J . Phys. Chem. 1992,96,7971-7975 (57) Meyer, W. J . Chem. Phys. 1973, 58, 1017. (58) Diercksen, G.H. F.; Sadlej, A. J. Theor. Chim. Acta 1983, 63, 69. (59) Mulder, F.; van der Avoird, A. D.; Wormer, P. E. S . Mol. Phys. 1979, 37, 159. (60) Amos, R. D. Chem. Phys. Lett. 1986, 124, 376. (61) Moskowitz. J. W.: Harrison. M. C. J. Chem. Phvs. 1965.43. 3500. (62j Verhoeven,’J.; Dynamus, A.’ J. Chem. Phys. 19i0, 52, 3222: (63) Murphy, W. F. J. Chem. Phys. 1977,67, 5877. (64) McClcllan, A. L. Tables of experimental dipoles moments, Vol. 1; W. H. Freeman: San Francisco and London, 1963. (65) Ermler, W. C.; Kern, C. W. J. Chem. Phys. 1974,61, 3860. (66) Bartlett, R. J. Annu. Rev. Phys. Chem. 1981, 32, 359. (67) Bartlett, R. J. Comparison of ab Initio Quantum Chemistry with Experiment for Small Molecules; Reidel: Dordrtcht, 1985. (68) Schaefer, H. F., I11 Methods of electronic structures theory; Plenum: New York, 1977. (69) For further details see: Szabo, A.; Ostlund, N. S. In Modern Quantum Chemistry: Introduction io Advanced Electronic Structure Theory: MacMillan Publishing Co.: New York, 1982. (70) For further details scc: Robb, M. A. In Computational Techniques in Quantum Chemistry and Molecular Physics; Diercksen, G.H. F., Suttcliffe, B. T., Veillard, A,, Us.; Reidel: Boston, MA, 1975. (71) Ciszek, J. J . Chem. Phys. 1966, 45,4256. (72) For further details scc Bartlett, R. J. J. Phys. Chem. 1989,93, 1697. (73) Brucckner, K. A. Phys. Rev. 1955, 97, 1353. (74) Pople, J. A,; Head-Gordon, M.; Raghavachari, K. J . Chem. Phys. 1987, 87, 5968. (75) Herzbcrg, G. Infrared and Raman Spectra of Polyatomic Molecules; D. van Nostrand Co.: New York, 1945. (76) Pople, J. A.; Seeger, R.; Krishnan, R. Int. J. Quantum Chem. Symp. 1977, 11, 149. 1771 Bloor. J. E. J. Mol. Srruct. I T H E X H E M 1991. 234. 173. (78) Zeiss,’G. D.; Scott, W. R.; Suzuki, N.; Chong, D.’P.; Langhoff, S. R. Mol. Phys. 1979, 37. 1543. (79) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2657. (80) Hehre, W. J.; Ditchfield, R.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1970, 52, 2769. (81) Pietro, W. J.; Levi, B. A.; Hehre, W. J.; Stewart, R. F. Inorg. Chem. 1980, 19,2225. (82) Pietro, W. J.; Blurock, E. S.;Hout, R. S.;Hehre, W. J.; DeFrees, D. J.; Stewart, R. F. Inorg. Chem. 1981, 20, 3650.
7971
(83) Pietro, W. J.; Hehre, W. J. J. Comput. Chem. 1983, 4, 241. (84) Way, P.; Fogarasi, G.; Pang, F.; Bogg, J. E. J. Am. Chem. SOC.179, 101, 2550. (85) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J. Am. Chem. SOC.1980, 102, 939. (86) Gordon, M.S.;Binkley, J. S.; Pople, J. A,; Pietro, W. J.; Hehre, W. J. J. Am. Chem. Soc. 1982, 104, 2797. (87) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J. Chem. Phys. 1971, 54, 724. ( 8 8 ) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Shaefer, H. F., 111, Ed.; Plenum: New York, 1977. (89) Amos, R. D.; Gaw, J. F.; Handy, N. C.; Carter, S . J . Chem. Soc., Faraday Trans. 2 1988,84, 1247. (90) DeFrees, D. J.; Levi, B. A.; Pollack, S. K.; Hehre, W. J.; Binkley, J. S.;Pople, J. A. J. Am. Chem. Soc. 1979, 101, 4085. (91) Schlegel, H. B. J. Comput. Chem. 1982, 3, 214. (92) Fletcher, R.; Powell, M. J. D. Comput. J. 1963, 6, 163. (93) Billingsley, F. P., 11; Krauss, M. J . Chem. Phys. 1974, 60, 4130. (94) Silco, R. N.; Cool, T. A. J. Chem. Phys. 1976,65, 117. (95) Waclawek, W.; Hurvic, J. Rocz. Chem. 1965, 39, 1509. (96) Takaji, K.; Kojima, T. J. Phys. Soc. Jpn. 1971, 30, 1145. (97) Blukis, U.; Kasai, P. H.; Myers, R. J. J. Chem. Phys. 1%3,38,2753. (98) Krisher, L. C.; Saegebarth, E. J. Chem. Phys. 1971, 54,4553. (99) Kurland, R. J.; Wilson, E. B., Jr. J . Chem. Phys. 1957, 27, 585. (100) Meighan, R. M., Diss. Abstr. 1965, 25, 4427. (101) Kolos, W.; Wolniewicz, L. J. Chem. Phys. 1967, 46, 1426. (102) Bridge, N. J.; Buckingham, A. D. Proc. R. Soc. London l966,295A, 334. (103) Mtinter, J. S . J . Chem. Phys. 1972, 56, 5409. (104) Albasiny, E. L.; Cooper, J. R. A. Proc. Phys. Soc. 1963.82, 289. (105) Applequist, J.; Karl, J. R.; Fung, K. K. J. Am. Chem. Soc. 1972, 94, 2952. (106) Ramaswamy, K. L. Proc. Indian Acad. Sci. 1936, A4,675. Stuart, H. A. Z . Phys. 1930.63, 533. (107) Metzger, R. M.; Rhee, C. H. Mol. Crysr. Liq. Crysr. 1982,85, 81. (108) Maryott, A. A.; Buckley, F. Natl. Bur. Stand. Circ. 1953, No. 537. (109) Aroney, M. J.; LeFevre, R. J. W.; Singh, A. N. J. Chem. Soc. 1965, 3179. (110) d’Alelio, G.F.; Reid, E. E. J . Am. Chem. Soc. 1937, 59, 109. (1 11) van Eijck, B. P.; van Ophdeusen, J.; van Schaik, M. M.M.; van Zoeren, E. J. Mol. Spectrosc. 1981, 86, 465.
Fundamental Aspects of Lithlum Ion Transfer Xiaofeng Duan and Steve Scheiner* Department of Chemistry & Biochemistry, Southern Illinois University, Carbondale, Illinois 62901 (Received: May 4, 1992)
The transfer of the Li+ ion from one water molecule to another is studied in (H20-Li-OH2)+ by ab initio calculations, and the results are compared with analogousproton transfer in (H20-H-OH2)+. In both cases,the equilibrium geometry contains a centrally located Li or H ion, although R(0-0) is considerably longer in (H20-Li-OH2)+. Only a small stretch of the H bond is needed to yield a double-well potential, whereas the barrier does not appear in the Li potential until R(O-0) has been stretched by 1 A. The Li-transfer barrier rises much more gradually with further intermolecular stretch than in the case of the proton. Similarly, the Li barrier is less sensitive to angular deformations. Whereas the proton-transfer barrier is enlarged monotonically with each addition to the basis set, the behavior of the Li analogue relates instead to the dipole moment calculated for the water monomer. Many of these discrepancies can be understood on the basis of the highly ionic nature of the Li bond.
Introduction
In comparison to the volumes of data and interpretation that have built up over the years concerning the hydrogen bond,’-3 the analogous lithium bond remains largely unexplored. An interaction of this type was first observed in 19754using spectroscopic measurements of LiCl and LiBr combined with nitrogen bases in matrix isolation. The Li-X stretching frequency was found to shift in a direction similar to that observed in H bonds but by a much smaller amount. Another parallel was drawn to the possibility that the bridging Li, like the proton in a H bond, is capable of transferring from one group to the other. This pos-
sibility was indicated by a minimum in the curve which plots the relative frequency change vs a normalized difference in proton affinity of the two group^.^ Recent years have seen a rapid accumulation of insights into proton transfer from both experimental and theoretical perspect i v e ~ . ~It. ~has been learned, for example, that the barrier to transfer rises very quickly as the H bond is elongated and that angular deformations from linearity can produce not only increases in the transfer barrier but also strong perturbations in the relative energies of the two minima in the transfer potential?J Systematic ab initio calculations have revealed the sorts of errors likely to
0022-365419212096-7971$03.00/0 0 1992 American Chemical Society
7972 The Journal of Physical Chemistry, Vol. 96, No. 20, 1992
Duan and Scheiner
TABLE I: SCF Geometry and Dipole Moment of the H20-Li+ Complex' P, cr(H20), r(Li-O), r(O-H), WiOH), A deg D D A 4-31G 6-31GS 6-311G* 6-311+GS* a C*,
1.8158 1.8585 1.8323 1.8449
0.9558 0.9540 0.9447 0.9477
124.8 126.8 126.2 126.8
3.792 4.125 3.954 4.126
2.542 2.150 2.310 2.170
Z = H'
n
symmetry.
be incurred in the potential by various deficiencies in the basis set or by partial treatments of electron correlation.' Very little is known about the possibility of a Li+ ion transferring between two subunits. Szozcsniak et d.'O concluded that a transfer from LiCl to any of a number of amines was unlikely, based upon their calculations with a small basis set. This observation is not unexpected since the transfer would lead from a neutral pair to an ion pair, highly unfavorable in the gas phase; similar effects are valid for proton transfers as A simultaneous transfer of bridging H and Li centers in the conversion of H2NLi-OH2 to H,N.-LiOH seems feasibleI2since, again, there is little charge separation generated. In contrast, the transfer of H+ or Li+ between two neutral molecules as in (H20-H-OH2)+ provides a better testing ground since the complex is of ion-neutral type regardless of whether the H+ is more closely associated with the molecule on the left or the right. In part, for this reason, (H20-*H-.0H2)+ has been a prototype system for investigating the fundamentals of the proton-transfer p r o c e ~ s . ' ~ JThe ~ present work focuses on the Libonded analogue in which the central hydrogen is replaced by lithium. Direct comparison of the two complexes affords a consistent basis on which to draw conclusions about the source of any differences observed.
Computational Details The GAUSSIAN-R set of ab initio computer codes15was employed to carry out all calculations. Four basis sets were applied in this work. The smallest one, 4-31G,I6 is of split-valence type. 6-31G*I7 is similar but involves polarization functions of d type on the 0 and Li centers. Two triplevalence sets, 6-311G* and 6-31l+G**, were also considered.I8 The latter adds p-type polarization functions to hydrogen atoms as well as s and p diffuse functions on the other atoms. Electron correlation was evaluated via Mdler-Plesset (MP) perturbation theory to the second and third orders.I9 Structure and Energetics of (H20-Li-OH2)+
The complex of Li+ with a single water can be thought of as a building block of (H20-Li-OH2)+, making its study a useful prerequisite to examination of the full complex. The geometry of (H20-Li)+ was fully optimized, and the resulting details of its structure are summarized in Table I. The first column indicates a fairly long 0-Li bond, about 0.8-A longer than the 0 - H bond in (H@-H)+. This distinction is consistent with the larger size of Li and the weaker nature of the former bond which will be discussed in more detail below. Also listed in Table I are the dipole moments of both the (H20-Li)+ complex and the neutral water molecule, computed with each basis set. The geometry of (H20-Li-OH2)+ was fully optimized with all the basis sets mentioned at the SCF, MP2, and MP3 levels. As shown in Figure 1, this complex adopts a D u structure in which the two water molecules are planar and staggered with respect to one another. (An eclipsed planar structure has negligibly higher energy than the staggered one: 0.23 kcal/mol with 6-31G*. Frequency calculations verify it is not a real minimum but a transition state through which the two HOH groups rotate nearly freely around the 0-0 axis.) In comparison, the arrangements around the oxygen atoms are pyramidal in (H20-H-OH2)+, as illustrated also in Figure 1?* In either case, the bridging Z atom (Li or H) is located at the midpoint of the 0-0 axis. This central position is consistent also with the case where the donor and acceptor groups are both anions, viz., OH-, NH,, or CH3-, and
W
Z=LP Figure 1. Geometries of (H20-Z-OH2)+, Z = H, Li. The HOH bisectors make an angle of some 120' with the 0-0 axis when Z = H and 180' for Z = Li for which the two HOH units are staggered, Le., 4(HOOH) = 90°.
TABLE II: Geometry and E n e m of the (H&-LI-H,O)+ r(Li-O), r(H-01, B(LiOH), 4-31G
SCF MP2 MP3
6-31G*
SCF MP2 MP3
6-311GS
SCF
MP2 6-31 1+G** SCF MP2
Complex
A
A
del3
E, au
1.8393 1.8515 1.8519 1.8838 1.8806 1.8937 1.8596 1.8588 1.8729 1.8820
0.9545 0.9764 0.9735 0.9530 0.9738 0.97 15 0.9437 0.9605 0.9466 0.9633
124.6 125.1 125.1 126.7 127.2 127.1 126.1 126.2 126.7 127.5
-159.194 14 -1 59.454 22 -1 59.455 65 -159.375 86 -159.761 55 -159.76485 -1 59.425 13 -159.88908 -1 59.45096 -159.94422
TABLE III: Atomic Charge and Mulliken Overlap Population of the (H20-Z-OH2)+ Complex" overlap atomic charge population Z Z 0 H, Z.s.0 O*-*H, Li+ 0.903 -0,985 0.517 0.038 0.259
H+
0.662
-0.919
0.544
0.104
0.253
'Calculated with the 6-31 lG* basis set.
the overall complex has a negative charge, e.g., (HO-Li-NHJ-.20 Calculations of a similar type were carried out also for the analogous (H3N-Li-NH3)+ complex where each water molecule is substituted by ammonia. Here, too, the Li center adopts a central position, midway between the two N atoms. The two q u a l r(Li-N) distances are consistently longer than the r(Li-O) distances in (H20-Li-OH2)+ by about 0.015 A at all levels of theory. An important distinction between the two complexes is the r ( Z - 0 ) separation, which is some 1.2 A in (H20-H-OH2)+ but 1.9 A in (H20-Li-OH2)+, as indicated in Table 11. While the former represents a stretch of some 0.2 A as compared to the (H20-H)+ monomer, comparison of Tables I and I1 indicates very little perturbation of the CbLi bond length of (H20-Li)+ upon complexation with a second water molecule. Correlation seems to exert only a minor influence upon the geometries of these complexes with lithium, as judged by comparison of SCF and MPn entries in Table 11. Previous work has provided a number of strong indications that the Li bond is considerably more ionic than is the H bond.10*21-23 This distinction is apt to be especially true in the case of a system with an overall positive charge, like those considered here. One verification of the higher degree of ionic character comes from a Mulliken analysis of the 6-31 1G* wave functions, reported in Table 111. The charge computed for the Li center in (H20Li-OH2)+ is 0.903, notably higher than the 0.662 charge on the proton in (H20-H-OH2)+.Also of note is the much lower overlap population between the central atom and the oxygens in the case of Li, indicating weaker covalent character in the bond. A second window into the comparative natures of the bonding is via the interaction energies. We define E l as the complexation
The Journal of Physical Chemistry, Vol. 96, No. 20, 1992 1913
Fundamental Aspects of Lithium Ion Transfer TABLE I V First rad Second Bood Energiesa (kcrl/mol) of
(Ht+Li-OHdt El
4-31G
HF MP2 MP3
6-31G*
HF MP2 MP3
6-31 lG*
HF MP2 MP3
6-311+G**
HF MP2 MP3
-
47.85 (183.2)b 48.97 48.24 39.55 (173.1) 41.62 40.99 41.62 (176.9) 43.68 43.07 36.40 (174.0) 35.57 35.75
E2 42.25 (42.66)b 43.63 42.98 35.01 (33.50) 37.44 36.87 36.50 (32.72) 39.26 38.69 31.69 (30.77) 31.71 31.89
-
TABLE V Energy Barritr for Litbium Transfer (kcrl/mol) R = 4.6 A R = 5.0 A R = 5.4 A R 4-31G SCF 0.09 2.72 6.85 MP2 0.01 1.91 5.84 MP3 0.01 2.06 6.08 6-31G* SCF 0.00 1.61 4.83 MP2 0.00 1.06 4.22 0.00 1.20 4.42 MP3 6-311G* SCF 0.02 1.98 5.40 MP2 -0.03 1.59 5.06 MP3 -0.01 1.80 5.35 6-311+G** SCF 0.02 1.78 4.87 MP2 -0.03 1.24 4.1 1 MP3 -0.01 1.47 4.46
= 5.8 A 11.19 10.25 10.40 8.27 7.87 8.06 9.04 8.89 9.18 8.15 7.31 1.73
a well on either side. As an example, the transfer potentials for the case of R(O*-O)= 5.4 A are displayed in Figure 2 at three levels of theory for the largest basis set considered here, 6placed by H. 311+G**. One may note that the potential has double-well character at each level of theory. The minima occur at nearly the exact same r(0-Li) distance in each case, 1.9 and 3.4 A. The only significant difference is that the SCF barrier is slightly higher 5 than the correlated MP2 and MP3 values. Table V reports the Li+-transfer barriers computed for a set of different R ( 0 - 0 ) distances and with various combinations of basis set and correlation for each. As in the case of proton transfers? MP2 barriers are smaller than SCF values, with MP3 in between these two extremes (but closer to MP2). Also like 2 the H+ case,the barrier rises as the intersxygen distance increases. On the other hand, the sensitivity of barrier to intermolecular W1 stretch is much weaker for Li+. Taking the MP3/6-311+G** barriers as an example, a 0.4-A stretch from 5.0 to 5.4 A raises the barrier by 3 kcal/mol. In contrast, a recent computation of the H analoguegaindicated a larger 6 kcal/mol increase in the - 1 1.5 2.0 2.5 3.0 3.5 4.0 proton-transfer barrier as a result of only a 0.16-A stretch of R(O--O). A perhaps more dramatic comparison arises from a r(O-Li), 1.2-A stretch. At the SCF/6-311G* level, the Li+-transfer barrier Flgum 2. Li-transfer potentials computed with the 6-31 1+G** basis set increases by 9 kcal/mol when R(O-0) is stretched from 4.6 to for (H20-Li-OH2)+with R ( 0 - 0 ) = 5.4 A. Energy scale is relative to 5.8 A. In contrast, the 1.2-A stretch in the H+ case from 2.5 to the lowest point in each minimum. 3.7 A raises the barrier by over 60 kcal/mol. While the magnitudes of the barrier increases are indeed smaller energy of Li+ (or H+) with a single water molecule, while E2 refers for Li+ as compared to proton transfer, the O-Li+ bond strength to the interaction energy of the first-formed (H20-Z)+ complex is considerably weaker than in the case of O-.H+. Taking the with a second water. Table IV lists the values of these quantities HF level 4-3 1G calculations as an example, Table IV reveals that calculated at several levels of theory for the Li+ ion. It may be the diasociation energy of H20-Li+ is 47.85 kcal/mol, as compared fvst noted that these energies are fairly insensitive to correlation. to 183.2 kcal/mol for H20-H+. When related to this standard, Despite a good deal of dependence upon the basis set, one aspect the energy bamer increases for the Li+ and proton transfers are of these data stands out: E , and E2 are surprisingly similar to comparable. More specifically, when R ( 0 - 0 ) of the (H2& one another. The binding energy of a second water is only 4-5 Li-OH2)+ system is stretched by 0.4 A from 5.0 to 5.4 A, the kcal/mol smaller than the interaction energy of the first water HF/4-31G barrier climbs by 4.13 kcal/mol, which is 8.6%of the with a naked Li+ ion. The contrast with the proton is striking original O-.Li+ bond strength. A stretch of similar magnitude in that the first binding energy is some 4 or 5 times larger than for (H20-H-OH2)+ from 2.55 to 2.95 A raises the barrier by 15.4 Et. The similarity of the two quantities in the case of Li+ argues kcal/mol, which is 8.4%of El for H20-H+. One can carry the for the highly elcctmstatic nature of these complexes as compared percentage analysis one step further by considering also the bond to the proton where the very large value of El is due to formation stretch. The 0.4-A stretch used in the example above represents of a strong covalent bond. As another indication that the theo11% of the optimized R ( 0 - 0 ) in (H20-Li-OH2)+ but 17% for retical methods are appropriate to this problem, our m a t reliable (H20-H-OH2)+. From this perspective, the quotient of the estimate of the Li+ binding enthalpy of water, 34.8 kcal/mol, percentage barrier increase divided by the percent bond stretch computed with the 6-3 11+G** basis set at the MP3 level, and is larger in (H20-Li-OH2)+ than in the H-bonded analogue. corrected for vibrational and translational effects, is in excellent agreement with the experimentalmeasurement of 34 k c a l / m ~ l . ~ ~ Previous work has demonstrated that the proton-transfer bamer in (H20-H-OH2)+, as well as a number of similar complexes, Eaergy M e r for Lithium Tranefer rises with each increment in the size and flexibility of the basis As indicated above, the equilibrium R O-*O) distance of the set being a ~ p l i e d .The ~ situation is rather different in the case (H20-Li-OH2)+ complex is about 3.7 and has the lithium of Li. As is evident from Table V,the largest barriers of all are directly centered between the two 0 atoms. We now consider computed with the smallest basis set, 4-3 1G. Adding polarization the case where this inter-oxygen separation is stretched in order functions lowers the bamer, but it is aglain raised when the valence to consider how this affects the Li-transfer potential. For each part of the set is improved to 6-3 1 1G* and suffers another decrease intersxygen distance chosen, the internal geometries of the two upon addition of diffuse functions. water molecules were left as in the fully optimized structure: As illustrated in Figure 3, this oscillatory behavior is reproduced planar and staggered with respect to each other. by the computed dipole moment of the water monomer. These It was found that for all R(O.-O) distances less than 4.6 A, parallels may be understood on the basis of the highly electrostatic the transfer potential is of symmetric single-well type. For longer nature of the Li bond. The electrostatic interaction between the separations, a k m e r appears in the middle of the potential with charge on the Li+ ion and the dipole moment of neutral water ' E l : (H20-Li)+ H 2 0 + Li+. El: (H20-Li-OH2)+ (H20Li)+ + H20. *Value in parentheses refer to the case where Li is re-
A
1
7974 The Journal of Physical Chemistry, Vol. 96, No. 20, 1992
Duan and Scheiner
TABLE VI: Transfer Barrier (kcrl/mol) in Distorted Configurationswith tbe 6-311CSBasis Set
R = 4.6 A R = 5.4 A
I
a2
a, = O
SCF a1 = a2
a1 = -a2
al = 0
a l = a2
a I = -a2
al = 0
0.0 20.0 40.0 0.0 20.0 40.0
0.019 0.163 0.778 5.403 5.842 7.129
0.019 0.144 1.155 5.403 6.162 8.735
0.019 0.094 0.872 5.403 6.106 9.388
-0.025 0.044 0.602 5.064 5.566 6.896
-0.025 -0.025 0.703 5.064 5.855 8.446
-0.025 -0.038 0.452 5.064 5.792 8.848
-0,013 0.094 0.690 5.346 5.855 7.185
\
MP2
MP3 al = a2 -0.013 0.038 0.897 5.346 6.156 8.785
a1 = - a 2
-0.013 0.01 3 0.640 5.346 6.099 9.381
I .n. 2.3 3
7 d
8
6
2
5; (d
Y-
c
5
w 1 4 ‘
4-31G
I
6-31G*
6-311G’
6-311+G**
lines refer to the dipole moment computed for water, with its scale on the right.
Figure 4. Parameters used to define angular distortions in (H20-LiOH2)+. a,and a2refer to the angle between the O.-O axis and HOH bisector of Li donor and acceptor molecules, respectively. Both of these angles are positive in the example shown above.
resists pulling these two apart. Since the transfer barrier involves separating Li+ from water to some extent so as to reach the 0-0 midpoint, it is not surprising to see these barriers correlate so well with the dipole moment of water. The more covalent character of the 0-H bond endows the ion-dipole interaction with less relative importance in the case of proton transfers. The parallel basis set sensitivity of the Li+ affinities, reported as E l in Table IV, and the equilibrium r(0-Li) distances of the (H20-Li-OH2)+ complex in Table I1 reinforce the fundamental importance of the dipole moment of water in studying these processes. Angular Distortions. Previous calculations had revealed that the energy barrier for proton transfer is highly sensitive to angular distortions of the H bond.”J3Js The types of distortions considered are described in Figure 4 where either or both of the two water molecules may be turned such that their HOH bisectors make angles of al and a2with the 0-0internuclear axis. As was done previously for proton transfer, the Li was allowed to follow its lowest energy path between the two HOH molecules, keeping frozen the remainder of the geometry. Three modes of distortion were investigated. In the first case, the donor molecule was not distorted at all ( a l = 0). A second mode is conrotatory in the sense that both molecules are turned by equal amounts in the same direction (aI= a2). Misorientation in opposing directions comprises the disrotatory mode (aI= -a2). Transfer potentials were computed for R ( O 0 ) = 4.6 and 5.4 A. The effects of each sort of misorientation upon the lithiumtransfer barrier are reported in Table VI at the SCF and correlated levels. The small negative barriers refer to the situation where, at a correlated level, the midpoint geometry is actually slightly more stable than the end point, as optimized at the SCF level. The salient patterns are illustrated in Figure 5 where the solid curves make it evident that the barrier rises gradually if only one of the molecules is misoriented. The broken curves indicate that rotation of both molecules causes a somewhat larger barrier in-
I 40
a , degs
Figure 3. Li-transfer barriers in (H20-Li-OH2)+ with R(O-0) = 5.4
A, shown as solid lines and using the vertical scale on the left. Broken
I
I 20
2
Figure 5. Transfer barriers computed for bent configurations of (H20Li-OHJ+ at the SCF/6-311GS level.
crease,especially the disrotatory mode. Theae trends are consistent with what was observed earlier for proton transfer^.^^.^^ Just as noted above in the case of sensitivity to distance, the barriers rise much more gradually with angular distortion for Li+ as compared to proton transfer. Taking the al = -a2 mode with R = 4.6 A as an example, the barrier incream only 0.85 kcal/mol when the rotation angle changes from 0 to 40’. In contrast, the energy barrier of (H20-H-OH2)+ increases by about 14 kcal/mol for the same misorientation when R(O-0) = 2.55 A. A prime source of the lesser sensitivity of the Li transfer to angular distortion is the considerably longer Li bond. The equilibrium 0-0 distance is 3.7 A, but the barrier appears only for distances longer than 4.6 A. As a result, the inter-oxygen distances pertinent to Li transfers are 5 A or longer, while the separation is half this amount in the case of proton transfers. At these longer distances, the directionality of the 0-Z bond is weakened considerably. To illuminate this characteristic, calculations were performed on the simple H20-Z+ ion with r(0Z) distances typical of the systems being examined. Using the 63 11G+basis set, it was found that bending the proton of H20-H+ around by 40’ from the HOH bisector raises the energy of this ion by 30 kcal/mol for r = 1.275 A, which corresponds to the midpoint when R(O-0) = 2.55 A; the distortion energy is 26 kcal/mol when r = 1.475 A. In contrast, 40’ distortion angles in H20-Li+ result in much smaller destabilizations of leas than 10 kcal/mol for r(0Li) = 2.3 or 2.5 A; the midpoints of the R(O-0) = 4.6 and 5.0 A Li transfers. The greater sensitivity of the H interaction has been ascribed to the inclusion into the interaction of overlap effects which are largely absent for Li but which have strong directional depenThis assertion may be tested by comparing the results for H+ or Li+ to a positive point charge with neither orbitals nor electrons. As mentioned above, a 40’ distortion of the proton in H20-H+ raises the energy by 26-30 kcal/mol, depending upon the internuclear separation. When the proton is replaced by a point charge at the same distance from the water, the distortion energy for 40’ nonlinearity is reduced by 8-10 kcal/mol. Substitution of Li+ by a point charge, on the other hand, results in very little change in distortion energetics. This distinction between the proton and lithium cation supports the idea that there are overlap effects present for the former that are absent for the latter. The weaker dependence of the Li-transfer barrier to angular distortion may be understood also on the basis of electrostatics.
Fundamental Aspects of Lithium Ion Transfer A prime factor in the deformation energy of the H or Li bond arises from the weakening of the attractive force between an ion like H20-Z+ and the neutral H 2 0s u b ~ n i t . Lengthening ~ ~ ? ~ ~ their separation attenuates the magnitude of this force as well as its dependence upon misorientation. summary
There are a number of similarities between the H and Li bonds present in (H20-H-OH2)+ and (H20-Li-OH2)+, respectively. The fully optimized geometry of each contains a centrally located Z nucleus where Z = H, Li. In either case, as the two water molecules are separated from one another, the Z-transfer potential changes from a single- to a double-well function. The barrier separating the two minima is enlarged as the waters are further removed. Angular deformations of either type of bond away from linearity also raise the transfer barrier. In either case, the correlated barriers are lower than those computed at the SCF level. There are a number of important differences between the H+ and Li+ transfers. In the first place, the equilibrium R(O-0) distance is 3.7 A for (H20-Li4H2)+, which compares with only 2.4 A in (H20-H4H2)+. A barrier does not appear in the Li-transfer potential until the inter-oxygen distance has stretched by nearly 1 A from its equilibrium length. The increase in barrier height with further stretch is considerably more gradual than in the case of the proton transfer. The same is true with respect to the lesser sensitivity of the Li transfer barrier to imposed nonlinearities. These differences can be largely explained on the basis of the larger size of Li as compared to H and the more ionic character of the Li bond. Another significant distinction involves the variation in calculated barrier height with basis set. Whereas the proton-transfer barrier seems to increase monotonically with each increment in the basis set, the Li analogue is directly related instead to the magnitude of the dipole moment of the water molecule, another indication of the importance of electrostatics in Li bonding. It is unlikely that any of the central conclusions reported here will be changed appreciably by additions to the basis set or by an alternate means of including electron correlation. The highly electrostatic nature of the Li bond allows even moderate-sized basis sets to produce very reasonable quantitative results. For example, the Li+-transferbarriers computed here with the 4-31G basis set are only slightly higher than the 6-31 1+G** results. Correlation is not a major factor here. SCF barriers are generally only slightly larger than the values computed at the MP3 level. With regard to the M~ller-Plesset treatment of correlation, previous work has demonstrated its effectiveness in comparison to other approaches such as CI and coupled cluster9 when treating proton transfers.
Acknowledgment. We are grateful to a reviewer for suggesting an alternate viewpoint for considering the barrier increases. Financial support was provided by the National Institutes of Health (GM29391).
The Journal of Physical Chemistry, Vol. 96, No. 20, 1992 7975
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