Volume 29
Inorganic Chemistry
Number 1 January 10, 1990
I
0 Copyright 1990 by the American Chemical Society
Communications Utility of the Semiempirical INDO/l Method for the Calculation of the Geometries of Second-Row Transition-Metal Species In recent years the use of second-row transition metals and their compounds in catalysis and advanced materials has spurred interest (e.g. Y in high-temperature superconductors,' Tc radiopharmaceuticals,2 Mo3 and Ru4 oxidation catalysts, Rh5 hydroformylation catalysts, and the Pd6 catalyst in the Wacker process). However, the application of quantum chemical methods to transition-metal compounds in general, and the second- and third-row transition Secmetals in particular, has been fraught with difficultie~.~.~ ond-row transition-metal complexes have received less attention due to the greater number of electrons and orbital^.^.^ It is our aim to show that a semiempirical method such as the INDO/1 method,"' while not specifically parametrized for geometries, can yield important results. As with any method, caution must be exercised not to apply the method to problems that are beyond the level of theory employed, or the model invoked. Designing a successful semiempirical theory is a reasonably complex endeavor. To date much of our research has been focused on the calculation of optical properties. The efficiency of the INDO model has extended its use to the calculation of molecular geometries,I2 and its successes in this area are remarkable in view of the little attention paid to this property in the parametrization of the basic theory." Previous studies on second-row transi-
Whangbo, M.-H.; Evain, M.; Beno, M. A.; Williams, J. M. Inorg. Chem. 1987, 26, 1831. Melnik, M.; van Lier, J. E. Coord. Chem. Rev. 1987, 77, 275. Mimoun, H.; Seree de Roch, 1.; Sajus, L. Tetrahedron 1970, 26, 37. Dobson, J. C.; Seok, W. K.; Meyer, T. J. Inorg. Chem. 1986,25, 1513. Cotton, F. A.; Wilkinson, G. Advanced Inorganic Chemistry, 3rd ed.; Wiley: New York, 1972; p 790. See ref 5, p 797. Some of these problems are discussed in: Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry; Veillard, A., Ed.; Reidel: Dordrecht, The Netherlands, 1986. Salahub, D.; Zemer, M. C. The Challenge of d and f Electrons. ACS Proceedings, 1989. The @ parameters were calculated by using the equations in ref 9a and are described more fully in ref 11. (a) Poyle, J. A,; Beveridge, D. L. Approximate Molecular Orbital Theory; McGraw-Hill: New York, 1970. (b) Pople, J. A.; Dobosh, P. A.; Beveridge, D. L. J . Chem. Phys. 1967, 47, 2026. All the parameters other than @ (see above) are taken from atomic spectroscopy, or from model ab initio calculations that were focused on reproducing molecular electronic spectra, as described in the following references: (a) Zerner, M. C.; Loew, G.; Mueller-Westerhoff, U. J. Am. Chem. Soc. 1980, 102, 589. (b) Bacon, A. D.; Zerner, M. C. Theor. Chim. Acta 1979,52,21. (c) Anderson, W.; Edwards, W. D.; Zerner, M.C. Inorg. Chem. 1986, 25, 2728. Anderson, W.P.; Cundari, T. R.; Drago, R. S.;Zerner, M. C. Manuscript in preparation. (a) Head, J. D.; Zetner, M. C. Chem. Phys. Len. 1985,122, 264. (b) Head, J. D.; Zerner, M. C. Chem. Phys. Lett. 1986, 131, 359.
tion-metal complexes using an INDO-type model have proven f r u i t f ~ 1 , ' ~although J~ they have not been applied to the variety of compounds considered here. These methods are somewhat different from the present model, as discussed in detail elsewhere." The basis set chosen for these studies is single-!: for the 5s and 5p AOs and double-!: for the 4d. The radial extents of these orbitals are chosen to match overlaps of multiple-!: functions between the given metal and nitrogen, to within 5%, from a separation of 1-3 A. The values of ,6 used for this study are given in Table I. The results of geometry optimizations on model systems are given in Table 11. The results are quite good. The average percent error for all species is 4.4% ( N = 48) or 10 pm (measured by [x(RINm- Re)z/N]'/2.N is the number of distinct M-X bonds; e.g., in a trigonal-bipyramidal structure N = 2 (M-X,, and M-X,). The average error for each individual transition metal ranges from 2.6% for Ru (3 pm, N = 4) and N b (5 pm, N = 7) to 9.7% (22 pm, N = 4) for Ag. There is average error of 3.3% for ions ( N = 15) and 3.7% for metal-oxo diatomics. There is a 3.3% (10 pm) average error for coordinatively saturated molecules, i.e. coordination number 1 4 about the central metal. For coordinatively saturated molecules errors in the experimentally determined bond lengths are unknown in many cases. For the cases where experimental errors are known, they are relatively small for bonds to larger atoms but significant for smaller atoms. In MoOzCl2 the uncertainty is A10 and f 3 pm for the Mo-0 and Mo-Cl bonds, re~pective1y.l~ Thus, calculated errors may range between 1.8% and 12.4% for the Mo-0 bond. A comparison of INDO/l and ab initio calculations for experimentally characterized systems is of interest. The average errors for the INDO/l and a b initio results are 6.5% (10 pm) (1 3) The application of similar models to main group geometries as well as to hydrogen-bonded species (using AMI) has been successfully carried out by Dewar and his -workers (MINDO). For a review of these and other methods for the calculation of main group molecular properties, see: Sadlej, L. Semi-Empirical Methods of Quantum Chemistry; Wiley: New York, 1985. Clark, T. Handbook of Computational Chemistry; Wiley: New York, 1985 and references therein. (14) There have been several studies on specific second transition series complexes using the INDO theory of ref lob. See, for example: Krogh-Jespersen, K.; Westbrook, J. D.; Potenza, J. A.; Schugar, H. J. J . Am. Chem. SOC.1987,109,7025 (for Ru). van der Lugt, W. T. A. M. Int. J . Quantum Chem. 1972, 6, 859 (for Rh). (15) Sakaki, S.;Nishikawa, M.; Tsuru, N.; Yamashita, T.; Ohyoshi, A. J . Inorg. Nucl. Chem. 1919, 41, 613. (16) (a) Pietro, W. J.; Hehre, W. J. J . Comput. Chem. 1983, 4, 241. (b) Pyykk6, P. Chem. Rev. 1988.88, 563. (17) (a) Huber, K. B.; Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand, New York, 1979; Part IV. (b) Sutton, L. E. Interatomic Distances; Chemical Society: London, 1958; p S8. (18) Roch, M.; Weber, J.; Williams, A. F. Inorg. Chem. 1984, 23, 4571. (19) Bauschlicher, C. W.; Nelin, C. J.; Bagus, P. S.J . Chem. Phys. 1985, 82, 3265. (20) (a) Krauss, M.; Stevens, W. J. J. Chem. Phys. 1985, 82, 5584. (b) Goddard, W. A.; Carter, E. A. J . Phys. Chem. 1988, 92, 2874. (21) Norman, J. G.; Kolari, H. J. J. Am. Chem. SOC.1978, 100, 791.
0020-1669/90/1329-0001%02.50/0 0 1990 American Chemical Society
2 Inorganic Chemistry, Vol. 29, No. 1, 1990 Table 1. fi Bonding Parameters (eV)" Y Zr P, = P p -1.0 -1.0 fid -14.14 -1 7.03
Nb -1
.o
-19.81
Communications
Mo
Tc -1.0 -23.55
-1.0 -21.83
Ru -1.0 -26.29
Rh -1.0 -27.17
Pd -1.0 -27.59
Ag -1.0 -27.94
"See refs 9 and IO. Table 11. INDO/I Geometry Ootimization Results % error
R,(calc) species" YO (22') YF ('Z') YCI ('E+) YH ('E+) YH('A) YF' (22+) ZrO ('E') ZrC14d ('A,) ZrCldd ('A,) ZrC16" ('AI ) ZrMe4d ('AJ ZrF73-f ('A) ZrO ('A) NbF72-r ('Al) NbO (T) NbF5h ('Al') N b(02)4'-' NbN ('A) MoH, ('AI&
Mo (%)
Mo ( 7 ~ ) MoF6 ('Aig) MoO,CI,' M0(02):-' RuO (5A) RuO' (4A) RuCP#' ('AI') Ru04 ('AI) RhCI," (IA, ) Rh(NH,),Clq' RhC (%+) Rh2form4 (D4h) PdH (2Z') PdO ('2') PdO ( ' T ) PdC142-s PdF2- ('Al8) AgCI ('2') AgF ('2') Ago AgH ( I F )
e*)
bond Y-0 Y-F Y-CI Y-H Y-H Y-F Zr-0 Zr-CI Zr-CI Zr-CI Zr-C Zr-F Zr-0 Zr-F Nb-0 Nb-F,, Nb-F, Nb-08, Nb-0, Nb-N Mo-H Mo-O
Mo-0 Mo-F
Mo-O Mc-CI Mo-08, Mo-0, Ru-0 Ru-O Ru-C Ru-O Rh-CI Rh-CI Rh-N Rh-NtmIl, Rh-C Rh-Rh Rh-0 Pd-H Pd-0 Pd-0 Pd-CI Pd-F Ag-CI Ag-CI Ag-F Ag-0 Ag-H Ag-H
INDO/I 174 189 239 173 178 187 166 234
X 249 204 212 167 198 162 186 184 207 209 160 174 161 192 182 162 237 197 192 171 178 224 170.5 253 243 214 217 166 257 207 168 185 189 255 208 26 1
X 22 1 209 175
X
ab initiob
193 (NR)/194(R) 201 (NR)
244 (ST03G) 240 (NR)/238 (R) 237 (ST03G)
185 (ST03G) 185 (ST03G)
R.(exptl)C 179 193 240 192 191 (2A) 171 232 f 1 232 f 1 245 227c 210 178 197 168 188 188 201j 204j 169
I
187 (NR) 185 (R) 171 (NR) 206 (NR)k
22 1 170.4 250 240 2234 223q 161 239' 204' 153
186 (SDCI+Q)k 185 (SDCI+Q)' 178 (ST03G) 242 (NR)/233 (R) 177 (ST03G) 212 (SCF+CI+Q)k 161-174 (NR) 168-180 (R)
X +1.6 -10.1 +0.9 +6.2
ab initio
+0.5/1.0
+5.2 +3.4/+2.6 +4.4
+os
-3.6 -1.1 -2.1 +3.0 +2.5 +5.3 -7.01-5.9
-1.6 -1.6
-5.8 183 175 f IO 228 f 3 20oi 197'
174 (NR)"' 175 (NR)" 215 (ST03G)
INDO/ 1 -2.8 -2.1 -0.4 -9.9 -9.4 -2.0 -2.9 +0.9
230 189 228
-6.8 -0.5 +7.4 +3.9 -1.5 -2.5 -2.3 +1.7 +1.4 +0.06 +1.2 +1.3 -4.0 -2.7 +3.1 +7.5 -I .5 +9.8 -0.5 +2.2 +10.9 +10.1 +14.5
X 198 200 162
X
+11.6 +4.5 +8.0
-2.7
-21.9 +6.1/+2.2 -10.6 +6.0 -0.6 to 7.4 +3.7 to 11.1
'The symmetry of the lowest energy electronic state, as determined by the INDO11 method, for a particular multiplicity is given in parenthesis. The symmetry of the molecule is given in those cases in which the choice is not obvious. Diatomics are, of course, C,,, and six-coordinate molecules are octahedral. NR: nonrelativistic, a b initio calculation, extended basis set R: relativistic, ab initio calculation, extended basis set. ST03G: nonrelativistic, a b initio calculation with the minimal basis set STO-3Gas reported in ref 16a. N R and R are from the review of Pyykk6.'6b CBond lengths given for diatomic and polyatomics are from Huber and Herzberg". and S ~ t t o n , " respectively, ~ unless otherwise noted. dTetrahedral geometry, T,+ e Estimated by Pietro et ai.'& from Zr(CH2C6H5).. 'Pentagonal bipyramid, f&. #capped octahedron, C3,. Trigonal Bipyramid, Dyh. For NbFs Pietro and Hehre16' cite equivalent experimental Nb-F bond lengths for both the axial and equatorial F. This must be viewed with some caution, sinc NbF, exists as a trimer in the gas phase. Also, there is the possibility of fluxional behavior (see: Hargittai, M. Coord. Chem. Reu. 1988, 91, 35). 'Dodecahedral, DW jSee ref 18. kSee ref 19. 'C, "'See 20a. "Seeref 20b. PEclipsed Conformation, Dsh. qExperimental error uncertain. 'See ref 21. JSquare planar, D4h.
and 5.6% (15 pm; 10 pm excluding the STO-3G calculation of AgCI), respectively. A n investigation of geometrical isomers in coordinatively saturated systems was performed to see if INDO could reproduce experimental results for the geometry of the global minimum.
ZrC14 was geometry optimized within the constraints of both Td (tetrahedral) and D4,, (square-planar) symmetry. The DM local minimum is calculated to be 28.3 kcal mol-' higher in energy than the Td global minimum, in agreement with experimental" and theoretical considerations.22 For d8 PdCld2-, the Dlh isomer is
3
Inorg. Chem. 1990, 29, 3-5
lower in energy, in agreement with experiment, than singlet and Isolation and Characterization of triplet tetrahedral minima by 176 and 6.3 kcal mol-', respectively. IrHzC!($-H2)[P(i-Pr)3]2: A Neutral Dihydrogen Complex In our previous of v2-tetraperoxides, M(02)42-, small of Iridium distortions of each M 0 2 fragment from a symmetrical, isosceles triangle geometry were observed, i.e. one M-O bond shorter than The nature of metal-hydrogen interactions in iridium polythe other. INDO/I calculations were able to reproduce this hydride complexes has been the focus of several recent studies.14 experimentally observed distortion for Nb(OJ4> and M O ( O ~ ) ~ ~ - .All ~ ~reported iridium nonclassical, v2-dihydrogen2-'complexes have The five-coordinate complex NbFS was optimized within the been cationic while the neutral iridium polyhydride complexes constraints of D3* (trigonal-pyramidal) and C, (square-pyramidal) that have been studied appear to be classical In symmetry. These minima are calculated to be within l/z kcal mol-' contrast, we have isolated IrHzCl(v2-H2)[P(i-Pr),], (1) in which of each other. The specific geometry a t each minimum is of dihydrogen is coordinated to a neutral iridium center. The interest. For the TBPS and SQP5 geometries the Nb-FaX and metal-hydrogen interactions in 1 exhibit dynamic behavior that Nb-Fkl bonds, respectively, are calculated to be longer than the we have examined both in solution and in the solid state. This Nb-F, and NbFnpicalbonds, respectively, in keeping with basic dynamic behavior is remarkably different than that which has been electronic structural arguments.24 observed2' for cationic q2-hydrogen iridium complexes. For seven-coordinate structures NbF:- and ZrF7>, the different We initially obtained 1 through treatment of THF solutions polytopes were compared in two distinct ways. First, the M-F of IrC13.3H20 and 2 equiv of P(i-Pr)3 with 2 equiv of sodium bonds were kept fixed ("frozen") and idealized (in terms of bond naphthalide under an atmosphere of hydrogen (Scheme I). angles) seven-coordinate structures assumed. Second, these Filtration of the reaction mixture, followed by removal of the THF idealized, frozen structures were allowed to relax, for NbF7", by solvent, produced an oil from which orange crystals of 1 arose submitting them to a geometry optimization. Three seven-coupon standing under an atmosphere of H2. The crystals were ordinate polytopes2s were considered: the pentagonal bipyramid found to contain an equimolar amount of napthalene. The po(PBP7), capped octahedron (C07), and capped trigonal prism lyhydride complex l is stable only in the solid state under an (CTP7). These structures are calculated to be close in energy, atmosphere of hydrogen and slowly converts to IrH2C1[P(i-Pr),],6 as expected. For the frozen approximation the PBP7 is favored (2), through elimination of H2 under 1 atm of argon. In solution, on the basis of smaller nuclear-nuclear repulsions. For the fully 1 was found to establish an equilibrium with 2 through the reoptimized NbF," structures the C 0 7 was calculated to be the versible loss of H2 (Scheme I).7 Prompted by these observations, global minimum by 3 kcal mol-' versus the PBP7. The CTP7 we have discovered that 1 can be prepared more conveniently relaxes to the PBP7. In the PBP7, NbF?-, the Nb-F, bonds are through the reaction of 2 with H2 either in solution or the solid shorter than the Nb-Fq bonds, in keeping with previous analyses.25 state. Thus, a pentane solution of 2 placed under 1 atm of hyIn the geometry optimization of Rh(NH3)&12+, an interesting drogen and allowed to stand at room temperature gives rise to result is obtained: R(RH-Cl) = 243 pm, R(Rh-N) = 214 pm, orange crystals* of the less soluble 1 in 70-80% yield. and R(Rh-N,,,,,) = 217 pm. Thus, the INDO/1 geometry opScheme I timization correctly describes the well-known "trans" influence;23 Le., the bond trans to C1- is longer than those which are cis. H2 Although this work does not represent an exhaustive study of IrC13.3H20 + 2P(i-Pr)3 + 2NaCloH8 the INDO/ 1 model for the calculation of geometric quantities IrH2Cl(v2-H2)[P(i-Pr)3]2 * IrH2Cl[P(i-Pr),l2 + Hz for second-row transition-metal species, the results allow several conclusions to be drawn. First, INDO/1 does as good a job in The ' H NMR spectrum of a sample of 1 in CD2CIzsolution predicting geometries as does minimal basis set a b initio calcuat 22 "C under 1 atm of hydrogen exhibits a broad ( w ~ i=, ~700 lations on large, coordinatively saturated molecules. Second, the Hz) singlet at ca. -17 ppm. Reduction of the hydrogen pressure INDO/ 1 method in the majority of the cases studied here reby partial evacuation results in the resonance sharpening and produces the energy ordering of geometric isomers. moving up field toward a limiting value of -33.0 ppm, the chemical It should be emphasized again that no exhaustive or compreshift which is observed for the hydride resonance of 2 under an hensive investigation has been made of the INDO/1 parameters. atmosphere of argon at 22 "C. A sample of 1 that was dissolved That the model works as well as it does with so little effort testifies in CD2CI2, freeze/pump/thaw degassed and allowed to stand to the strength of the model. We believe that very useful results under an atmosphere of argon for 12 h was seen to produce a can be obtained by this model, but as always, the proper care of hydride signal identical with that observed for 2 (6 -33.0 ppm, interpretation must be exercised. JpH = 13 Hz). Conversely, spectra identical with those of 1 under Acknowledgment. This work was supported in part by a grant from the US.Army through a CRDEC (Aberdeen, MD) Center Garlaschelli, L.; Khan, S. I.; Bau, R.; Longoni, G.; Koetzle, T. F. J. Am. Chem. SOC.1985, 107, 7212-7213. of Excellence Award to the University of Florida. Additional Crabtree. R. H.: Lavin.. M.:. Bonneviot. L. J . Am. Chem. Soc. 1986.108. funding by the National Science Foundation is gratefully ac4032-4037. knowledged. (a) Rhodes, L. F.; Caulton, K. G. J. Am. Chem. SOC.1985, 107,
-
(22) Burdett, J. K. Molecular Shapes; Wiley: New York, 1980; p 65. (23) Cundari, T. R.; Zerner, M. C.; Drago, R. S. Inorg. Chem. 1988, 27, 4239. (24) Whangbo, M.-H.; Burdett, J. K.; Albright, T. Orbital Interactions in Chemistry; Wiley: New York, 1970. (25) Hoffmann, R.; Beier, B. F.; Muetterties, E. L.; Rossi, A. R. Inorg. Chem. 1977, 6, 5 5 . (26) Purcell, K. F.;Kotz, J. C. Inorganic Chemistry; Saunders: Philadelphia, PA, 1977 p 704. (27) Present address: Department of Chemistry, Bloomsburg University, Bloomsburg, PA 17815.
Department of Chemistry and Quantum Theory Project University of Florida Gainesville, Florida 32611
Wayne P. Anderson" Thomas R. Cundari Russell S. Drago* Michael C. Zerner*
Received June 30, 1989
0020- 1669/90/ 1329-0003$02.50/0
259-260. (b) Lundquist, E. G.; Huffman, J. C.; Folting, K.; Caulton, K. G. Angew. Chem., Int. Ed. Engl. 1988, 27, 1165-1167. (a) Heinekey, D. M.; Payne, N. G.; Schulte, G. K. J. Am. Chem. SOC. 1988, 110,2303-2305. (b) Zilm, K. W.; Heinekey, D. M.; Millar, J. M.; Payne, N. G.;Demou, P. J . Am. Chem. Soc. 1989,111,3088-3089. Hamilton, D. G . ; Crabtree, R. H. J. Am. Chem. SOC.1988, 110, 4 126-4 1 33. Werner, H.; Wolf, J.; Hohn, A. J. Organomet. Chem. 1985, 287, 395-407. A similar equilibrium has been suggested (Mura, P.; Segre, A,; Sostero, S.Inorg. Chem. 1989,28,2853-2858) as part of the solution behavior of Ir'vH2C12[P(i-Pr)3]2.However, the solution behavior of 1 (see below) does not suggest further equilibria with paramagnetic Ir(IV) species. 'H NMR (300 MHz, 20 "C in CD2C12under 1 atm H2): 6 2.36 (m, 6 H), 1.26 (m, 36 H), -17.0 (br s). 31P(lH)NMR (122 MHz, 20 "C in CD2C12under 1 atm H2): 6 51 ppm (br s). Anal. Calcd: C, 39.15; H, 8.40; CI, 6.42. Found: C, 39.94; H, 8.40; CI, 6.66. IR (KBr in gas cell under H2): uh(+ 2204 (vw) and 2152 (m) cm-' (deuteride uM+ 1568 (vw) and 1540 (m) cm-I). As has been the case with previously isolated dihydrogd complexes of iridium, no absorptions assignable to the H-H modes of 1 could be conclusively identified in comparison with the IR spectrum of the HD-substituted complex.
0 1990 American Chemical Society
