J . Phys. Chem. 1991,95, 5463-5410
5463
Ab Initio Molecular Orbital Studies of s s M ~"0, , and "9s Chemical Shielding In Transition-Metal Compounds J. E. Combariza, M. Barfield,* and J. H. Enemark* Department of Chemistry, University of Arizona, Tucson, Arizona 85721 (Received: November 28, 1990)
Ab initio LORG (localized orbital-local origins) methods are used to calculate molybdenum, oxygen, and sulfur isotropic ( n = M),Mo(CO)6, and MoNCb-. With and tensor shielding data for the series of oxothiomolybdateanions the exception of Mo(CO), the isotropic chemical shift data are overestimated, but the method provides an excellent correlation of the experimental chemical shifr frends in this series of anions. With less than a 5% change in the diamagnetic shielding contributions, shielding in the oxothiomolybdates is dominated by the paramagnetic contributions. The sensivity of the paramagnetic Mo shielding contributions to the quality of the basis sets on both the metal and the ligands is no worse than that noted in distributed origins methods applied to first and second-row elements. Within the LORG algorithm Mo isotropic shieldings are examined in terms of the diamagnetic and paramagnetic contributions associated with inner shells, bonds, and lone pairs. Except for Mo(CO)~,where the paramagnetic contributions arise almost entirely from the ta orbitals of the metal, the Mo shieldings are dominated by paramagnetic contributions from the bonds and the lone pairs of the ligands. Calculated results for the ligand nuclei (S and 0) follow the observed trends for ''0 and ))S chemical shift data in the oxothiomolybdates. The excellent correlation, which is noted for all of the calculated and experimental 9 S M ~"0, , and ))S chemical shift data with the computed Mo 4d atomic orbital populations, provides a useful method for relating the experimental data for the three different nuclei in the oxothiomolybdates. It seems likely that the same factors are implicated for the oxothio compounds of vanadium and tungsten as these exhibit the same chemical shift trends as the oxothiomolybdate anions.
Modern high-field multinuclear NMR spectrometershave made experimental NMR data available for nearly every transition metal in the periodic table, and chemical shift data for a large number of chemically related compounds are available. The experimental metal NMR data show many puzzling features in their chemical However, in spite of the rapid growth of techniques for studying metals, and the large amount of available NMR data, the understanding of transition-metal chemical shifts is still extremely primitive! Molybdenum-95NMR6 provides examples of unexplained shielding trends. In recent years ab initio molecular orbital methods for chemical shielding have been extensively applied to first- and second-row elements7-" but have not generally been applied to transition-metal complexes. Because of the well-known gauge dependence of chemical shielding, coupled Hartree-Fock (CHF) and the equivalent finite perturbation theory (FPT) procedures with a common origin have been generally unsatisfactory for elements (1) Webb, G. A. In NMR ojNnvly Accessible Nuclei; Laszlo, P., Ed.; Academic Press: New York, 1983; Vol. 1, p 79. (2) Harris, R. K.; Mann, B. E. NMR und the Periodic Table;Academic Press: New York, 1978. (3) Lambert, J. B.; Riddell, F. G., Eds. The Multinucleur Approuch to NMR Specfroscopy; Reidel: Boston, 1983. (4) Mason, J. Mubinucleur N M R Plenum: New York, 1987. (5) Rehder, D. Magn. Reson. Rev. 1984, 9, 125. (6) Minelli, M.;Enemark, J. H.; Brownlee, R. T. C.; OConnor, M. J.; Wedd, A. G. Coord. Chem. Rev. 1985,68, 169. (7) Kutzclnii, W. Isr. J. Chem. 1980,19, 193. Schindler,M.; Kutzclnigg, W. J. Chem. Phys. 1982, 76, 1919. Schindler, M.;Kutzelnigg, W. J. Am. Chem. Soc. 1985, 105,1360. Schindler, M. J . Am. Chem. Soc. 1988,110, 6623. (8) For a m i e w of shielding calculations with emphasis on IGLO results see: Kutzclnigg, W.; Fleischer, U.; Schindler, M.In NMR Baric Principles u d Progress: Diehl, P., Fluck, E.. Kosfeld, R., Eds.; Springer: Berlin, in press. (9) Hansen, As. E.; Bouman, T. D. J . Chem. Phys. 1985. 82, 5035. Bouman, T. D.; Hamen, Aa. E.; Voigt, B.; Rettrup, S. Inr. J. Quunfum Ch" 1983,23,595. Bouman, T. D.; Hansen, Aa. E. Chem. Phys. Lrrr. 1988,149 (510). (IO) Facclli, J. C.; Grant, D. M.; Bouman, T. D.; Hanscn, Aa. E. J . Compur. Chem. 1990.11, 32. (1 1) For reviews of the theory of shielding see, for example: Jameson, C. J. In Nuclear Mugneric Resononce; Specialist Periodical Reports; The Chemical Society: London, 1989; No. 18, and previous chapters in this series. (12) Ditchfield, R. Mol. Phys. 1974, 27, 789. (13) Rohlfing, C. M.; Allen, L. C.; Ditchfield, R. Chem. Phys. 1984,87, 9.
0022-3654/91/2095-5463$02.50/0
in the first and second rows of the periodic table. This is largely attributable to cancellation errors between diamagnetic (positive in sign and accurately calculated almost independent of the basis set) and paramagnetic terms (these are negative in sign and have an accuracy which is quite dependent on the quality of the basis sets). To avoid these origin dependence problems, C H F computations with a common origin required saturation of the basis sets. Introduction of distributed origins methods improved the quality of shielding computations with modest basis sets. The fmt of these was based on the method of gauge-invariant atomic orbitals (GIAO).I2 Subsequently, the introduction of the individual gauge for localized molecular orbitals (IGLO) method by Kutzelnigg and Schindler7v8led to a large number of calculations of shielding for elements in the first and second rows. Localized origins methods provide a better description of the paramagnetic contributions. Since the latter vanish if the origin is at the center of spherical orbitals, and localized quantities such as bonds and lone pairs tend to be roughly spherical, the resulting decrease in paramagnetic shielding magnitudes produces smaller cancellation errors for the total shieldings. It has been suggested that localized molecular orbital methods7+' may be easier to carry out than those based on gauge-invariant atomic orbitals GIA0I2 but give comparable results if basis sets of similar quality are used." The basis-set dependence of the IGLO method was investigated and it was concluded that the results were adequate to predict major trends with basis sets of double-{quality and that the results were satisfactory for carbon, for example, with triple{ plus polarization functions. More recently, the random phase approximation ( M A ) has been used in the context of localized orbitals-local origins (LORG)9 for shielding calculations. The LORG method9 also leads to appropriate damping of basis set errors associated with remote groups and the results are similar to the IGLO method.l0 The LORG method, however, as presently implemented is more amenable to studies of transition-metal shielding. Although experimental chemical shift data for transition-metal compounds are there are only a few previous nonempirical studies."Js The studies of Nakatsuji et al.lS made use of a common origins approach and finite perturbation theory (14) A preliminary account of this work on Mo shielding has appeared: Combariza, J. E.; Enemark, J. H.; Barfield, M.; Facclli, J. C. J. Am. Chem. Soc. 1989, 111,7619. (15) Nakatsuji, H.; Kanda, K.; Endo, K.; Yomzawa, T. J. Am. Chem.Soc. 1984,106,4653. Kanda, K.; Nakatsuji, H.; Yonnawa, T. J. Am. Chem. Soc. 1984, 106, 5888.
0 1991 American Chemical Society
5464 The Journal of Physical Chemistry, Vol. 95, No. 14, 199‘I
TABLE I: Buir scb U d L tbe LQRC c.ledr(k.r basis A
B
atom Mo
0,s
contraction (433321/433 11 /42l) 3-21 +G
Mo
(433321/43311/4211) 4-31+G
Mo
N,0, S, CI
(433321/43311/4211) 4-31+G*
O
4-3 1G
0,s
polarization and diffuse functions exponents sp(0) sp(S) d(Mo) sp(0)
sp(S) C
D
d(Mo) d(O) d(S) d(N) d(CI) sp(N) sp(C1)
0.084 0.045 0.045 0.084 0.045 0.045 1.154 0.421 0.864 0.514 0.0639 0.0483
(FFT), which is equivalent to coupled Hartree-Fock (CHF) methods of SCF-MO theory, to investigate compounds of transition elements (Cu, Zn, Ag, Cd, and Mn). Even though modest basis sets were employed, the computed results reproduce a number of the experimental trends.IS More recently, these techniques have been applied to other transition elements including oxothioDiamagnetic conmolybdates and o~oselenomolybdates.’~~’~ tributions can be calculated accurately even with minimal basis sets and semiempiricalI8 or even empirical calculation^.'^ Moreover, for metal shielding in symmetrical, or nearly symmetrical molecules, the coupled Hartree-Fock methods, which have the metal as a common origin, seem to compensate for problems of inadequate basis sets. Observation of the enormous chemical shift ranges for metals’*2’ prompted a large number of semiempirical studies of transition-metal ~hielding,2~**~ including several concerned specifically with molybdenum.u Typically, semiempirical methods are based on Ramsey’s perturbation formulation2sbut invoke an yaverage excitation energy” AE and closure in the second-order perturbation expression for the paramagnetic contribution to the shielding. Alternatively, empirical methods attempt to correlate the experimental chemical shifts with l/AE, where AE corresponds to some experimentally measured low-lying electronictransitions in the molecules of intenst. Serious problems with such an analysis are corrected, in part, by assuming that the shielding arises entirely from the metal orbitals and introducing empirical parameters in the numerator of the shielding expression. The resulting “nephelauxetic effects” are presumed to be related to the substituent dependence of expectation values of ( P )for the metal. Presented here are ab initio tensor and isotropic molybdenum, oxygen, and sulfur shielding data for a number of molybdenum compounds. The dependence of calculated results on the quality of the basis sets is investigated by means of the LORG algorithm? With the modest basis sets employed the results are only in moderate agreement with the experimental data, but the correand 33Schemical shifts of lation of the trends in the 95Mo, ‘‘0, oxothiomolybdates is exceedingly good. Furthermore, the negative chemical shift for Mo(CO)~,which has 0 formal oxidation state, is well reproduced. Calculated oxygen and sulfur chemical shifts for the oxothiomolybdate anions are compared with the experi(16) Nakatauji, H.; Sugimoto, M. Inorg. Chem. 1990,29,1221. (1 7 ) Nakatauji, H.; Inouc, T.; Nakao, T. Chem. Phys. Lett. 1990,167.11 1. (18) Barfield, M.; Grant, D.M.J, Chem. Phys. 1977,67, 3322. (19) Flygarc, W.; Goodiman, J. 1. Chem. Phys. 1968. 49,3122. Gierke, T. D.; Flygarc, W. J. Am. Chem. Soc. 1972,94, 7277. (20) Roctot, W. G.; Yu, F. C. Phys. Rev. 1951,81,20. (21) Freeman, R.; Murray, G. R.; Richarda, R. E. Proc. R. Soc. London Ser. A 1957. 242, 455. (22) Griffith. J. S.; Orgel, L. E. J. Chem. Soc., Faraday Soc. 1957, 53, 601. (23) Juranic, N. Coord. Chem. Rev.1989, 96.253, and references cited therein. (24) Grievor, R. A.; Muon,J. Polyhedron 1986,5.415. Grieves, R. A.; Muon, J. J. Chem. Soc., Dalton Trans.1906, 1313. (25) Ramsey, N. F. Phys. Rev. 1950, 78,699.
Combariza et al. mental data. Theoretical results for nuclei in the ligands of transition metal have not heretofore been reported. Computational hocedurea
Basis Sets and Molecular Geometries. Ab initio shielding computations were performed with basis sets of varying quality, and designated A-D as defined in Table I. The basis set A computations were carried out using the GAUSSIAN 86 program% to obtain the SCF wave functions and a version of WAC 8.327 to obtain the chemical shieldings. The basis sets are those of Huzinagaz8for the (SF) state of molybdenum (433321/43311/ 421), which is of double-{ quality for all of the metal valence orbitals and for the ligands. Two single primitives were used to describe the 5p orbital of Mo with exponents optimized for atomic calculations. Basis sets for the ligands (in the A set) are (3-21G)29 and an extradiffuse sp function was added to account for the negative charge on the anions.m Exponents for the sp functions on oxygen and sulfur are those of Chandrasekhar et al.” The optimized Mo-O bond length of the molybdate system is 1.7841 A with this basis set. Experimental values for Mo-O bond distances are in the range 1.75-1.78 A, with an average characteristic distance of 1.77 A in isolated MOO,]^-?^ The optimized value was used for all calculations in the oxothiomolybdate series. Similarly, point-by-point optimization for [MoO3Sl2-led to an Mo-S distance of 2.15 A, which was also used for all of the calculations in these molecules. This Mo-S distance compares favorably with an experimental value of 2.17 (4) A.33 Internal angles for these anions were assumed to be tetrahedral in conformity with the evidence for [Mo0412- and [ M O O ~ S ] ~ - . ~ ~ J ~ Calculations for Mo(CO)~with basis set A are at the 3-21G level for the ligand atoms but do not include the extra-{ diffuse sp functions. Results are also given for Mo(CO)~(basis set D) at the 4-31G level for the C and 0 atoms. The CO distance in Mo(CO)~was taken as 1.16 A, which is the internuclear distance for CO with this basis set, and the M0-C distance was chosen as 2.1 1 A, as deduced from point-by-point energy optimization. Experimental distances from electron diffraction data are r(C-0) = 1.145 A and r(M0-C) = 2.063 A.35 Set B calculations were also performed with GAUSSIAN WAC 8.3 programs with the geometries described for basis set A. A problem arises on using these basis sets with orbital exponents optimized for atoms: the optimized 3d orbital exponents for compounds with first-row transition elements lead to a charge density that is too close to the metal to give effective bonding. S i r l y , the exponents representing the 4s orbitals usually appear to be too diffuse and extend too far away from the bonding region. Following the suggestion of Hay,Man extradiffuse d function was included. The exponent 0.045 in Table I was obtained by energy optimization for the [Moo4]*-anion and is in good accord with the value of 0.0432 used by Bauschlicher et aL3’ This basis set (26) Frisch, M. J.; Binkley, J. S.; Schlegcl. H. B.; Raghavachari, K.; Melius, C. F.; Martin, R. L.; Stewart,J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; &frees, D. J.; -a, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Poplc, J. A. GAUSSIAN w; CamegiaMellon Quantum Chemistry Publishing Unit, Pittsburgh, PA, 1984. (27) human. T. D.; Hanren, Aa. E.,Program No. 556. QCPE,Indiana University, Bloomington, Indiana, 1988. (28) Huzinaga. S.Gaussian Basis Sets for Molecular Calculations; Elsevier: New York, 1984. (29) Ditchfield, R.; Hehre, W. J.; Pople, J. A. J . Chem. Phys. 1970, 52, 5001.
(30) Frisch, M.J.; Poplc, J. A.; Binkley, J. S.J . Chem. Phys. 1984,80, 3265. (31) Clark, T.; Chandrasckhar,J.; Spitznagel,G. W.; Schleyer, P. v. R. J . Comput. Chem. 1983, 4, 294. (32) ScWer, F. A. Acta Crystallogr. Ser. B. 1975,31, 2294. Leciejewicz, J. Z . Kristallogr. 1966, 121, 158. (33) Schiifer, H.; Schiifer, G.; W e b , A. Z. Nuturfwsch. 1964, 198, 76. (34) Lutz, 0.;Nolle, A.; Kroncck, P. Z . Naturforsch. 1976, 31A, 454; l f i , 32A, 505. (35) Amcdcn, S. P.; s i p , H. M. Acta Chem. S c u d 1966, 20, 2711. (36) Hay, P. J. J . Chem. Phys. 1977,664377. (37) Walch, S.P.; Bauschlicher, Jr., C. W.; Nelin, C. J. J . Chcm. Phys. 1983, 79, 3600.
Chemical Shielding in Transition-Metal Compounds
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5465
TABLE E
Ab Initio LQRG RewlCl for Mo Shidhg in tbe Seriea of Oxothiomdybdates, Mo(CO), rad MoNQ- Compand with tk Experimental I h t P bhld
species' [Mad"'
A
B
"'
[MoOpS]
[Maw-'
[MOOS,]*-* [ MOS,]~-'
Mo(CO)d
C A
B C A
B C A
B C A B C A
B
od
0.p
UT
CalCd
exptP
4d orbital populn
5379.5 5388.2 5297.2 5385.0 5399.8 5295.3 5421 .O 5361.8 5315.2 5474.8 5508.0 5362.0 5569.1 5589.4 5441.3 4658.2 4646.8 4280.4
-6334.2 -6395.5 -6167.9 -7173.2 -7219.1 -6686.2 -8154.2 -8168.6 -7490.9 -9257.4 -9208.3 -835 1.1 -10485.4 -10334.8 -9313.0 -3799.2 -3755.2 -7053.0
-954.7 -1007.8 -686.4 -1788.2 -1819.3 -1 390.9 -2733.2 -2806.8 -2175.7 -3782.4 -3700.3 -2989.2 -4916.3 -4744.9 -3871.8 859.1 891.3 -2773.6
0 0 0 833.5 811.8 702.7 1778.5 1799.0 1507.4 2827.7 2692.5 2367.7 3961.6 3737.1 3185.4 -1813.9 -1898.6 2087.2
0 (0)
3.547 3.761 3.307 3.822 3.881 3.570 4.1 IO 4.115 3.872 4.409 4.424 4.191 5.016 4.733 4.191 6.215 5.804
497 (451) 1067 (997) 1654 (1586) 2259 (2209) -1856
MoNCI;' A 1106' 'Entries in columns 3 - 6 are in ppm. Basis sets are given in Table I. bGeometrical data are given in the text. 'Values relative to [Mo04J2-. dMeasured in aqueous solution by Lutz et al., ref 34. Values in parentheses were measured in acetonitrile by Do et al., ref 44, and by Gheller et al., ref 42. A value of -1875 ppm for Mo(CO)~was reported by: Bailey, J. T.; Clark, R.J.; Levy, G. C. Inorg. Chem. 1982, 21, 2085. 'Energies for the basis sets A-C are -4270.06, -4271.21, and -4271.34 au, respectively. /Energies for the basis sets A-C are -4591.20, -4593.56, and -4593.69 au, respectively. #Energies for the basis sets A-C are -4912.23, -4915.90, and -4916.05 au, respectively. *Energies for the basis sets A-C are -5233.47, -5238.25, and -5238.41 au, respectively. 'Energies for the basis sets A-C are -5554.61, -5560.60, and -5560.76 au, respectively. )Energies for the basis sets with 3-21G and 4-31G basis sets on the ligands are -4645.02 and -4647.73 au, respectively. 'Energy for MoNC14- using 4-31+G* on the ligands is -5862.97 au. 'Minelli, M.; Young, C. G.; Enemark, J. H. Inorg. Chem. 1985, 24, 1111. can be described as triple-{quality (433321/43311/4211) for the d orbitals on the metal. For set B computations of the oxothiomolybdates the ligand basis sets were 4-31+G.30J8 Because of the large number of ligand atoms in Mo(CO)6, the 4-31G basis sets (set D in Table I) were used on carbon and oxygen. Geometry optimization for Mo(CO), with this basis set led to r(C-0) = 1.133 A and r(Mo-C) = 2.11 A. The MO calculations with basis set C were performed with a version of the program GAMESS'~ (which seemed to offer some advantages for SCF calculationsinvolving transition metals) and WAC E.&' In this case the quality of the basis set was improved by inclusion of polarization functions on the ligands. Exponents for the d functions on 0 and S in Table I were taken from the compilation of Huzinaga.28 Results for MoNCI4- were only obtained with basis set C, and the X-ray geometry r(Mo-N) = 1.637 A, r(Mo-Cl) = 2.344 A, and L(N-Mo-Cl) = 103.1°.41 Modules were written to interface the SCF programs (GAUSSIAN 86 and GAMES) with the version of WAC program which permitted computations of shielding by means of the LORG a l g ~ r i t h m . ~ Computations were performed on IBM 4381 and 3090-VF computers. The computation time of the Mo shielding in Mo(CO),, which was performed with a triple-{ basis set for Mo and 4-31G basis sets for carbon and oxygen, required 0.9 h for the SCF part and 3.9 h for the shielding (LORG) calculation on an IBM 3090-VF computer.
Results and Diecussion A. Basii Set and Geometry Dependence. Entered in Table I1 are the calculated diamagnetic contributions ad, paramagnetic contributions up, and the total isotropic shielding uT for the molybdenum compounds of this study. These were obtained with basis sets A-C. An exception is Mo(CO), for which the smaller (38) Ditchfield, R.;Hehre, W. J.; Pople, J. A. 1.Chem. Phys. 1W1,54, 724; Hehre, W. J.; Lathan, W. A. 1.Chem. Phys. 1972, 56,5255. (39) Dupuis, M.;Spangler, D.; Wendoloaki, J. J. National Resource for Computations in Chemiatry Software Catalog, Program Q G O I , 1980. Schmidt, M.W.; Boatz, J. A.; Baldridge, K. K.; Soreki, S.;Gordon, M.S.; Elbert, S.T.; Lam, B. QCPE 1987, 7, 115. (40)Bouman, T.;Hanren, Aa. Program RPAC. Elwtronic Excitation Propcrtia and Nuclear Magnetic Shielding in the Random Phase Approximation, Venion 8.4; private communication, 1989. (41) MOller, U.;Schweda, E.;Strithle, J. Z.Nufurforsch. 19133,388,1299. Knopp, B.; Ldrcher, K. P.; Strihle, J. 2.Nuturforsch. 1977, 328, 1361.
set D (see Table I) was used. In fact, it was not possible to obtain the basis set C results for Mo(CO), because the integral files were too large to permit calculations with available resources. Data in Table I1 clearly show that the total molybdenum shielding and the changes in the shielding are dominated by the paramagnetic terms. In fact, for the [Mo0,,S~c,,,]2- (n = 0-4) anions in Table I1 the changes in the diamagnetic contributions are less than 5% throughout the series. Prior to our communicati~n,~~ this behavior had only been noted for Mn.15 This is precisely the result expected for transition elements having partly filled d subshells. Since the diamagnetic contributions are relatively insensitive to basis set quality, it can be seen from the data in Table I1 that the dif€ercnca between calculated and experimental results are primarily due to improperly calculated paramagnetic terms. The total paramagnetic contribution in Mo(CO), has the smallest magnitude in Table 11. The paramagnetic term is actually exceeded in magnitude by the diamagnetic term even though the latter is about a 1OOO-ppm smaller than for the other molecules in the table. As noted above, it makes no sense to compare calculated diamagnetic and paramagnetic contributions based here on a distributed origins approach with those obtained by other groups using a common origin. In Table I1 the calculated Mo chemical shifts for the three basis sets are compared with the experimental data34.42-'sin aqueous solution referenced to [Mo0412-. The 95Moshifts differ by as much as 70 ppm from values, which were measured in acetonitrile and which are included in parentheses in Table 11. Calculated chemical shift results are referenced to the [Mo04]* values with the same basis set. The comparison of theoretical results for isolated molecules with experimental data in condensed phases is difficult especially in circumstances such as these where the data are known to be extremely solvent dependent. Since these computations are only at the triple-S level for the valence orbitals of the metal, overestimation (larger absolute value) of the paramagnetic contributions was expe~ted.4~'In the IGLO (42) Gheller, S.F.;Hambley, T. W.; Rodgen, J. R.;Brownloe, R.T. C.; O'Connor, M.J.; Snow, M.R.; Wedd, A. G. Imrg. Chem. 1984,23,2519. (43) Kroneck, P.; Lutz, 0.;Nolle, A. Z.Nuturforsch. 1980, 354 226. (44) Do, Y.;Simhon, E. D.; Holm, R. H. Inor Chem. 1985,21, 1831. (45) Belton. P. S.; Cox, I. J.; Hams, R. K.; &onnor, M. J. Ausr. 1. Chcm. 1986, 39,943.
5466 The Journal of Physical Chemistry, Vol. 95, No. 14, 1991
Combariza et al.
TABLE Ilk c.lestcd !W&bg Tensom for nMo, ‘‘0, d% in the Oxothiowlybdates, d nMo in Mo(C0)‘ d MoNQ-O species 4Mo) 40) 4) [M~,I2[ MoO3SI2-
[Mo02S212[MOOSJ2[ M ~ d ”
-686.2 0.0 0.0 -1777.5 0.0 0.0 -3137.0 0.0 0.0 -2434.5 1.7 0.9 -3871.8 0.0
0.0 ~ o ( c 0 ) ~ MoNC1;
891.3 0.0 0.0 -4237.3 0.0 -0.4
0.0
0.0
-686.3 0.0
0.0 -686.3
0.0
0.0
-1777.5 0.0
0.0 -617.6 0.0 0.0 -2126.6 -1.8 1 .O -4104.3 0.0 0.0 -3871.8
0.0 -1268.4 0.0 -5.0 -2428.7 -0.1 0.0 -3871.8
0.0 0.0 0.0 -4237.3 0.3
-268.0 -564.2 268.0 -470.2 -442.7 -126.1 0.0 -1034.2 0.0 -0.3 -1422.8 -0.2
-268.0 268.0 -564.2 125.0 -216.5 -794.7 647.3 0.0 -1088.8 1.2 -0.7 -229.5
-126.1 0.0 0.0 -629.6 0.0
0.0 -173.4 -338.5 287.6 -366.8 474.5 474.5
0.0 -126.1 0.0 0.0 361.0 -458.4 -339.0 217.8 -497.1 474.5 -366.8 474.5
0.0 0.0 750.8 0.0 -341.8 157.1 216.1 -375.2 -692.5 474.5 474.5 -366.8
0.0 0.0
891.3
0.0
-564.2 -268.0 -268.0 -985.6 -470.2 72.8 -561.9 0.0 517.2 -1421.8 0.9 0.3
891.3 -0.2 0.2 153.9
and [MOS,]~- the Cartesian axes are along the C2axes. In [MO02S212-the 0 and S atoms lie in the yz and the z axis is along the Mo-S bond and the tensor is for the oxygen atom in the xz plane. The coordinate system for [MoOS3I2- is analogous. The Mo-N bond is along the z axis in MONCIi, and one of the chlorine atoms is in the yz plane.
OAll values are in ppm. In
xz planes, respectively.
For
and LORG methods satisfactory chemical shift results are often obtained for first- and second-row elements if the basis sets are triple-t plus a set of polarization functions. The improvement in the paramagnetic term with basis set size can be ascribed to the expansion of the virtual orbital space. Because the metal ions of this study have so many core and lone pair orbitals, the ratios of the number of virtual orbital orbitals to the number of occupied orbitals are actually less than for double-f basis sets in hydrocarbons.”” Currently available resources do not permit expansion of the basis sets to provide the desired flexibility in the virtual space. The calculated Mo chemical shifts for the oxothiomolybdates with basis sets A-C in Table I1 are plotted as a function of the experimental data in Figure 1. As expected, the calculated values improve substantially with the quality of the basis set asymptotically approaching the experimental values, which are depicted by the open triangles in Figure 1. Even for basis set C the disparities between the theoretical and experimental values are as large as 900 ppm. However, this represents no more than a 10% error in the paramagnetic contributions in Table 11. The monotonic Mo deshielding in the anions, resulting from successive replacement of oxygen by sulfur, is well-reproduced by the calculated results. In fact, for the best basis set (C) the correlation coefficient 9 is 0.9999 in the linear regression between the computed bM0(calcd) and experimental GMo(exptl)95Moshift data for the oxothiomolybdates in Table I1 G~~(calcd) = 1.41 5GMO(exptl)- 2 ppm (1) where the standard deviations in the slope and intercept are 0.009 and 17 ppm, respectively. The calculated chemical shielding for Mo is exceedingly sensitive to geometry around the position of the optimum geometry. For example, shortening the M e 0 bond of [MoO4I2-by 0.022 A from the value used here leads to a 317 ppm increase (more positive) in the calculated Mo chemical shielding. This is an important finding because older bond length data for this molecule are almost certainly too long by about 0.05 A, e.g., 1.83 A.“ As a consequence, the use of this longer Mo-0 bond length would ~
~
~~~
(46) Calculations using the coupled Hartrce-Fwk method with a common origin give results for firat- and second-row elements which a n not generally
as good as the distributed origins methods with the same basis set. The CHF
methods applied to transition metals appear to underestimate the paramagnetic term, giving fortuitously better results for a given basis set. (47) Orendt, A. M.; Facelli, J. C.; Beeler, A. J.; Reuter, K.; Horton, W. J.; Cutta, P.; Grant, D. M.; Michl, J. J . Am. Chem. Soc. 1988, IIO, 3386. (48) Donohue, J.; Shand, W. J . Am. Chem. Soc. 1947,69, 222.
4000
I
I
io00 ~,,dexptl), ppm
AB/ I
I
2000
1
Figure 1. A plot of the calculated Mo chemical shifts GMo(~l0d)in the oxothiomolybdate series versus experimental values GMo(exptl) relative to 0,set A; 0,set B; 0 , set C; A, exptl.
lead to a more negative value of the Mo shielding for [Mo0,12-, and fortuitously better resultsI6 with smaller basis sets than the ones used here. The molybdenum tensor shielding data for all of the compounds of this study and the oxygen and sulfur tensor data for the 0x0thiomolybdate anions are entered in Table 111. Because of difficulties of solid-state NMR measurements for quadrupolar nuclei, there appear not to be experimental data for comparison at this time. However, there is substantial interest in theoretical values of tensor components, especially in metals where the shielding anisotropies can be very large. The tensors in Table 111 exhibit the expected a ~ y m m e t r i e s associated ~~s with nuclei in sites of varying symmetry. For example, Mo in an octahedral site has only a single independent component, whereas 0 in [Mo02S212has five independent components. It is not clear why the tensor data for [MoOJ” deviate by a few ppm from the symmetry rules. Smaller deviations from the symmetry rules occur in the Mo shielding tensor in MoNC1,-. B. Molybdenum SWding in Oxothiamolybdate ~00,&,-,,,]~AniA major goal of theoretical studies of molecular pmpertm is one of finding a simple conceptual basis for interpretation of (49) Buckingham, A. D.; Malm, S. M.Mol. Phys. 1971, 22, 1127. (50) Hansen, Aa. E.; human, T. D. J . Chem. Phys. 1989, 91, 3552.
Chemical Shielding in Transition-Metal Compounds I
I
I
I
I
I
1 ,
The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 5467 ad
UT
up
2-
2-
2-
2-
2-
q,,(MO) Figure 2. A plot of calculated (0, basis set C) Mo chemical shifts bM,,(calcd) and the experimental data (0) c$&(exptl) for the oxothiomolybdate anions versus the calculated (basis set C) 4d orbital population q4d(W.
the experimental results. Shielding phenomena in transition-metal compounds are particularly interesting, but most molecules have 4-6 ligands each with a number of atoms. It is difficult to envision the feasibility of the computational procedures of the type used here for a few relatively simple molecules. There have been a number of attempts to rationalize the NMR data via correlations with low-lying electronic transitions. However, in contrast to the shielding, satisfactory values for excitation energies are not obtained at the Hartree-Fock level. Moreover, theoretical NMR shielding formulations, which use a single excitation energy, would give exceedingly poor results. An alternative criterion, which is presented here, makes use of the dependence of calculated and experimental chemical shifts on the p and d atomic orbital populations. Although this procedure also does not have a rigorous theoretical basis, it does offer some promise of a common theme and 33S)chemical shifts in for relating the various (95Mo,"0, these anions. As noted previously, the LORG method gives the total shielding as the sum of diamagnetic contributions associated with inner shells, bonds, and lone pairs. This also provides an alternative but rigorous description of factors involved in the shielding. 1. Correlation with 4d Orbital Population on Molybdenum. The excellent correlation between Mo chemical shifts and Mo atomic charges, which was noted for the oxothiomolybdate series in our earlier comm~nication,'~ is not followed as well with the larger basis sets used here. Although changes in the ab initio 4d atomic orbital populations on Mo are still the major factor in the Mo atomic charges, the basis set C results exhibit a large jump in the 5s orbital populations for [MoO4I2-in comparison with [MoO3SI2-. Since the molybdenum 5s atomic orbitals play a negligible role in the paramagnetic shielding trends for these anions, it will be of interest to examine the correlation with the calculated Mo 4d atomic orbital populations. The latter are entered in last column of Table 11. The resulting 4d orbital populations of molybdenum increase monotonically as oxygens are replaced by sulfur atoms in conformity with the expectation that sulfur atoms attract electrons less strongly than oxygen atoms. Although the d-orbital demities do not explicitly enter theoretical expressions for the paramagnetic shielding, it is reasonable to expect that such terms would be related to the occupation of p and d atomic orbitals which have nonzero angular momentum. Since the diamagnetic terms vary by less than 5% in the anions, it should also be adequate to consider the relationship to the total calculated or experimental chemical shifts. Plotted in Figure 2 are the calculated ( b i s set C LORG) results for the Mo chemical shifts b ~ , ( c a l c d )of the oxothiomolybdatesand the experimental data bMo(expt1) as a function of Mo atomic charges q4(Mo) (basis set C). Least-squares analysis gives the result &, (calcd) = 275Oqa(Mo) - 91 17 ppm with correlation coefficient = 0.9992. In addition, the experimental Mo chemical shift data are plotted
3
I
2-
Figure 3. Schematic diagrams showing the calculated (basis set C) diamagnetic contributions d,paramagnetic contributions d,and total Mo shielding uT associated with the bonds and lone pairs of the ox* thiomolybdate anions. Since shielding contributions from each type of bond are the same by symmetry, it is sufficient to tabulate values for a single Mo-O or Mo-S bond for each species in Figure 3.
in Figure 2 as a function of the 4d orbital population qU(M0). These data give a comparable relationship bMo(exptl) = 1942qM(Mo)- 6437 ppm with correlation coefficient ? = 0.9986. 2. Bond and Lone-Pair Contributions to Molybdenum Shielding. Observation of the monotonic increase in the chemical shift (decrease in shielding) in the oxothiomolybdate series might suggest at the simplest level that each Mo-S bond has a paramagnetic contribution which is about 500 ppm more negative than an Mo-O bond. Of course, the situation is more complicated as can be seen from an analysis of the local (LORG) contributions to the total shielding. Depicted schematically in Figure 3 are the calculated local diamagnetic contributions d,paramagnetic contributions up, and total calculated isotropic shielding values uT for Mo which arise from the bonds and lone pairs in the oxothiomolybdate anions. The large positive diamagnetic contributions, which arise primarily from the Mo inner shells, are not listed in Figure 3. These data show that progressive replacement of sulfur by oxygen lead to relatively small changes (less than 30 ppm per bond or lone pair) in the diamagnetic contributions within the oxothiomolybdate series. The magnitudes of bond paramagnetic contributions for both Mo-O and Mo-S increase monotonically (-1181 ppm per bond for Mo-O in [MoO4I2-to -1731 ppm per bond in [MoS4I2-) in the series. Differences of total bond paramagnetic contributions between successive members of the series are -426, -564, -545, and -667 ppm. This trend is completely consistent with the monotonic deshielding noted in the experimental data. Moreover, progressive substitution by sulfur leads to more negative values of the Mo paramagnetic lone-pair contributions for both 0 and S (paramagnetic contributions from all lone pairs range from -1440 ppm in [M0O4I2-to -2540 ppm in [Ma4]*) in Figure 3. Differences of total lone-pair paramagnetic contributions between successive members of the series are -241, -205, -225, and -246 ppm. Thus, the experimentally observed trends in the chemical shifts, upon progressive oxygen replacement by sulfur, arise from the greater deshielding associated with all of the bonds and lone pairs! C. Shielding in Mo(CO)~and MoNq-. Shielding data for Mo(CO)~and MoNCl,' are entered in Tables I1 and 111. Calculated results for these molecules are quite different than for the oxothiomolybdate anions. In particular, Mo(CO)~corresponds
Combariza et al.
5468 The Journal of Physical Chemistry, Vol. 95, No. 14, 1991 Ud
UP
UT
TABLE IV: Comprrkm of Expwl”t8l SbkMag Dah for O X O t h i O m h k 3 , OXotbiorrsrhta,d exptl’ exd
CXPtl’
0 [WO,]” 0 [V04l5 0 [M00jSI2833 [WO3S]” 290 841 [VO3S]” 720 [M00$3z]2- 1067 [ W O Z S ~ ] ~1787 [VO#J)1280 2760 [VOSf [MOS,]~2259 [WOS I*MOOS^]^1940 1654 [WS,$3769 [VS,] -1416 Mo(CO)~ -1856 W(CO)6 -3483 V(CO),‘Reference 34. *Reference 42. W(CO)(: Malisch, W.; Malisch, R.; Colquhoun, I. J.; McFarlane, W. J . Orgonometof. Chem. 1981, 220, C1. CReference51. V(CO)6: Rehder, D.; Bechtold, H.-Ch.; Kcceci, A.; Schmidt, H.; Sewing, M. 2.Noturforsch. 1982, 378,631. [M004I2-
core:
3094
89
3983
dxy:
04
-1049
-965
dxz:
04
-1049
dyz:
84
-1049
- 965 - 965
4Ooo
/I
Figure 4. Schematic diagrams showing the calculated (basis set D)
diamagnetic contributions ad, paramagnetic contributions OP, and total Mo shielding uT associated with the bonds, lone pairs, and d orbitals of Mo(CO)(. Because of symmetry, it is sufficient to give only those contributions associated with one of the M A 4 moieties of Mo(CO)(. &J
up
/I
M=W
/
UT 7 -
I
Figure 5. Schematic diagrams showing the calculated (basis set C) diamagnetic contributions ad, paramagnetic contributions aP, and total Mo shielding uT associated with the bonds and lone pairs of [MoNC14]-.
to the situation in which Mo has a formal charge of 0. The calculated molybdenum chemical shift of -1898 ppm (basis set D) for Mo(CO)~is in fortuitously good agreement with the experimental values of -1 856 and -1 875 ppm in Table 11. Factors that could lead to agreement for a modest basis set include choice of bond length, relatively poor basis set, and gas-tesolution shifts, e.g., a situation perhaps analogous to the sinslearigin CHF results in the oxdhiomolybdate series.I6 However, from the following discussion of the factors involved in the shielding in MO(CO)~, it seems likely that the computed chemical shifts are probably insensitive to the assumed bond lengths. Given schematically in Figure 4 are the d and aP contributions and the total Mo shielding a’ (basis set D) associated with the bonds, lone pairs, Mo m,and d orbitals of MO(CO)~ The total contribution of all six of the Mo-C bonds to the total calculated Mo shielding is only -135 ppm! Furthermore, the total contribution of all bonds and lone pairs to the total calculated Mo shielding is only -204 ppm. The major factors in the approximately 900 ppm positive shielding are the 3894 ppm diamagnetic Mo con contribution and the paramagneticshielding contribution of -3148 ppm from the d orbitals (dx,,, d,, and d ) on Mo. Clearly, the original argument of Griffith and Orgel%regarding shielding in complexes of octahedral symmetry is followed remarkably well. Since the angular momentum operators, which enter the expressions for the shielding, transform as t5, the ground state of A,, symmetry will give nonzero paramagnetic shielding components from states of TQ.symmetry. As predicted?2 only small corrections arise from mixing of the e* orbitals due to the effects of u bonding. Shielding results for Mo(CO)~imply that the chemical shift range for Mo(0) should be relatively insensitive to the nature of the substituents. In contrast to the very large range of shielding for other Mo compounds, almost all of the data for Mo(0) fall between -1400 and -1800 ppma6 For MoNC14- the calculated Mo chemical shift (basis set C) of 2087 ppm is not in impressive agreement with the experimental value of 1106 ppm, but it is consistent with about a 10% overestimation of the paramagnetic contribution in Table 11. The Mo
&(exptl),
ppm
Figure 6. Experimental chemical shift data bM(exptl) in oxothiotungstates (0,M = W) and oxothiovanadates(0,M = V) plotted versus the experimental values bMo(eXPt1) for the oxothiomolybdates.
formal charge is again 6, but a major difference from the oxothiomolybdate anions is the Occurrence of the M o z N bond. Depicted schemically in Figure 5 are the calculated diamagnetic contributions 8,paramagnetic contributions 8, and total isotropic shielding values u*, for Mo which arise from the bonds and lone pairs in MoNCl,-. The total shielding arising from the three equivalent Mo-N triple bonds is -4216 ppm in Figure 5. In contrast, the four Mo-Cl bonds give a total of only -1740 ppm. The lone pair of nitrogen contributes substantially more (-599 ppm) than each of the lone pairs on chlorine (-86 ppm); however, the 12 of the latter make a substantial contribution to the total. D. chq”of Treads for Mwith Metals in F’irst and Third TrPIIsitioa Series: Vurrdium, Tungsten, md Rhenium. Any transferability of the Mo shielding results to other elements offers the potential for interpretation without additional computation. The available experimental chemical shift data for r e p resentative compounds of molybdenum, vanadium and tungsten are entered in Table IV and plotted in Figure 6. In fact, the correlation between the experimental chemical shift data for the oxothiomolybdate series and the corresponding oxothiotungstate series in Table IV and Figure 6 is remarkably good4s Gw(exptl) = 1.6666,,(exptl) 6 ppm (2)
+
with standard deviations of 0.003 and 6 ppm in the slope and intercept, respectively. Not surprisingly, the correlation is not as good if data for the carbonyls (in Table IV) are included. Because of the analogous chemistry, a good correlation of the Mo chemical shifts of the oxothiomolybdatesand oxothiovanadates might be expected. Literature data for the oxothiovanadatesare also given in Table IVS1and are plotted in Figure 6. The range for vanadium (1933 ppm) is only slightly smaller than Mo in this ~~~~~~~
~
~
~
(51) Bachofer, S.J.; Hayden, Y.T.; Edwards, J. O., unpublirhed results cited by: Hagen, K.1.; Schwab, C. M.; Edwards, J. 0.; Sweigart,D.A. Inorg. Chem. 1986, 25,918.
The Journal of Physical Chemistry, Vol. 95, NO. 14, 1991 5469
Chemical Shielding in Transition-Metal Compounds
TABLE V Ab Initio LORG R d b for Oxygen SWdhg in tk Series of Oxothiolwlybdates with Basis Seb A-C
witb tk
ExpCriaclltrl V 8 h "
60
d
speciesb H,(T
[MoO,l2[MoSOJ
'-
A
300.7
B C
290.3
A
B C A
B C C A
CalCd
exptl'
2p orbital populn
859.4 979.6 817.8 1050.2
525 (544)
4.951
313.6
443.9
450.1 447.4 449.9 456.6 453.6 456.6
[MoOS3l2-
UT
UP
194.1 462.1 464.2 471.5
-558.7
-1002.6 -1 139.4 -101 1.6 -1 199.4 -1366.8 1 194.6 -1 376.4 -1 569.5
-689.3
-564.2 -759.5 -910.3 -741.0 -919.8
-1375.4
-1352.0 -1525.0 -1739.8 -1 500.0
-895.0
-1060.7
4.860
585 (624)
1211.0
1054.6 1220.5 1676.2 1195.7 1361.5 1587.0 1325.4
633 (696)
699 (759)
5.OOO 4.889
4.860 4.943 4.840 4.787
4.879 4.799 4.7 17 4.829
-1286.3 B -1024.7 469.3 C ovalus in columns 3-7 are in ppm. Basis sets are given in Table I. *Structural data are given in the text. eChemical shifts relative to ''0 in H 2 0 for the corresponding basis set. dReferenceS44-46. 'An experimental geometry was used with r(0-H) = 0.96 A and LHQH = 104.5'.
and bv(exptl) is related to bM0(exptl) by means of the relationship bv(eXpt1)
0.8626~~(eXptl) - 98
(3 )
with 9 = 0.987. For the analogous compounds of rhenium [Reo4]-and [ReSJ the shift of the latter relative to the former is 2586 ppm.5) and, by analogy to the data for W and V,it should be possible to make reasonable predictions for the other members of this series. In view of the many unexplained chemical shift results for transition metals, there is a remarkably good relationship between the oxothiometal compounds which include first- through third-row transition series metals. E. shiekding in tbe Ligand Nuclei: I7Oand '5. The chemical shifts of both 170and 33Sin the series of oxothiomolybdate (and oxothiotungstate) anions have been measured in aqueous solution and in acetonitrile, and correlated with the 9SMoshifts in these The few existing theoretical studies of NMR shielding in transition-metal compounds have ignored the shielding of the atoms in the ligand even though theoretical chemical shifts of atoms in the first and second rows have been studied extensively.8J1*J5 The ligand shielding data offer additional potential for the interpretation of structure and bonding in transition-metal compounds and can be obtained routinely along with the metal shielding computations. Entered in Table V are the computed oxygen isotropic shielding data for the oxygen-containing molybdenum com unds of this study for basis sets A-C, and the experimental 0 chemical shifts measured in aqueous solution and in acetonitrile." Since HzOis the usual reference compound for I7Ochemical shifts, the HzOisotropic shielding data for basis sets A-C are also entered in Table V. The LORG (basis set C in Table V) value for the 170shielding in H20is 314 ppm, which is in reasonable agreement with the IGLO value of 305 ppm for a comparable basis set.7 The experimental gas-phase shielding value is 357 ppm." The calculated oxygen chemical shifts for the oxothiomolybdates in Table V were obtained relative to the H20value for the equivalent basis set. Experimental "0chemical shift data in this series are exceedingly dependent on the nature of the solvent, exemplified here by changes as large as 60 ppm measured in H20versus acetonitrile. As a consequence, it is more difficult to ascribe the disparities in the theoretical (hypothetical gas phase) and experimental data to basis set and other inadequacies in the theoretical computations. The agreement for oxygen chemical shifts is far from quantitative, possibly a consquence
P
(52) Dwek, R. A.; Luz, Z.; Shporer, M. J. Phys. Chcm. 1970, 74,2232. MOller, A.; Krickemeyer, E.; Wgge. H.;Penlt, M.; Rehder, D. Chlmfu1986, 40. 50. (53) Do, Y.; Simhon, E. D.; Holm,R. H.Ituwg. Chcm. 1985, 24,4635. (54) Fowler, P. W.; Raynca, W.T.; Mol. Phys. 1981, 43, 65. (55) Schtndler. M. J. Chcm. Phys. 1988, 88, 7638.
9,JMo) Figure 7. Plots of the calculated (basis set C) chemical shifts for oxygen [O, bO(calcd)]and sulfur [0,$(calcd)] and the experimental chemical shift data for oxygen [O, bo(exptl)], and sulfur [A,Gs(exptl)] in the oxothiomolybdateanions versus the calculated (basis set C) 4d orbital
populations qM(Mo)for molybdenum. of the relatively small virtual orbital space provided by the basis sets used here. Since a substantial improvement in the Mo shielding results was noted on inclusion of polarization functions on the ligands, it seems likely that the comparable improvements for oxygen and sulfur shieldings will be obtained on inclusion of f orbitals on molybdenum. Moreover, within the series of oxothiomolybdates there is a good correlation between the calculated bo(calcd) and experimental chemical shift data bo(exptl), and this can be examined in terms of the least-squares result bo(calcd) = 2.593b0(exptl) - 469 ppm (4) with correlation coefficient 9 = 0.989, and the standard deviations in the slope and intercept are 0.186 and 24 ppm, respectively. Because of the correlations of the calculated and experimental Mo chemical shift data with the 4d atomic orbital population for Mo,it was of interest to see if the I7O data also exhibited a comparable dependence. Entered in the last column of Table V are the 2p atomic orbital populations qtp(0)for oxygen with basii sets A-C. The increases in the 4d populations with oxygen replacement by sulfur occur almost entirely because of population transfer from the oxygen 2p and the sulfur 3p atomic orbitals in the series. Both the calculated (basis set C) and experimental chemical shifts exhibit a linear dependence on the 2p populations, but the reason for slopes opposite to those for Mo in Figure 2 is not yet clear. Possibly, since oxygen replacement by sulfur is two bonds removed the most important electronic changes are associated with the molybdenum. In fact, the oxygen 2p and mo-
Combariza et al.
5470 The Journat of Physical Chemistry, Vol. 95, No. 14, 1991
TABLE VI: Ab Initio LORG R d t s for sulhv Skldlng in the scrim of OxotLlomdybdates with B M Sets ~ A C Compnred with the Ex~erimeotdIhW species SO4'-'
d
up
A
B C
[MoS03]'-
A 1098.1 -1103.2
B 1101.4 -1092.4
C 1097.6 [MOS202]'- A 1107.1 B 815.9 C 1110.4 [M&Sjl2- A 1121.9 B 1123.9 C 1119.7 [MoS,]' A 1130.3 B 1134.2 C 1129.1
-931.4 -1372.9 -359.6 -1147.5 -1610.1 -1596.1 -1335.6 -1794.0 -1785.1 -1495.9
6s 3p orbital calcd exptId popuh 202.1 0 0 236.4 290.0 -5.6 207.8 -25 4.800 9.1 227.3 4.809 166.2 123.9 5.130 -265.8 467.9 123 4.729 -543.7 780.1 4.690 -37.2 327.2 5.034 488.2 690.3 240 4.664 -476.0 712.4 4.593 -215.9 506.0 4.913 -663.7 865.8 345 4.617 -651.0 887.4 4.541 -366.8 656.8 4.848
2
"Value in columns 3-7 are in ppm. Basis sets are given in Table I. bGeometrical data for the anions are given in the text. CChemical shifts relative to SO,'- for a given basis set. dReference 45. 'For these calculations r ( S - 0 ) = 1.49 A and the geometry is assumed to be tetrahedral.
lybdenum 4d populations are related, and somewhat better linear correlations for the oxygen chemical shift data are found with the Mo 4d orbital populations from Table I1 as depicted in Figure 7: bo(calcd) = 5O0qa(M0) - 754 ppm (9= 0.987) and bo(exptl) = 193q2,(0) - 109 ppm (? = 0.996). Although the relationship of the chemical shift to orbital populations is not rigorous, it does provide a way of rationalizing the observed relationships between the shielding of the metal and the ligands.45 Entered in Table VI are the computed sulfur isotropic shielding data (basis sets A-C) for the sulfur-containing molybdenum compounds of this study and the experimental 33Schemical shift data in aqueous solution. Since SO4*-is the usual reference for "S chemical shifts, the calculated S042-shielding data for basis sets A-C are also entered in Table VI. Previous ab initio results for sulfurss~include an isotropic shielding value for the reference compound (319.8 ppm) based on a coupled Hartree-Fock calc ~ l a t i o n . ~The ~ calculated sulfur chemical shifts for the oxothiomolybdates in Table VI were obtained relative to the value for an equivalent basis set. Again, within this series there is excellent correlation between the calculated bs(calcd) and experimental chemical shift data bs(exptl), and this can be represented by the least-squares result bs(calcd) = 1.447bs(exptl) 156 ppm (5)
+
with ? = 0.9995. The similarities, which have been n~ted,'~ between the 9 s M ~ , "0, and % experimental chemical shifts for the oxothiomolybdate anions suggest that these stem from a common source. In analogy to the results for Mo and 0,the "S calculated and experimental chemical shift data are correlated with the 3p atomic orbital populations q3 (S)on sulfur. The latter quantities were obtained with the three ksis sets and arc entered in the last column of Table VI. Again, even better correlations are found between the sulfur chemical shifts and the Mo 4d orbital populations. The calculated (56)T w l l . J. A.: Lazzeretti, P.; Vaughan, D. J. J . Mugn. Reson. 1987, 73, 334.
sulfur chemical shifts &(calcd) and experimental data &(exptl) are plotted in Figure 7 as a function of the Mo 4d orbital populations from Table 11. Linear regression analyses of the calculated (basis set C) and experimental data in Table VI give the results bs(calcd) = 412qa(M0) - 1486 ppm (9= 0.996), and bs(exptl) = 597qa(Mo) - 1997 ppm (? = 0.998). Conclusions
Calculations of shielding by means of distributed-origins methods are reported for several transition-metal compounds of molybdenum. It is demonstrated that the localized orbital-local origins (LORG)9 method satisfactorily reproduces the large 9SMo deshielding on successive oxygen replacement by sulfur in the oxothiomolybdate anions. The results clearly show that ab initio MO computational techniques for nuclear shielding can be used very effectively for qualitative interpretation of the experimental trends in chemical shifts of transition-metal compounds. The sensitivity of the calculated results to the quality of the basis sets has been investigated and appears to be no worse than the situation for many first- and second-row elements. Satisfactory chemical shifts were obtained with basis sets which are not excessive even for elements of the second transition series, but it will be of interest to expand the virtual orbital space, for example, by inclusion of f orbitals on the metal. Reasonable metal shielding results have been obtained without the inclusion of configuration interaction or relativistic effects, which would be a formidable complication at this time. Within the LORG algorithm the Mo shielding contributions are investigated in terms of diamagnetic and paramagnetic contributions from inner shells, bonds, and lone pairs. Although the shielding in Mo(CO)~and (by analogy) other nearly octahedral Mo(0) compounds is clearly dominated by the contributionsfrom the orbitals of the metal, this is not at all the case for the Mo(6) compounds of this study. This conclusion differs from other studis of transition-metal shielding based on coupled Hartree-Fock theory with a common gauge origin, and which give very small total shielding contributions for the ligands.15J6 The feasibility of computations of the chemical shifts of the ligand atoms, e.g., "0and 33S, is also demonstrated, and the trends for these nuclei are found to parallel those for Mo in the oxothiomolybdate anions. From these analyses it now appears that the monotonic deshielding, which is observed for molybdenum, oxygen, and sulfur, are related to the monotonic increase of about 0.3 units in the 4d orbital populations as oxygen is successively replaced by sulfur. Because of the excellent correlations between the 95Mochemical shifts of the oxothiomolybdates and the metal shifts in oxothio compounds of vanadium and tungsten, it seems very likely that the same electronic factors control the shielding.
Acknowledgment. We extend thanks to Prof. T. Bouman for providing preliminary versions of the RPAC program and for making valuable comments on the manuscript, to Dr. Julio C. Facelli for assistance with the implementation of the RPAC program, and to Dr. A. G. Wedd for pointing out some important references. We also express our appreciation for support from the U.S.Department of Agriculture under Grant No. 84-CrCr1 - 14 16 and the Cornel1 National Supercomputer Facility, a resource of the Center for Theory and Simulations in Science and Engineering, which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of the Corporate Research Institute.
