J. Phys. Chem. 1988, 92, 1378-1382
1378
Lithium and Sodlum Catlon Affirtittes of H2, N2, and CO David A. Dixon,* E. I . du Pont de Nemours & Company,t Central Research & Development Department, Experimental Station, Wilmington, Delaware 19898
James L. Cole, School of Physics,. Georgia Institute of Technology, Atlanta, Georgia 30332
and Andrew Komornicki Polyatomics Research Institute, 1101 San Antonio Road, Suite 420, Mountain View, California 94043 (Received: July 1, 1987)
The Li' and Na+ affinities of H2, N2,and CO have been calculated by ab initio molecular orbital theory with extended basis sets. Geometries were gradient optimized at the self-consistent field (SCF) level. Force fields were calculated at the SCF level at stationary points as were correlation corrections at the Cl(SD) level with a correction for higher order excitations where appropriate. The optimum geometries are C, (bent) for MH2+ and C,, (linear) for MCO+, MOC', and MN2+. The Li+ affinities (AH at 300 K) for H2, CO (at 0),CO (at C), and N2 are 4.8, 12.0, 14.6, and 11.8 kcal/mol, respectively, at the correlated level. The Na+ affinities (AH at 300 K) for H2, CO (at 0),CO (at C), and N2 are 2.8, 7.6,9.6, and 7.4 kcal/mol, respectively, at the correlated level.
Introduction The binding of atomic ions to molecules plays an important role in a variety of processes. The binding of protons to molecules has been studied in detail both experimentally' and theoretically,* protonated species being important in media whose diversity ranges from solutions to dense interstellar clouds. It is now possible to calculate the proton affinity (the energy released on binding a proton) of small molecules as accurately as to measure it experimentally. There has also been significant interest in the binding of metal ions to molecules. Experimental studies have focused primarily on the binding of transition-metal ions3 and alkali-metal ions.4 At various levels of sophisti~ation,~-~ there have also been a number of recent theoretical studies of the binding of alkali cations to small molecules. We have been involved in the accurate calculation of molecular proton affinities,IO and these calculations are important in establishing the absolute proton affinity scale.' We have now extended our studies to the binding of alkali cations, specifically Na' and Li+, to small molecules employing the same techniques as used previously in our accurate proton affinity calculations. Here we report the Li+ and Na+ affinities of H2, N2, and CO. Metbod The atomic ion affinity (AIA) of a base (B) is defined as -AjY(rxn l ) , where M+ is an atomic cation. B
+ M+
-
MBf
(1)
The theoretical evaluation of AIA(B) is given by eq 2, where AIA(B) = -AH(rxn 1 ) = -AEoclcc- AZPE
+ AEvib(n+ S/RT
AEoelsis the electronic energy difference between reactants and products at 0 K and AZPE is the difference in zero point energies between the base (B) and ion-base complex (MB'). The term AEvib(T)corrects for the change in the population of vibrational levels as a function of temperature. The final term includes the translational and rotational changes assuming classical behavior and a AnRT term required to convert an energy to an enthalpy, assuming ideal gas behavior: this term becomes 2RT if B is linear and MB+ is nonlinear. We assume that M+, B, and MB+ are in their ground electronic states, an assumption which should be valid for alkali ions but may not be so for other metals. 'Contribution No. 4421.
0022-3654/88/2092-1378$01.50/0
Equation 2 requires knowledge of the structures, energies, and force fields for B and MB+ and the energy of M+. The geometries of B and MB+ were determined with the programs HONDO'~ and GRADSCF'~by using analytic gradient methods13 at the self-consistent field (SCF) level. The SCF geometries were used for determining the force fields by analytic second derivati~es'~ with the program GRADSCF. Configuration interaction calculations including all single and double excitations, CI(SD), from the SCF reference configuration were carried out at the S C F geometries. The effect of higher order excitations due to unlinked clusters was approximated by the use of Davidson's approximation, CI(SDQ).15 The CI(SD) calculations were done with the GUGA formalism16 as implemented in the program HONDO. We also calculated the correlation energy at the MP-2 level" using the program GRADSCF. (1) Lias, S.G.; Liebman, J. F.; Levin, R. D. J . Phys. Chem. Ref. Data 1984. -13. - ,695. --(2)Dixon, D. A.; Lias, S. G. In Molecular Structure and Energetics; Liebman, J. F., Greenberg, A. Eds.; VCH: Deerfield Beach, FL; Vol. 2,p 269. (3) Elkind, J. L.; Armentrout, P. B. J . Phys. Chem. 1987,91, 2037. (4)Castleman, A. W., Jr., Peterson, K. I.; Upschulte, B. L.; Schelling, F. J. Int. J. Mass Spectrom. Ion Phys. 1983,47,203. ( 5 ) Ikuta, S.Chem. Phys. Lett. 1984,109, 550. (6) Del Bene, J. E. J. Comput. Chem. 1986, 7,259. (7) Woodin, R. L.; Houle, F. A,; Goddard, W. A. Chem. Phys. 1976,14, 461. (8) Del Bene, J. E.; Frisch, M. J.; Raghavachari, K.; Pople, J. A,; Schleyer, P. V. R. J. Phys. Chem. 1983,87,73. (9) (a) Staemmler, V. Chem. Phys. 1975,7,17. (b) Staemmler, V. Chem. phys. 1916, :7, 187. (IO) (a) Ri,aemer,W. P., Komornicki, A,; Dixon, D. A. Chem. Phys. 1986, 105,87.(b) Dixon, D. A.; Komornicki, A,; Kraemer, W. P. J . Chem. Phys. 1984,81,3603.(c) Komornicki, A.; Dixon, D. A. J . Chem. Phys. 1987,86, 5625. (d) Eades, R. A.; Scanlon, E.; Ellenberger, M. R.; Dixon, D. A,; Marynick, D. S.J . Phys. Chem. 1980,82,2840. (1 1) (a) Dupuis, M.; Rys, J.; King, H.F. J . Chem. Phys. 1976,1 1 1. (b) King, H. F.; Dupuis, M.; Rys, J. National Resourcefor Computer Chemistry Software Catalog, Vol. 1; Program Q H 0 2 (HONDO) 1980. (12)GRADSCF is an ab initio gradient program system designed and written by A. Komornicki at Polyatomics Research. (13)(a) Komornicki, A.; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977,45,595. (b) McIver, J. W.; Komornicki, A., Jr. Ibid 1971, 10, 303. (c) Pulay, P. In Applications of Electronic Structure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977;p 153. (14)King, H. F.;Komornicki,A. NATO ASISer. C. 1986,No. 166,207. King, H. F.; Komornicki, A. J . Chem. Phys. 1986,84,5645. (15)Langhoff, S. R.;Davidson, E. R. Int. J . Quantum Chem. 1974,8,61. (16)(a) Brooks, B.; Schaefer, H. F., I11 J. Chem. Phys. 1979,70,5092. (b) Brooks, B.; Laidig, W.; Saxe, P.; Handy, N.; Schaefer, H. F., 111 Phys. Scr. 1980,21,312. (17)(a) Moller, C.; Plesset, M. S. Phys. Reu. 1934,46,618. (b) Pople, J. A,; Binkley, J. S . ; Seeger, R.Int. J . Quantum Chem. Symp. 1976,10, 1.
-.
-..
0 1988 American Chemical Society
Li and N a Cation Affinities of H2, N2, and CO
TABLE II: Calculated Vibrational Swctra
TABLE I: Molecular Geometries molecule
r(A-B)'
H,b L;H2+( C,)' LiH2+(C,,) NaH2+(Cb)d NaH2+(C,,) NZg LiN2' NaN,'
0.734 0.743 0.734 0.739 0.734 1.074 1.068 1.069 1.107 1.121 1.095 1.118 1.097
cob
LiOC+ LiCO+ NaOC' NaCO'
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 1379
r(M-A)'
@I,
molecule 2.094 2.141 2.485 2.602 2.097 2.503 1.954 2.241 2.357 2.614
'Bond distances in A. bReference lob. e6(HLiH) = 20.1". (HNaH) = 16.9". eReference loa.
Our previous work on proton affinities has shown the need for adequate basis sets in order to accurately calculate these affinitim. We employed the same basis sets for H and the second row atoms, C, N, and 0 as have been used previously.Ihvb The basis set for H is of triple quality with exponents and coefficients from Dunning,'* augmented by two sets of p functions with exponents of 1.4 and 0.35 giving a basis set of the form (5s2p)/[3s2p]. The basis sets on C, N , and 0 are of triple j- quality, and again the exponents and coefficients are from Dunning.'* This basis set was augmented with d functions expressed as two-term contractions of four gaussian functions with effective Slater exponents of 2.0 (C), 2.1 (N), and 2.2 (0)for the inner d, and an effective Slater exponent of 0.8 for the outer d. The basis set has the form (1 ls6p4d)/[Ss3p2d]. The s basis set for Li+ is taken from Gerber and SchumacherI9 and the p portion is from Dunning and Hay," augmented by a d function determined as a two-term Gaussian fit with an effective Slater exponent of 1.5. The final Li+ basis has the form (lls4p2d)/[5s2pld]. The Na+ basis set is from McLean and Chandlerz' for the s and p portion and is augmented by a single d function determined by a two-term Gaussian fit with an effective Slater exponent of 1.1. The final Na+ basis set has the form (13~9p2d)/[6sSpld].
Results Geometries. The SCF geometries of the diatomics employed here were determined in previous workloa,band will not be discussed. All of the geometry results are given in Table I. There are two possible structures for binding an alkali ion to H2, an asymmetric linear structure, C,,, and a structure where the M+ , symmetry has equal bond distances to the hydrogens with C (bent). At the S C F level, the C,, structure is a maximum with a degenerate direction of negative curvature while the symmetric , symmetry. Both structures structure is a minimum with C resemble an H2onto which an alkali ion is weakly bonded. The largest change in the H2 bond distance as compared to isolated H2 is found for H2Li+ (C,) where we find that this bond length , structures is 0.01 A longer. The M+-H bond distances in the C are shorter than those in the C,, structures with differences of 0.05 A for LiH2+and 0.12 A for NaH,+. For further comparison, the bond distances in LiH and N a H are 1.596 and 1.887 A, respectively:2 while those in LiH+ and NaH+ are 2.191 and 2.593 A, respectively.z3 The addition of an alkali ion to N, or CO leads to a significantly larger interaction than results with Hz. On the basis of our previous proton affinity work,'O"Vbonly the asymmetric linear C,, structures were considered. The second derivative calculations (18) Dunning, T. H.; Jr. J . Chem. Phys. 1971, 55, 716. (19) Gerber, W. H.; Schumacher, E. J. Chem. Phys. 1978, 69, 1692. (20) Dunning, T. H., Jr.; Hay, P. J. In Methods of Elecfronic Strucfure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977; p 1. (21) McLean, A. D.; Chandler, G.S. J . Chem. Phys. 1980, 72, 5639. (22) Huber,K. P.; Herzberg, G. Constunts of Diatomic Molecules; Van Nostrand-Reinhold: New York, 1979. (23) Rosmus, P.; Meyer, W. J. Chem. Phys. 1977, 66, 13.
cm-'
4582 2417 2692 N2 4466 LiH2+(C,,) LiH,'(C,,) 4585 NaH2+(C2,) 4518 NaH,'(C,,) 4586 LiN2' 2749 NaN,' 2743 2532 LiCO' LiOC+ 2298 2509 NaCO' NaOC' 2323 H2
co
1, km/mol
02,
cm-I
I,
W3r
1,
km/mol cm-l km/mol
0 144 0 47 205 28 108 29 17 69 296 84 257
704 531i(e) 306 382i(e) 183(e) 142(e) 236(e) 119(e) 179(e) 114(e)
7 31 8 9 41 6 15 62 0.4 11
446 251 558 144 351 167 341 385 177 185
43 61 7 11 147 32 130 156 29 34
show that the linear structures are all minima. The interaction of Li+ with N z leads to a bond distance that is shorter than the Li-H bond distance in LiHz+ (C,,); a similar resdt is found for the Na-N bond in NaNz+ versus NaH2+. In both cases the Nz bond length decreases by -0.005 A versus that in the isolated molecule. The alkali ion can bind at either the C or the 0 in CO. Addition of M+ at the oxygen leads to a shorter metal-ligand bond than does addition at the carbon, and there is an overall lengthening of the CO bond relative to isolated CO. Addition of M+ to C leads to a shortening in the CO bond relative to isolated CO. The Li+ interaction is expected to be larger than the Na+ interaction and, indeed, the difference in CO bond lengths between LiCO+ and LiOC+ is more pronounced than that found for NaCO+ and NaOC+. This behavior follows that observed in HCO+ and HOC+ where the interaction is still stronger and an even larger effect is observed.lob The M-N distances in MN2+ lie intermediate to the M-C and M-0 bond distances in MCO+ and MOC?, and the M-0 bond distances in MOC' are shorter than the M-H bond distances in MH2'. Vibrational Spectra. The positions of the molecular vibrations and the infrared intensities are given in Table 11. The calculated frequencies are approximately 10% higher than the experimental values because of our neglect of anharmonic and correlation corrections. The experimental frequencies and percent errors for the diatomics are 4401 (4.0%), 2359 (12.4%), and 2170 (10.2%) cm-I for diatomic Hz, N2, and CO, respectively.22 The calculated frequencies for LiH2+ and NaH2+ clearly show that the C, structures are minima while the C,, structures are maxima with the degenerate bend corresponding to a negative direction of curvature. For LiH2+ (C,), the Hz stretch decreases by 116 cm-l as compared to its value in the free molecule consistent with the slight increase found in the H2bond distance. The bend is at much lower frequency, 704 cm-I, and the asymmetric stretch is even lower at 446 cm-'. All transitions are predicted to have some intensity in the infrared. The most interesting change is in the H2 stretch, which while inactive in the free molecule is predicted to have an intensity of 47 km/mol in the ion. For linear LiH2+, the H2 frequency is essentially the same as that in the monomer while the asymmetric stretch of Li+ with respect to the H2 is only 251 cm-I. The intensities of these transitions are , structure; the intensity significantly higher than those in the C of the H2 stretch in the C,, structure is more than 4 times the intensity in the C2,structure. The behavior of NaH2+ is similar to that of LiH2+. The Hz stretch in the Czustructure is only 64 cm-' below that of free H2, while this stretch in the C,, structure is 4 cm-I above the H2value. The asymmetric stretch frequencies are lower in the C,, and C,, structures being only 144 cm-I in the latter case. The bend in the C,, structure also shows a significant decrease. The intensities of the Hz stretch have decreased somewhat and the intensity for the C,, structure is now only 4 times that of the C,, form. In the C,, structure, the charge generates an external electric field along the molecular axis. The field induces a dipole moment due to the parallel component of the polarizability resulting in a n infrared active vibration. In the C, structure, the induced moment is perpendicular to the largest component of the vibration and thus has a smaller effect.
1380 The Journal of Physical Chemistry, Vol. 92, No. 5, 1988
Dixon et al.
TABLE HI: Total Electronic Energies (au)
molecule Lit Nat
H2 N2
co
LiH2+()C, LiH2'(C,J NaH2'(C2,) NaH2'(C,,) LiN2+ NaNzt LiCO+ LiOC+ NaCO' NaOC+
E(SCF)
E(CI-SD)
-7.236 21 1 -161.664 909 -1.132992 -108.983 946 -1 12.779 692 -8.377 535 -8.370642 -162.802 481 -1 62.798 28 1 -1 16.237 896 -270.659 450 -120.036 638 -120.036957 -274.457 023 -274.457 782
-1.170 764 -109.287 995 -1 13.066 092 -8.415091 -8.408 963 -162.840 106 -162.836 370 -116.542379 -270.963 721 -120.325 075 -120.320963 -274.745 132 -274.741 819
TABLE I V Energetic Qunutities Required for Determining Lit and Nat Affinities" molecule AEO,&CF) AEO ,i,(Cl-SD) AEO ,i,(CI-SDQ) LiH2'( C,) 5.23 5.09 0.90 1.25 2.87 2.78 0.24 0.44 11.36 11.13 11.40 6.74 6.65 6.79 14.38 13.01 14.29 11.45 13.21 11.71 8.96 7.79 8.87 6.79 6.56 8.27
E(Cl-SDQ)
E(MP-2)
-1.162721 -109.307 956 -113.080024 -8.407 103 -8.400 7 17 -162.832 109 -162.828 213 -116.561 904 -270.983 464 -120.340852 -120.331 937 -224.760 736 -214.153 162
-109.315 523 -1 13.090674
-1 16.569 842 -270.991 171 -120.349 808 -120.345 138 -274.169 855 -274.766 042
AEo,I,(MP-2) 5.13 1.12 2.81 0.37 11.13 6.65 15.45 9.85 9.69 5.54
AZPE 1.48 0.37 1.15 0.22 1.11 0.72 1.31 0.94 0.89 0.42
-AH,, 4.81 2.38 2.83 1.72 11.75 7.43 14.57 12.01 9.57 7.64
All energies in kcal/mol.
For LiN2+, the symmetric stretch frequency has increased by 57 cm-' over that in isolated N 2 consistent with the decrease in the N2 bond length. The asymmetric stretch at 351 cm-' is higher than the corresponding value in LiH2+. The degenerate bend is a much lower frequency, 183 cm-I. Essentially the same results are found in NaN2+. The N 2 frequency is again made IR active by placing a charge on the molecular axis. As found in binding a metal ion to Hz, displacing the charge further from the N 2 (Li+ vs Na+) decreases the I R intensity. The intensity of the asymmetric stretch is also much larger in LiN2+ versus NaN2+. There are two structures for M+ bonded to CO, bonding to the carbon leads to a decrease in R ( C 0 ) just as found for N 2 while bonding to oxygen leads to an increase in R ( C 0 ) . Thus for LiCOt, the CO stretch increases by 115 cm-', while for LiOC+, the C O stretch decreases by 119 cm-I. The asymmetric stretch, in contrast, is higher in LiOC+ than in LiCO+. The bending frequency in LiCO+ is almost double the value in LiOC'. As expected, the same trends are observed in the Na+ clusters although they are not as pronounced as those in the Lit clusters. The intensities of the C O stretch show an interesting behavior. Bonding M+ to the carbon decreases the intensity as compared to that associated with the diatomic, while bonding to the oxygen leads to an increase in the intensity. As observed for the alkali ion-Nz complexes, the asymmetric stretch is quite intense for Li+ but weakens considerably as a result of Nat binding. In both cases, the binding of M+ to oxygen leads to a larger intensity than binding at carbon. Similarly, the bends are more intense for Li+ binding than for Na' when M+ is bonded to oxygen. Energetics. The total electronic energies are given in Table 111, while the energetic quantities required to calculate -AH(rxn l), the AIA(B), are given in Table IV. Before discussing the metal ion affinities, we consider how the electronic energies, AEoelec,change with the quality of the calculation. The effect of correlation energy on the binding of M+ to H2 is very small, and the CI-SD calculations (full C I in the valence space) are in good agreement with the MP-2 results. Correlation leads to a decrease of 2.7% in the M+-H, binding energy for LiH2+; for NaH2+the decrease is 3.2%. These results should be compared to the 2.4% increase found in evaluating the binding of a proton to H,. The correlation effect on binding Mt to N, is also very small and we find no correction at the MP-2 level. At the CI-SDQ
level, correlation increases the binding energy by 2.1% for LiN2+, which can be compared to an increase of 2.6% found for HN2+ (the proton affinity of N2);for NaN2+, the correlation effect corresponds to a 1.4% increase. At the SCF level, the energy for binding M+ to carbon is below that for binding to oxygen. This situation reverses at the correlated wave function level. The percent increase due to correlation for binding at carbon is 10.5%, while the percent decrease due to correlation for binding at oxygen is 15.4%. Thus at the CI-SDQ level LiCO' is 2.9 kcal/mol more stable than LiOC+. The correlation correction at the MP-2 level overestimates this energy difference, making LiCO' too stable and LiOC' too unstable. The predicted magnitude of binding Na+ to carbon increases through correlation by 13.9%, while the correlation correction for binding at oxygen leads to a 26.1% decrease, making NaCO+ 2.4 kcal/mol more stable than NaOC+. Again the MP-2 correction over-estimates this energy difference. The binding of a proton to CO leads to two different correlation effects on the proton affinity.lob Correlation corrections for addition of H+ to carbon lead to an increase of 2.4% in the proton affinity, while the corrections for addition to oxygen lead tu a decrease of 5.5%. However, the energies of HOC+ and HCOt differ substantially (AEoelcc(SCF) = 31.8 kcal/mol, AEoelec (CI-SDQ) = 41 kcal/mol with HCO+ being the most stable) and thus the AE's at the S C F and correlated levels are in the same direction. In contrast, the absolute values for binding Li+ or Na+ to C O are much smaller, 5-15 kcal/mol, than those for binding a proton to CO, 140 kcal/mol. Considering the small magnitude of AI3 for the binding of an alkali ion, it is not surprising that the binding energy at oxygen is slightly larger than that at carbon at the SCF level and that this trend is reversed at the C1 level. We consider also that the direction of the dipole moment reverses when comparing calculations at the SCF and C1 levels. Since the SCF value for the dipole moment is in the wrong direction, it will favor binding at oxygen. Correlation corrections reverse the direction of the dipole moment leading to the stronger interaction of a positive charge at carbon. Because the interaction energies are small and the interactions are at long range for an alkali cation interacting with CO, the direction of the dipole moment is important in giving the correct qualitative prediction. For a proton, the chemical binding effects outweigh the long-range dipolar forces
Li and N a Cation Affinities of H2, N2, and CO and the correct predictions are given at the S C F level. In order to calculate the metal ion affinities, we must include the AZPE terms and the appropriate temperature corrections. The changes due to AZPE are not inconsequential. They result primarily from the bends and the asymmetric stretch in MB+ since the symmetric stretch in MB+ is essentially cancelled by the zero point energy of the diatomic. The AZPE terms are approximately cancelled by the temperature-dependent corrections at 300 K. The binding affinities of Li+ and Na+ to N 2 are much larger than the binding affinities of H2. The Li+ affinity of CO is 24% greater than that of N2, while the proton affinity of CO at carbon is 19% higher than that of N2. The Na+ affinities for CO and N2 are significantly lower than the Li+ affinities. The Na+ affinity of CO a t carbon is 29% greater than that for N2. The only available experimental data on the binding energies of these ions corresponds to the Na+ affinity of N2 and CO, which has been determined by Castleman and co-workers."a The calculated Na+ affinity of N2is 7.4, in excellent agreement with the experimental value of 8 kcal/mol. However, the experimental value of 13 kcal/mol found for the Na+ affinity of CO appears too high on the basis of the theoretical value and the expected trends in ion binding affinities. The actual value is expected to be near 10 kcal/mol. The calculated ratio of the Li+ affinities for N2 and CO is 1.24, while the calculated ratio for Na+ is similar at 1.29; this is not consistent with the experimental ratio of 1.76. Comparison to Other Studies. There have been a number of other studies of the binding of M+ to H2, N2, and CO. Cardelino et al.24have calculated the eometry of LiH2+at the S C F level. They find r(Li-H) = 2.049 and r(H-H) = 0.747 8,as compared to our values of 2.094 and 0.743 8,,respectively, and determine a slightly larger interaction for Li+ with H2 (as compared to the present calculation). Their calculated value for AEoelecis 5.5 kcal/mol, which is slightly higher than our value. There is, however, some question as to the accuracy of their calculated value since a consistent basis set was not employed for the three relevant quantities required for the determination. Poshusta and ~ o - w o r k e r performed s~~ early ab initio calculations on LiH2+ using a minimum basis set of 4 Gaussian orbitals. They correlated the four electrons within three valence-bond wavefunctions, which leads to a severe overestimate of the core correlation in LiH2+as compared to an isolated Li+ ion. They find a AEocI, of 13.6 kcal/mol, which is clearly too large. They obtain bond distances of 2.05 8,for r(LiH) and 0.82 8,for r(H-H), which differ from our values, and underestimated wIas 4000 cm-' and overestimated w j as 1100 cm-'. They also obtain a lower value of 700 cm-l for w2 in good agreement with our value. Using the diatomics-in-molecule (DIM) method, Wu and Ellison26studied LiH2+ and found a structure with r(H-H) = 0.741 8,but found a long value for r(Li-H) of 2.65 8,. Their value for AEocls of 2.5 kcal/mol is approximately a factor of 2 too small. Lester2' has employed a large contracted basis set of the form [5s,3p/6s,3p] (in the order Li/H) to study the Li+/H2 surface. He constrained r(H2) at 1.4 au (0.74 8,) and found r(Li-H) = 2.03 A with a binding energy of 5.64 kcal/mol. His value for r(Li-H) is shorter than the current determination by 0.06 8, and his binding energy is slightly greater, 0.4 kcal/mol. Some of this difference in binding energy is due to our better energy for Li+, 0.14 kcal/mol lower. Kutzelnigg and co-workers2*employed a basis set of the form (9~4p/5~2p)/[6~4p/3~2p] and the IEPA-PNO method for electron correlation in their study of Li+ interacting with H2. Here, some of the basis functions are employed as bond functions, which can lead to problems in ener y calculations. At an Li-H distance of 2.02 A ( r ( H 2 ) = 0.741 ), they find a value for AEoclecof 5.64
1
1
(24) Cardelino, B. H.; Eberhardt, W. H.; Borkman, R. F. J. Chem. Phys. 1986, 84, 3230.
(25) Poshuta, R. D.; Haugen, J. A.; Zetik, D. F. J . Chem. Phys. 1969,51, 3343. (26) Wu, A. A.; Ellison, F.0.J . Chem. Phys. 1967, 47, 1458. (27) Lester, W. A., Jr. J . Chem. Phys. 1970, 53, 1511; 1971, 54, 3171. (28) Kutzclnigg, W.; Staemmler, V.; Hoheisel, C. Chem. Phys. 1973, I , 27.
The Journal of Physical Chemistry, Vol. 92, No. 5, 1988 1381 kcal/mol at the SCF level and a value of 5.75 kcal/mol at the level of IEPA-PNO. Their use of bond functions probably biases their results so as to predict a complex that is too stable. Del Bene6 has recently calculated the Li+ affinity of CO using a variety of basis sets and included correlation corrections at the MP-2, MP-3, and MP4-SDQ levels. With her best basis set (6-311 G(2d)) she obtains values for AEoels binding at oxygen of 14.1 (SCF), 10.4 (MP-2), and 11.8 (MPCSDQ) kcal/mol as compared to our values of 13.2 (SCF), 9.9 (MP-2), and 11.4 (CI-SDQ) kcal/mol. The agreement is quite satisfactory. She calculated an Li+ affinity at oxygen of 11.3 kcal/mol at 298 K as compared to our value of 12.0 and a value of 14.5 kcal/mol for binding at carbon as compared to our value of 14.6 kcal/mol. Considering the differences in basis sets, geometries (unreported), and methods for treating correlation, the agreement is excellent. Ikuta5 has calculated AEoelec terms for the binding of Li+ and Na+ to CO and N 2 using the 6-31G* basis set and the MP-3 level for treating electron correlation. Geometries were obtained with the 4-31G or 3-21G basis set, which is far below the level of the present calculations. Thus for Li+-N2, his Li-N bond distance is 0.043 A shorter than the present value, yet there is no change in r(N-N) as compared to the diatomic. For NaN2+,his value for r(Na-N) is far too short, 0.180 8, shorter than the present value. Similarly his Li-C and Li-0 bond distances for LiCO+ and LiOC' are shorter than our values by 0.020 and 0.078 A, respectively. In agreement with the present calculations, Ikuta finds a decrease in r ( C 0 ) for LiCO+ and an increase in r ( C 0 ) for LiOC' as compared to the diatomic. Again, Ikuta finds r(Na-C) in NaCO+ to be 0.054 8, shorter than our value, and r(Na-0) in NaOC+ is 0.175 shorter than our value. Ikuta finds values of AEoelec of 14.8 (SCF) and 16.8 (MP-3) kcal/mol for L E O + , 16.1 (SCF) and 14.5 (MP-3) kcal/mol for LiOC', and 12.4 (SCF) and 14.1 (MP-3) kcal/mol for LiN2+. These SCF values are all too large and the final correlated values are still in error, also being too large. Furthermore, the difference in energy between LiCO+ and LiOC+ is too large at the SCF level (favoring LiOC+), a consequence of the small basis set and inadequate geometry employed in Ikuta's study. For the binding values of 9.5 (SCF) and 11.7 of Na', Ikuta calculates AEoelcc (MP-3) kcal/mol for NaCO+, 10.3 (SCF) and 9.4 (MP-3) kcal/mol for NaOC+, and 7.5 (SCF) and 8.7 (MP-3) kcal/mol for NaN,'. Again the values of AEoelecare too large as compared to the present values. Using a basis set of similar quality to our basis set, Staemmlerg has studied the interaction potential of Li' with N2 and CO. Most of these studies were done at the SCF level with the diatomic bond distance fixed at its unperturbed value. Correlation calculations were done with the CEPA-PNO method at selected points. In both systems, his total energies are significantly higher than our total energies. In studying Li+ interacting with N,, Staemmler basis set and found AEoelcc used a (9~4p2d/Ss3p)/[5~3p2d/5~3p] (SCF) = 13.02 kcal/mol at r(Li-N) = 2.1 1 A, somewhat higher than our value. With a smaller basis set, he found AEoeI, = 13.55 kcal/mol at the S C F level and AEoelec= 14.84 kcal/mol at the correlated level, which shows a larger correlation effect than found by us with a larger basis set. He noted that for N2 and CO interacting with Li+ correlation has little effect on the geometries. basis set, Staemmler found With a (9~5p2d/Ss2p)/[5~3p2d/5~2p] AEoelec = 14.53 kcal/mol for Li+ at oxygen and AEoel, = 12.22 kcal/mol for Li+ at carbon. Although the difference is larger than what we find, the trend, which indicates that binding at oxygen is more stable than binding at carbon at the SCF level, is correctly given. Correlation reverses these values giving AEoelec= 14.30 kcal/mol at carbon and AEO,,,, = 12.45 kcal/mol at oxygen. Staemmler's value for the magnitude of the interaction at carbon is in good agreement with our value, while his value for binding at oxygen is slightly high.
+
Conclusions The alkali binding affinities of H2, N2, and CO are small, C 15 kcal/mol. Alkali ions bind to H2 to give a C,, (bent) structure and bind to N2 and CO to give C,, (linear) structures. The
1382 The Journal of Physical Chemistry, Vol. 92, No. 5, 1988
binding affinities a t 300 K for H2are very small, 4.8 kcal/mol for M+ = Li+ and 2.8 kcal/mol for M+ = Na+. For the other two molecules, the affinities are somewhat higher. The alkali ions bind preferentially at carbon in co but this result is Only found a t the correlated level. The binding affinities at CO are 14.6 kcal/mol for M+ = Li+ and 9.6 kcal/mol for M+ = Na+. The
Additions and Corrections binding affinities for N2 are smaller than those for CO and are 11.8 kcal/mol for M+ = Li+ and 7.4 kcal/mol for M+ = Na+. Registry No. Li', 17341-24-1; Na+, 17341-25-2; H,, 1333-74-0; N2, 7727-37-9; co, 630-08-0; LiH2+, 12281-02-6; NaH2+, 12664-45-8; LiN2+,38682-57-4; NaN2+,38682-60-9; LiOC+, 97664-93-2; LiCO+, 74551-73-8; NaOC', 97664-94-3; NaCO', 85625-87-2.
ADDITIONS AND CORRECTIONS 1987, Volume 91
Young Kee Kag, George Ngmethy, and Harold A. %beraga*: Free Energies of Hydration of Solute Molecules. 1. Improvement of the Hydration Shell Model by Exact Computations of Overlapping Volumes. Page 4108. Insert after the first paragraph in the left-hand column: It may happen that some pairs of the volume segments or, VI', us, vi, ut, or u,' in Figure 3 overlap each other, instead of being located next to each other, as shown in the figure. This occurs when the plane of intersection of two spheres does not lie between the centers of the two spheres. Whenever this happens, one of the volume segments u, or u,' in eq 16 must be subtracted rather than added. If the term to be subtracted is u,, then the following changes must also be made: in eq 20, 6, is replaced by xr - Or and 4, is replaced by a - +,, and in eq 29, X, - 6, is replaced by X, - 6 , - a. Analogous changes must be made if the term to be subtracted is u;. While these changes were not mentioned explicitly in the paper, the computer program used in the calculations of the free energies of hydration in the paper and in the two accompanying papers (ref 28 and 29) takes proper account of any such changes.
