately, often demanding very large basis sets. For the CHFPT calculations, we have expanded the Cd d basis set over that employed for split valence calculations, using six primitive d Gaussian functions,lgcontacted to a set of three, a set of two, and a single function, Le. (6) [321], and adding diffuse p Gaussians with exponents of 0.16 and 0.04. Our best basis set for CdC142-is, in the usual contracted Gaussian notation [6sSp3d/4~3pld], Even with these large bases the contribution of distant core orbitals to up is smaller than it should be. McConnel120has shown that the only effect of distant charge distributions on u should vary as the anisotropy in the magnetic susceptibility of the distant group divided by the cube of the distance. Thus, for isotropic distant groups, ad and up should exactly cancel.20 Such cancellation is also found to high accuracy in perturbation theory approaches which utilize different origins for different occupied localized MOkZ1Our CHFPT method, which employs a common origin for all electrons, does not automatically give such cancellation, and thus gives total shieldings that are too large if the surrounding atoms have deep cores. We can, in a somewhat ad hoc manner, correct for this by subtractingfrom ad a distant core contribution, given by the formula of Flygare and Goodisman22as
-
Aucorr= 17.75x(1/Ri0) i
where Riois the distance from the origin to nucleus i (an adjacent C1 or 0 atom) and the sum is over all the core electrons on adjacent C1 and 0 atoms. We report these final corrected values of u as umrrin Table X. We have previously shown that the relative 67Zn NMR shieldings of ZnC142-, Zn(CN)42-, and Zn(OH)42-, for which unequivocal experimental data exist, are well described by this CHFPT approach.23
Computational Results The general goal of thii research was first to calculate structural and spectroscopic properties for the simplest complexes (i.e. the unhydrated species) and then to compare these results with experimental data. Calculations on the hydrated complexes were then undertaken, and the available diffraction and spectral data were used to help identify the overall symmetries of the species that exist in solution. Unhydrated and Hydrated Zinc Species. We fmt compare our calculated results for the unhydrated zinc chloride complexes with those of the previous theoretical workag This is done in order to determine if the present pseudopotentialsand bais sets give adequate results to ensure that subsequent calculations would be comparable. The calculations differ in that previously an allelectron formalism and polarized split valence bases were used.g Calculated equilibrium bond distances for the zinc chloride complexes and hexahydrated Zn2+cation are given in Table I. The calculated Zn-Cl bond lengths using the ECP show an increase from the previously calculated all-electron polarized split valence values of -0.1 A. This difference is consistent for all the complexes studied. The ECP calculated Zn-O bond length for aquated Zn2+is better predicted but is still slightly long. Our calculated Raman frequencies are all smaller than the previously
6496 The Journal of Physical Chemistry, Vol. 96, No. IS, 1992 TABLE I: Calculated and Experimental Zn-Cl and Zn-0 Bond Distances (A), and ToWly Symmetric Raman Frequencies (em-') (in Parentheses) present previous work wnrk9" (ECP) exatl ZnCP ZnC1,
2.03 (502) 2.07 (380)
2.13 (433) 2.17 (326)
ZnCIy ZnC1:-
2.18 (326) 2.31 (297)
2.28 (280) 2.41 (253)
Zn(OH2):+
2.09 (400)
2.15
a All-electron, polarized
2.07 (361) (gas phase24) (305) (aq2') (286) (aq25) 2.30 (275) (aq25*26) 2.25 (crystal) 2.08 (as) (385-40Oz7)
split valence.
TABLE 11: Calculated and Experimental C d c l and Cd-0 Bond Distances (A) (Symmetries in Parentheses) Calcd exptl CdCl+ (CJ 2.30 2.33. 2.31' 2.24 h a s phase2') CdC1, (D-L) 2.576'7aqiv29) 2.553 (aq av29) CdCIy (D3h) 2.45 2.57, 2.52" 2.45 (crysta130) CdC1d2- ( T d ) 2.56, 2.53 CdC15'- (D3h) 2.66, 2.72" 2.32 2.31 (aq2'v3') Cd(OH2)6*+(oh)
. -..,
Butterworth et al. TABLE III: Calculated Cd-Cl ToUly Symmetric Raman Frequencies (em-') for the Unbydmted CdClnpnComplexes and Related Experimeatal Data calcd exDtl CdCP 40 1 CdC12 326 327 (calcd gas phase33) 280 (aq") CdCIy 282 265 (aq3') CdC1:237 260 (aq") TABLE I V Calculated C d 4 and Cd-0 Bond Distances (A) (Symmetries in Parentheses) for the Hydrated CdCIn(H20):-" Complexes CdCl Cd-O CdCMOHz)4 (4)" CdC1z(OH2)2 ( T d ) CdCI3(OH*)- (Td)" CdCl,(OH2)2- (&)" CdC13(0H2)2-
2.53 2.42 2.49 2.54 2.46, 2.60 X 2
2.35 2.32 2.36 2.38 2.45
'
a
Polarized SV* all electron calculation.
-
calculated values by 14%but again this difference is consistent for all the complexes and is consistent with the calculated bond lengths. In addition to being an all-electron calculation, the previous work included ligand 3d polarization functions in the basis. The previous stretching frequencies were too large, as expected near the HartreeFock limit, and had to be scaled down by about 5% to match experiment. The species ZnC1," is known to exist in solution with no waters of hydration, so that the "bare" gas-phase anion should, therefore, be expected to be an adequate model if artifacts produced by the unbalanced negative charge are not too large. Our calculation on ZnClz is also directly comparable to experimental data obtained in the gas phase. The calculated Raman frequencies for both these species are 10%lower than the comparable experimental values, in line with the calculated longer bond lengths. If we assume that our calculated Raman frequencies are consistently in error by this amount then some conclusions about hydration can be drawn from the results. The experimental value for ZnC1, in solution (305 cm-I) is lower than both the experimental and calculated values in the gas phase and suggests that the ZnC12is strongly assOciated with waters of hydration in solution. Results for the ZnC1,complex indicate that it is less strongly associated with waters of hydration as the Raman frequency measured in solution is -2% higher than the calculated gas-phase value. We would expect this frequency to be somewhat reduced if there existed a significant water-anion interaction. These results are in agreement with previous work9 and consistent with the expected trend for these complexes. In our previous work, we evaluated the Zn NMR shieldings for both bare ZnC1,2-" species and several aquated species. Based on a comparison of calculated and experimental NMR parameters and available X-ray and Raman data we arrived at the following set of species as most probable: ZnC1(OHz)s+(pseudooctahedral), ZnCl,( OHZ)4(pseudooctahedral), ZnCl,( OHz) (pseudotrigonal bipyramidal), and ZnC14z- (tetrahedral). Near the end of this paper we present results for some additional zinc chloride species which support our previous conclusions and make possible some general comparison with the Cd chloride results. Cadmium Chloride Species. Unhydrated CdC1,2-" Species. Results for the CdCl,Z-nspecies and for Cd(OHz)6z+are given in Table 11. Our calculated value of the Cd-Cl bond length in CdC12 is -0.1 A greater than that determined in the gas phase, in line with our findings for ZnClz. Indeed, our calculated bond lengths for both ZnClz and CdClz calculated at the ECP level agree well with those reported by Stromberg et al. for ZnCIz at
-
"Optimization was performed constraining the local metal atom symmetry as indicated.
the all-electron level and for CdClz at the ECP level.1° These authors have also shown that electron correlation has little influence on the calculated bond lengths, which gives us added confidence in the SCF calculations described herein. For CdCLzour calculated bond length is 0.12 A greater than the crystal value,Ma difference that is also similar to that found for ZnC14z-. X-ray studiesz9of aqueous CdClz indicate that the cadmium cation possesses overall octahedral symmetry, with a mean Cd-Cl bond length of 2.576 A. Both the calculated and experimental bond lengths for CdClzin the gas phase (Table 11) are considerably shorter than this value, a finding consistent with a strong association with waters of hydration in solvation that results in an increased metal-halide distance. The same experimental study also indicated that on addition of ZnClz to the solution the mean environment of the cadmium changed. The number of metalhalide bonds identified for the new species was three, with a mean Cd-Cl bond length of 2.553 A. This value is greater than the calculated gas- hase value for CdClr by only about 0.1 A, compared to -0.2 for CdC12,which suggests a weaker water-metal interaction than in the dichloro complex. The calculated Cd-0 bond length of 2.32 A for hexaaquated Cd2+shows essentially exact agreement with the experimental value of 2.31 A determined from X-ray diffraction st~dies.~'.~' However, it is expected that our calculated value is an overestimate by up to about 0.1 A, so that the effect of further complete solvation is anticipated to increase the Cd-0 bond length by up to this amount. On the basis of our calculations of the hexahydrate, the calculated hydration energy of Cd2+(1333 kJ mol-l) is lower than the value for Zn2+ (1497 W mol-'), a trend in line with experiment.jZ The lower hydration energy relative to the zinc species is consistent with a decreased water-cation interaction brought about by the larger radius of the cadmium cation. This effectively reduces the electric field experienced by the hydrating water molecules and so reduces the hydration energy. We now discuss the calculated Raman frequencies for the unhydrated species shown in Table 111. The calculated value for CdClZis essentially the same as the experimental value. For CdC14z-,the Raman frequency that we predict is 10% lower than the experimental value, in line with our findings for the Zn species, and suggests that CdC142-is not strongly hydrated in solution. As in the case of the zinc complexes, there is a sisnificant increase in Raman frequency on going from CdC12- to CdC13-, which is not found experimentally, which reflects the stronger hydration of the latter species. Hydrated Cadmium Chlorides, CdCl,,(H20),*n. Bond lengths for the optimized structures of the hydrated cadmium chloride complexes are given in Table IV. Raman data suggest that the
s
-
Spectra of Cd Complexes
The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 6497 TABLE VI: Calculated and Exwrimental Cd-Br Bond Distances (A, calcd ._.._
CdBrt (C-,,) CdBr, (D,,d CdBr3- (D3h) CdBr4,- ( Td)
w -
Figure 1. Optimized structure of CdC13(OH2)T TABLE V: Hydration Energies per Added H20 (kJ/mol) Calculated for the Optimized Shyctures of the Cadmium Complexes
Cd(OH2)62+(0,+) 222 CdCl,(OH2)T(D,h)' 31 CdCI(OHJs+(Oh) 140 CdCl,(OHZ)-(Td)" 40 CdCl2(OH2),(Oh)' 71 CdCI3(OH2)248 CdClAOHzMTd) 87 a Optimization was performed constraining the local metal atom symmetry as indicated. symmetry of the CdClq complex in solution approximates to D3*, with the chloride ligands occupying the equatorial, and the water molecule the axial, positions of a bipyramid. However, an unconstrained optimization gave the structure shown in Figure 1, with one inequivalent short Cd-Cl bond, and two longer Cd-Cl bonds, closer to the two water molecules. An attempt was made to optimize the structure of CdC&,- bound to two water molecules using an overall octahedral structure as the starting point. No stable minimum energy configurationcould be located, in line with experimental data suggesting CdC14,- is not hydrated. The calculated Cd-Cl bond lengths for the hydrated species are all longer than the corresponding values in the unhydrated species. This lengthening is found to be much greater for the mone and dihalide octahedral complexes than it is for the trihalide tetrahedral structures, due to the greater perturbation of the CdCln fragment by the solvating molecules. The smallest increase in the calculated Cd-Cl bond lengths upon hydration occurs for the trichloride complex which also has the longest calculated Cd-0 bonds. These features are consistent with a lower hydration energy. X-ray diffraction studiesB of CdCl, in aqueous solution obtained a mean Cd-Cl bond length of 2.576 A for a species suggested to be CdC12(0H2)4. This bond length is considerably longer than the calculated gas-phase bond length for CdCl, (Table 11) but is only slightly longer than the predicted bond length for the octahedral complex (Table IV). On addition of ZnC1, to the solution, a species which may be CdC13(H20)- is found with a reduced Cd-Cl bond length of 2.553 A, but with an essentially unaltered Cd-0 length. These findings are in accord with our calculations (Table IV) where a reduction in the Cd-Cl bond length of 0.04 A is predicted on going from octahedral to tetrahedral coordination, but with little change in the Cd-0 length between the two species. The calculated hydration energies for the cadmium species are shown in Table V. We note the predicted large decrease as the number of coordinated halide atoms increase, which would suggest a very small hydration energy for the tetracoordinated s p i e s in line with the lack of hydration suggested from Raman studies. For the unhydrated species, a plot of the calculated symmetric frequencies (Table 111) versus the reciprocal of the calculated bond length (Table 11) gives a good straight line plot in agreement with the analysis of Kanno. If we assume that the Cd-Cl and Cd-OH, stretching vibrations can be separated in the CdCl,(OH2),2-" complexes, this relationship leads to estimated Cd-Cl stretching frequencies of 258,252,291,248, and 266 cm-'for CdC1(0H2)5+, CdC12(0H& CdCl2(OH2),, CdC13(OH2),-,and CdC13(0H2)-,
2.43 2.47 2.60 2.73
exatl ---r--
2.63 (melts5) 2.39 (gas phase2*) 2.59 (crystals6)
TABLE MI: Calculated Totally Symmetric Raman Frequencies (cm-I) for the Unhydrated Cadmium Bromide Complexes and Related Experimental Data calcd exptl CdBr' (C-,,) 281 200 (aq) CdBr2 (D-h) 205 186 (aqs7),205 (gas phase) CdBrr (Dsh) 173 168, 173 (a(137,34) CdBr2- ( T d ) 142 159, 161, 166 (aq37934) 161 (melt3*) TABLE VIII: Calculated Cd-Br and Cd-O Bond Distances (A) (Symmetries in Parentheses) for the Hydrated CdBr,(H20):-" Complexes" Cd-Br Cd-O CdBr(OHz)st (4) 2.62 2.36 (ax) 2.33 (e¶) CdBr2(OH2)4 (4) 2.70 2.35 CdBrz(OH2)2 ( T d ) 2.56 2.32 C ~ B ~ ~ ( O H(D3h)' Z)F 2.70 2.38 CdBr3(OH2)-(Td)O 2.64 2.36
'Optimization was performed constraining the local metal atom symmetry as indicated. TABLE I X Hydration Energies/H20 (kJ/mol) Calculated for the Optimized Structures of Cadmium Bromide Complexes CdBr(OH2)st( o h ) 133 CdBr3(OHz); (D3h)" 32 CdBrdOHA (oh) 68 CdBr3(OH2)-(Td)" 40 CdBr2(0H2)2 ( T d ) 82 a As
in Table VIII.
respectively. These estimates are in the experimental range but are probably not sufficiently accurate to allow a confident determination of speciation by comparison with the limited experimental data. Cadmium Bromide Species. Unhydrated CdBrnh Species. The calculated bond lengths for the cadmium bromide species (CdBr>-", n = 1-4) are given in Table VI. For CdBr, the Cd-Br bond length is in acceptable agreement with experiment and shows a similar deviation from experiment as was found for CdC12 For all the bromides, the Cd-Br distance is predicted to be -0.15 A greater than that of the corresponding chlorides. This agrees with the experimental increase in the cadmium-halide bond length on going from CdCl, to CdBr4-, but as with the chloride, the deviation found between the calculated and experimental bond length is somewhat larger than that for gaseous CdBr,, presumably also due to solid-state effects. For CdBr+, our calculated bond length is smaller than that obtained experimentally from the melt (2.63 A). However, Raman data for the melt are similar to those for CdBr4,-, which casts some doubt as to whether the species present is actually CdBr+. Turning to the calculated Raman frequencies, both the experimental and calculated values decrease with increased coordination, as expected (Table VII). As was found for CdCl,, the calculated value for CdBr, is the same as the gas-phase value. Through the series CdBr', CdBr2,CdBr3-, CdBrP, the calculated overestimation of the Raman frequency is progressively reduced, compared to the experimental aqueous values, until for CdBr42the calculated value is less than that measured. These comparisons indicate reduced solvation as coordination increases and suggest that the tetrabromide is essentially unsolvated. We may use the magnitude of the difference between our calculated (gas phase) Raman frequencies and those measured in aqueous solution to speculate on the relative effects of hydration for the chloride and bromide species. The overestimation (in
6498 The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 TABLE X Cdcuhted NMR !Mddhgn for Cd Complexes: Absolute Shieldings a d Shifts Compared to Cd(OH2)62t
Cd(OH2)62t Cd Cd2+ CdCP CdCI(OHJ5’ CdC12 CdCh(OH2)2 CdCMOH2)4 CdClC CdCIS(OH2)CdCI3(OH2)c CdC1F2 R = 2.453 A (expt) R = 2.574 A (calc) CdCIs” R = 2.53, 2.56 A (expt) R = 2.72, 2.66 A (calc)
Anm,. exptl“ 0 -1106“
4059 4781 4769 4370 3955 3880 3804 3848 3724 3755 3882
calcd 0 -722 -710 -311 104 179 255 211 335 304 177
3608 3802
451 257
451-474’
3741 3955
318 104
247-329c 188, 172d
awn.
89b 114b
TABLE XI: Experimental Cd Chemical Shifts (ppm) for Various Cd(I1)-Halide Complexes halide CdX+ CdX2 CdXc CdX12c189 114 296 474 Br74 66 380 365 Ifast exchangeo 49 29c 148 70 slow exchangeb 20 43 122 101
” Reference 6. Reference 41. Value considered unreliable in ref 6 because of the small concentration of the Cd12 species in all solutions. TABLE XII: Calculated Cd NMR S h i e l d i q for CdBr2, CdBry, and
296b
CdBr.*-
Aa-..
Reference 39. Reference 6. Limit for Cd(C104)2 dissolved in concentrated HCI or LiCl in ref 6. dShieldings for CdCIs3-in solids in ref 6.
percentage) of the frequencies is somewhat larger for the chloride than for the bromide species and suggests the expected reduction in solvation for the latter. This may lead to a change in geometry, from octahedral to tetrahedral, at an earlier stage of halide coordination, for the bromide, compared to the chloride species. Hydruted Cadmium Bromides, CdBr,,(H@),;”-n.The calculated equilibrium geometries are summarized in Table VI11 and the hydration energies are given in Table IX. As was found for the hydrated chloride species, the Cd-O bonds in the bromides are all somewhat longer than the calculated value for Cd(OH2)62+, reflecting the reduction in the Cd charge upon halide complexation. The effect of replacing CI by Br is most evident for CdX(OH2)5+, where a slight increase in the Cd-O bond length is seen for the bromide. This is reflected in the reduced hydration energy calculated for the bromide complex (Table IX). For the other hydrated bromides, the Cd-0 bond lengths are essentially the same as for the chlorides in line with the calculated hydration energies of these species which show little difference for the two halide series. However, there is a lack of experimental X-ray diffraction data for the solvated bromides which prevents a more detailed discussion of our calculations. clllcllllnted NMR sbieldimgs. In Table X, we present calculated values of a, for Cd,Cd2+,Cd(OH2)2+,the unhydrated CdC1;“ series, and their hydrated analogs, using ECP double4 optimized geometries unless otherwise noted. We first observe that Cd(OH2):+ is deshielded by about 700 ppm with respect to the free Cd atom (or the free Cd2+ion), in reasonable agreement with the experimental estimate of 1100 ppm deshielding. Compared to Cd(OH2)62+,the usual reference species expected in Cd(NO& aqueous solutions, most of the other species are deshielded. Comparing the ‘bare” chloride series CdZ+,CdCl+, CdC12,CdClq, and CdCh”, we see progressively larger deshielding until CdCly, but a smaller deshielding for CdCh2-at the calculated equilibrium geometry. The difference between Cd(OH2)62+and CdC142shieldings match= those obtained from experiment for the CdCb2anion in crystals against the Cd(OH2)62+cation in aqueous Cd(N03)2 solution, only if we use the experimental Cd-Cl distance; using the calculated value the deshieldmg of CdCb2- is 200 ppm smaller. Experimental shieldings for Cd(C104)2 dissolved in concentrated HCl or LiCl are on the order of 250-330 ppm deshielded with respect to Cd(OHz)62+.Such values might be consistent for CdC142-with a longer bond distance than in the crystal, approaching the calculated value of 2.574 A in the free ion. At high C1- concentration the formation of CdClS3-(or even CdCh4-) is also p i b l e . Using allelectron polarized split valence bases as in ref 9 we calculate Cd-Cl bond distances in CdCIS3of 2.66 A (equatorial) and 2.72 A (apical), values which we expect to be too long because of the unbalanced 3- charge. The ex-
-
Butterworth et al.
a,,,
CdBr, CdBr,CdBr2-
calcd geom calcd geom (R = 2.60) calcd geom (R = 2.73) exptl geom (R = 2.59)
3862 3770 3870 3654
calcd 197 289 189 405
exptP 66 380 365-387
“ Reference 6. perimental values for CdCIS3-in one crystalline environment are 2.56 A (eq) and 2.53 A (ap).& The calculated and experimental geometries of CdCb3- give considerably different shieldings but, in each case, they are more shielded than CdC13-. It thus appears that, for the bare CdCl,Z-” species, the most deshielded is CdCIq. Inspection of the calculated shieldmgs for the hydrated species indicates that a pseudooctahedral CdCI(OH2)5+gives a shielding decrease of 104 ppm with respect to Cd(OH2)6’+, in good agreement with the experimental value of 89 ppm. In a qualitative way we see that each H 2 0in Cd(OH2)62+deshields the Cdz+ion by about 120 ppm, while each C1- in CdCLZ-deshields it by about 240 ppm, so replacement of one H 2 0 by a C1- should deshield Cd(OH2)6’+ by roughly 120 ppm. For the CdCI2species the situation is more complicated. The Cd shielding changes only slightly as two or even four H 2 0 molecules are coordinated to it. Each additional H 2 0 molecule contributes to the deshielding of the Cd2+but at the same time the coordination of Cd by H 2 0 increases the Cd-Cl distance and thus reduces the deshielding due to C1-. On the basis of a comparison of calculated bond distances with those from solution X-ray diffraction, the CdC12(OH2)4species appears the most probable. Its calculated deshielding of 21 1 ppm is larger than the experimental value of 114 but the latter depends upon the assumed equilibrium constants. NMR studies on frozen solutions of Cd12 in the slow-exchange limit give the Cd NMR shieldings shown as the last line of Table XI, which differ substantially from those obtained by analyzing the fast-exchange data using assumed equilibrium constants. For bare CdClq the calculated deshielding is 335 ppm, not too much different from experiment. Addition of one H 2 0 molecule expands the Cd-Cl distance from 2.45 to 2.59 A giving a slight increase of the shielding and coordination of a second H 2 0 causes even further shielding. On the basis of the good agreement of calculated and solution X-ray diffraction geometries, the CdC13(0H2)-species is probably favored. Although the CdBr,(OH2),bn species are too large at present for all-electron shielding calculations, we can gain some further understanding of speciation in the Cd bromide system by calculations on the high-symmetry bare halide species CdBr2,CdBr,-, and CdBr4’-, for which results are shown in Table XII. The shielding of CdBr4” vs Cd(OH2):+ agrees well with experiment if the experimental geometry of CdBr42-is used. The deshielding contribution of each Br- in CdBrt- is about 220 ppm, suggesting that replacement of one H 2 0 by Br- in forming CdBr(OH2)s2+ should give a dcshielding of about 100 ppm vs Cd(OH2)62+, reasonably consistent with the experimental value of about 72 ppm. The calculated deshielding for CdBr3- is 289 ppm, reasonably consistent with the experimental value of 380 ppm and indicative of rather weak involvement of H 2 0 in the coordination sphere. The experimental deshielding of the CdBr, s p i e s is only 66 ppm.
The Journal of Physical Chemistry, Vol. 96, No. 15, 1992 6499
Spectra of Cd Complexes TABLE XIII: Mulliken Sp Populations for the Cadmium Cations of the Hvdrated Comdexes no. of halide no. of halide ligands, n ligands, n (symmetry) CdCI, CdBr, (symmetry) CdCI, CdBr, 0 (oh) 0.20 0.20 3 (D3h) 0.62 0.66 1 (Oh) 0.30 0.34 3 (Td) 0.65 0.72 0.45 0.48 4 (Td) 0.69 0.73 2 (oh) 2 (Td) 0.54 0.60
hydrated value, and (3) the ML(OH2)5+species is slightly deshielded compared to M(OH2)62+.
~~
TABLE XIV Comparison of Calculated and Experimental AuValues (with Respect to Zn(OH,)J+) for ZnCI:-" and ZnCI.(OH~),'-"
ZnCi,2ZnClgZnC13(OH2)ZnCI3(OH2)~ ZnC12 ZnC~z(OH2)4 ZnCP ZnCI(OH2)5t
calcd 245 206 187, 191b 162, 15Sc 78 92d -267 91
exDtl 253 119
30
Positive Au,, corresponds to deshielding compared to Zn(OH2?62+, opposite sign convention to that used in ref 9. boptimized polarized SV geometries with C,symmetry (Garmer, D. L., personal communication), and with new C, geometry with close H-.-CI contact. c T w ~ different C,geometries, the second with lower energy and closer H-..Cl contacts. dNew lower energy optimized polarized SV &, geometry with He .H and C. C l vectors parallel.
Although we have not calculated the shielding for CdBr2(OH2)4, its change in geometry compared to Cd(OH2)?+ is similar to that for CdC12(0H2)4,suggesting a similar Shielding. We believe that the fast-exchange data underestimate the deshielding of this species. To gain a more qualitative understanding of the trends in Cd shielding it is useful to focus upon some aspects of the ground-state electronic structures of the complexes. According to the analysis of Nakatsuji and ~ e w o r k e r the s ~ magnitude ~ ~ ~ ~ of 8 should depend strongly upon the extent of donation of electron density from the ligands to the 5p orbitals of the Cd. We have previously verified such a semiquantitative relationship for Zn complexes? as originally On the basis of the Mulliken Cd 5p populations, PSpfor the hydrated complexes shown in Table XI11 and our calculated [up1values, we have constructed a plot of IuPI vs P5,and a similar plot of um vs Pg. Both plots show reasonably smooth but nonlinear variation, as seen before in the Zn case. Thus, from the ground-state charge distribution aP can be estimated but the scatter of the plot indicates that only a semiquantitative value of u,, can be obtained. In Table XIV we update our previous results for ZnC1,2-" hydrated complexes based on new calculated allelectron polarized split valence geometries for ZnC12(0H2)2(a species not previously considered), ZnCI2(OHJ4 (previously optimized as a higher energy rotamer) and ZnC13(OH2)-(previously optimized with symmetry constraints). Responding to questions from D. L. Garmer (personal communication to J.A.T.), we have found that our optimized total energies are considerably different for different rotamers, with the most stable rotamers allowing close H . 4 1 contacts, as for CdC13(0H2)2-in Figure 1. For example, rotating the H 2 0 ligand to allow for such H-bonding interactions lowers the total energy by 44 kJ/mol even if C, symmetry is retained. Reoptimizing in C1symmetry gives an additional 9 kJ/mol stabilization. Fortunately, the calculated NMR shieldings are insensitive to the rotamer used. For example, the two different C, geometry rotamers of ZnC13(OH2)2-differ in energy by 85 kJ/mol but in shielding by only 7 ppm. Our calculated Zn NMR shielding trends are thus similar to those for Cd. Thus, (1) the MC13- species becomes progressively more shielded as H 2 0 is added, (2) the addition of two H 2 0 deshields the MC12 species, but addition of four H 2 0 molecules increases the shielding back to near its un-
Conclusions Calculations of the geometries, symmetric stretching frequencies, and Cd NMR data for a series of "bare" and hydrated Cd chloride and bromide complexes are consistent with the following structural trends when comparison with experimental data is made. The CdX2- species are unhydrated, CdX3-are weakly hydrated, probably in a pseudotetrahedral geometry, while CdX2 and CdX+ are strongly hydrated, probably as pseudooctahedral complexes. As far as NMR data are concerned, the CdX(OH2)5+complexes are slightly deshielded with respect to Cd(OH2)62+,all the CdX2complexes (both bare and hydrated) are substantially deshielded (in disagreement with fast-exchange experimental estimates) and the CdXy species show slightly increased shielding as H 2 0 is added. CdXz- complexes have shieldings which match well against experimental values in solids only if experimental bond distances are used. The calculated shielding of CdCI5>is strongly dependent upon geometry, which may explain the apparent variability in shielding values for this species. Acknowledgment. This research was support by the National Science Foundation Grant No. EAR900654 and NATO Grant No. CRG90015 and by the SERC (U.K.) and the NERC (U.K.) Grant No. GR3/7132A.
References and Notes (1) (a) Craig, J. R.; Vaughan, D. J. Ore Microscopy and Ore Petrography; Wiley-Interscience: New York, 1981. (b) Crerar, D.; Wood, S.;Brantley, S.;Bocarsly, A. Can. Mineral. 1985, 23, 333. (2) (a) Barnes, H. L. Solubilities of Ore Minerals. in: Geochemistry of Hydrothermal Ore Deposits, 2nd ed.; Barnes, H. L., Ed.; Wiley-Interscience: New York, 1979. (b) Gerding, P.; Jonsson, I. Acta Chem. Scand. 1978, 22, 2247. (3) Ruaya, J. R.; Seward, T. M. Geochim. Cosmochim. Acta 1986, 50, 651. (4) Magini, M., Ed. X-ray Diffraction of Ions in Solution Hydration and Complex Formation; CRC Press: Boca Raton, FL, 1988. (5) Anderson, p. R.; Irish, D. E. J . Solution Chem. 1988, 17, 763. (6) Ackerman, J. J. H.; Orr, T. V.; Bartuska, V. J.; Maciel, G . E. J. Am. Chem. Soc. 1979, 101, 341. (7) Drakenberg, T.; Bjork, N-0.; Portanova, R. J. Phys. Chem. 1978,82, 2423. (8) Mennitt, P. G.; Shatlock, M. P.; Bartuska, V. J.; Maciel, G. E. J. Phys. Chem. 1981,85, 2087. (9) Tossell, J. A. J . Phys. Chem. 1991. 95, 366. (10) (a) Stromberg, D.i Sandstrom, M.; Wahlgren, U. Chem. Phys. Lett. 1990, 172, 49. (b) Stromberg, D.; Gropen, 0.;Wahlgren, U. Chem. Phys. 1989, 133, 207. (11) Nakatsuji, H.; Nakao, T.; Kanda, K. Chem. Phys. 1987, 118, 25. (12) Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985,82, 270, 285, 299. Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984,81, 6026. (13) Tatewaki, H.; Huzinaga, S.J. Chem. Phys. 1979, 71, 4339. (14) (a) Guest, M. F.; Kendrick, J. GAMESS User Manual, CCP1/86; Daresbury Laboratory, 1986. (b) Schmidt, M. W.; Boatz, J. A.; Baldridge, K. K.; Koseki, S.;Gordon, M. S.;Elbert, S.T.;Lam, B. QCPE Bull. 1987, 7, 115. (15) Kanno, H. J . Raman Spectrosc. 1987, 18, 301. (16) Buttersworth, P. Ab initio molecular orbital study of some transition metal complexes. Ph.D. Thesis, University of Manchester, 1991, (17) Lipscomb, W. N. Adv. Magn. Reson. 1966, 2, 137. (18) Tossell, J. A.; Lazzeretti, P. Phys. Chem. Mineral. 1988, 15, 564. (19) Huzinaga, S.,Ed. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (20) McConnell, H. M. J . Chem. Phys. 1957, 27, 226. (21) (a) Fleischer, U.; Schindler, M.; Kutzelnigg, W. J. Chem. Phys. 1974, 86,6337. (b) Hansen, A. E.; Bouman, T. D. J. Chem. Phys. 1985,82,5035. (22) Flygare, W. H.; Goodisman, J. J . Chem. Phys. 1968,49, 3122. (23) Tossell, J. A. Chem. Phys. Lett. 1990, 169, 145. (24) Hargittai, M.; Tremmel, J.; Hargittai, I. Inorg. Chem. 1986,25,3163. (25) Morris, D. F. C.; Short, E. L.; Waters, D. N. J . Inorg. Nucl. Chem. 1963, 25, 975. ( 2 6 ) Kruh, R. F.; Standley, C. L. Inorg. Chem. 1962, I , 941. (27) Ohtaki, H.; Johansson, G. Pure Appf. Chem. 1981.53, 1357. (28) Lister, M. W.; Sutton, L. E. Trans. Faraday Soc. 1941,406. (29) Paschina, G.; Piccaluga, G.; Pinna, G. J . Chem. Phys. 1983,78,5745. (30) Richardson, M. F.; Franklin, K.; Thompson, D. M. J . Am. Chem. SOC.1975, 97, 3204. (31) Ohtaka, H.; Maeda, M.; Ito, S.Bull. Chem. Soc. Jpn 1974,47, 2217. (32) Rosseinsky, D. R. Chem. Rev. 1965, 65, 467. (33) (a) Lowenschuss, A.; Ron, A.; Schnepp, 0. J . Chem. Phys. 1%9,50, 2502. (b) Strull, A.; Givan, A.; Loewenschuss, A. J . Mol. Spectrosc. 1976, 62, 283.
J. Phys. Chem. 1992, 96,6500-6504
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(34) Davics, J. E. D.; Long, D. A. J . Chem. SOC.A 1968, 2054. ( 3 5 ) Bengtsson, L.;Holmberg, B. Acra Chem. Scand. A 1976, 30. 249. (36) Bart, J. C. J.; Bassi, I. W.; Calcateria, M. Phosphorus Sulfur 1981, 9,347. (37) Macklin, J. W.; Plane, R. A. Inorg. Chem. 1970, 9, 821. (38) Clarke, J. H. R.; Hartley, P. J.; Kuroda, Y. J . Phys. Chem. 1972,76, 1831.
(39) Kruger, H.; Lutz, 0.;Schwenk, A.; Stricker, G. Z . Phys. 1974, 266, 233. (40) Epstein, E. F.; Bernal, I. J . Chem. Soc. A 1971, 3628. (41) Ackerman, M. J. B.; Ackerman, J. J. H. J . Am. Chem. Soc. 1985, 107, 6413. (42) Nakatsuji, H.; Kanda, K.; Endo, K.; Yonezawa, T. J. Am. Chem. Soc. 1984, 106,4653.
A Far-IR Study of Irradiated Amorphous Ice: An Unreported Oscillation between Amorphous and Crystalline Phases Reggie L. Hudson* Department of Chemistry, Eckerd College, St. Petersburg, Florida 33733
and Marla H. Moore Astrochemistry Branch, NASAIGoddard Space Flight Center, Greenbelt, Maryland 20771 (Received: February 26, 1992; Zn Final Form: April 14, 1992)
Far-IR spectra have been recorded for amorphous H20ice irradiated at 13-125 K with 0.7-MeV protons. Little or no changes were seen in the spectra of ices irradiated above -27 K. However, at lower temperatures, most prominently at 13 K, IR spectra showed that ice samples oscillated between a highly amorphous and a highly crystalline form with increasing radiation dose. A mechanism for the oscillation is proposed involving free radical storage.
Introduction Amorphous water ice occupies an important position in the chemistry of comets, interstellar grains, and planetary satellites and rings.' In each of these objects, ice has been exposed to Cosmic radiation, mostly in the form of high-energy protons.2 Since the temperatures of comets, grains, and the planets from Saturn outward are nearly always below 100 K,3 and often below 30 K, radiation chemical products, such as free radicals, are thought to be stored in the amorphous ice for long periods of time. In contrast with the importance of irradiated amorphous ices in astronomical environments, very few laboratory radiation studies on amorphous H 2 0 ice have been reported. Excellent work has been done on ice mixtures, normally ices made by freezing solutions, often very acidic or alkaline ones, from the liquid state.4 While these experiments have been invaluable for studies of ice structure and reaction mechanisms, the samples themselves were of little interest to astrochemists. Even in experiments where "neat" H20ice has been irradiated, it has nearly always been in the common hexagonal phase, Zh,irradiated at or above 77 K by radiation of low linear energy transfer (LET), such as electrons, X-rays, or @C y-raysSs Our own literature search, summarized in the first five lines of Table I, uncovered but three spectroscopic6 and two diffraction' studies of irradiated amorphous ice. This paper presents our recent work on amorphous ice irradiated from 13 to 125 K with a 0.7-MeV H+ beam. The experiments assess the stability of amorphous ice at low temperatures in a radiation environment. In addition, we describe an unusual radiation-induced oscillation between amorphous and crystalline phases of ice. A separate paper will explore the radiation chemistry of crystalline ice and its astrochemical implications.*
Experimental Section A common method of forming amorphous H20ice is to slowly condense water vapor onto a surface cooled below 130 K,and preferably below 77 K.9 Warming such an ice to 135-145 K causes crystallization to the cubic phase, and further warming produces the hexagonal phase above 170 K.Io Our experiments were done with these facts in mind.
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0022-3654/92/2096-6500$03.00/0
TABLE I: Laboratory Studies of Irradiated Amorphus Ice ref T (K) radiation used method of study 90 1.7-MeV e6a mid-IR 6b 97 0.53-MeV eUV-vis 6c 77 700-kV X-rays ESR 7a 28 100-keV ee- diffraction 225 SO-, 100-keV e7b e- diffraction this work 13-125 0.7-MeV p+ far-IR
Figure 1 is a schematic representation of the experimental setup. Located perpendicular to the figure, and not shown, was a closedcycle cryatat (T- 13 K). Experiments began by cooling a polished, circular 5 cm2 aluminum substrate to 13 K in the evacuated multisided sample chamber. Next, the source beam from a Mattson Polaris FTIR was reflected off the substrate, along the path shown in the figure, and then back to the spectrometer's detector. The resulting spectrum served as a background for spectral ratioing. Water vapor was then deposited slowly onto the cooled substrate under conditions chosen to assure that the solid formed was amorphous, as shown by its IR spectrum.e'' The ice thickness, based on the most recent optical constants,I2 was on the order of a few micrometers. IR spectra of the ice were recorded as 60-scan accumulations with 4-cm-' resolution from 100 to 500 cm-' A heater and thermocouple adjacent to the ice (not shown in Figure 1) permitted irradiations and measurements at temperatures above 13 K. The heater also was used in forming crystalline ice by warming an amorphous sample from 13 to 155 K,holding at 155 K for 5 min, and then recooling to the temperature of interest. A dedicated quadrupole mass spectrometer (QMS), shown interfaced to the sample chamber in Figure 1, allowed the analysis of gas releases from the ices during either irradiation or warmings. Irradiations were performed with 0.7-MeV protons (LET430 MeV cm-], range 13 pmI3) from a Van de Graaff accelerator at a current of 1 X lo-' A. Since the range of the protons always was greater than the thickness of the sample, the protons passed through the ice and came to rest in the aluminum substrate where 0 1992 American Chemical Society
