Static Dipole Polarizability of
the
Fluoride Ion
The Journal of Physical Chemisty, Vol. 83, No. 12, 1979
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Static Dipole Polarizability of the Fluoride Ion’ Andrrej J. Sadlej Institute of Organlc Chemistry, Polish Academy of Sciences, Kasprzaka 44, PL-0 1-224 Warsaw 42, Poland (Recelved October 27, 1978)
The reliability of the recent empirical value of the electric dipole polarizability of the free fluoride ion due to Coker (1.48 f 0.08 A3) is discussed by a comparison with the corresponding accurate theoretical data for the He isoelectronic series. It is concluded that the true free fluoride ion polarizability should be much higher than both the empirical value and the accurate CHF result of Cohen (1.56 A3). The calculations of the second-order correlation correction of the CHF polarizability of the F- ion by using three different GTO basis sets with explicit dependence on the external electric field strength (so-called EFV GTO bases) show that the correlation contribution is quite large and positive. These calculations lead to the free fluoride ion polarizability as large as about 2.4 A3. The discrepancy between the theoretical and empirical estimates is interpreted in terms of the medium effects. Similar discrepancies for the heavier halide ions are also expected. It is also pointed out that the proportionality between the polarizabilityvalues and the inverse fourth power of the screened nuclear charge does not in fact provide any reliable criterion for the accuracy of the polarizability data for negative ions.
Introduction Although the free ions represent well-defined physical entities, they can be rarely studied in almost isolated form. Therefore, the determination of several physical properties of free ions is usually quite difficult, if not impossible. Among such properties the electric dipole polarizabilities of free ions seem to be of particular interest. The empirical values of free ion polarizabilities can be estimated from the polarizability data for ionic crystals or from the solution polarizabilities of salts. The corresponding indirect methods have recently been reviewed and extensively discussed by Cokera2s3It is quite obvious that the estimation of free ion polarizabilities must involve a number of additional assumptions regarding the effects of the ion surroundings or the partition of salt polarizabilities into the contributions of separate ion^.^-^ This makes the empirical free ion polarizabilities always uncertain to some extent. The degree of this uncertainty appears to be much higher for negative than for the positive i o n ~ . ~ B Another source of free ion polarizabilities follows from theoretical calculation^.^ In principle, the theoretical approach may lead to the corresponding exact values. However, this level of accuracy can hardly be reached for larger than two-electron system^.^,^ The majority of theoretical free ion polarizabilities corresponds at best to the Hartree-Fock (HF) level of accuracy. The polarizabilities computed within the so-called coupled HartreeFock (CHF) perturbation scheme5#* suffer from the neglect of the electron correlation effect~.~JO Both, the intrinsic inaccuracy of computational methods currently in use and the uncertainty of empirical estimates result in several serious discrepancies between the theoretical and empirical polarizabilities of free i o n ~ . 2 J J -The ~~ most striking differences between the CHF and the empirical data are for free halide ions and deserve careful analysis. The present paper will be mainly concerned with the free fluoride ion. However, our comments and conclusions should have a much wider range of applicability. In the next section the most representative empirical and theoretical data for the polarizability of the free fluoride ion are reviewed and discussed. The subsequent section is concerned with the analysis of the correlation contributions to the CHF polarizabilities. Then, the results 0022-3654/79/2083-1653$01 .OO/O
of our calculations, including some necessary computational details, are presented. They lead to the conclusion that the actual value of the dipole polarizability of the fluoride ion should be much higher than both the CHF value and the most recent empirical estimate of C ~ k e r . ~ B A similar conclusion also appears to be valid for heavier halide ions. The discussion is supplemented by some critical remarks concerning the extrapolation of halide ion polarizabilities from the polarizability data for a given isoelectronic series. Survey of the Polarizability Data for the Fluoride Ion One of the best known and commonly accepted standard sets of empirical free ion polarizabilities is due to Fajans and his c o - ~ o r k e r s .In ~ the case of free fluoride ion the polarizability value (0.95 A3) derived by these authors from the study of molar refractions of salts at infinite dilution was in satisfactory agreement with the older value (1.05 A3) suggested by Pauling.16 It was rather surprising that the first reliable CHF calculations by Cohenl’ predicted fluoride ion polarizability as large as 1.56 A3.Qualitatively similar but supposedly less accurate result (1.40 A3) was also obtained by Lahiri and Mukherji.12 The high accuracy of Cohen’s CHF result is also confirmed by the present calculations. Since the CHF scheme does not include electron correlation e f f e c t ~ , ~they J ~ could have been blamed for the observed discrepancy. However, for the isoelectronic Ne atom the correlation contribution to the polarizability was known5J6to be positive and rather small (about 10% of the CHF result). Thus, including the correlation effects in the case of the fluoride ion was expected only to increase the CHF value. Nevertheless, Fajand7 defended his much lower value of the free fluoride ion polarizability. This problem has also been discussed by the present author13 who favored the larger CHF value and suggested a revision of the empirical polarizability data for free halide ions.13J4 The discrepancy between the CHF and the empirical polarizability value for the fluoride ion remained unresolved until very recently. Some new ideas in this respect have been given by C0ker~9~ who proposed a new repartitioning scheme for Fajans’ molar solution polarizabilities. Moreover, Coker has carefully considered the solvent perturbation effects and utilized some recent accurate 0 1979 American Chemical Society
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The Journal of Physical Chemistty, Vol. 83, No. 12, 1979
TABLE I: CHF and Accurate Polarizabilities for the He Isoelectronic Series (in aua ) HHe Lit CHF~ 93.0 1.322 0.189 accurateC 206.39 1.38335 0.192456 correlation correction 113.4 0.061 0.003
The conversion factor to A3 is 0.148185. Taken from ref 19. These are the central values reported in ref 6.
polarizability values calculated for small ions. The free fluoride ion polarizability derived by Coker from the repartitioning of molar solution polarizabilities3is 1.48 f 0.08 A3. This result was also supported by the corresponding crystal polarizability data2J8and is rather close to the available CHF values of Cohenll and Lahiri and Mukherji.12 If one assumes that the correlation contribution amounts to roughly 10% of the exact value, Coker’s result evidently favors that by the latter authors. It is of note, however, that in spite of the agreement between his empirical polarizability and the CHF data, Coker finally concluded that3 “the solution polarizabilities ... actually require a polarizability for the fluoride ion greater than 1.4 A3”. Coker’s treatment of molar solution polarizabilities, though more refined than the previous one by Fajans and his co-workers, is still subject to several more or less documented assumptions. It will be shown, for instance, that the polarizability values of negative ions cannot be 2 proportionality criterion,15 rationalized by using though it works pretty well for positive i0ns.l’ By using the available accurate polarizability data for two-electron systems6 one can also conclude that the correlation contribution to the polarizability of negative ions should be much larger than that for the isoelectronic noble gas atoms. A more detailed analysis of these data shows that the empirical polarizability of the fluoride ion estimated by Coker is still too low.
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Reliability of the CHF Polarizabilities for Negative Ions Recently, Glover and Weinhold have computed the exact lower and upper bounds for the electric dipole polarizability of the isoelectronic series Li’, He, and H-.6 Their results give very precise estimates of the exact polarizabilities of these systems. Since the corresponding CHF polarizabilities are also a ~ a i I a b l e , ~one ~ J can ~ precisely determine the correlation contributions to the CHF values. The relevant numerical data are collected in Table I. First of all, the data of Table I indicate a complete failure of the CHF method in predicting the polarizability of the H- ion. For this ion the total correlation contribution amounts to more than 50%. However, the relative weight of the correlation correction to the CHF polarizability rapidly decreases with increasing nuclear charge. Thus, for the He atom the CHF polarizability is already acceptable and only a rather unimportant difference is observed for the lithium cation. These data clearly indicate that one has to be rather careful when estimating the correlation corrections to the CHF polarizabilities of ions from data for neutral systems. Accurate polarizability calculations for negative ions represent quite a problem even within the HF approximation?O The HF method tends to overestimatethe effect of electron-nucleus attraction, leading to the charge density distribution less difuse than it should be. On the other hand, the outer regions of the charge density distribution are extremely important for accurate prediction of the system response to external electric field perturbation. Also within the standard CHF scheme8 one has
Andrzej J. Sadlej
to be quite careful when selecting the basis set funct i o n ~ . ~For ~ -this ~ ~reason the CHF polarizability of the fluoride ion computed by Cohenll seems closer to the corresponding HF limit than the value reported by Lahiri and Mukherji.12 The tendency of the HF method to produce too contracted orbitals for negative ions is also to some extent reflected by the sign of the correlation correction to the CHF polarizabilities. This correction, as already indicated, is positive for the H- ion. According to the analysis of Werner and MeyerZ1it should be also positive for systems with a noble gas electron configuration. The magnitude of the correlation correction for the H- ion also indicates that one can expect quite large correlation contributions for F- and heavier halide ions. I t would mean then, that the agreement between Coker’s empirical value and the CHF polarizability of the free fluoride ion is rather fortuitous. It has recently been observedlO that the total correlation contribution to the CHF polarizability is quite accurately approximated by a second-order correlation correction. The exact polarizability a can be expanded as a = a@)
+ pa(1)+ y2a(2)+ ,..
( 1)
where p is the ordering parameter with respect to the correlation ~erturbation.lO>~~ If the total Hamiltonian of a given system in an external electric field is partitioned into the field dependent HF part and the field dependent correlation perturbation,1°then the first term in expansion (1) is the CHF polarizability, i.e. .(a) = ~ C H F (2) and a(l) I
0
(3) The following term in (1) is the “true”lo correlation correction to the HF result. However, this correction is evaluated with a field-dependent correlation perturbation operator, and thus, it has some two-body contributions summed to infinit~.~JO It is perhaps this feature, which determines the effectiveness of the method approximating the exact a by the sum a ~CH+ F 4%~ (4) The subscript CHF in the last term is used to indicate that this is the second-ordercorrelation correction with respect to the CHF approximation. More recent results for He and Nez5show that the polarizabilities computed according to eq 4 differ from the exact ones by less than 2%. Thus, one can conclude that the contribution of higher-order terms is relatively small. Moreover, for both He and Ne the higher-order terms lead only to a small increase of the final polarizability value. It is important that eq 4 appears to approximate the exact polarizability of systems with a noble gas electron configuration from below. Since this approach is utilized in the present paper for the fluoride ion, one can expect that our results give the lower limit for its polarizability. On the basis of the analysis presented in this section the contribution due to CY~AFis also expected to be quite substantial. Moreover, approximation (4) may not be as good as it was for neutral systems. In the case of the fluoride ion the higher order terms of (1)can be relatively large, though they are rather unlikely to dominate over the second-order term.
Calculation of the Electric Dipole Polarizability of the Fluoride Ion Computational Methods. The first step in our approach involves the calculation of the CHF perturbed wave
Static Dipole Polarizability of the Fluoride Ion
The Journal of Physical Chemistry, Vol. 83, No. 12, 1979
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TABLE 11: Results of Calculations for the Fluoride Iona function and the CHF polarizability. The polarizability calculations are known to require quite extensive and basis setb appropriately selected basis sets.21-23Recently, some of A B C these difficulties of the ordinary CHF scheme8-26 have been 9 9 . 4 58612 9 9 . 4 5 8 2 3 9 9 9 . 4 5 8 4 4 6 considerably diminished by using basis sets with explicit -0.264840 -0.291123 -0.263943 dependence on the external electric field p e r t u r b a t i ~ n . ~ ~ , ~ ~ 0.689 0.897 ~ c H F ( , ~ ) 0.481 ~ Using these so-called electric-field-variant (EFV) bases 1.562 1.568 ~ c H F ( ~ ) 1~. 3 3 6 allows not only the reproduction of the best known CHF 0.877 0.515 e&(?)” 0.499 data for small atoms and molecules2s~29 but also extends 2.445 Oif 1.835 2.077 the practical limits of the applicability of the CHF method to molecules as large as C2H4 or C2H2.30The important For the dea Energies are in au, polarizabilities, in .A3. scription of basis sets see the text. ‘ The estimated HF point is that the EFV bases are derived from ordinary limit is - 9 9 . 4 5 9 3 6 au (ref 37). The CHF results calcuGTOZ7or ST028sets currently in use in atomic and lated using the corresponding field independent basis sets, molecular calculation^.^^^^^ The basis set dimension rei.e., for h = 0. e The results obtained using the corremains the same as for the unperturbed system. However, sponding EFV GTO bases and the optimized values of h = the ordinary CHF scheme requires some extension.33 The ^h. f Estimate of the free fluoride ion polarizability accordnear-HF accuracy of the EFV CHF polarizabilities caling to eq 4. culated with relatively small basis sets (no polarization set was composed of 35 CGTO’s with the following confunctions are included) is obtained at the expense of the traction scheme (14.8.2/8.5.2). As shown by the results variational optimization of the second-order perturbed presented in the next section set C does not only reproduce energy with respect to a single parameter, e.g., A. This the best CHF polarizability of the fluoride ion but also parameter enters each function of the EFV basis set and accounts for quite a portion of the second-order correlation represents the magnitude of the orbital origin shift due energy. to the external electric field. The polarizability calculations have been performed by Computationally the numerical, i.e., finite perturbation,34 using the finite perturbation ~ c h e m e which ~ ~ ” ~is formally approach to the calculation of the EFV CHF polarizaequivalent to the analytic CHF a p p r o a ~ h . The ~ ~ ~nu~?~~ bilities appears to be far more convenient than the analytic merical approach was applied for both the field-indemethod.33 A detailed discussion of the finite perturbation pendent and field-dependent (EFV) GTO bases. The numerical approach is given e l s e ~ h e r e . This ~~!~ method ~ reported calculations correspond to an external field is completely followed in the present paper and results in strength equal to 0.005 au. This field strength is small an optimized (with respect to X) EFV CHF polarizability enough to give quite accurate polarizabilities for the value. As a by-product one obtains the field-dependent fluoride ion and is simultaneously large enough to produce o_rbitalsdetermined for the optimal value of X = A, Le., ui significant changes in the second-order correlation energy. (X; F) where F denotes the electric field strength in a given Higher field strength values would result in a nonnegligible direction. When expanded into a power series with respect contribution of higher-order polarizabilities, while smaller to F these orbitals will give the perturbed CHF onefield values would lead to correlation energy chan es too electron functions of the appropriate order. small to be used for the numerical calculation of a1&:”fiF?2’33 In order to calculate the correlation correction c@LF, one Within the EFV GTO CHF calculations, the optimiuses the standard second-order correlation energy forzation of the scale factor X was performed according to the m ~ l a .However, ~~ the corresponding orbitals are those method described p r e v i o ~ s l y .The ~~~ optimized ~~ values detsrmined previously during EFV CHF calculations, i.e., X2’ were found to be 0.1158, 0.1080, and 0.1129 for basis of ui(h;F). Thus, the second-order correlation energy will A, B, and C, respectively. sets depend on the external electric field strengthlo and its second-order derivative with respect to F can be again Results computed numerically. This procedure, though in a The main results of our calculations are collected in slightly different context, has already been discussed by Table 11. They include the total SCF energy (ESCF), the Adamowicz and the present author.1° It is worth noting and the CHF posecond-order correlation energy (E@)), that the EFV CHF calculations as well as the calculation larizability calculated with the field-independent bases A, of by this method require a rather high numerical B, and C. Then the results of the EFV GTO calculations accuracy. are presented, Le., the CHF polarizability, aCHF(X), calComputational Details. In order to provide the highest culated for the optimized value of X and the corresponding accuracy to our calculations at the H F level, three subA). second-order correlation correction, sequently extended basis sets of contracted Gaussian The data of Table I1 clearly show why the initial basis orbitals have been used. The first set (A) employed in the set A was subsequently extended. Even in the EFV GTO present study is the optimized CGTO set of Clementi et approach this set does not properly account for electron It is composed of 13s, 8p, and Id primitive GTO density changes due to an external electric field. On contracted to 7s, 4p, and Id CGTO. Energetically this set augmenting set A with s- and p-type GTO’s with low is fairly close to the H F limit for the fluoride ion.37 orbital exponents, the EFV set B leads to the CHF poHowever, the representation of the outer region of the larizability of comparable accuracy as that calculated by electron density distribution is expected to be rather poor, Cohen.ll Both Cohen’s and the present result are higher since the s- and p-type GTO exponents are relatively high. than the polarizability value reported by Lahiri and For this reason, the second set (B) was generated from set Mukherji.12 However, the latter authors employed the A by the addition of s- and p-type GTO’s with exponents STO unperturbed wave function of Clementi et ale3which equal to 0.035 and 0.032, respectively. These were selected presumably suffers from the same deficiency as set A of by the assumption that the orbital exponents approxithe present paper. A further extension of set B was inmately form a geometric progression. The third set (C) tended to improve the calculated second-order correlation was obtained from set B by the addition of another d-type energy. This extension is completely immaterial for the GTO (orbital exponent equal 0.6). Thus the largest basis EFV CHF polarizability value but leads to a substantial
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The Journal of Physical Chemistry, Vol. 83,
No. 12, 1979
.,$A&,).
increase of both E@)and a The second-order correlation energy values computed in this paper can be compared with the total correlation energy of the fluoride ion calculated by Diercksen et al.39 For the valence shell contribution these authors obtained40 about -0.1976 au. However, they used a much smaller basis set than that employed in the present study. Comparing the appropriate numbers, one can expect that our result for E@)calculated with basis set C should be rather close to the exact second-order energy. This observation also helps to assess the quality of the .,$AF value obtained for set C. Obviously, increasing the basis set size will result in a further but rather small lowering of the second-order correlation energy and will presumably slightly increase the second-order correlation correction to the CHF polarizability. Nevertheless, according to our calculations this correction is positive and quite substantial. Its value calculated for basis set C leads to a total electric dipole polarizability for the fluoride ion as large as about 2.4 A3. This value is much higher even than the recent empirical estimate of C ~ k e r , though ~ , ~ it agrees with a general comment by this author3l4l that the free fluoride ion polarizability should be at least as large as 1.4 A3.
Discussion and Comments In view of the mentioned general remark by Coker3there is no point to claim any serious discrepancy between the empirical and the theoretical estimates of the free fluoride ion polarizability. However, the polarizability value finally given by this author2i3amounts only 1.48 f 0.08 A3 and one should try to explain why it is much lower than our result. First of all,our calculations do not account for the higher order correlation corrections to the CHF polarizability. Such corrections will, however, involve rather hi h excitations and usually they are small compared to a k F . As already pointed out the second-order treatment is quite sufficient for neutral ~ystems~O+'~ and is believed not to fail in the case of negative ions. It could be that the higher-orders contribute in this case more than in the case of neutral atoms (ca. 2% for He and Ne). However, this will not change the main result of the present paper. Thus, the explanation of the difference between Coker's estimate and the present value must be looked for elsewhere. It seems that this difference can be rationalized in terms of rather peculiar features of negative ions. In free negative ions the extra electron is loosely bound to the system and thus, the whole system is highly susceptible to external perturbations. Even a very small perturbation due to the ion surrounding will result in considerable changes in the electronic structure of negative ions. This is clearly illustrated by the orbital contraction effects studied long ago by Burns and W i k n ~ The . ~ ~orbital contraction due to medium effects leads to a considerable lowering of the polarizability of negative ions. Thus, one can ask if the medium effects can be properly accounted for when extracting the polarizabilities of negative ions either from crystal data or from salt refractivity measurements. According to the present author, a complete and satisfactory treatment of these effects is not possible because of a very high sensitivity of negative ions to relatively small external perturbations. Thus, the empirical polarizability values obtained, e.g., from the solution polarizabilities of salts, should be considered as apparent polarizabilities of free ions, for they already account for some portion of the medium effects. The knowledge of accurate hyperpolarizabilities and multipole polarizabilities of free negative ions would be helpful in this respect. Unfortunately, these
Andrzej J. Sadlej
data can hardly be obtained even at the HF level of accuracy. Similarly as for the fluoride ion, the C1- ion polarizability appears also to be higher than the corresponding empirical value. The recent CHF result by Bounds et amounts to 4.25 A3, which is higher than Coker's empirical value2 (3.94 f 0.2 A3) and the previous CHF result (3.76 A3) of Lahiri and Mukherji." Our recent EFV CHF calculations for this ion44gave 4.54 .A3 and they presumably represent near-HF accuracy. The correlation contribution to the polarizability of the C1- ion is also expected to be positive. Thus, the true polarizability of the free chloride ion will again be larger than both the empirical and the CHF value. Although no sufficiently accurate data are available at the moment for heavier halide ions, one can rather safely assume that the empirical polarizabilities determined by Fajans et alq4and by Coker2p3are in this case too low as well. It also seems appropriate to comment on the usefulness of accurate theoretical polarizabilities of negative ions in the interpretation of experimenta1 data. It has already been pointed out that the theoretical and empirical polarizabilities of free negative ions should be treated as two distinct quantities. Neither the empirical free ion polarizabilities can be directly compared with the results of theoretical calculations nor the theoretical data can be directly inserted into the empirical formulae. However, the present study shows that the empirical free ion polarizabilities should be smaller than the exact theoretical values for negative ions. The difference between the exact and the empirical polarizability of negative ions can be used as a measure of the ion-solvent interaction effects in solutions. This is perhaps the most interesting aspect of theoretical calculations for such idealized systems like free negative ions. Finally, we wish to comment on some assumptions used to justify the estimated polarizability values within a given isoelectronic series. It was shown by Pauling16 that for a given isoelectronic series the electric dipole polarizabilities should be approximatelyproportional to the inverse fourth power of the screened nuclear charge. By using a single screening constant, one limits the validity of this proportionality to two-electron systems or to the contribution of a single shell. However, it is far more important that the calculated polarizabilities must correspond to what is called the uncoupled HF appr~ximation.~~ In the case of CHF polarizabilities one has the contribution of the socdled self-consistency terms45@whose dependence on the screened nuclear charge is in general different from (2S)-4. This is well illustrated if the CHF polarizability of the H- ion is estimated from the data of Table I for He and Li+. The result of this extrapolation3is 67.8 au, Le., it is much lower than the directly computed CHF value (93 ad9). The same procedure applied to the exact polarizability values results in 80.0 au for the H- ion and does not even predict 50% of the accurate polarizability of H-. Our example clearly indicates that the proportionality suggested by Pauling is of no use for negative ions. It follows also that the fact that the empirical estimate of the polarizability of the free fluoride ion fits the d I 4 2 plot for the Ne isoelectronic series cannot be considered as an argument in favor of the empirical value. However, for neutral atoms and for positive ions the self-consistencyand the correlation contributions to the polarizability are much smaller and this makes the use of Pauling's c r i t e r i ~ n ~ ' ~ ~ ' * ~ ~ more legitimate. For the same reason the empirical polarizabilities of positive ions determined by Coker2p3appear to have rather high accuracy.
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The Journal of Physical Chemistty, Vol. 83, No. 12, 1979
Electron Affinity of the Water Dimer
Acknowledgment. The author is indebted to Professor
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D. F.-T. Tuan, S.T. Epstein, and J. 0. Hirschfetder, J . Chem. Phys., 44, 431 (1966). A. J. Sadiej, unpublished results. G. Diercksen and R. McWeeny, J . Chem. Phys., 44, 3554 (1966). A. J. Sadlej, Chem. Phys. Lett., 47, 50 (1977). A. J. Sadlej, Acta fhys. Polon., A53, 297 (1978). A. J. Sadlej, Mol. Phys., 34, 731 (1977). A. J. Sadiej, Mol. Phys., 36, 1703 (1978). S.Huzinaga, J . Chem. Phys., 42, 1293 (1965); C. Salez and A. Veillard, Theor. Chlm. Acta, 11, 441 (1968); L. C. Snyder and H. Basch, "Molecular Wave Functions and Propertles", Wlley, New York, 1972; F. B. van Duijnevek, "Gaussian Basis Sets for the Atoms M e for Use in Molecular Calculations", IBM Research Report, 1971. E. Ciementi, IBM J. Res. Dev., Suppl. 9, 1 (1965). J. L. Dodds, R. McWeeney, and A. J. Sadlej, Mol. Phys., 34, 1779 (1977). H. D. Cohen and C. C. J. Roothaan, J. Chem. Phys., 43, S34 (1965); H. D. Cohen, lbld., 43, 3558 (1965). S.T. Epstein and A. J. Sadlej, Inf. J . Quantum Chem., in press. S. Wilson and D. M. Silver, Phys. Rev. A , 14, 1949 (1976). H. Kistenmacher, H. Popkie, and E. Ciementi, J. Chem. Phys., 58, 5627 (1972). E. Ciementi, J. Chem. Phys., 38, 996 (1963); E. Clementi, A. D. McLean, D. L. Raimondi, and M. Yoshimine, phys. Rev. A, 133, 1274 (1964). G. H. F. Diercksen, W. P. Kraemer, and 8. 0. Roos, Theor. Chlm. Acta, 38, 249 (1975). The correlation energy of the F- ion has not been explicitly given in ref 39. The value in the text was obtained as the difference between the valence shell correlation energy of H,O.-F- at the H20-F- dlstance of 100.0 au and the valence shell correlation energy of the isolated water molecule. The corresponding data were taken from Table 3 and Table 10 of ref 39. H. Coker, private communication. G. Burns and E. G. Wikner, Phys. Rev., 121, 155 (1961). D. G. Bounds, J. H. R. Clarke, and A. Hinchliffe, Chem. Phys. Lett., 45, 367 (1977); D. 0. Bounds and A. Hinchliffe, lbld., 56, 303 (1978). A. J. Sadlej, unpubllshed results. P. W. Langhoff, M. Karplus, and R. P. Hurst, J . Chem. Phys., 44, 505 11966). A. J. 'Sadlei, Mol. Phys.,21, 145 (1971); A. J. Sadlej and M. JaszuAski, ibid., 22, 761 (1971). D. F.-T. Tuan and K. K. Wu, J. Chem. Phys., 53, 620 (1970). D. F.-T. Tuan and A. Davidz, J. Chem. fhys., 55, 1286 (1971).
H,Coker for his comments concerning the empirical values of the free fluoride ion polarizability. Dr. M. Jaszufiski is thanked for making his 4-index transformation program available to the author. References and Notes Thls work was supported by the Institute of Low Temperatures and Structure Research of the Pollsh Academy of Sciences under Contract NO. MR-1.9.4.3. H. Coker, J. Phys. Chem., 80, 2078 (1976). H. Coker, J . Phys. Chem., 80, 2084 (1976). N. Bauer and K. Fajans, J. Am. Chem. Sac., 64, 3023 (1942). A. Dalgarno, Adv. Phys., 11, 281 (1962). R. M. Glover and F. Weinhold, J . Chem. Phys., 65, 4913 (1976). J. S. Sims and J. R. Rumble, Jr., Phys. Rev. A , 8, 2231 (1973). R. M. Stevens, R. M. Pitzer, and W. N. Lipscomb, J . Chem. Phys. 38, 550 (1963). T. C. Caves and M. Kardus. J . Chem. fhvs., 50, 3649 (1969). L. Adamowicz and A. J. Sadlej, Chem. fhys: Lett., 53, 377 (1978). The dlagramrnatic analysis of the CHF scheme shows that there are certain types of the correlation-like diagrams which contribute to the second-order perturbed energy (see ref 9). However, these diagrams are in fact only due to modification of the HF potential and they do not represent the correlation effects. What is meant by the true correlation contribution to second-order energies is represented by diagrams with a least one closed ring. H. D. Cohen, J. Chem. fhys., 45, 10 (1966). J. Lahiri and A. Mukherji, Phys. Rev., 153, 386 (1967); 155, 24 (1967). A. J. Sadlej, Mol. fhys., 22, 705 (1972). A. J. Sadlej, 2.Naturforsch. A , 27, 1320 (1972). L. Pauling, Proc. R. SOC.London, Ser. A , 114, 181 (1927). C. Matsubara, N. C. Dutta, T. Ishihara, and T. P. Das, Phys. Rev. A , 1, 561 (1970). K. Fajans, J. Phys. Chem., 74, 3407 (1970). H. Coker. J . Phvs. Chem. Solids. submitted for Dublication. K. T. Chung and R. P. Hurst, Phys. Rev., 152, 35 (1966). R. Ahirichs, Chem. Phys. Lett., 34, 570 (1975). H.J. Werner and W. Meyer, Phys. Rev. A , 13, 13 (1976). H.-J. Werner and W. Meyer, Mol. Phys., 31, 855 (1976). P. Swanstrbn, W. P. Kraemer, and G. Diercksen, Theor. Chlm. Acta, 44, 109 (1977).
Theoretical Study on the Electron Affinity of the Water Dimer Danlel M. Chipman Radiation Laboratory,t University of Notre Dame, Notre Dame, Indiana 46556 (Received February 15, 1979) Publlcatlon costs asslsted by the US. Depattment of Energy
Ab initio SCF calculationson properties of an isolated dimer of the water molecule are reported. The calculated geometry and force constants of the neutral dimer are in good agreement with other calculations and, where comparisons are possible, with experiment. The dipole moment and ionization potentials are also reported. This work represents the first realistic attempt at a quantitative determination of the electron affinity of the water dimer. It is found that the neutral dimer and its anion have virtually identical equilibrium geometries and force constants. The excess electron is in a very diffuse orbital, being weakly bound by the long-range dipole field of the neutral molecule. The calculated vertical electron affinity at the equilibrium geometry is only 0.0002 eV. Other points on the potential surface show much higher vertical electron affinities (the highest being 0.009 eV) and indicate that vibrational excitation will cause the experimental electron affinity to have a significant temperature dependence.
I. Introduction As part of a continuing program to elucidate the structure and process of formation of the hydrated electron, calculations have been undertaken on the electron The research described herein wm supported by the Office of Basic Energy Science of the Department of Energy. This i s Document No. NDRL-1940 of the Notre Dame Radiation Laboratory.
0022-3654/79/2083-1657$01 .OO/O
affinity of an isolated dimer of the water molecule. The results are ah0 of significance in interpretation of the electron scattering spectrum of water vapor. Relevant to this is a Previous study' of the electron affinity of an isolated water monomer, in which it was found that the Cahlated Born-Oppenheimer binding energy of the excess electron is SO Small at COnfigUrationSnear the equilibrium geometry (a maximum of about eV) that coupling @ 1979 American Chemical Society
