388 1
Inorg. Chem. 1990, 29, 3881-3890 Acknowledgment. This research is supported by grants from the swiss National Science Foundation. We thank Mrs. C, Kosinski for technical help. Supplementary Material Available: Tables of nitrate (Table TI) and
bound MeCN (Table T2) vibrations in solutions of Ln(NOh in acetonitrile and figures showing calibration curves for DMSO in acetonitrile (Figure FI) and absorbances of bound and free DMSO in solutions of Ln(N03), in acetonitrile (Figure F2) (8 pages). Ordering information is given on any current masthead page.
Contribution from the Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712
AM1 Parameters for Sulfur Michael J. S . Dewar* and Yate-Ching Yuan Received August 17, I989
AMI has been parametrized for sulfur. Calculations are reported for a wide range of sulfur-containing molecules. The calculated heats of formation and other properties of organosulfur molecules are much superior to those from MNDO and superior overall to those from PM3. AMI calculations for several reactions agree well with experimental values. The results for compounds of sulfur in its higher valence states are also satisfactory, except for SF,, where the error is probably due to the neglect of d AOs.
Table 1. Optimized AMI Parameters for Sulfur
Introduction Organosulfur chemistry has developed very rapidly in recent years' and now plays an integral role in organic chemistry. New types of structures found recently2in organosulfur compounds have enlarged our general knowledge of bonding and the electronic distributions in molecules. Many new reactions of compounds containing sulfur are now widely used in organic ~ynthesis,~ and many new types of biologically important organosulfur compounds have been d i s ~ o v e r e d . ~ The need for an effective theoretical treatment of organosulfur compounds is therefore clear. Use of a b initio procedures is restricted in this connection, as in many others,s by the computing time they need. Computational studies of chemical problems by adequate a b initio methods are frequently impracticable. These comments apply with special force to studies of chemical reactions, which require not only extensive exploration of potential surfaces but also the use of relatively high-level a b initio procedures, involving the use of split-plus-polarization basis sets and allowance for electron correlation. Sulfur presents more problems than the "organic" elements in this connection because it contains more orbitals and because the formal charge on it varies greatly, becoming very large in its higher valence states (SIv, Sv'). In organic chemistry, these difficulties have been largely solved by the development here of effective parametric ("semiempirical") procedures, in particular M N D 0 6 and AMI ,' which give results comparable" with those from quite good a b initio methods at less than one-thousandth of the cost. They are generally much superior to ones using minimum basis sets." However, determined attempts to parametrize M N D O or AMI for phosphorus or sulfur failed. No set of parameters could be found that gave satisfactory results for compounds containing them in all their valence states. Jn hindsight, this failure was due to one of the major problems met Senning, A., Ed. Sulfur in Organic and Inorganic Chemistry; M. Dekker Inc.: New York, 1971 and 1982; Vols. 1 and 4.
Kresze, G. In Sulfur, its Significance for Chemistry,for the G e e , Bio, and Cosmosphere and Technology: New Developments in The Field or Organic Sulfur Chemistry; Muller, A., Krebs, B., Eds.; Studies in Inorganic Chemistry, Vol. 5 ; Elsevier Science Publishers: Amsterdam, 1984; pp 93-120. (3) Bernardi, F.; Csizmadia, I. G.; Mangini, A. Organic Sulfur Chemistry; Elsevier Science Publishers: Amsterdam, 1985. (4) Muller, A.; Krebs, B.; Sulfur, its Significance for Chemistry,for the G e e , Bio, and Cosmosphere and Technology; Elsevier Science Publisher: Amsterdam, 1984; Chapter IV. See e.g.: Dewar, M. J. S. Int. J . Quantum Chem. 1988, 22, 557. Dewar, M. J. S.; Thiel, W . J . Am. Chem. SOC.1977, 99. 4899. Deward, M. J. S.;Zoebisch, E. G.;Healy, E. F.;Stewart, J. J. P. J . Am. Chem. Sor. 1985, 107, 3902. (a) Dewar, M. J . S.;Storch, D. M. J . Am. Chem. Soc. 1985, 107, 3898. (b) Dewar, M. J. S.;O'Connor, B. M. Chem. Phys. Lert. 1987,138, 141. 0020-1 669/90/ 1329-388 1$02.50/0
optimized params lJ,/eV
Up,/eV
Z,/au ZpIau &/eV
yg Gss
GPP GSP
GP2 HSP
KI K2 K3
LI
L2 L3
MI M2 M3
AM 1
MNDO
-56.694056 -48.71 7049 2.366515 1.667 263 -3.920566 -7.905278 2.461 648 11.786329 10.039 308 8.663 127 7.781 688 2.532 137 -0.509 195 -0.01 1 863 0.01 2 334 4.593 691 5.865 73 I 13.557 336 0.770665 1.503 313 2.009 173
-72.242 281 -56.973 207 2.312962 2.009 146 -10.761 610 -10.108433 2.478 026 12.880000 9.900000 11.260000 8.830 000 2.260 000
PM3 -49.895 371 -44.392 583 1.891 185 1.658 972 -8.827465 -8.091 415 2.269 706 8.864667 9.968 164 6.785 936 7.970 241 4.041 836 -0.399 191 -0.054 899 6.000 669 6.001 845 0.962 I23 1.579 944
in developing semiempirical treatments such as AMI, i.e. the fact that the hypersurface representing the mean error as a function of the parameters (parameter hypersurface) usually has numerous minima and it is not easy to find the optimum one. While we would normally have continued the search for a better minimum, we were not unnaturally misled by the fact that split-plus-d basis sets have to be used in a b initio studies of compounds of P and S and the natural assumption that the same might be true in AMI. Recently, however, Dewar and Jie9 succeeded in finding a better minimum on the parameter hypersurface for phosphorus, leading to a set of parameters that reproduced the properties of compounds containing it in both its valence states, and we have now likewise succeeded in finding a set of parameters that deals effectively with the even worse case of sulfur, where three valence states are involved. The effect of d AOs can apparently be largely compensated via the parametrization. However, as noted below, there are exceptional molecules where AMI gives poor results and where the error can reasonably be attributed to d AOs, or changes in AOs, playing an unusually large role. A similar situation exists in the case of anions. In a b initio studies of anions, it is necessary to use a basis set containing diffuse AOs to allow for the orbital expansion due to negative charge. Yet, AMI gives good results (9) Dewar, M. J. S . ; Jie, C. THEOCHEM 1989, 187, 1-13.
0 1990 American Chemical Society
3882 Inorganic Chemistry, Vol. 29, No. 19, 1990
Dewar and Yuan
Table - It. Calculated AMI and Observed Heats of Formation and Comparison of Errors for A M I , MNDO, PM3, and S l N D O l error molecule expa calcd AM 1 MNDO PM3 SINDOlb 28.0' 17.5 -10.4 8.9 9.0 -19.6 (-19.5) -5.5c.d -4.4 1.1 -I .8 -0.1 5.0 (2.4) - 1 1.1C.d 0.5 -2.6 -10.6 2.3 5.3 ( 1 . 1 ) -0.5 -1.6 -16.2' -16.7 7.0 2.1 -1.1 -2.4 -21.1' -23.5 9.0 1.6 -18.2' -1 5.6 2.6 2.0 4.8 21.2 -3.8 -1.6 -4.2 -2.2' 5.8 7.0 -7.0' -9.5 -2.5 -3.7 3.9 - I 1.4' -20.3 -8.9 -10.6 -2.5 -22.9' O
S
H
-6.9
-2.8
2.4
26.9'
25.7
-1.2
-3.5
0.8
22.0c
22.4
0.4
-1.7
3.0
-9.3 -15.6 -21.6 -4.2 -16.7 -4.0 -29.0 -39.4 -51.8 -70.3 -75.8 -81.2 -25.4 - I 39.3 -174.7 -14.6 -59.2 -39.2 29.9 27.4 27.6 22.1 1.9 64.1 -3.3 9.9 41.6 15.3 30.7
-0.3 -1.4 -2.0 1.6
-2.0 0.1 1.1
4.9 -5.2 -2.7 18.8 22.9 22.0 11.0 -23.8 -10.6 2.2 7.0 3.0 4.9 -3.6 -3.4 -16.2 2.8 -19.5 -3.4 15.9 6.6 -7.8 11.1
-8.1 -8.8 -7.8 -9.0 -9.0 -9.1 11.0 38.2 40.6 142.8 146.4 143.8 138.9 50.4 158.6 9.3 65.2 3.7 2.8 12.7 6. I -14.9 -3.3 -1 2.6 -10.4 15.4 10.8
2.7'
17.8
0.9#
-9.0' -14.2' -19.6' -5.8' -17.8' -3.0' -33.9' -34.0' -49.1' -89.1' -98.7' -103.4' -36.4' - 1 15.5' -164.1 -16.8f -66.2f -42.2' 25.OC 3 1 .Oc 3 1 .Oc 38.3' -0.9d 83.6 O.ld -6.0 35.0' 24.OC 19.6
