J. Am. Chem. SOC.1992, 114, 6469-6475
IV. Conclusions These show that the LDAP-PW method can produce accurate structural parameters for molecules. The data suggest that the method wl&h uses plane waves, pseudopotentia1s:and supercells may be a useful alternative to standard ab initio quantum-mechanical methods for calculations on chemical systems. Future work will include more realistic density functionals and tests of energetics of chemical transformations. In addition, research is continuing to develop more efficient energy mini(35) Baughcum, S. L.; Duerst, R. W.; Rowe, W. F.; Smith, Z.; Wilson, E. B. J. Am. Chem. SOC.1981, 103, 6296.
6469
mization algorithms and superior pseudopotentials. These changes will improve the efficiency and accuracy of the method for the study of Periodic and aperiodic chemical and b ~ ~ & m k system. al
Acknowledgment. This research was supported in part by the florida StateUniversity SupercomputerComputations Research Institute, which is partially funded by the U.S. D~~~~~~~~~of Energy through contract N ~~.~ - F C 0 5 - 8 5 E R 2 and 5 ~ 0oNR contract No. N0()()1486-K4158. we also achowldge computer time provided by the florida StateUniversitv Comoutinn center. -, the MIT Supercomputer Facility, and the San Diego SipercomPuter Center. One of us (A.M.R.) is Supported by a Joint S M C e S Electronics Program fellowship.
Ab Initio Prediction of the Structure and Stabilities of the Hypermagnesium Molecules: Mg20, Mg30, and M g 4 0 Alexander I. Boldyrev,+,*Igor L. Shamovsky,$and Paul von R. Schleyer**+ Contribution from the Institut fur Organische Chemie, Friedrich- Alexander Universitat Erlangen- Nurnberg, Henkestrasse 42, 8520 Erlangen, FRG, and Institute of Chemical Physics of the Russian Academy of Sciences, Kosygin Street 4, 1 I7334 Moscow, Russia. Received August 21, 1991
Abstract: The concept of hypermetalation, characterized by molecules with unprecedented stoichiometries, is extended to the magnesium-xygen combinations, Mg20, Mg,O, and M&O. Their equilibrium geometries and fundamental frequencies were calculated at the HF/6-31GS and correlated MP2 (fu11)/6-31G* levels. Extensive searches of possible structures and electronic states were carried out. The global minima are as follows: linear Mg2O (D+ both singlet IZg+and the triplet 3Z,- states), planar Mg,O (D3h, 3Al'), and Mg40 forms slightly distorted from the square planar arrangement (DU,'Al and planar MgOMg, (C,, lA1)structures have nearly the same energy). These Mg20,Mg,O, and Mg40 species are stable with regard to all possible decomposition pathways. Representative dissociation energies are the following: Mg20, 74.5 kcal/mol into MgO + Mg at QCISD (T)/6-311+G(3df)+ZPE; Mg30, 26.7 kcal/mol into Mg20+ Mg at QCISD(T)/6-31 l+G*+ZPE; and Mg,O, 7.9 kcal/mol into Mg,O + Mg at MP4SDTQ/6-31 l+G*+ZPE. Magnesium-magnesium bonding contributes significantly to the stability of Mg30 and Mg40.
Introduction
Hypermetalation, involving metal stoichiometries exceeding normal valence expectations, should be a general phenomenon exhibited by many if not all metals. Hyperalkali metal molecules are now well-documented. Many hyperlithium molecules, OLi4, OLi5, OLi6, NLiS, CLis, OLi6, BLi5, BeLi4, BeLi4, BeLi6, etc., were discovered by calc~lation.'-~Li30, Li40, and L i 5 0 have been observed by mass spectrometry and atomization energies determined.loJ1 There is similar evidence for Na2C1,12Na30, and C S ~ O The . ~ ~"suboxides" of rubidium Na40, K 3 0 , and cesium, e.g., Rb202,Cs70, and Csl103,have been charact e r i ~ e d . ' ~ .Bonding '~ interactions between ligand atoms contribute to both the structure and the stability of these species.'-9 Despite K 4 0 , 1 3 3 1 4
Universitat Erlangen-Ntirnberg. *Russian Academy of Sciences.
having the usual stoichiometry, SiLi4 also is instructive. Metal-metal bonding contributes to the surprising preference for a (1) Schleyer, P. v. R.; Wurthwein, E.-U.; Pople, J. A. J. Am. Chem. SOC. 1982, 104, 5839.
(2) Schleyer, P. v. R. In New Horizons of Quantum Chemistry; Lowdin, P.-O., Pullman, A., Eds.; Reidel: Dordrecht, The Netherlands, 1983; pp
__
95-105
(3) Schleyer, P. v. R.; Wuthwein, E.-U.; Kaufmann, E.; Clark, T. J. Am. Chem. SOC.1983, 105, 5930. (4) Gutsev, G. L.; Boldyrev, A. I. Chem. Phys. Lerr. 1982, 92, 262. (5) Pewestorf, W.; Bonacic-Koutecky, V.; Koutecky, J. J. Chem. Phys.
1988, 89, 5194, (6) Fantucci, P.; Bonacic-Koutecky, V.; Pewestorf, W.; Koutecky, J. J. Chem. Phys. 1989, 91, 4229. (7) Klimenko, N. M.; Musaev, D. G.; Gorbik, A. A.; Zyubin, A. S.; Charkin, 0. P.; Wurthwein, E.-U.; Schleyer, P. v. R. Koord. Khim. 1986,12, 601 (in Russian). (8) Schleyer, P. v. R. Pure Appl. Chem. 1984, 56, 151. (9) Savin, A.; Preuss, H.; Stoll, H. Reu. Roum. Chim. 1987, 32, 1069.
0002-786319211514-6469$03.00/0 0 1992 American Chemical Society
Boldyrev et al.
6470 J. Am. Chem. SOC..Vol. 114, No. 16, 1992 1.782
I. 78. (1.821)
M 3 102
1.939 (1.982)
n l.8Bl
1.8S4 (1.8781
3.678 3.647)
)&
I
@
Figure 1. Optimized geometries of the magnesium oxides (bond length in A and valence angles in deg). Geometries a t MP2(fu11)/6-31G* are given in parentheses. Other data a t HF/6-31G*.
nontetrahedral, C, point group ge~metry.~***~ We have recently investigated the hyperaluminum molecules, A130 and A140, computationally:20 planar A130 (the C,, Y-shaped (2A1)and T-shaped (2B2)forms have nearly the same energy) and planar 40 lAlg)structures were predicted to be the global minima. Both of these species are very stable with regard to all possible decomposition pathways. There also is mass spectrometric evidence for A130.21 We have now extended our ab initio investigations to the hypermagnesium molecules, Mg20, Mg30, and M h o . While experimental and theoretical studies of the MgO monomer are e ~ t e n s i v e , ~we~ -have ~ ~ not been able to find any information on
the isolated Mg20, Mg30, and M a 0 molecules. However, M&O and MgsO clusters as models for oxygen chemmrption on metal magnesium surfaces were e ~ a m i n e d , but ~ ~ .full ~ ~optimization of the geometries and characterization via frequency calculations were not carried out. Hypermagnesium RMg,Hal molecules containing linear -Mg-Mg-Mg- chains have been studied.35 However, the extra Mg atoms are bound in these molecules by only 2 kcal/mol (6 kcal/mol when n = 2).
(10)Wu, C. H.; Kudo, H.; Ihle, H. R. J. Chem. Phys. 1979, 70, 1815. (11) Wu, C. H. Chem. Phys. Lett. 1987,139,357. (12) Peterson, K. I.; Dao, P. D.; Castleman, A. W., Jr. J. Chem. Phys. 1983,79,777. (13) Dao, P. D.; Peterson, K. I.; Castleman, A. W., Jr. J. Chem. Phys. 1984,80,563. (14)Wurthwein, E.-U.; Schleyer, P. v. R.; Pople, J. A. J. Am. Chem. Soc. 1984,106,6973. (1 5 ) Fallgren, H.; Martin, T. P. Chem. Phys. Lett. 1990,168,233. (16)Simson, A. Bonding (Berlin) 1979,36, 81. (17)Borgstedt, H. V. Top. Curr. Chem. 1986,134, 125. (18)Schleyer, P. v. R.;Reed,A. E. J . Am. Chem. Soc. 1988,110,4453. (19)Reed,A. E.;Schleyer, P. v. R.; Janoschek, R. J. Am. Chem. Soc. 1991,113,1885. (20)(a) Boldyrev, A. I.; Schleyer, P. v. R. J. Am. Chem. Soc. 1991,113, 9045. (b) Schleyer, P. v. R.; Boldyrev, A. I. J. Chem. Soc., Chem. Commun. 1991, 1536. (21)Cox, D. M.; Trevor, D. J.; Whetten, R. L.; Rohlfing, E. A.; Kaldor, A. J. Chem. Phys. 1986,84,4651.
(22)Liu, B.; Olson, R. E.;Saxon, R. P. J . Chem. Phys. 1981,74,4216. (23)Meyer, W.; Rosmus, P. J. Chem. Phys. 1981,74,4217. (24)Bauschlicher, C. W., Jr.; Lengsfield, B. H., 111; Liu, B. J. Chem. Phys. 1982,77,4084. (25)Langhoff, S.R.; Bauschlicher, C. W., Jr.; Partidge, H. J. Chem. Phys. 1986,84,4414. (26)Veits, I. V.; Gurvich, G. V. Zh. Fiz. Khim. 1957,31,2306. (27)Drowart, J.; Exsteen, G.; Verhaegen, G. Trans. Faraday Soc. 1964, 60,1920. (28)Cotton, D. H.; Yenkins, D. R. Trans. Faraday Soc. 1969,65,376. (29)Zeegers, P. J. I.; Townsend, W. P.; Winefordner, J. D. Spectrochim. Acto, Part B 1969,26,234. (30)Farber, M.; Srivastava, R. D. High Temp. Sci. 1976,8, 195. (31) Srivastava, R. D. High. Temp. Sci. 1976,8,225. Field, R. W. J. Mol. Spectrosc. (32)Ikeda, T.; Wong, N. B.; Hams, D. 0.; 1977,68,452. (33) Sakoto, C. Phys. Reu. 1984,B30, 1754. (34)Broughton, J. Q.;Bagus, P. S . Phys. Reu. 1987,112,2813. ( 3 5 ) Jasien, P. G.;Dykstra, C. E. J. Am. Chem. Soc. 1985, 107, 1891.
Computational Methods Geometries of MgO, Mg20, Mg30, and M h o were optimized employing analytical gradients36with a polarized split-valence basis
Structure and Stability of Hypermagnesium Molecules Table I. Calculated Total (E,,J and Relative (AE)Energies of Mannesium Oxide SDecies" sDecies
(S* . .) 0
E,,,. .".,au
AE.kcal/mol
-199.595 61 -74.783 93 -274.323 83 -474.101 72 -474.029 55 -474.027 97 -473.932 1 1 -673.732 20 -673.727 37 -673.677 66 -673.66479 -673.645 86 -873.32545 -873.293 32 -873.290 56 -873.283 70 -873.281 41 -873.257 42 -873.228 59 -873.145 53
2.006 0 2.002 (0) 0.0 0 (0) 45.3 (2) 46.3 0 106.4 (0) 0 2.362 (0) 0.0 (2) 3.0 2.130 0 (0) 34.2 0 (0) 42.3 54.2 0 (0) 2.749 (0) 0.0 0 (0) 20.2 0 (1) 21.9 0 (0) 26.2 0 (1) 27.7 0 42.7 0 60.8 0 112.9 "UHF/6-31G8 was employed for open-shell species, RHF/6-31G* for closed-shell. The number of imaginary frequencies are given in parentheses.
set (HF/6-31G*)37*38 and at correlated MP2(full) levels (UHF and UMP2 for open-shell systems). The results are summarized in Figure 1. Fundamental frequencies, normal coordinates, and zero-point energies (ZPE) were calculated by standard FG matrix methods. The MP2(fu11)/6-3 lG* equilibrium geometries were used to evaluate electron correlation in the frozen-core approximation both by Moller-Plesset perturbation theory to full fourth order3gand by (U)QCISD(T)" methods using the 6-311+G* and 6-3 11+G(3df) basis sets. The UHF wave functions for open-shell systems were projected to pure spectroscopic states (PUHF, PMPZ, PMP3, and PMP4).41 Analytical frequencies at MP2(fu11)/6-31G* were carried out with the CADPAC program.42 GAUSSIAN 90 (CONVEX version)43was used for the other calculations. The total energies at HF/6-31G* and at different correlated levels are presented in Tables I and 11. Dissociation energies and harmonic frequencies are given in Tables I11 and IV, respectively. For estimation of the stability of the hypermagnesium molecules with respect to all possible dissociation pathways, reference data for the Mg(lS) and O('P) atoms, as well as for the MgO (lZ+, 311) molecule, were calculated. The total energies at HF/6-3 1G* and at different correlated levels using the 6-31G*, 6-31l+G*, and 6-311+G(3df) basis sets are included in Tables I and 11. Results MgO. The IZ+ MgO ground state arises from the singlet coupling of the 3s electron of Mg+ to the pu1p?r4open shell of 0-. This state is not well represented by a single reference configuration, reflecting the fact that the charge distribution is intermediate between Mg+O- and Mg2+02-.22-25Therefore, H F and correlated methods (like MP4) based on a single configuration reference state cannot be expected to give reasonable values for the dissociation energy. In the best available theoretical study, Langhoff et aLzs estimated the dissociation energy of the XIZ+ Schlegel, H. B. J . Comput. Chem. 1982, 3, 214. Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. Frisch, M. J.; Pople, J. A,; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (39) Krishnan, R.; Pople, J. A. Znt. J. Quantum Chem. 1978, 14, 91. (40) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J . Chem. Phys. 1987, 87, 5968. (41) Schlegel, H. B. J . Chem. Phys. 1986, 84, 4530. (42) Amos, R. D.; Rice, J. E. CADPAC: The Cambridge Analytic Deriuatiues Package, Issue 4.0, Cambridge, England, 1987. (43) GAUSSIAN 90 (CONVEX version): Frisch, M. J.; Head-Gordon, M.; Trucks, G. W.; Foresman, I. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M. A.; Binkley, 1. S.; Gonzales, C.; DeFrees, D. I.; Fox, D. I.; Whiteside, R. A,; Seeger, R.; Melius, C. F.; Baker, 1.; Martin, R.; Kahn, L. R.; Stewart, I . 1. P.; Fluder, E. M.; Topiol, S.; Pople, J. A. Gaussian Inc.: Pittsburgh, PA, 1990.
J. Am. Chem. Soc., Vol. 114, No. 16, 1992 6471
state of MgO indirectly by using the total energy of the 311state of MgO, obtained at the CISD level with a large basis set (12~9p12d6f/8~6p4d2f),,+(1 1s7p9d3f/6s4p3d1f)ol and by correcting for the experimental X12+-a311energy separation. The resulting De (MgO, '2') is 63.4 kcal/m01.~~The value of De(MgO, l2') recommended by Huber and Henberg& is 80.7 kcal/mol, which is a reinterpretation of the Srivastava r e ~ u t , ~ ' taking into account the presence of the low-lying 311 state. However, Huber and Herzberg" pointed out that 'the dissociation energy MgO (to Mg(IS) O(3P)) is quite uncertain". Because our dissociation energies for MgO ( I F ) oscillated along the MP2-MP3-MP4 series (see Table 11), we estimated De of MgO (IZ') by employing the procedure of Langhoff et al. (seeabove).25 We added the experimental X1Z+-a311energy separation (0.326 eV45)to the total energies of MgO (aQ) calculated at QCISD(T)/6-311+G* and at QCISD(T)/6-311+G(3df) (both at optimized MP2(full)/6-31+G* geometry). The resulting De (MgO, I Z ' ) is 58.8 kcal/mol at QCISD(T)/6-311+G(3df)+ZPE. We also used these estimated total energies of MgO (lZ+) in our evaluations of the Mg20, Mg30, and M a 0 dissociation energies, as discussed below. Mg20. We have examined three MgzO forms at HF/6-3 1G*: linear M g U M g (Dmh),linear Mg-Mg-O (C-,), and M g U M g (C,,), all in singlet and triplet states (see Table I). The triplet 3Z; linear Mg-O-Mg structure with a ( lo,)2( 1 ~ ~ ) ~ configuration is an absolute minimum ( 2 ~ ~ ) ~ ( 2 uIT , , ))O~valence ( (no imaginary frequencies) at this level. Modest spin contamination ( ( S 2 )= 2.002) was found for the triplet linear structure at UHF. The linear singlet Mg-0-Mg structure [(lag)2(luJ2( l?r,)4(2ug)2(2a,)0configuration] is not a minimum and lies 46 kcal/mol above the ground state. Another linear singlet structure, Mg-Mg-O [(la)2(2a)2(l?r)4(3u)2(4a)2(2~)o], is a local minimum (no imaginary frequencies), but is higher in energy than the dissociation products MgO('2') + Mg('S). Optimization of triplet C, Mg20leads to the linear D..h % ( ); ground-state configuration. The singlet C2,structure of Mg,O is a local minimum. But this structure is highly flexible (the bamer toward linearization is only 5.2 kcal/mol), and its relative energy is 41 kcal/mol. At this uncorrelated level, the stability of the M g 2 0 forms is Dmh(32;) < Cz,('A1) < Dmh('Ze+)
