J. Phys. Chem. 1992, 96, 6962-6969
6962
use of empirical correction factors is advocated.22 The reason for these isotope effects is complex, as their size is determined by the sum of oppositionally directed changes which take place on reducing the hydrocarbon. The calculations predict unequivocally that the effect cannot be simply linked to the charge of the C atom at which substitution occurs. Appendix. Force Constant Difference Matrix
The force constant difference matrix given in Chart I shows the difference in force constants between the neutral benzene molecule and the corresponding radical anion (in mdyne/A). A positive number signifies a bond which becomes weaker on reduction. As the matrix shows, almost all force constants change on reduction. The largest changes occur in the carbon framework of the ring; the C-H bonds vary only slightly. This means that the calculated isotope effect can only be caused by coupling of the many vibrations in the molecule. Acknowledgment. Use of the services and facilities of the Dutch National NWO/SURF Expertise Center CAOS/CAMM, under Grants SON 326-052 and STW NHC99.1751, is gratefully acknowledged. We thank Drs. J. H. Borkent and G. Schaftenaar of this center for many helpful comments and Prof. J. Cornelisse and Dr. H. P. J. M. Dekkers for their on-going interest in this project. Furthermore, we thank Prof. J. J. P. Stewart for helpful correspondence. Registry No. D2,7782-39-0; I3C, 14762-74-4; benzene, 7 1-43-2; pyrene, 129-00-0.
References and Notes (1) Ellison, G. B.; Engelkind, P. C.; Lineberger, W. C. J . Phys. Chem. 1982,86,4873.
(2) Jackson, R. L.; Hiberty, P. C.; Brauman, J. I. J . Chem. Phys. 1981, 74, 3705. (3) Stevenson, G. R.; Reiter, R. C.; Espe, M. E. J. Am. Chem. Soc. 1986, 108, 532. (b) Ibid. 1986,108, 5760. (c) Stevenson, G. R.; Espe, M. E.; Reiter, R. C.; Lovett, D. J. Nature 1986, 323, 522. (d) Stevenson, G. R.; Peters, S. J.; Reidy, K. A. Tetrahedron Lett. 1990, 31, 6151. (4) Stevenson, G. R.; Reidy, K. A.; Peters, S.J.; Reiter, R. C. J. Am. Chem. Soc. 1989, I l l , 6578. ( 5 ) (a) Stevenson, G. R.; Lauricella, T. L. J. Am. Chem. SOC.1986, 108, 5366. (b) Stevenson, G. R.; Sturgeon, B. E.; Vines, K. S.; Peters, S. J. J. Phys. Chem. 1988, 92, 6850. (6) Stevenson, G. R.; Reiter, R. C.; Espe, M. E.; Bartmess, J. E.; Crowder, C. J. Am. Chem. SOC.1987, 109, 3847. (7) Goodnow, T. T.; Kaifer, A. J. Phys. Chem. 1990, 94, 7682. ( 8 ) Marx, D.; Kleinhesselink, D.; Wolfsberg, M. J . Am. Chem. SOC.1989, 111, 1493. (9) Stevenson, G. R.; Sturgeon, B. E. J. Org. Chem. 1990, 55, 4090. (10) Hempenius, M.; Zuilhof, H. Unpublished data. (11) (a) Stewart, J. J. P. J. Comput. Chem. 1989, 10, 209. (b) [bid. 1989, 10, 221. (c) Paneth, P. J. Phys. Org. Chem. 1991, 4 , 635. (12) Brodersen, S.; Langseth, A. Mat.-Fys. Ski. Dan. Vidensk. Selsk. 1959, 1 (7), 1. (13) It is therefore sensible to speak of a significant improvement on the AM1 results by PM3 in this case. See for a recent discussion on this topic: Dewar, M. J. S.;Healy, E. F.; Holder, A. J.; Yuan, Y.-C. J. Comput. Chem. 1990, 11, 541. Stewart, J. J. P. J . Comput. Chem. 1990, 11, 543. (14) See for a clarifying discussion: Grossjean, M. F.; Tavan, P.; Schulten, K. J. Phys. Chem. 1990, 94, 8059. (15) Blom, C. E.; Altona, C. Mol. Phys. 1977, 34, 177 and references therein. (16) Tavan. P.: Schulten. K. Bioohvs. J . 1986. 50. 81. (17) Moore; J. C.; Thorton, C.; C&z.r, W. B.; Devlin, J. P. J . Phys. Chem. 1981, 85, 350. (18) Devlin, J. P.; McKennis, J. S.;Thorton, C.; Moore, J. C. J . Phys. Chem. 1982,86, 2613. (19) Hinde, A. L.; Poppinger, D.; Radom, L. J. Am. Chem. Soc. 1978,100, 468 1. (20) Jeanmaire, D. L.; Van Duyne, R. P. J. Am. Chem. SOC.1976, 98, 4029 and references therein. (21) Bozio, R.; Girlando, A.; Pecile, C. J. Chem. SOC.,Faraday Trans. 2 1975. 71. 1237. (22) Hess, B. A.; Schaad, L. J.; Carsky, P.; Zahradnik, R. Chem. Reu. 1986, 86, 709.
Ab Initio Molecular Orbital Study of Electronic Structures of doso-Borane Anions B, Hn2- and c/mo-Carboranes C2Bn-2Hn w
Keiko Takano, Michiyo Izuho, and Haruo Hosoya* Department of Chemistry, Ochanomizu University, Bunkyo- ku, Tokyo I 1 2, Japan (Received: February 3, 1992)
Ab initio molecular orbital (MO) calculations were performed for a series of closo-boranes B,,H;- (5 In I12) and closo-carboranes C2Blr2Hn( 5 In I 12) with deltahedral skeletons to study the peculiar properties, such as electron deficient and three-center two-electron bonds. By use of the MOs of high quality of double {, the electron density distributions in these compounds were calculated and analyzed in detail through the analytical 'spherical charge analysis" by Iwata and electron density contour mapping. It was found that the external BH bonds in both closo-boranes and closo-carboranes have almost similar homopolar bonding character of the typical two-center two-electron bond. The oxidation states of B and C atoms in the series of boranes and carborane isomers were interpreted in terms of the modified oxidation numbers assigned from the spherical charge analysis. Inspection of the contour maps of the deformation electron density on a variety of planes in the deltahedral molecular skeleton reveals that the central planar ring in a three-dimensional cage molecule has the same tendency for the charge distribution and stability as that in planar cyclic conjugated systems.
Introduction
Chemical properties of boron compounds cannot be understood using only the classical concept of a valency of 3 for boron. The clusters, hydrides, and cage compounds containing boron atoms have a variety of bonding characteristics, such as electron deficiency in the three-center two-electron bonds. Boron hydrides are called boranes and form unique structural classes of compounds with polyhedral skeletons of boron atoms, e.g., closo-, arachno-, and nido-boranes.' Figure 1 shows the deltahedral skeletons of boron atoms for the closo-borane series, which have the highest
symmetry among them. Their unusual chemical features derived from variations of the nature of the chemical bond await reasonable theoretical interpretation. During the first half of this century, experimental chemistry of boron hydrides was developed mainly by Stock and his coworkers.2 Sidgwick summarizes the early history of the boron hydride^.^ Their interesting theoretical and structural features were mainly due to the works, respectively, by Longuet-Higgins4 and Lipscomb.s Recently boron chemistry has been refocused from different points of view, e.g., energetics for the geometrical
0022-365419212096-6962%03.00/0 0 1992 American Chemical Society
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 6963
Electronic Structures of B,H,2- and C2BW2Hn
A D OIRI
l b
0
I-t H(l)
16)
(5)
H
,-
BH151
-*-,
BH[31
-
CHI11
-
N
-
H(9)
CH4 I
I
(8)
17)
Figure 1. Deltahedral skeletons of a series of closo-borane anions B,,H;( n = 5-12) and isoelectronic closo-carboranes C2BW2H,, ( n = 5-12)
TABLE I: Topological Properties of c h o -Borane Family, B,,H?- (n = 5-12\
point closo-boranes" group (1) (2) (3) (4) (5) (6)
B5HS2-
B,H,~-
BsHB2BgHJBIOHl2(7) BIIHlI2(8) B I ~ H I ? -
no. of faces
no. of edges
no. of vertices 5
8 io 12 14 16 18 20
9 12 15 18 21 24 27 30
D3h
Oh D~~ DM D3h
Du Cb Ih
6
7 8 9 10 11 12
distribution of the degree of B atoms 3
4
5
0 0 2 4 6 0 2 8 0 2 8 0 0 1 2
2 0 0 0 0
3 6 5 4 3
6 0 0 0 0 0 0 1 0
Their skeletons are shown in Figure 1. stabilization: chemical reactions such as elimination reactions of H2 and BH3 from boron hydrides,' heat of formation: topological analysis of three-dimensional a r ~ m a t i c i t yand , ~ so on. For interpretation of these electron deficient chemical bonds of boron compounds detailed analysis of the accurate wave functions and electron density distribution is necessary. In this respect we have performed a systematic study on the electronic structure of the series of closo-borane anions BnH,2- and isoelectronic closo-carbonanes C2BW2H,with closed deltahedral structures by the use of the analytical "spherical charge analysis" and electron density mapping with a b initio Gaussian-type molecular wave functions. Method of Calculation
Ab initio RHF calculations with STO-6GI0 and MIDI-411 bases were performed for the singlet ground states of the series of closeborane anions, B,H:(n 5-12), as listed in Table I, and their isoelectronic clo$o-carborane molecules, C2BW2Hn(n = 5-12). Their deltahedral skeletons except for H atoms are shown in Figure 1. The geometries of the compounds studied were either taken from the experimentally determined datal2or estimated by using the parameters optimized with a b initio RHF/STO-3G calculations by Ott et a1.6 The calculated total and orbital energies for closo-borane anions, B,H,Z- (n = 5-12), are listed in Table II.I3 By use of the M O s of high quality of double ( (MIDI-4),
the electron density distributions in these compounds were calculated and analyzed in detail through the spherical charge analysis by Iwata14 and electron density contour mapping. The analytical spherical charge analysis can be applied to any compound as long as its G T (Gaussian type) wave functions are a ~ a i l a b l e . ' ~The ~ ' ~spherically averaged electron density, po(R), and its increment relative to the summed up values of the component atoms, Apo(R),are defined as
atom
ApdR) = PO(R)- C Poi(R) I
where N ( R ) is the number of electrons in a sphere with radius R, and the subscript i refers to the contribution of the component free atom i. These quantities can be written down in terms of the Gaussian and error functions. The central position of the sphere for the calculation can be chosen at any point if necessary. In this paper the radial dependency of the Apo(R)values around each atom and the center of the molecule is mainly examined. Ab initio M O program package MOLYX by Iwata's group of Keio University was used after a slight modification on SONY NEWS 821/711 in our laboratory, HITAC M680H in the IMS (Institute for Molecular Science), and HITAC M682H/M680H in the University of Tokyo. Spherical Charge Analysis around Hydrogen Atoms
A linear relationship between the Apo(R) value around the specified atom and its oxidation state has been found not only in inorganic but also in organic molecules.'6-18 A positive Ap,(R) value expresses the increment of electron density upon molecule formation and corresponds to lowering of the oxidation state. Figure 2 shows the radial dependency of the ApO(R)values around the hydrogen atoms in 1,2-dicarba-cIoso-pentaborane (1,2-C2B3HS)with CH4 as the reference. All the curves apparently collapse into two groups depending on the kind of the bonded atom, boron or carbon. The ApPo(R) values in Figure 2 suggest that the H atom bonded to B is less oxidized than that bonded to C. It is remarkable that the oxidation state of H does not depend on
6964 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
Takano et al. the degree of the bonded B or C atom. Further, the Apo(R)values around H atoms bonded to B are almost the same in the bonding region in the anionic closo-boranes, B,,HR (n = 5-12), and neutral closo-carborane molecules, C2BW2H,(n = 5-12). The Apo(R)values around H atoms bonded to C coincide quite well in the bonding region (0.5 < R < 0.8 A) with the reference curve of CH4, in which the modified oxidation number of the H atom has been assigned +1/2.16 This suggests that the H atoms bonded to C in closo-carbonane molecules C2BP2Hnare oxidized half as much as the H atoms bonded to 0 as in organic and inorganic compounds hitherto studied. The Apo(R) curves around H atoms bonded to B in Figure 2 have almost the same shape in the bonding region with those in borazine B3N3H6,boroxine B303H3, and diborane B2H6 (external H) molecules. These facts suggest that the BH bond in closoborane anions B,H," and in closo-carborane molecules C2BP2Hn has the same two-center two-electron ordinary bonding character and that the extra charge of -2 in the closo-borane family is mainly distributed within the threedimensional cage of B atoms. Thus the so-called exohydrogens are expected to have properties independent of the skeletal moiety not only geometrically but also electronically. Since the Apo(R) curve of the exo-hydrogen atom is similar to that of the neutral H2 molecule, we can assign zero for the oxidation number of the exo-BH-hydrogen atom. As will be discussed below in detail, the exo-BH bond can be deemed as a homopolar bond. Then, the assignment of our modified oxidation number for the series BHO, CH112,NH314,and OH' is found to be reasonable. With regard to the bridging hydrogen atoms in diborane B& and pentaborane B5H9with a square pyramidal structure, the electronic density distribution around them is found to be similar with each other, but quite different from that of the exo-hydrogen atoms. The Apo(R) curves around the bridging hydrogen atoms have almost the same shape with those of the NH314atoms in organic molecules. The higher oxidation state of the bridging hydrogen atoms relative to the exo-hydrogen reflects the electron deficiency in the three-center two-electron BHB bond.
Detailed Annlysis of XH Bonds A variety of XH bonds are examined using the spherical charge analysis extensively to grasp the overall electronic characteristics of XH bonds and H atoms, especially the polarity of XH bonds. Figure 3 shows the radial dependency of the Apo(R)values around the H atoms bonded to X atoms (X = H, B, C, N, 0, F,Si, P, S,Cl) in the representative molecules, respectively, H2, 1,5-C2B3H5 (1,5-dicarba-cl~~pentaborane), CHI, NH3, H20, HF, SiH4,PH3, H2S, and HCI. Stepwise change of the Apo(R) value in the bonding region is seen among the curves. This means that the oxidation state of H atoms changes stepwise according to the kind of bonded atom. In Figure 4, the Ap0(0.6A) values around the H atoms in the bonding region of XH bonds are plotted against the difference of the Pauling's electronegativity, A = xx - XH. It is clearly seen that the plots for the second and third row atoms lie, respectively, on the two straight lines with almost the same slope. Even with the same electronegativity, movement of electrons around the hydrogen atom bonded to the atom of the third row is larger than that of the second row. Thus the oxidation state of the hydrogen atoms depends on both the electronegativity and the size of the bonded atoms. The Apo(R) curve around the so-called exo-hydrogen atoms bonded to the B skeleton in one of the closo-carboranes, 1 3 C2B3HS,is quite similar to that of H2 molecules in the bonding region from 0.5 to 0.8 A, as shown in Figure 3. This suggests that BH bonds are nonpolar similar to the homopolar hydrogen molecule. The proximity of the points of B and H in Figure 4 also supports this inference. Spherical Charge Analysis around B and C Atoms Topological properties of the closo-borane family with deltahedral skeletons are listed in Table I. Generally the carbon and boron skeleton of the closo-carborane family, C2BP2Hn ( n = 5-12),
Electronic Structures of B,,H?- and C2BW2H,
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 6965
A G OIRJ m
X- ’k
I
0
H-
[HI
8-IHI
I
I
8131
C-lHl
N-IHI
0-lHl
F-lHl
-
Si -(HI
P-IHl S-(HI CI-IHI
Figure 3. Difference spherically averaged electron density ApPo(R) around the hydrogen atom bonded to X atoms (A’= H, B, C, N, 0, F, Si, P, S, Cl) in H2,l,5-C2B3H5, CH4,NH,, H20,HF, SiH4,PH,, H2S,and HCI.
APo(0.6P\)
,.,*I
ST 0.01 p C.
-0.01
t
@F
Figure 4. Plots of Apo(0.6A) values around the hydrogen atoms in the bonding region of XH bonds vs the difference of the Pauling’s electronegativity between X and H atoms (A = xx - XH).
has a lower symmetry than the present closo-borane. The vertex degrees for these skeletons vary from 3 to 6. By a comparison of the Apo(R)values around the B and C atoms, it was found that the degree of the skeletal atoms is closely related to the Apo(R) values regardless of its atomic species. Namely, the Apo(R)value around the skeletal atom decreases in the following order: C with smaller degree, B with smaller degree, C with larger degree, and B with larger degree. Figure 5 shows a typical example of the radial dependency of the Apo(R)values around the B and C atoms described above in 1,2-C2B3H5with the C, symmetry. The oxidation numbers of the skeletal atoms in most carboranes can be assigned without any inconsistency from the comparison among the same atomic species. These assignments are durable to the cross-reference check of the Apo(R)values for the skeletal atoms. We could assign the oxidation numbers of the so-called exohydrogens as B W and CH+’12for all the members of the borane and carborane families. The Apo(R)values around these H atoms are all coincident with each other and differ from that of the bridging H atoms. The assignment of CH+’/*is quite consistent
I
I
I
6966 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
Takano et al.
5
2'
0
2r
I
Figure 6. Contour plots of the deformation electron density for the closo-borane anions B5H5" with the deltahedral skeletons (a) in the central ring plane and (b) on the plane vertical to the central ring.
respectively shown in Figure 6a, Figure 7, and Figure 8a. In the B5HS2-anion there is only a slight electron density increment in the BB bond region, contrary to a substantial increment around the exo-hydrogen atoms. The center of gravity of the electron density increment in the BB bond region is displaced off the line connecting the two B atoms and outward of the ring, suggesting the existence of the so-called 'banana bond". The electron density increment can be seen on the four- and fivemembered ring planes much more than on the three-membered one in Figures 6-8. Contour electron density plots on the plane vertical to the central ring shown in Figures 6b, 7,and 8b also correspond to the charge
distribution pattern observed as above. As illustrated schematically in Figure 9, the trigonal and pentagonal bipyramids have opposite electron density patterns. This is consistent with the modified oxidation numbers for the component atoms in the B,,H:+ (n = 3, 4, 5) anions and C2BP2H, (n = 3, 4, 5 ) molecules, as listed in Tables 111and IV. It is noteworthy that the central planar ring even in a three-dimensional molecule has the same charge distribution and stability as planar cyclic conjugated molecules. The stability of c l a s w a h " e isomers has a close relationship with the charge density distribution of closo-boranes mentioned above. lrS-C2B3HS and l,7-C2BSH7are considered to be the most
The Journal of Physical Chemistry, Vol. 96, No. 17, 1992 6967
Electronic Structures of B,H,2- and C2BW2H,
/
\
\
I
1
6
Figure 7. Contour plot of the deformation electron density for the closo-borane anions B6H2- with the deltahedral skeleton in the central ring plane. TABLE III: Modified Oxidation Numbers and Apo Values with MIDI-4 Bash (App,(0.55A) X l@in P a r a t b e e ) for B Atoms in BJI;H,"(a = 5-12) rad Sum of the Modified Oxidation Numbers of AU the Atoms in Each Anion ~
species
modified oxidation no."
B5Hs2-
TABLE I V Modified Oxidation Numbers and Ap0 Values with and C MIDI-4 Basis (Apo(o.55A) X l@in P a r e n t h ) for B (0) ( 0 )Atoms in C2BP2H, ( a = 5 1 0 ) and Sum of the Modified Oxidation Numbers of AU the Atom in Each Molecule
~~~
sum of the modified oxidation no. -13/10
species 1,5-C2B3HS
modified oxidation no.'
sum of the modified oxidation no.
4
0
(6.0)
B6H62-
-2
1,6-C2B,H6
/K
%Po
0
(6.0)
114(4.5)
B7HT2-
+,2
-2
(11.6)
BsHS2-
-2
B9H9'-
-21/10
BI OHlo2-
-2
BI IH I I 2-
-0
-2
"The assignment of H atoms (BHO) is not shown. and least stable, respectively, among their own structural isomers. In the former the carbon atom with larger electronegativity than boron lies at the position of caps coincident with the localization of electron density, b,as shown in Figure 9a. This agrees with the results by Ott et a1.6
1,7-C2BsH7
0
0
"The assignment of H atoms (BHO, CH+'/2)is not shown.
Concluding Remarks The electronic structure of the hydrides of boron and carbon atoms with three-dimensional deltahedral skeletons can be understood by the spherical charge analysis and contour mapping of the electron density distribution with the Gaussian-type molecular orbital wave functions of double-{ quality. By crossreference of the Apo(R) values around the component atoms, it was found that the external BH bonds have homopolar bonding character of the typical two-center two-electron bond contrary to the three-center two-electron bonds containing the bridging hydrogen atom. The modified oxidation number of the H bonded to the B atom was assigned as zero (BHO) in accord with the already assigned values, CH+'12, NH+3/4, and OH+'. The spherical charge analysis around the H Atoms bonded to a variety of atoms (X = H, B, C, N, 0, F, Si, P,S, C1) revealed that the
6968 The Journal of Physical Chemistry, Vol. 96, No. 17, 1992
Takano et al.
n
7
3
h
0 3'
4
f
2
v 7
0 7'
Figure 8. Contour plots of the deformation electron density for the closo-borane anions B7H7*with the deltahedral skeletons (a) in the central ring plane and (b) on the plane vertical to the central ring.
polarity of XH bonds depends not only on the electronegativity but also on the size of the bonded atom. A detailed discussion will be given with such as the concept of charge capacity named by Huheey and absolute hanines introduced by Pearson.2' Studies in this direction are in progress. A series of closo-borane B,H," anions have n external exohydrogen atoms for which the modified oxidation number is assigned zero. From the contour maps of eiectron density the central part of the cage seems to be electronically empty. These facts suggest that the extra charge of -2 in the closo-borane BnH,2anion is localized mainly on the surface of the deltahedron. The
common feature of the localization of the electron density distribution in the molecules containing cyclic groups can be extended to three-dimensional cage molecules. For example, the opposite pattern is observed in the electron density distribution for the trigonal and pentagonal bipyramids. The oxidation state of each component atom of closo-borane BnH;- anions and closocarborane C2Brr2Hnmolecules can also be understood from the modified oxidation numbers assigned from the spherical charge analysis. Thus both overall and local features of electron density distribution in three-dimensional cage molecules were made clear. In addition to the present series of closeboranes and arboranes,
J. Phys. Chem. 1992,96,6969-6973
lbr
la
IC)
Figure 9. Schematic pictures of localization of the electron density in the
closo-boranes and clmmrboranes with the trigonal bipyramidal, octahedral, and pentagonal bipyramidal skeletons. quantum chemical calculations are being performed on organoboranes, nido- and arachno-boranes,and their isomers containing bridging hydrogen atoms.
Acknowledgment. We thank Professor Suehiro Iwata of Keio University for his helpful advice on our calculations. We also thank the Computer Center, Institute for Molecular Science, Okazaki National Research Institutes, for the use of the HITAC M680H computer. References and Notes (1) Bailer, J. C., Jr., Emeleus, H. J., Nyholm, R.,Trotman-Dickenson, A. F., Eds. Comprehensive Inorganic Chemistry; Pergamon: Oxford, U. K.,
1973. (2) Stock, A. Hydrides of Boron and Silicon; Cornel1 University Press: Ithaca, NY, 1933.
6969
(3) Sidgwick, N. V. The Chemical Elements and Their Compounds;Oxford University Press: Oxford, U. K., 1950; Vol. 1, p 338. (4) (a) Bell, R. P.; Longuet-Higgins, H. C. Nature 1945, 155, 328. (b) Longuet-Higgh, H. C. J. Chim. Phys. Phys.-Chim. Biol. 1949,46,268. (c) Longuet-Higgins,H. C.; Phil, M. A. D. Q.Rev., Chem. Soc. 1957, I I. 121. (5) Lipscomb, W . N. Boron Hydrides; Benjamin: New York, 1963. (6) Ott, J. J.; Gimarc, B. M. J . Compur. Chem. 1986, 7, 673, and their related papers. (7) McKee, M. L. J. Am. Chem. SOC.1990, 112, 6753. (8) McKee, M. L. J. Phys. Chem. 1990,94,435. (9) King, R. B.; Dai, B.; Gimarc B. M. Inorg. Chim. Acta 1990,167,213. (IO) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969, 51, 2657. (1 1) Tatewaki, H.; Huzinaga, S.J . Comput. Chem. 1980, 1, 205. (12) Landolt-Mrnstein, New Series 11-7. Structure Data of Free Polyatomic Molecules; Springer-Verlag: Berlin, 1976. (13) Positive energies for the HOMOS and next-HOMOS suggest that each of them is unstable as a free dianion. For example, discussions on the stability of B6Hs2-anions as a free dianion and in the crystal field are given in: Fowler, P. W. J. Chem. Soc., Faraday Tram. 2 1986,82,61. (14) Iwata, S Chem. Phys. Lett. 1980,69, 305. (15) Takano, K.; Hosoya, H.; Iwata, S.J . Am. Chem. Soc. 1982, 104, 3998. (16) Takano, K.; Hosoya, H.; Iwata, S.J . Am. Chem. Soc. 1984, 106, 2787. (17) Takano, K.; Hosoya, H.; Iwata, S.J . Chem. Soc. Jpn. 1986, 1395. (18) Takano, K.; Okamoto, M.; Hosoya, H. J . Phys. Chem. 1988, 92, 4869. (19) Takano, K.; Yoshimura, R.;Okamoto. M.; Hosoya, H. J. Phys. Chem. 1990.94, 2820. (20) (a) Jemmis, E. D.; Schleyer, P. v. R. J . Am. Chem. Soc. 1982,104, 4781. (b) Jemmis, E. D. J. Am. Chem. Soc. 1982, 104, 7071. (21) Politzer, P. J. Chem. Phys. 1987, 86, 1072 and references cited therein.
Theoretical Study of the Bonding of the First- and Second-Row Transition-Metal Positive Ions to Methylene Charles W. Bauschlicher, Jr.,* Harry Partridge, J. A. Sheehy, Stephen R. Langhoff, and Marzio Rosit NASA Ames Research Center, Moffett Field, California 94035 (Received: February 18, I992)
The geometries of the molecules formed by the interaction of the fmt- and second-row transition-metal cations with methylene are optimized at the modified coupled-pair functional (MCPF) level of theory using large Gaussian basis sets, and their dissociation energies are computed employing both the MCPF and internally contracted averaged coupled-pair functional (ICACPF) methods. The compufed binding energies are generally in good agreement with the available experimental results, although the calculations indicate that the experimental values for ScCH2+, TiCH2+,and NbCH2+ are probably too large. The nature of the bonding in each case and trends in the bonding patterns across the transition-metal rows are discussed.
I. latroductioa The transition-metal methylidene cations have been postulated as intermediates in a variety of reactions, and therefore an understanding of their bonding characteristics and a determination of the metal-CH, bond strengths are of interest. Toward this end, there have been several t h ~ r e t i c a l l -and ~ experimentalg" studies of the transition-metal-cation-methylene systems. Previous theoretical results have suggested a t least two bonding mechanism~.~-'Carter and GoddardzJ have described the M+-C interaction (where M represents a transition-metal atom) in CrCH2+ and RuCH2+as a covalent double bond arising from the 3Bl state of CH2, and Harrison and c o - w ~ r k e r sfound ~ , ~ the same type of bonding in M H 2 +and CrCH2+. Carter and Goddard2 pointed out that the metal-dr-carbon-pr overlap is small, leading to a poor description of the bonding at the self-consistent-field (SCF) level of theory. Planelles et al.' concluded that the bonding in CuCH2+ is electrostatic in origin, resulting from the interaction of IS Cu+ with 'Al CH2. This is favored over a bonding scheme involving the 3Bl ground state of methylene, even though the latter 'Current address: Department of Chemistry, University of Perugia, I06100, Perugia, Italy.
is 9 kcal/mol lower in energy than the former," because in the complex the excited state has a pair of electrons directed toward the cation, whereas the ground state of CH, can point only a single electron at the metal ion. By contrast with the case for covalently bonded systems, an SCF calculation yields a good description of the electrostatically bonded CuCH2+. Armentrout and co-workers* recently presented experimental results for the fmt transition row MCH2+compounds. They found a linear relationship between their binding energies and the metal cation promotion-plus-exchange energies, which they defined in each case as the energy difference between the metal cation ground state and the state derived from a d 5 occupation, plus the exchange energy lost upon formation of a double bond with the ligand (see also ref 13). Armentrout et al. concluded that their plot indicated significant metal 4s contribution to the bonding, although they noted that FeCH2+deviated somewhat from the linear relationship. Carter and GoddardI3 had predicted, however, that a linear relationship should exist between the binding energies and the lower of the dns and dn+' promotion-plus-exchange energies. In this work we compute the metal-ligand binding energies for the MCH2+ compounds derived from the first and second transition-row atoms. We find covalent double bonds in molecules
0022-3654/92/2096-6969$03.00/00 1992 American Chemical Society
