Chemical Physics 64 (1982) 437-446 North-Holland Publishing Company

APPLYING THE POLARIZATION MODEL TO SELECTED IONIC SUBSTANCES

Paul TURNER, Elaine Eisler DAVID and Carl W. DAVID Department of Chemistry, University of Connecticut, Storrs, Connecticut 06268, USA

Received 3 August 1981

The polarization model is applied to Li+ and F- in their interactions with water and with themselves. The model is alsO applied to NHa and NH: in their interactions with water. Results on applying the polarization model to PO:-, HPO;-, H*POi and Hap04 in their interactions with water are reported. Finally, results on CO:-, HCO<, HaCOs and CO2 are reported.

1. Introduction

The polarization model is an attempt at treating water as a collection of associated protons and oxide ions held together in familiar molecular form but capable of dissociating into a proton and a hydroxide anion [I] (and technically, into another proton and a free oxide anion). The a priori ionic point of view of the model suggests that it should be useful in studying species disolved in water which themselves are “ionic” in character. The first non-water extension of the model was made by StiUinger [2] in which it was shown that the same physical model could ac- count for several aspects of the interactions in spe- cies of the form

H pither + or - m n

This paper deals with many of the substances which can be successfully handled in the context of the polarization model. Calibration of the halides and the alkali metals, as well as SOi- and SO3 ap- pear to represent viable future efforts, but they are not included here. In section 2, we rediscuss the cali- bration of the Li+---H20 interaction. Section 3 treats the results of the prior calibration of the F----H20 interaction. Section 4 deals with the solvation of LiF, based on the added calibration of the Li+---F- inter- action in terms of the polarization model. Section 5 introduces the CO, and CO$- calibration. Section 6 reports results on the hydration of the PO:- anion.

Section 7 is concerned with the system NH, and NH: with water. Finally, in section 8, we discuss future applications of the model, and attempt to draw some conclusions about the future of fully empirical po- tential energy computational schemes.

The time delay between writing and accepting, on the one hand, and accepting and publishing on the other hand, makes it a given that the potpourri of re- sults presented here will be slightly incomplete by the time these words are read.

2. The Li+ cation interacting with water

Since the polarizability of the Li+ cation is only 0.03 A3, i.e., virtually zero, this mono-valent cation is almost isoelectronic with the proton from the point of view of the polarization model. Of course the Li+ cation is less strongly bound to water (about -34 kcal/mol) than the proton (about - 170 kcal/mol), and the Li-0 bond length (about 1.9 A) is greater than then H-O bond length in the equivalent hy dronium ion (about 1 A). The previous calibration of the polarization model for the Li+ cation [3] incor- porated these facts in the calibration function for “frozen” water using the planar (rigid) geometry in- dicated ab initio computations [4] *. It was found in

* However, note that non-additive terms have been found necessary to successfully imitate the ab initio hypersurface; see ref. [5].

0301-0104/82/0000-0000/$02.75 0 1982 North-Holland

438 p. Turner et al/The polarization model

that calibration that upon relaxation of the geometry of the complex Li(HZO)+ the H-O-H angle in- creased, the O-H bond length increased, the Li-0 distance decreased, the bond strength increased, and the complex became non-planar.

This calibration was criticized [6] mainly on ener- getic grounds. Since the quantum mechanical evi- dence for planarity of the complex is in some doubt [7 1, it seemed reasonable to re-calibrate the polariza- tion model function for the Li-0 interaction, SO that in the relaxed complex, the binding energy would be -34 kcal/mol. This entails weakening the interaction, relative to the prior calibration. Since the Li+ cation is attracted to the oxide ion of water via a Coulomb interaction, a term must be added to this coulombic interaction which is repulsive in character. The func- tion which gives a 1.9 A Li-0 bond length and simul- taneously gives a proper binding energy (after relaxa- tion) is: 13600 e-3*4r kcal/mol. This function gives the typical non-planar behaviour which the model has emphasized in the past. This non-planarity amounts to a tilt of the plane of the water relative to the Li-0 axis, so that the geometry of the coordina- tion of the water to the cation is approximately mid- way between the planar (found by most quantum mechanical computations) and the tetrahedral (ex- pected on the basis of lone pair arguments) confor- mations.

It appears as if the facts are consonant with a non- planar hydrated Li+ cation. Newsome et al. [8] find that the coordination number of the Li+ cation varies from 3 to about 6 (in round figures) with molality, as does the tilt angle, and that the tilt angle is close to the tetrahedral value, but a bit smaller, At low concentrations they estimate the angle between the Li-0 axis and the H-O-H bond angle bisector to be about 40’ based on a rigid water with OH distances ’ of 1 A and H-O-H angle of 105.5’ (they use D-O-D). Recently, a simulation by Szasz et al. [9] has been reported in which Li+ cation interacts with ST2 water, and the molecular dynamic sirrntlation in- dicates that the water is tilted from the Li-0 axis.

It is of some interest to ask whether or not this new, presumably improved, calibration will success- fully predict the “expected” geometry of the 4hy- drated Li+ cation [IO]. That geometry is, of course, the tetrahedral arrangement of 4 waters, where each water presents its oxygen to the Li+ cation. Older ex

perimental information exists as to the structure of the Li+ cation in concentrated solutions [ 1 l] and that information also suggests that the planes of the four nearest neighbor water molecules are canted relative to the Li-0 axis, and that the time average structure of the 4-hydrated complex is symmetrically tetrahedral.

The revised polarization model prediction for the structure of the 4-hydrated Li+ complex in the gas phase is the unsymmetric structure predicted using earlier versions of the model. Its energy was found to be -4228 kcal/mol. The structure is almost identical to the one obtained for the 4-hydrated proton, and emphasizes the fact that the polarization model pre- dicts that the 4-hydrated proton (H90i) is a di-hy- drate of the symmetric H,O: cation. (The H30+ ion, the hydronium ion, is not discernable in the H, 0; cation structure!) The Li+ equivalent structure is identical in overall structure, with two water ligands in the “second” coordination sphere of the Li+ or the first coordination sphere of the Li(HZO)l. Both of these outer waters are hydrogen bonded to the interi- or waters.

Since it is impossible to guarantee that any mini- mum energy configuration found by our simple step- ping procedure is the global minimum energy struc- ture, we decided to obtain the energy of the 4-hy- drated lithium cation with proton position minimiza- tion, holding all oxygens in symmetric equivalent po- sitions tetrahedrally about the central cation. The re- sulting minimum energy, which occurred at an Li-0 distance of 2.5 A, was -4210 kcal/mol. Further, complete relaxation of structure from this local min- imum energy configuration showed that this local minimum was stable with respect to 0.1 A steps.

2.1. Charge assistance in hydrogen bonding

We have found that the hydrogen bond strength of the complex Li*(H20)--HZ0 cation has an extraor- dinarily large binding energy, due to polarization ef- fects of the Li+ cation on the nearer neighboring water. The second nearest neighboring water molecule to the Li” is (1) bound to the Li(H,O) cation with -19.7 kcal/mol of binding energy, more than double the normal binding energy of the hydrogen bond in the polarization model (-6.8 kcal/mol for PM4), and (2) the O-O bond length in the complex is 2.56 A

P. Turner et al/The polarization model 439

which is substantially shorter than the 2.95 A ex- pected for the gas phase water dimer hydrogen bond length. Such effects have been predicted previously [121-

3. The F- ion

Arshadi et al. [ 133 have measured the binding energy of the F--(H,O) complex and found it to be about -23.3 kcal/mol. This value has also been ob- tained in ab initio quantum mechanical computations both by Diercksen and Kraemer [ 141 and Kistenmacher et al. [ 151. The F--O distance in the linear complex is computed to be about 2.5 A.

In prior work, we [ 161 indicated that a suitable fluoride-oxide interaction function could be con- structed as a linear combination of two mixing rules, a geometric and an arithmetic one, where the F-F and O-O interactions are averaged. The final result reported was:

where the total interaction is now:

However, the F--O predicted distance in the com- plex is 2.68 A in the totally relaxed geometry, rather than the 2.5 A expected *.

The expected structure of the fluoride ion in solu- tion is tetrahedral, with four protons of four equiv- alent waters pointing directly at the F- ion. We have attempted to locate the minimum energy structure of the F(H20)z anion as predicted by the polariza- tion model. The result is far different from the above expectations; the structure is not tetrahedral. Three of the waters bind as expected but one water mole- cule (the fourth) is hydrogen bonding to another water molecule rather than binding to the F- ion. The energy of this structure was found to be -4210.7

* It should be remembered that the complicated functional form chosen for the mixed iziteraction is not a burden in simulation studies, as all special functions in our simulations are precomputed and accessed using table look-up proce- dures. Thus, no time is lost computing complicated func- tions during actual run time simulations.

kcal/mol, which corresponds to a binding energy of -79 kcal/mol tied up in 3F--water interactions and one hydrogen bond.

Doubting that this structure could be the lowest energy structure, we carried out a series of minimiza- tions with all oxygens tetrahedrally and symmetrically located about the F- anion, with only protons free to relax their locations in an effort to lower the ener- gy of the complex. The lowest tetrahedral complex found, with a F--O distance of 3.1 A, had an energy of -4075.7 kcal/mol. This complex was resistant to further relaxation when the oxide anions were freed from their tetrahedral constraint, implying that the tetrahedral structure corresponds to one whose ener- gy lies in a local minimum on the energy hypersurface which is connected by 1 atom moves to the minimum energy structure by an energy barrier.

3.1. HF-H20

It is of some interest to compute structures and energies of substances which are subject to some ex- perimental verification. The HF-H20 complex has had its structure measured [ 171 and its energy [ 181 and force constants [ 191 computed. With no adjust- able parameters left, the polarization model predicts a structure similar with the one found, with an O-F distance of 2.74 A (measured 2.66 A) with a binding energy of -14.1 kcal/mol (quantum mechanical values between -8.5 and -15.7 kcal/mol), and dipole moment magnitude = 4.79 D (compared to pa = 4.05 D). We regard the agreement as good.

3.2. Hydra ted HF

Giguere and Turrell [20] have proposed that the predominant species in aqueous hydrofluoric acid is the ion complex, H,O+- - -F-, the complex being sta- bilized by an extraordinarily strong hydrogen bond between the fluoride anion and the hydronium ion. If such were the case, it would represent a rather rare occurrence of a documented structural modification which was solvent induced. Thus, the gas phase species, H,O---HF which is known to be the stable dimer, is proposed to be solvent stabilized into the form H,O+---F- . We have computed the energy and minimum energy geometries of HF encapsulated by eight waters in the hope of discovering whether or

440 P. Turner et aLIThe polarization model

not the polarization model gave any indication of a gy. This correction function, which is a term binding possible stability reversal. Li’ to F- has the final form:

(332.1669/r)(lO e-2.470r - 1) Even starting from solvated H,O+---F- the polari- zation model predicts that the eight solvated species is HF, not the seven solvated H,O+---F-. Our best minimum energy structure appears to have HF sur- rounded by four nearest neighbor waters, with the other waters occupying second, and possibly third coordination “spheres”. The total net stabilization energy, relative to gas phase HF and eight isolated gas phase HZ0 molecules, is -54.3 kcal/mol. It would have been more exciting to have found a solvent stabilized ion pair such as the one suggested. But, even when we have wrenched the proton away from the fluoride anion, and created a situation such as H30+---H&)---F-, we observe the proton migrating during energy minimization to the fluoride. We therefore cannot give encouragement to performing accurate quantum mechanical computations on the solvated HF molecule.

+ 7 e-18(r-1.44)2 + 5.97874 x 1010 e-16.3014r

_ 8.71 e-33.83(r-1.6)2.

3.3. H3F;

We were interested in studying the collision of Li+ with F- when both cation and anion were solvated. Presumably, the waters which lay on the Li-F axis, which would act to shield the cation from the anion, would ultimately be forced off the Li-0 axis, as the two ions were brought into close proximity. Then, we would have a solvated ion-pair. In such an ion-pair the Li-F interaction would be directly the term (above) and a polarization term (which would be slightly modified from the value in solitary LiF by the adjacent charges and polarizable point particles of the solvent water). Therefore, we expected to see two r(LiF) domains, one where water acted as a dielec- tric medium, shielding the Li+ cation from the F-

Desmules and Allen [21] have computed the ab initio energy and geometry of the ion HF---H---HE+. They found that the complex has unusually short bond lengths. We have computed, using the polariza- tion model, the energy and geometry of this ion. The energy turns out to be -9 13.0 kcal/mol, which means that the total energy tied up in the two hydrogen bonds is -30 kcal/mol of ion. This is very large, but not quite so large as that reported by Desmules and Allen, i.e., -39.6 kcal/mol. Further, they compute an rFmF of 2.307 A and we obtain 2.36 A with a per- fect trans conformation. Our agreement with their results is moderate.

4. LiFinsohtion

We have calibrated the Li+---F- interaction ac- cording to the polarization model. In order to do this, we computed the polarization energy as a function of the Li-F distance, and subtracted that from the total interaction energy given by Brumer and Karplus [22]. The resulting numerical function represents a correc- tion function which, when applied to the polarization energy, results in the Karplus and Brumer total ener-

w. F lH>O’>--‘FH (HxG:)

9 ‘L : --F) (ANC.STROYl

Fig. 1. Energy of the cluster Li(HzO)$---F(H20): as a func- tion of the Li-F distance. Regions correspond to r(Li-F) < 2.5 A, 2.15 A < r(Li-F) G 4.5 A, and r(Li-F) > 4.5 A.

P. Turner et aLIThe polarization model 441

anion, and one where the waters were pushed aside, and the ion-pair existed.

Instead, as can be seen from fig. 1, three domains were found. In ref. [ 1 b] detailed drawings of the LiF(H,O), system illustrate that the hydrolysis of water is taking place under the influence of the cation and anion. The system selects a water dimer (HZO)z and breaks it apart.

5. CO, and CO;-

The CO:- anion lies about 144 kcal/mol lower in energy than the system CO, and 02-(23). The CO:- anion is planar, while CO, is linear. The C-O bond length in the CO;- anion is ~1.3 A while the bond length in CO, is x1.16 A. It is a non trivial effort to reconcile all these data in the context of a model which has all the properties of 02- fured. Our calibra- tion is predicated on the assumption that the carbon “ion” in both CO;- and CO2 bears a +4 charge. Con- sistent with this assumption is the assignment of zero polarizability to Cti in the model. Under these as- sumptions, the following function has been found to work:

LJ(~~-~) = 332.1669 [(+4)(-2)/r t (8.0/r)e-2.2r]

t 91.79[(1 - e-6-O(r-lJ3))2 - 11,

which can be seen to be related to a Morse potential. Using this potential energy function for the C-O in- teraction, we obtain a total energy of -4036.5 kcal/mol for CO;- and -3892.3 kcal/mol for CO,. The C-O bond length in CO, was found to be 1.37 A while the C-O bond length in CO, was found to be 1.24 A; the slightly deviations from the desired values represent part of the compromise required to main- tain D3n symmetry in the anion, while preserving CO2 with no dipole moment!

We have computed the energy of the HCOT anion in this calibration of the polarization model to be -4559.3 kcal/mol. Unfortunately, the C-O bond distance of the oxide bound to the proton is too large, being 1.78 A rather than the 1.43 A value reported by Jonsson et al. [24] as found by ab inito computa- tions, or 1.38 A as reported by Keesee et al. [25] as found by CNDO/2 computations.

There seems to be no evidence that the hypotheti- cal “carbonic acid” exists, and the polarization model, in this calibration, supports such a view. In the gas phase, H2CO3 has been computed to have an energy of -4844.2 kcal/mol. However, this must be a local minimum in the energy hypersurface, as the energy of infinitely separated CO, and H,O adds up to -4925.3 kcal per mole equivalent of H2CO3. Thus carbon dioxide and water are energetically favored over carbonic acid, at least in the gas phase.

It is of some interest to attempt to hydrate the various species discussed above, in order to see if the polarization model predictions are in accord with other computations, and measurements on these species. It turned out to be impossible to hydrate CO:- anion. No matter what starting configuration one starts with, the reaction

CO;- + H,O + HCOT + OH-

occurs spontaneously. The computation of the solvation energy of gas

phase HCO; requires, as has been pointed out by Castleman [25] averaging over various relative con- figurations of the anion and the water. They report instead the energy of interaction between a rigid water and a HCOT anion as being -29.6 kcal/mol in the most favorable geometry that they could find. We have found configurations of the two with interaction energies of -25.0 and -26.4 kcal/mol, in reasonable agreement with the CND0/2 results. Further, Jean and Volatron [27 ] report values ranging from about -24 to - 16 kcal/mol, in moderate agreement with our results here.

5.1. (CO2)2

The CO, dimer has an energy of -7785.3 kcal/mol. This means that it is bound by al/2 kcal/mol (of dimer) relative to two infinitely separated CO2 mole- cules. In gross agreement with the fact that the mole- cule has no dipole moment, the dimer (shown in fig. 2) has the two molecules oriented close to mutually perpendicular. One can “see” how the beautiful solid structure of CO2 emerges from the interactions be- tween molecules. The C-C distance in the gas phase dimer is predicted to be e6.6 A.

442 P, Turner et aL / The polarization model

Fig. 2. me lowest energy conformation of (CO2)2 as found by the polarization model. See ref. [ 261 for a nice drawing of the crystal structure of COz.

6. The PO:- anion

me calibration of the polarization model for phos- phate [28] anion means that it is possible to study the interaction of this anion, the HPO4- amon, the H,PO, anion, and H$O4 with each other and with water.

The calibration for the P-O interaction depends on declaring the charge on the phosphorous ion to be +5, and the polarizability zero. Then it is possible to invent a function which gives the right bond lengths in P,O,, (see fig. 3) and structure [29] and a reason- able set of energies:

(332Jfj&#‘)(-10 + 130 e-3*34gr) - 75 e-g(r-1-54)2.

Since the PO:- anion is so large, and one of the high- est charged anions in existence, we turned first to the question of how large the anion was i.e., how many waters were bound to the anion [30] *. It is unrea- sonable to believe that we can carry out a full mini- mization of one POj- anion with, say, 30 bound waters, with any hope of finding the global minimum energy structure. Therefore, we have carried out our computations in stages. First, we solvated the anion with 6 waters, and found a minimum energy structure

* This question was prompted by a deviation in the rate of peritoneal solute cleamnce of PO:- from expected, whose explanation was sought in the size of the hydrated anion.

w

Fig. 3. The lowest energy structure of P.+O,,, as found by the polarization model.

which had all six waters approximately equidistant from the central phosphorous ion. This 6-hydrate had the expected structure, with one proton from each ligand facing in toward the PO:- anion.

Next, we added 8 waters to the 6-hydrate, and re- minimized the energy. The 14-hydrated anion stabil- ized after a very large computational effort. The final structure for the 14 hydrate of PO:- was found to have an energy of - 19949.7 kcal/mol. Removal of any of the peripheral waters from this hydrated anion cost about 13 kcal/mol, thereby implying that all 14 waters are strongly bound to the anion. We then added a fifteenth water to the complex, and remini- mized. The newest ligand penetrated the second co- ordination sphere of the anion. We conclude that there are more than 14 waters in the first two coor- dination spheres of the PO:- anion. The 15th water required about 16 kcal/mol to separate it from the 14hydrate. This energy is commensurate with the other removaI energies, and we therefore conclude that we have not yet fully solvated the anion up to the second coordination layer. (We were forced to stop at 15 waters because the minimization algorithm has become too unwieldy.)

The size of the hydrated anion is equally difficult to know. The most distant water in the 15-hydrate has its oxygen 6.4 A from the anion center (the $’ “ion”), while the next farthest water is 6.2 A away,

P. Turner et al/The polarization model 443

Among these 15 waters, there are a total of 8 water- water hydrogen bonds. In addition, every oxygen of the PO:- anion has two nearest neighbor water protons al.5 A away. Thus each oxide of the anion is a double donor from two solvent waters. Thus there are actually eight waters in the first coordination sphere. The oxygens of these 8 waters lie between 3.7 and 3.9 A from the central phosphorous. Every water of these 15 has a proton pointed inwards, toward the anion. The onset of “water structure” is not apparent in the 15-solvated anion.

It is very important in this particular case to qualify our statements about minimum energy structures. There is certainly good reason to believe that the sphere of enclosure for the first two solvation layers for this anion is about 6 A in radius. But we have no- ticed in other studies that the minimization algorithm we use gets stuck in small dimples of the energy hy- persurface when the number of particles rises to very high values. Therefore, we have been forced in such cases to carry out Monte Carlo minimizations which have resulted in extraordinarily large drops in energy from previously minimized energy configurations. Since we are as yet unable to carry out such a Monte Carlo minimization in this particular case we cannot state that the absolute minimum energy configuration has been found.

7. NH3 and NH;

Although the polarization model has been cali- brated for the interaction of nitrogen with protons (in fact, it has already been recalibrated) it has not been calibrated for the interaction of nitrogen with oxide anion. We have attempted this calibration based on the quantum mechanical computations of Kollman [3 l] and find the function

u(N-0) = 332.166/r

t 27.396/[ 1 + e2.0(r-2.68)]

+ 26 ,-10.5(r- 2.5)

to be adequate to reproduce the energy of HNi---OH;! and N-O distance at -27.1 kcal/mol and 2.68 A respectively. From this calibration, the calculated values for the NH3---HZ0 dimer agree well with the

earlier optimized 4-3 1G ab initio values of Kollman [321.

We have investigated the hydration of NH, and the singly charged NH: up to the addition of the fifth water. Due to the large proton affinity of NH3, the first water functions better as a hydrogen donor than as an acceptor by 2.16 kcal/mol. Both of monohy- drates (donor and acceptor) are distinct and consider- ably more stable than the isoelectronic NH:-OH-, which is 83.6 kcal/mol less stable than H,N---H-OH.

The fifth water molecule enters the second coordi- nation sphere of the NH,.

In the case of the ammonium cation, all waters up to and including the 4th are acceptors, forming a tetrahedral arrangement about the nitrogen. Analo- gously to the neutral ammonia, the 5th water donates to one of the other waters, beginning the formation of a second hydration sphere.

8. Discussion

The generality of the polarization model is stunning. The model is the lineal descendant of the ST2 [33] model which attempted to treat water as a rigid moi- ety with no possible chemistry. It is also related to the central force model [34] which acted as a bridge be- tween the rigid models and the ionizable model under discussion here. Each model has improved on its “fa- ther”, and each has generated a “son” model *. It follows that there must be some other model lurking in the wings which will encompass and sub- sume the polarization model in the same way as it has superceded its predecessors.

In one sense the computations reported here re- present a challenge to that yet to be invented model. The next model must account for all of the water facts, all of the HF facts, and all of the ammonia facts which have been successfully incorporated into this model. Further, it must improve upon the results which are in some doubt as reported here. We here attempt to summarize the obvious conflicts between the polarization model predictions and intuition (and/ or experiment).

Both Li’ and F- are expected to be tetrahedrally

* Mother-daughter works also.

444

Table 1 Collected results on ions

Description Energy (kcal/mol)

carbonate -4036.5 -3892.4 -7785.3

-4559.3 -4844.2 -5617.2,-5618.6

-5877.99

-5889.5

phosphate anion -5005.4

-5589.6

-6047.0

-6368.9

-11764.6

-9636.2

-19445.9

-6101.0

-7188.5

-9331.4 -11484.0

-19949.7

ammonia -1818.6

-1975.3

-2862.1

-3905.2

-4945.9

-5984.2

-7032.6

-1975.3 -3035.3

-4091.8

-5145.1

-6195.4

-7229.6 water -1032.9

P. Turner et al/The polarization model

Formula

cog-

co2

co:

HCO;

HZC03

HCO;---(H20)

HzCO3 ---(H20)

CO:----(H20)2

PO:-

HPO:-

H2PO;;

H3P04

H4P201

p205

p4010

~o’----H~o J”-

PO4 ---(H20)2

POJj----(HzO)4

PO:----(H20),5

POi----(HzO)14

NH3 NH+4

NH3---(H20)

NHr-(H~Oh NH3---(H20)3

NH3---(H20j4

NH3---(H20)5

NH; NH:---(H20)

NH&(H20)2

NH:---(HzO)a

NH+4---(H20)4

NH&(H20)5 ’

Hz0

solvated by water. Recently Szasz et al. [35] re- ported that in their simulations of LiI the Li’ cation is six fold coordinated, with tilted water molecules, and an r(Li-0) of about 2.13 A has been found, based on an ST2 type potential with modifications. Since this is a dense phase computation, and the ex- periments are also carried out in dense phase, we have no direct evidence that the gas phase Li(H20)+

cation is tetrahedral. There exists the possibility that the gas phase hydrated cation is not tetrahedral, but becomes so when packed into liquid water. Of course, another possibility is that the cation, even in liquid water is only time average symmetric, and that mole- cules are constantly moving in and out of the first coordination sphere. Most likely, however, the gas phase ion is tetrahedral, and the calibration is in error. It certainly would be possible to correct this error by widening the bowl of the potential energy, i.e., change the force constant of the L&-water interaction. No attempt at fitting this value was made in light of the absence of any experiment as to the value of the force constant in the Li’---OH2 gas phase cation.

We suspect, on even less grounds, that the F- anion anion interaction with water is slightly flawed, even though it is based on high quality quantum mechani- cal computations. Again, one suspects that the force constant is in error, and that during coordination the F-O distance increases relative to the mono-hydrate, as three more waters are coordinated.

The HF-HZ0 results are quite gratifying. On the other hand, the HF---H---FH results are only modest, much to our chagrin. Lisy [36] has called for a re- calibration of the F-F interaction based on experi- mental measurements of the infrared frequencies for sets of (HF), rings. It would appear that such a re- calibration is in order. We also need to point out that the polarizability we use for F-, 0.8207 A which was found by interpolation between values for neon, oxide in water, and nitrogen in ammonia, disagrees sharply with theoretical values almost twice as large [371*

The LiF results, of course, depend to some extent on the calibration of the Li+ and F- calibrations with water. But, the general idea that the ion pair as- sists in splitting the water via the water dimer forming a zwitterion of the form H,O+---OH- prior to trans- ferring a proton to F- anion to form HF, seems to be quite exciting. One of the major values of calculations such as ours is to suggest new structural possibilities which are subject to some form of experimental veri- fication.

The carbonate results seem to be reasonable. It is interesting, and pleasing, to find the model correctly predicting that carbonic acid is unstable relative to carbon dioxide and water. It is also gratifying to see that CO$ anion is not stable in water, but undergoes

P. Turner et al/The polarization model 44s

elementary hydrolysis to HCOT and OH-, in agree- ment with elementary chemical principles.

We note in passing that the inability of the polari- zation model to simultaneously treat both CO, and CO is not dismaying, since formally, the carbon “ion” in CO is in the +2 state, and the model is incapable of treating multiple ionization states.

The phosphate anion studies undertaken so far seem quite promising, but it remains a disappoint- ment that we could not completely hydrate the PO:- anion up to two full coordination spheres. We await development of a Monte Carlo simulation program for clusters of polarization model substances, before attempting anything larger than the 15 waters we have considered so far. The application of the model to PO:-, HPOi-, H,POT and H,PO, appears to be quite exciting.

It is interesting to note that whereas CO;- is un- stable relative to water, and shows this instability by hydrolysing, PO:- which is also unstable relative to water, does not show this same kind of hydrolysis. Thus the monohydrate of PO:- lies at higher energy than HPOi- and OH-. It is clear that the polarization model is predicting a barrier to hydrolysis in PO:- which is not present in CO$.

The ammonia and ammonium results also appear to be quite promising, and we look forward to con- sidering solutions of NH,OH in the near future. We have had extraordinary difficulty in obtaining the 4- fold hydrate of NH,, as competition between direct attachment of the 4th water to NH,(H,O), can pro- ceed by two avenues. In the end, we found a most stable arrangement which contained no water-water hydrogen bonds, but it was an effort.

Many of the results of computations using the po- larization model are difficult to compare with experi- ment, due to a lack of experimental data on gas phase clusters. It would be preferable to employ the polari- zation model directly in normal statistical mechanical simulations, either Monte Carlo or molecular dynam- ics, attempting to treat thermodynamic (e.g., infinite) systems. Unfortunately, the polarization model pre- sents a host. of extra complications for periodic boundary condition simulations which have not yet been properly addressed. Nevertheless, it would appear that the polarization model’s computational problems are worth the effort of exploring. Recently, others have also come to the conclusion that retaining pair-

wise additive potential energy functions in describing realistic systems requires the non-additivity that a po- larization model supplies. Thus Clementi [38] re- ported that significant non-additivity in the energy of the system Li(H20)z required a polarization term in addition to the standard pair-wise additive terms in order to obtain reasonable agreement with the ab initio energy surfaces he had generated.

Barnes et al. [39] has also begun using a polariza- tion interaction term in simulations on water, attempt- ing to better model the real interactions that take place in dense phases. Further, Boyd and Kesner [40] has employed a “polarization model” with the polar- izability located in chemical bonds, to do some inter- esting conformational computations.

From the results reported here, and the prior suc- cesses of the polarization model; from the successes of Clementi et al., it would appear as if polarization models are “on the right track”. Improvements in the model, when they come, will most likely evolve from the existing model, in a continuous and intelligible manner. Therefore, the computations reported here represent a base from which future models can be measured.

Acknowledgement

This work was supported in part by a grant from the National Institutes of Health, GM-26525, for which we are immensely grateful. Generous extra grants of computer time from the University of Connecticut Research Computer Center are acknowl- edged with deep thanks. This paper represents an enormous computational effort, and the generosity of the gift of this computer time has made this work realizeable. Finally, it is a great pleasure to acknowl- edge the continued help, guidance, and advice of Dr. Frank Stillinger.

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