6680
J . Phys. Chem. 1986, 90, 6680-6684
Thermodynamics of Ionic Solvation: Monte Carlo Simulations of Aqueous Chloride and Bromide Ions Charles L. Brooks 111 Department of Chemistry, Carnegie- Mellon University, Pittsburgh, Pennsylvania 1521 3 (Received: February 12, 1986: I n Final Form: August 5, 1986)
The methods of thermodynamic perturbation theory have been used to calculate the relative thermodynamic properties for the hydration of chloride and bromide ions in dilute solution. The direct evaluation of derivatives of the partition function is carried out to compute the relative energy and entropy of hydration from a single simulation. The results from this method are of greater precision than those computed from differencesinvolving independent simulations. Thus, a potential computational savings of one-half may be obtained by use of the finite difference formula developed within. The influence of interaction truncation on the relative thermodynamic properties is also discussed. Substantial errors of lC-2.5% in the relative free energy of hydration may be attributed to truncation effects. A simple model for ion-water energetics and structure is used to analyze the origin of this truncation effect and it is shown that differences in the phase and/or amplitude of the ion-water distribution functions are responsible for the majority of the influence.
I. Introduction Calculating relative thermodynamic properties for solutions may lead to a deeper understanding of the thermodynamic forces which govern many chemical, biochemical, and pharmacological processes. A number of statistical mechanical approaches have been developed which permit one to make these basic thermodynamic c0nnections.l Most of these techniques are based on the methods of umbrella sampling’ and the closely related thermodynamic perturbation theory.* The umbrella sampling procedure introduces a biasing potential which makes possible efficient sampling within a particular window of configuration space. By carrying out calculations in several overlapping windows and piecing together the results, free energy surfaces may be c o m p ~ t e d . ’ , ~ - ~ Umbrella sampling techniques have been used by Beveridge and co-workers to study the rotational and conformational potential of mean force for the small biopolymer n-alanyla~etamide~ and Jorgensen and co-workers have used similar methods to study the free energy surface for the linear displacement of chlorine in models for SN2reactions in water and DMF.5 In the thermodynamic perturbation approach, relative free energies are computed by “perturbing” one species, e.g., a molecule or group of atoms, into This is achieved by generating configurations of the reference or “unperturbed” system in accord with a specific statistical mechanical ensemble and computing the probability of replacing or “mutating” one group of atoms. The resulting free energy difference for this process is then given by’-2
When the two systems being compared are too different a modified approach has to be used. In this approach, several computations are performed using a hybrid or “mixed” potential function2
u, = xu, - (X
- 1)Ul
in which A is sampled over a range of values connecting Uoto U1. The net relative free energy change is now computed from6,’ 1 dAA(X) A, -Ao = dX (3)
7
( I ) Valleau, J. P.; Torrie, G. M. In Statistical Mechanics, Part A, Berne, 6.J., Ed.; Plenum: New York, 1977, Chapter 5. (2) Tembe, B. L.; McCammon, J. A. Compur. Chem. 1984, 8, 281. (3) Berkowitz, M.; Karim, 0. A.; McCammon, J. A,; Rossky, P. J. Chem. Phys. Lett. 1984, 105, 577. (4) Mezei, M.; Mehrotra, P. K.; Beveridge, D. L. J . Am. Chem. SOC.1985, 107, 2239. ( 5 ) (a) Chandrasekhar, J.; Smith, S. F.; Jorgensen, W. L. J . Am. Chem. SOC.1985, 107, 154. (b) Chandrasekhar, J.; Jorgensen, W. L. J . Am. Chem. SOC.1985, 107, 2974. I
,
.. _
,
Applications of the perturbation approach have been made to several problems of interest in chemistry and biochemistry. These include the free energy of cavity formation in water,6 the solubilities of inert gases in water,7 and the relative free energy of hydration of methanol and ethane.* In recent work by McCammon and co-workers, it has been applied to the calculation of relative binding affinities in host-guest systems of pharmacological and biological r e l e ~ a n c e . ~This method should provide an important tool in the study of biochemical and biophysical phenomena. Therefore, it is important to further explore the use of these approaches to calculate thermodynamic properties, and the extension of the methods to allow greater accuracy and precision to be obtained in studies of specific systems, In this paper we focus on a process which is of basic interest in chemistry and has been reasonably well characteiized in an earlier study,I0 the relative hydration of chloride and bromide anions in water. We explore the direct calculation of thermodynamic derivatives and the effect of potential truncation on relative thermodynamic properties. Investigation of the former point is of great practical concern since it reduces the required computation while maintaining or increasing the precision in the calculated quantities. The latter is of interest in the assessment of the accuracy which may be achieved by the use of simulation methods for the calculation of thermodynamics. Our results indicate that the precision in computed thermodynamic properties may be enhanced by use of the finite difference thermodynamic expressions developed below. On the other hand, we find that the finite distance truncation of electrostatics has a “nonsystematic” effect on these properties. The outline of the remainder of this paper is as follows. In section I1 we present the theoretical formulation and computational methods used. Results for the systems studied are presented and discussed in section 111. We conclude with a brief summary in section IV. In an Appendix we present the model used to assess truncation effects. 11. Theory and Computational Model A . Theory. The standard thermodynamic perturbation theory
as discussed above and in ref 1 and 10 was employed. This formalism relates the ratio of partition functions to the probability of replacing a system with potential Uoby a system with potential U1‘ (6) Postma, J. P. M.; Berendsen, H. J. C.; Haak, J. R. Faraday Symp. Chem. SOC.1982, 17, 55. (7) Swope, W. C.; Andersen, H. C. J. Phys. Chem. 1984, 88, 6548. (8) Jorgensen, W. L.; Ravimohan, C. J . Chem. Phys. 1985, 83, 3050. (9) Lybrand, T. L.; McCammon, J. A,; Wipff, G. Proc. Natl. Acad. Sci. U.S.A..in Dress. (IO) Lybrand, T. L.; Ghosh, I.; McCammon, J. A. J . Am. Chem. SOC. 1985, 107, 7793.
0 1986 American Chemical Society
The Journal of Physical Chemistry, Vol. 90, No. 25, 1986 6681
Thermodynamics of Ionic Solvation (4)
TABLE I: Parameters for the Intermolecular Potential Functions Q? A1/2, W, molecule
The free energy difference is derived from the relationship (5)
The energy and entropy are related to the temperature derivative of eq 5
s1 - so =
- W l
- A,)
aT kB1n
-
(2)
+ kB{
a In Qi/Qo
aT
)
N,V
(6a)
In addition to the ratio of partition functions, eq 6a and 6b require knowledge of the temperature derivative of this ratio. This derivative may be approximated by the finite difference formula
(a
lnaY)N,v
E
In [Q(T + AT)] - [Q(T- AT)] 2AT In [Q(T + AT)/Q(T- AT)] (7) 2AT
Using this approximation and the fact that'
we may rewrite eq 6a and 6b asll
group
HzO (SPC)b 0 HzO (SPC) H
c1-
c1
Br-
Br
esu
(kcal/mol)l/2
-0.82 0.41 -1 -1
A6
(kcal/mol)'/2
793.3
A'
25.0
0
0
5054.9 5863.0
57.51 59.31
"8is 332.16 kcal/mol A. bThe molecular geometry of SPC water is RoH = 1.0 A and AHoH = 109.5O. where we have explicitly displayed subscripts on the angle brackets ((-.)T,o) to indicate the reference state used in the averages and 1 1 L*(T) = -- (10) TfAT T We note that one may view the temperature perturbations in a fashion analgous to interaction perturbations. In fact, our computational implementation of eq 9a and 9b uses this idea. B. Computational Model. Monte Carlo simulations were carried out to evaluate eq 4, 5 , and 9 for the mutation of aqueous Br- to aqueous C1-. Only two points, X = 1 and X = 0 in eq 2, were used in the calculations. This choice is probably sufficient for the case a t hand, as already pointed out by Lybrand et al.1° The simulations were run in the Canonical or NVT ensemble at 300 K using standard sampling procedures and periodic boundary conditions. Three systems were considered, they consisted of one solute atom, either Br- or C1-, and the solvent, water. In two of the simulations, one with Br- as solute and the other with C1-, 123 water molecules were included in a box of edge length 15.55 A. The interactions in this case were truncated based on molecular centers 7.775 A. In the third simulation 214 waters were included and Br- was the solute. The interactions in this case were truncated at 9.43 A and the size of the simulation box was 18.856 A. Thus, a dilute aqueous solution of ions was represented. Metropolis sampling was used to move the water molecules, and the ions were held fixed in the center of the box. The step sizes for translation and rotation were adjusted to yield an acceptance ratio near 60%. Equilibration of the system was carried out for 75K N-molecule moves. At this point the solvent-solvent and solvent-solute energies and the structural properties were stable. After the equilibration period, the simulations were carried out for an additional lOOK N-molecule moves for the 123 molecule solvent cases and 50K N-molecule moves for the 214 molecule solvent case. During this period calculations for the perturbation of one solute to the other were performed using a sampling frequency of 20 N-molecule moves. Thus, for the simulations involving 123 water molecule, 5000 independent configurations were used, and for those with 214 water molecules, 2500 configurations were used. The method of block averages was employed to estimate the errors in the computed quantities.12 In the finite difference temperature derivatives, a AT of f 1 0 degrees was used. It should be noted that temperature perturbations may be viewed as analogous to interaction perturbations and thus similar cautions apply to the extent of perturbation employed. As we show below, perturbations of f 1 0 degrees around a reference temperature of 300 K give good precision. The intermolecular potential functions used are those described by Lybrand et al.1° The water model was the SPC model of Berendsen et al.13 and the ions were represented by charged van der Waals spheres. For convenience these parameters are given in Table I. Standard geometric mean combination rules were used in combining the interaction terms, Le., A , = (A,,-AJJ)1/2 and
c, = (ClI.C,,)l/2.
(1 1) We note that other thermodynamic derivatives may be computed in an analogous manner. For example, in the Canonical ensemble we may compute the pressure from the finite volume change analogue of eq 7
a In Q(V P=k.?-(T)
In
N.T
[QW+ A V / Q ( v - AVl
==w
AV
(12) Schifere, S.; Wallace, D. J . Chem. Phys. 1985, 83, 5203. (13) Hermans, J.; Berendsen, H. J. C.; VanGunsteren, W. F.; Postma, J.
P. M. unpublished results.
6682 The Journal of Physical Chemistry, Vol. 90, No. 25, 1986
Brooks
-
TABLE II: Thermodynamic Properties (in kcal/mol) for Dilute Aqueous Solutions of Cl- and Br-" CIBr-
direct
finite difference
weighted
Br-
-
CIfinite
direct
weighted
difference ~
AQ
2.64 f 0.32
LIE*
4.29 f 4.75
1.88 & 4.88
TSSb
1.65 f 3.37
-0.76 f 3.45
ECI-H~O
-138.60 f 4.28
EB~-H~o E,,+,,o
3.30 f 0.66
-2.56 f 0.26 (-2.49 f 0.42) -4.29 f 4.75
-1.88 f 4.88
0.66 f 0.71
-1.65 f 3.37
0.76 f 3.45
-138.93 f 4.29 -135.33 f 4.48
-135.63 f 4.47
-1047.1 f 8.6
-137.21 f 5.25 (-136.00 f 7.20) -134.31 f 5.23 (-132.70 f 6.40) -1042.3 f 10.1 (-2139.9 f 12.4)
-2.70 f 1.16 (-3.54 f 1.09) -0.14 f 1.18 (-1.05 f 0.82) -137.52 f 5.25 (-136.30 f 7.20) -134.82 f 5.20
aValues in parentheses were computed from a simulation of Br- ion in 214 water molecules. bComputed from the differences between two simulations for "direct" and "weighted" quantities; values denoted as finite difference were derived from the same simulation, 111. Results
where the subscript Br denotes an average over the Br-(aq) simulation; (iii) from eq 8b. The estimates of statistical uncertainties given in Table I1 are f o and are obtained from averages over blocks of 5000 N-molecule moves. Several observations may be made concerning the results. First we note that the free energy changes BrC1- (AA = -2.56 i= 0.26 kcal/mol) and C1-- Br- (AA = 2.64 f 0.32 kcal/mol) are consistent with each other. Furthermore, they are in good agreement with the value computed from the 214 molecule simulation (-2.49 f 0.4 kcal/mol) and are in fair agreement with the earlier calculations by McCammon and co-workers1° (AA = 3.35 f 0.15 kcal/mol for C1Br-). The difference between our results for the two different sized systems may be accounted for by truncation effects, as discussed below. The differences between the present calculations and the earlier work may be due to a number of factors, including the differences in interaction truncation distance. For example, McCammon and co-workers have only averaged their results over 350 configurations. In addition, slight differences in the average temperature and density can lead to differences in the thermodynamic properties. Next consider the ion-solvent energies, and consequently the relative energy change AE, computed from the three methods outlined above. All ion-solvent energies are in excellent agreement with each other and, furthermore, are in line with results reported for solvation of C1- in TIP4P water by Jorgensen et aLI4 The fact that the energies derived from the finite difference formula, eq 9b, are in good agreement suggests that temperature perturbations may provide a viable approach to exploring the temperature dependence of thermodynamic properties. In fact, in a recent study a similar approach has been employed to compute the temperature dependence of the free energy of water.I5
The energy differences are in somewhat poorer agreement, however, as differences in a single simulation; Le., using the finite difference formula, the values computed are substantially more precise. This is a reflection of the fact that fluctuations within an individual simulation tend to be correlated and thus result in greater precision than can be achieved by making comparisons between different simulations. For example, compare the results for AE computed from the single simulation finite difference formula to those which result from the comparison of two simulations. The large variation of AE associated with computing small differences in large numbers suggests that more statistics are required to calculate converged relative energies and entropies when different simulations are being compared. An encouraging note is that the finite difference method gives AE and TAS at an acceptable level of precision. Thus, the advantage of using this method is to increase the precision and reduce the required computational time by one-half. The entropy change, like the energy change, is computed as the difference of two very similar numbers. Thus, the statistical significance of AS is unclear in the present calculations. However, we note that the observed entropy change is very small. This is consistent with the similarity between the ion-water interactions for both Br- and C1-, and the observed similarities in the distribution functions, e.g., the first peak and first minimum in,,g occur at the same separations, 3.51 and 3.91 A, respectively, for both solutes. Also, we note that the entropy changes computed by using the single simulation finite difference formula are more precise than those computed on the difference between quantities calculated from separate simulations. B. Solute-Solvent Structure. The ion-oxygen and ion-hydrogen radial distribution functions computed from the two simulations with 123 water molecules are shown in Figure 1. The ion-oxygen distribution functions display two well-defined peaks. Comparing the results for C1- and Br- we note that the first peak in the distribution functions occurs at nearly the same position but the C1--0 peak is higher. Comparison of the second peaks also shows the increased intensity pattern for C1--0. In addition, the peaks are now slightly out of phase, with the second C1--0 peak occurring at a larger value of r. These results are in ~ we qualitative agreement with those of other ~ 0 r k e r s . IFinally, note that the sharp peak which is visible at -6.8 A in the ionhydrogen distribution functions is probably due to the truncation of the ion-water interaction. This is consistent with the integral equation predictions of Brooks et a1.l6 C. TruncationEffects. Interaction truncation effects are known to alter the structure and energetics of liquids and solutions.16 For aqueous ions, Jorgensen and co-workers find that changes in the cutoff from 7.5 to 8.5 A can cause changes in solvation energies of 15% or more.I4 Thus, one would like to assess the extent of this error on the relative thermodynamic properties. This point
(14) Chandrasekhar, J.; Spellmeyer, D. C.: Jorgensen, W. L. J . Am. Chem. SOC.1984, 106, 903.
(15) Sussman, F.; Goodfellow, J. M.: Barnes, P.; Finney, J. L. Chem. Phys. L e f t . 1985, 113, 372.
In this section we present the results for structural and thermodynamic properties describing dilute aqueous solutions of chloride and bromide ions. A . Thermodynamics. The computed thermodynamic properties are presented in Table 11. These properties are AA, AE, and AS for the processes Br-(aq) Cl-(aq) and CI-(aq) Br-(aq), as well as the values of Esolvent-ion and Esolventsolvent. The property Eso,vent-ion may be derived from (i) the direct interaction of ion and solvent, say Br- and HzO, in the simulation of dilute aqueous Br-; (ii) the perturbed ion-solvent interaction weighted by the probability function, for example
-
-
-n20
-
-
The Journal of Physical Chemistry, Vol. 90, No. 25, 1986 6683
Thermodynamics of Ionic Solvation
0.2 7
I
I
--1
3.0 T
I
v
M
1 1.0 c
2.0
'
0.0 0.0
'
1.5
,
3.0
I
1
4.5
6.0
-0.2
7.5
7.0
r
I1
3.0 i
h
LI
v
~
M
2.0 f
1.0 I
0.0
'
0.0
1
8.0
9.0
10.0
=out
5.0 ----T--l i 4.0
L/
I
I
1
1
I
1
I
1.5
3.0
4.5
6.0
7.5
r Figure 1. Computed radial distribution functions between oxygens of water and anions (-), or hydrogens of water and anions (---) for (a) Cl- in dilute solution and (b) Br- in dilute solution. The radial separation, r, is A.
provides a motivation for studying the Br-(Cl-)-H,O system. We find from a comparison of the present results with those from earlier work that some differences occur and may be attributed to truncation effects (also, see below). However, the differences in relative free energies, entropies, and energies are difficult to quantify from the present data due to large standard deviations associated with all of the calculated quantities. To provide an independent estimate of truncation errors, we have derived a simplified model for the ion-solvent interactions and structure. This model, which is detailed in the Appendix, treats the long-range ion-water interactions as ion-dipole in nature, assumes a uniform orientational distribution of the dipoles at long distances, and models the ionspherical point dipole distribution as an extension of the ion-oxygen distribution function. In addition, we assume that the truncation effects are manifested only as errors in AE and not in hs: this is consistent with the assumption of no preferential dipole direction at long distances and is physically reasonable. From this model we compute the relative energy change resulting from the truncated ionsolvent interactions. This result is displayed in Figure 2. W e may make several points regarding the results of Figure 2. The first to note is the oscillatory behavior of 6(hE)lcy,.This feature arises from the phase and/or amplitude differences between the ion-water distribution functions and will certainly remain in more detailed treatments. It is interesting to note that judicious choice of the cutoff separation can result in complete cancelation of errors in AE, e.g. a cutoff of 8.25 8,for this system. However, a negative aspect of this oscillatory behavior is that the direction in which the error is incurred, i.e., whether the calculated difference is an under- or overestimate, is unknown. Next we turn to the "predicted" truncation difference between the present calculations, rcut= 7.775 A, r,,, = 9.43 A, and those
Figure 2. The interaction truncation correction, 6(AE),cu, in kcal/mol, is plotted vs. r,,, in A, for a simple model describing ion-water structure and interactions (see, section I11 and the Appendix). The truncation correction is for the perturbation CI-(aq) Br-(aq).
-
of Lybrand et al., rCut= 9.0 A.1o The differences in relative free energies predicted by the model are ~ 0 . 3 2kcal/mol for 7.78 vs. 9.0 and ~ 0 . 1 5kcal/mol for 7.78 vs. 9.43. This simple estimate thus predicts the correct ordering of the truncation effect; however, the values of the error differ from the simulation results. Despite this disparity, we believe that the main features which give rise to the differences for the case of similar ionic species are the phase and amplitude differences in the distribution functions; this physics is present in our model. Additional factors are also contributing. We anticipate that a large effect on the water structure around the ion is present due to the difference in interaction truncation distance^.'^^^^ The simplified model does not account for this feature as it extends the distribution functions indefinitely. Another obvious defect is the empirical modeling of the ion-water interactions as ion-point dipole. It will therefore be quite interesting to explore the truncation effects on thermodynamic properties using the recently developed integral equations methods. We are currently carrying out such a study for this system.I6
IV. Summary We have investigated the methodology for computing relative thermodynamic properties for solutions. The thermodynamic perturbation approach was extended to compute temperature derivatives of the free energy by finite differences and the results are encouraging for the systems investigated. The computed relative thermodynamic properties for the difference in the free energies of hydration for Br- and Cl- were shown to be independent of the direction of perturbation and in reasonable accord with experiment and a previous simulation study. In addition, the internal consistency provided by the single simulation finite difference methods we develop greatly improves the precision in the calculation of energies and entropies. We have also focused on the influence of interaction truncation on the relative thermodynamic properties. Comparison of the present results with an earlier simulation by Lybrand et al. on the same system but using an interaction cutoff distance other than that used here indicates that errors on the order of 30% may be incurred from truncation and convergence effects. The influence of truncation was illustrated by the results of a simplified model for ion-water interactions and structure. The model emphasizes that one effect of interaction truncation on energy differences is oscillatory in behavior, resulting from phase and/or amplitude mismatch between ion-solvent distribution functions. We are currently carrying out an integral equation study of C1- mutations to better characterize interaction aqueous Br-
-
(16) Brooks 111, C. L.; Pettitt, B. M.; Karplus, M. J . Chem. Phys. 1985, 83, 5897. (17) Brooks 111, C. L., manuscript in preparation.
J . Phys. Chem. 1986, 90, 6684-6687
6684
truncation effects. This study will be useful in providing some general trends in truncation effects on thermodynamic properties. Acknowledgment. Gratitude is expressed to the Research Corporation for partial support of this work. Special thanks is given to Dr. D. Fox for his assistance in the development of Monte Carlo codes for the CSPI-6420 array processors which were used in these calculations. Appendix. Truncation Effects on Ion-Water Energetics
In this Appendix we detail a simple empirical model for ionwater interactions and structure. This model permits us to estimate the extent of interaction truncation errors on the relative free energy of solvation for C1- vs. Br- in aqueous solution. The model is as follows. We assume the ion (Cl- or Br-)-water interactions may be represented simply as a van der Waals (1 2,6) plus an ion-dipole term between the ion and the oxygen atom on water
where r is the ion-oxygen separation, A and C a r e the ion-oxygen interaction parameters, constructed from Table I, and Meff is an empirical effective dipole moment (we adjust peffto give the appropriate contribution to v). The total ion-water interaction energy is now given by
eq A3 to the results from Figure 1 for r 3 3.91 8, the position ( r ) . We find for the chloride ions of the first minimum in G = -0.573, a = 0.113 k i P r ’ = 3.91 8,,k = 2.26 A-‘ and for r r = 3.91 A, k = 2.31 the bromide ion G = -0.502, a = 0.229 8-’, 8,-’.Substituting these values into eq A3 and computing EX-H20 from eq A2 with rcut= 7.775 A, we solve for Feffby comparison with the results from direct calculation of Ex-H20 in Table 11. We find keff = 11.75 and 11.73 kcal from a comparison with ECI--H~O and EB~--H~o, respectively. This provides a consistent empirical model which is used to estimate the effect of interaction truncation on the relative free energy of solvation, AA. The truncation error in the ionsolvent interaction energy may be obtained from ~ E X - H , ~=
2“peff P o J :
dr
exp[-ax-o(r -
( ~ x - 0
r i - o ) ] cos [k,-,(r - rfx-o)]+ I] (A4) Equation A4 results from neglecting the short-range van der Waals contributions, which may be shown to be negligible for distances r 3 7.0 A, and using eq A3 for gx-o(r). Carrying out this integration, we find Gx-o exp(-ax-orf? X
.
where gx4(r) is the ion-oxygen (water) radial distribution function and p o = 0.0334 A-’. We model gx4(r) in eq A2 for r 3 7.0 8, as gx-o(r) = Gx-0 exp[-a,-o(r
- r’x-o)l cos [kx-o(r - r’x-o)l + 1 (‘43)
The values for Gx4,
cyx4,
rk4, and k ,
are chosen by optimizing
with r” = rcut- rx-o. Thus, the truncation error in the energy difference 6(AE)rcu,= ~EcI--H,o - ~EB~-H,O
(‘46)
is given by the difference between eq A5 for X = Cl- and X = Br-. We have plotted this difference as a function of the interaction truncation distance, r,,,, in Figure 2. Registry No. Cl-, 16887-00-6; Br-, 24959-67-9.
Thermochemistry of Solvation of SF,- by Simple Polar Organic Molecules in the Vapor Phase L. Wayne Sieck Chemical Kinetics Division, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received: April 4, 1986; In Final Form: August 21, 1986)
The stabilities of SF6-.HR association ions, where HR is a simple aliphatic alcohol, H20, or (Me),SO, have been investigated by the technique of pulsed-electron-beam high-pressure mass spectrometry. Equilibrium constants were determined as a function of temperature in order to define AHo and ASo values for solvation. The binding energies are quite low, ranging from 10.5 kcal mol-’ for SF6-.H20to 14.7 kcal mol-’ for SF,;Me2S0. For ligands in which the nature of the bonding is expected to be similar, the binding energies increase nonlinearly with increasing acid strength of the ligand. On the basis of additional measurements involving I-eHR complexes, as well as existing literature values, the binding energies in SF6-.HR ions are found to be slightly higher than those for I-HR. The SF6-.HR complexes are less stable, however, due to their more positive dissociation entropies. Some comments are also included concerning the SF6-.SF6 dimer ion.
Introduction
Sulfur hexafluoride is a well-known gaseous dielectric with exceptional insulating properties. It has also found extensive use as an electron scavenger due to its very high nondissociative capture cross section and long lifetime with respect to auto&tachment.’ Much is known concerning the charge-transport (1) Hansen, D.; Jungblut, H.; Schmidt, W. F. J . Phys. D
and references therein.
1983, 16, 1623
processes occurring in SF6under the influence of electric fields,* and Streit has recently reported3 a detailed study of the electron transfer and other bimolecular ion-molecule chemistry initiated by SFs-using a flowing afterglow technique. In spite ofthe wealth of information that has been accumulated, nothing is known (2) de Urquijo-Carmona, J . J . Phys. D 1983, 16, 1603 and references therein. ( 3 ) Streit, G.E. J . Chem. Phys. 1982, 77, 826.
This article not subject to U S . Copyright. Published 1986 by the American Chemical Society
