J . Phys. Chem. 1988, 92, 2134-2136
2134
Absolute Proton Afflnltles of Li,, Na,, LIH, and NaH David A. Dixon,* Central Research & Development Department, Experimental Station, E. I . du Pont de Nemours & Company,' Wilmington, Delaware 19898
James L. Gole, 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: August 17, 1987)
The proton affinities of LiH, NaH, Liz, and Na2 have been calculated by ab initio molecular orbital theory with extended basis sets. Geometries were gradient optimized, and force fields were calculated at the SCF level. Correlation corrections were calculated at the CI-SD level for the valence electrons. The proton affinities are calculated to be 244.2, 261.8, 277.8, and 274.1 kcal/mol for LiH, NaH, Li2, and Na2. The Li+ affinity of LiH is calculated to be 56.4 kcal/mol, and the Na' affinity of NaH is calculated to be 49.7 kcal/mol.
Introduction The proton affinity of a molecule represents an important, fundamental, gas-phase thermodynamic property. With the recent advances in computer technology and software, it is now possible to calculate this thermodynamic property within the accuracy of experimental measurements.' This is especially true for absolute proton affinities, which are extremely difficult to measure experimentally. We have been interested in the calculation of proton affinitiesZand the properties of small metal cluster^.^ In this paper we report the proton affinities of LiH, NaH, Li2, and Na2. The proton affinities of these small systems are very large, in the range 240-280 kcal/mol. The Li' affinity of LiH and Na+ affinity of N a H are also presented.
TABLE I: Geometries and Vibrational Properties of Diatomics and Protonated Diatomics molecule bond dist," A Y,O cm" I, km/mol
Method The proton affinity, PA, of a molecule B is defined as -AH(eq
Rather large basis sets are required to accurately calculate proton affinities. We have employed the same basis sets used in our previous study of the binding of Li' and Na' to H2.I0 The
1)
B
+ H+
-
BH+
(1)
The expression for evaluating PA(B) is given by (2)l,where AEoels PA(B) = - A H ( q 1) = -AEoelec- A(ZPE)
+ AEvib(T) + ( 5 / 2 ) R T (2)
is the electronic energy difference between reactants and products at 0 K and A(ZPE) is the difference in zero-point energies of B and BH'. The term AEvib(T)corrects for the change in the population of vibrational levels as a function of temperature; we set A&,( T ) = 0. The final term includes the translational and rotational energy changes assuming classical behavior and a AnRT term required to convert an energy to an enthalpy assuming ideal gas behavior. This final (5/2)RTterm becomes 2RT if B is linear and BH+ is bent. The geometries for B and BH+ were determined with the program GRADSCF"using gradient methods5 at the S C F level. The force fields were determined at the SCF geometries using analytic second derivative techniques6 as was an MP-2 correlation energy correction.' These calculations were also done with GRADSCF. Configuration interaction calculations including all single and double excitations, CI-SD,from the valence orbitals were performed at the optimum S C F geometries. Since there are only two valence electrons, these are full-CI calculations in the valence space. The CI-SD calculations were done with the GUGA formalism' implemented in the program H O N D O . ~ 'Contribution No. 4484.
0022-3654/88/2092-2134$01.50/0
LiH NaH Li, Na2 Li2H+
1.623 (1.596) 1.912 (1.887) 2.790 (2.673) 3.221 (3.079) 1.68
Na,H+
2.00
1404 (1406) 1172 (1189) 340 (351) 152 (159) 380 423 (ug+) 1645 (a, ) 205 )',u( 339 (Tu) 1372 (uu+)
(q
257 333 0 0 988 0 560 0 1064 586
Experimental values in parentheses from ref 15.
(1) Dixon, D. A.; Lias, S. G. In Molecular Structure and Energetics; Liebman, J. F., Greenberg, A., Eds.; VCH: Deerfield Beach FL, 1987; Vol. 2 p 269. (2) (a) Kraemer, 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, K.; Ellenberger, M. R.; Dixon, D. A,; Marynick, D. S. J . Phys. Chem. 1980,84,2840. (3) (a) Ricbtsmeier, S.C.; Eades, R. A.; Dixon, D. A,; Gole, J. L. In Metal Bonding and Interactions in High Temperature Systems; ACS Symposium Series 179: Gole, J. L., Stwalley, W. C., Ed. American Chemical Society: Washington, D.C., 1982, p 177. (b) Eades, R. A,; Hendewerk, M. C.; Frey, R.; Dixon, D. A,; Gole, J. L. J. Chem. Phys. 1982,76,3075. (c) Partridge, H.; Dixon, D. A,; Walch, S.P.; Bauschlicher, C. W., Jr.; Gole, J. L. J. Chem. Phys. 1983,79,1859. (d) Richtsmeier, S. C.; Jagger, T.; Gole, J. L.; Dixon, D. A. Chem. Phys. Lett. 1985,117,274. (4) GRADSCF is an ab initio gradient program system designed and written by A. Komornicki at Polyatomics Research. ( 5 ) (a) Komomicki, A,; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977,45,595. McIver, J. W., Jr.; Komornicki, A. Ibid 1971,10, 303. (b) Pulay, P. In Applications of Electronic Structure Theory: Schaefer, H. F., 111, Ed.; Plenum: New York, 1977, p 153. (6) King, H. F.; Komornicki, A. In Geometrical Deriuatiues of Energy Surfaces and Molecular Properties, Jorgenson, P., Simons, J., Eds.; NATO ASISeries C.; Reidel: Dordrecht, The Netherlands, 1986; Vol. 166, p 207. King, H. F.; Komornicki, A. J . Chem. Phys. 1986,84, 5645. (7) (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,No. 10, 1. (8) (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., I11 Phys. Scr. 1980,21, 312. (9) (a) Dupuis, M.; Rys, J.; King, H. F. J . Chem. Phys. 1976,6J,111. (b) King, H. F.; Dupuis, M.; Rys, J. National Resource for Computer Chemistry Software Catalog, University of California-Berkeley: Berkeley, CA, 1980; Val. 1, Program Q H 0 2 (HONDO).
0 1988 American Chemical Society
Absolute Proton Affinities of Liz, Na,, LiH, and N a H TABLE 11: Total Energies (EH)" for Diatomics and Protonated Diatomics molecule
LiH NaH Liz Na2 LiH2+ NaH2+
Li2H+b Na2H+C
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2135 TABLE 111: Energetic Quantities for Calculating Proton Affinities" AEOelc
E(SCF)
E(CU
E(MP-2)
AEoela
molecule
(SCF)
(CI-SD)
(MP-2)
A(ZPE)
-7.984 145 -162.379 987 -14.870727 -323.692 564 -8.377 535 -162.802481 -15.311 475 -324.125 619
-8.018 350 -162.415 256 -14.899 142 -323.720235 -8.415091 -162.840 106 -15.345255 -324.159413
-8.009 177 -162.405 472 -14.888047 -323.709 331 -8.407 103 -162.832 109 -15.336777 -324.150737
LiH NaH
246.9 265.1 276.6 271.7
249.0 266.6 279.9 275.6
249.7 267.7 281.6 277.0
6.0 6.0
"EH= 1 hartree = 1 au. bE(SCF) = -7.236211 for Li+. CE(SCF) = -161.664909 for Na'.
hydrogen basis set is triple augmented by two sets of p functions with exponents of 1.4 and 0.35 giving a basis set of the form (Ss2p)/[3s2p]. The s basis set for Li is from Gerber and Schumacher," the p portion is from Dunning and Hay,I3 and the d function is a two-term Gaussian fit with an effective Slater exponent of 1.5. The final lithium basis set has the form (lls4p2d)/[5s2pld). The s and p basis set of McLean and ChandlerI4 for Na is augmented by a single d function determined from a two-term Gaussian fit with an effective Slater exponent of 1.1. The final sodium basis set has the form (13s9p2d)/ [6sSpld].
Results Geometries. The bond distances for the diatomics considered in this study are given in Table I. The calculated distances are longer than the experimental values,15 where the errors for the hydrides are small, (0.03 A, and the errors for the diatomic metals are larger, >Oslo A. The elongated bonds calculated for the dimers result primarily from the neglect of corrrelation corrections. Previous studies on Na2 have shown that inner shell-valence shell correlation corrections account for most of the bond shortening.16 The structures of LiH2+ and NaH2+ have previously been calculated.I0 The optimum structures were found to have C2, symmetry and to resemble an alkali-metal ion weakly bonded to H,. In Li2H+ and Na2H+, we find that the proton inserts into the alkali-metal diatomic bond, giving a linear Dmhstructure, M-H-M+. The M-H bond distances in M2H+ (Table I) are only slightly elongated as compared to those of the diatomic MH. For Li2H+,the elongation is 0.06 A whereas for Na2H+,it is 0.09 A. The linear structures found for M,H+ seem surprising since it is well-known that M3+ with M = H or an alkali metal is an equilateral triangle. The Mulliken charges suggest that the structure of Li2H+ is best described as Li'+-Hl--Lil+. Since the charge in M2H+is no longer distributed equally on all of the atoms as in M3+,electrostatic repulsions between the positively charged end atoms dominate to make the ion linear. Vibrational Spectra. The frequencies and infrared intensities of the molecular vibrations of several of the molecules considered in this study are given in Table I, whereas those for LiH2+and NaH2+ have been previously reported.I0 For the diatomics, the agreement with the observed freq~encies'~ is very good; all of the observed frequencies are found to be larger than the calculated values. This is in contrast to the usual observations at the S C F level where the calculated frequencies are greater than those observed and occur because the calculated bond lengths are too long. The infrared intensities for the polar LiH and N a H molecules are predicted to be quite intense. The lowest frequency for Li2H+ corresponds to the bending mode, with the symmetric stretch -40 cm-' higher. The asym(10) Dixon, D. A,; Gole, J. L.; Komornicki, A. J . Phys. Chem., in press. (11) Dunning, T. H., Jr. J. Chem. Phys. 1971, 55, 716. (12) Gerber, W. H.; Schumacher, E. J . Chem. Phys. 1978, 69, 1692. (13) Dunning, T. H., Jr.; Hay, P. J. In Methods of Electronic Structure Theory; Schaefer, H. F., 111, Ed.; Plenum: New York, 1977, p. 1. (14) McLean, A. D.; Chandler, G. S. J . Chem. Phys. 1980, 7 2 , 5639. (15) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (16) Partridge, H.; Bauschlicher, C. W.; Walch, S. P.; Liu, B. J . Chem. Phys. 1983, 79, 1866.
Li, Na2
AEOeI,
3.6 3.0
AH,, 244.2 261.8 277.8 274.1
'All energies in kcal/mol.
TABLE I V Energetic Quantities for Calculating Alkali-Metal Ion Affinities of LiH and NaH" enerw
LiH (Li')
NaH (Na')
AE0e,,(SCF) AEO,,,(CI-SD) AEO elc ( MP-2) A(ZPE) - A H 3 , = AIA
57.2 56.9 57.3 2.0 56.4
50.7 49.1 50.4 1.5 49.7
values in kcal/mol.
metric stretch is at a much higher frequency, -240 cm-I above that for diatomic LiH. The infrared active frequencies are predicted to be very intense, consistent with the large charge separation in the ion described above. Because of the degeneracy factor, the bend intensity is almost 2 times that of the asymmetric stretch. For Na2H+, the bend and symmetric stretch frequencies are reversed in order when compared to Li2H+. The symmetric stretch is very low in frequency, approximately half of the value in Li2H+, whereas the bend in NazH+ has only decreased by 40 cm-I with respect to Li2H+. The asymmetric stretch is again found to be 200 cm-' above the stretching frequency of isolated NaH. The infrared intensities in Na2H+are slightly increased relative to those in Li2H+although the charge separation in Na2H+ according to the Mulliken analysis, is not as great, Na0.8+-Ho.6--Na0 *+. Energetics. Total energies are given in Table 11, whereas the energetic quantities required to calculate proton affinities from (2) are given in Table 111. We consider first the effects of correlation on AEoclcc.The correlation corrections always lead to an increase in the proton affinity at the CI-SD level with the largest correction being 3.9 kcal/mol for Na2 and the smallest 1.4 kcal/mol for NaH. The MP-2 corrections consistently overestimate the effects of electron correlation where compared to the complete CI-SD results. The magnitudes of the proton affinities that we calculate in this study are striking. These proton affinities are some of the largest known for a neutral molecu1e.I The proton affinities of the metal hydrides M H increase with increasing atomic number of M whereas the proton affinities of M2 decrease. The magnitude of the increase in the proton affinities for the hydrides is larger than the decrease in proton affinity for the homonuclear diatomics. From the total energies given in this work and the total energies of Li+ and Na+ previously determinedlo (Table 11), we can determine the Li+ affinity of LiH and the Na+ affinity of NaH. These values are given in Table IV. The alkali-metal ion binding affinities are also quite high.I0 For example, the Li+ affinity of H2 is 4.8 kcal/mol while the Na+ affinity is 2.8 kcal/mol. Somewhat higher values are found for CO, where the Li' affinity is 14.6 kcal/mol and the Na+ affinity is 9.6 kcal/mol.
Discussion A major component that determines the energetics is charge transfer from the proton to the metal hydride or dimer. The ionization potential of hydrogen is 13.6 eV, which is much larger than the ionization potentials of LiH, Li,, and Na2, which are 7.7, 5.1 1, and 4.89 eV, respectively." In our model, we consider the differences in the proton affinity of H, and those of M H or M2. The proton affinity of H2 is 101.4 kcal/mol, and the charge is (17) (a) Lias, S. G.; Bartmess, J. E.; Homes,J. L.; Levin, R. D.; Liebman, J. F. J . Phys. Chem. Re5 Data, in press. (b) Stwalley, W. C., private communication.
2136 The Journal of Physical Chemistry, Vol. 92, No. 8. 1988 TABLE V Heats of Formation of MH,+ and M,H+" molecule A H ~ OPA)^ AHfo(AIA)c LiH,+ 154.8 157.6 NaH2* 138.7 141.3 Li2H+ 139.3 139.3 Na,H+ 126.4 129.2 AHfo in kcal/mol. bCalculated from proton affinity. CCalculated from alkali-metal ion affinity.
equally shared among the hydrogens. We can now compare the proton affinity of H2with those for the metal hydrides and dimers. The proton affinities for LiH, NaH, Li,, and Na2 are greater than PA(H,) by 142.8, 160.4, 176.4, and 172.7 kcal/mol, respectively. The ionization potentials for LiH, Li,, and Na2 are lower than the ionization potential of H2by 136.0, 195.8, and 200.8 kcal/mol, respectively. If we compare the ionization potential differences with the proton affinity differences, we note that charge transfer is the dominant effect leading to the large values for the proton affinities. Thus, to a crude approximation, the proton affinities of M H or M2 can be described by PA(MH or M,) = PA(H2)
+ IP(H) - IP(MH or M2)
(3)
From the known heats of formation" and the proton or alkali-metal ion (AIA) affinities we can calculate the heats of formation of the protonated species from MH M2
- - -
+ H+
+ H+
-PA
-PA
MH2+
M2H+
-AIA
-AIA
H 2 + M+
(4a)
+ M+
(4b)
MH
These values are given in Table V. The agreement between the two sets of values is reasonable but, considering the quality of the calculations, better agreement would have been expected. Almost exact agreement is found for AHf"(Li2H+) determined from the two methods. For the remaining three ions, the AHHp's determined from the metal ion affinities are 2-3 kcal/mol higher in energy. The AHf"%determined by the two methods allow us to estimate the errors in the heats of formation as 1.5 kcal/mol. The errors in the proton and alkali-metal ion affinities are of the same size or smaller consistent with previous calculations of proton affinities.l,, The errors in the affinities are most likely due to deficiencies in the basis sets. Errors in the geometries lead to small corrections of
