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Polyhedral hybrid approach to bonding in molecules containing transition metals
Volume 132, number 2
CHEMICAL PHYSICS LETTERS
5 December 1986
POLYHEDRAL HYBRID APPROACH TO BONDING IN MOLECULES CONTAINING TRANSITION METALS Richard P. MESSMER General Electric Corporate Research and Development, Schenectady, NY 12301, USA and Department of Physics, University ofPennsylvania, Philadelphia, PA 19104, USA
Received 1 July 1986; in final form IO September 1986
A polyhedral hybrid approach, based on generalized valence bond theory, is proposed to treat the electronic structure and bonding in transition metal molecules. A key feature of the approach is the ubiquity of “bent bonds” formed from overlapping hybrid orbitals.
On the basis of inductive reasoning from the results of recent generalized valence bond (GVB) calculations [ l-61, a set of postulates (referred to collectively as the polyhedral hybrid approach) are proposed regarding the bonding in transition metal molecules. This approach should prove to be not only a useful conceptual device in interpreting experimental situations, but also a vehicle to relate various future GVB calculations to a common theoretical structure. The basic tenets of the theory are outlined here and a few representative examples of applications to molecules are presented. A more comprehensive discussion of the theory, together with its application to many transition metal complexes, organometallic molecules, and transition metal clusters will be presented elsewhere. Over the last 12-l 5 years, a number of highly instructive and useful approaches to the understanding of bonding in molecules containing transition metal atoms have been developed [ 7- 121. The theoretical foundations of these approaches derive from molecular orbital (MO) theory, and thus ignore the physical consequences of potentially important electronic correlation effects. Hence, it is of some considerable interest to understand how electronic correlation effects might alter one’s view of bonding. The generalized valence bond (GVB) theory [ 13,141 offers the opportunity to study this situation as it treats some of the dominant electronic correlation
effects neglected in the MO theory. GVB calculations have recently led to three important findings regarding the effects of correlation on bonding: (1) well-defined covalent and dative bonds exist simultaneously in transition metal complexes [ 1,2]; (2) multicenter one-electron bonds exist in metal clusters and are likely the origin of “metallic bonding” [ 33; ( 3) equivalent multiple “bent bonds” ( R bonds) composed of overlapping atomic hybrid orbitals have been found to be more energetically favorable than the traditional o and rr bonds for cases of double [ 41, triple [ 51, and conjugated bonds [ 61. Given the above developments, particularly that regarding Q bonds, one is led to consider the consequences for describing bonding in transition metal molecules. These considerations lead to the polyhedral hybrid approach to bonding, whose basic postulates are now briefly outlined: (1) In transition metal molecules there are four limiting types of non-classical bonds of principal concern: (a) covalent, (b) dative, (c) metallic and (d) three-electron bonds. (2) Covalent bonds are composed of overlapping atomic hybrids on each of two sites having one electron per orbital; the two hybrids of a bond need not be directed along the internuclear axis. Dative bonds are also composed of overlapping atomic hybrids, however one hybrid contains two electrons and the other is empty (in a somewhat idealized descrip-
0 009-26 14/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
161
Volume 132, number 2
CHEMICAL PHYSICS LETTERS
5 December 1986
formed in addition to the three dative bonds it the hybrids above and below the trigonal plane are used for bonding. A trigonal bipyramidal geometry is obtained thereby, as in Ni( CN)2(PR3)3. For the ( 1OC) configuration, d2sp3hybrids (fig. 1c) suggest an octahedral coordination. As in the (1 OB) case, however, the hybrids above and below the plane each can be occupied by a single electron and these electrons can be singlet coupled into an angularly correlated pair. Then two covalent and two dative bonds can be formed with the remaining orbitals, leading to a square-planar molecular geometry. An example of such a molecule is Pt (NH3)*C12. If the electrons in the axial hybrids are uncoupled then two new covalent bonds can be formed as in Pt(NH3)2Cl, which has the octahedral geometry. In the Pt(lOD) configuration, d3sp3 pentagonal bipyramidal hybrids (fig. 1d) are formed which can accommodate six covalent bonds and one dative bond. The PtF6 molecule is an example; however, one of the fluorine ligands uses two coordination sites (one covalent and one dative) *. Note that the coordination number here is not the same as the ligancy. Some applications to transition metals in other columns of the periodic table are now considered. Three organometallic molecules are discussed first. The ferrocene molecule (fig. 2a) is derived from the Fe( 8B) configuration a with octahedral hybrids which can form two covalent bonds and four dative bonds. Each cyclopentadienyl (Cp) ring may be thought of as containing two sets of double Q bonds [4] and a radical orbital. One L-Jbond in each set makes a dative bond to the Fe and the radical orbital
tion); the hybrids again need not be along the internuclear axis, i.e. “bent bonds” can be formed. (3) The possible electronic configurations of a transition metal atom are described schematically in table 1 (using the Ni, Pd, Pt group as an example), where the nature of the polyhedral hybrids is determined by the singly occupied and empty orbitals. The A configuration for any atom always has the maximum number of doubly occupied orbitals; each succeeding configuration has one less doubly occupied orbital. The numerical prefix in the configuration designation corresponds to the number of valence electrons. (4) The number of dative bonds which can be formed is equal to the number of empty orbitals; the number of covalent bonds which can be formed is equal to the number of singly occupied orbitals. Each transition metal atom wants to share 18 valence electrons. (5) The geometry of a molecule is determined by the bonding characteristics of the individual atoms. These characteristics, in turn, are dictated by the possible polyhedral hybrids arising from the given electronic configuration. The application of these postulates is illustrated now for the Ni, Pd, Pt group. For the (10A) configuration, sp3 hybrids (fig. 1a) arise because of the formation of four equivalent orbitals from the empty s and three empty p orbitals, and thus a tetrahedral geometry with four dative bonds is expected as in Pd(PF3)4. The (10B) configuration results in dsp3 hybrids (fig. lb) giving a trigonal bipyramidal geometry. Two of the hybrids, one above and the other below the trigonal plane, can contain an electron each. They will slightly re-hybridize in order to overlap and form an angularly correlated electron pair, leaving three empty hybrids in the plane at 120” to each other. These orbitals can form three dative bonds as in Pd ( PPh3) 3. Two covalent bonds can be
t As there are clearly a number of symmetry-related structures in this case, the total wavefunction must be made up of a coherent superposition of all such possible (classically independent) structures, i.e. one must consider “resonance”. ff For Fe(8A), five dative bonds and a trigonal bipyramidal geometry would be expected as in Fe( CO) 5.
Table 1
162
Configuration
d,
d2
d3
d,
d5
s
p,
pz
p3
IOA 10B 1oc 10D 10E
2 2 2 2 2
2 2 2 2 I
2 2 2 1 1
2 2 1 1 1
2 1 1 1 1
00 1 1 1 1
0 1 1 1
0 0 0 1 1
0 0 0 0 1
Volume 132, number 2
CHEMICAL PHYSICS LETTERS
. +ib . (a)
0
(b)
& l
0
.
.’
.
(e)
Cd)
Fig. 1. Geometries of various sets of polyhedral hybrids: (a) tetrahedron; (b) trigonal bipyramid; (c) octahedron; (d) pentagonal bipyramid, (e) square antiprism.
makes a covalent bond, which leads to the observed geometry. There are several equivalent classical structures (“resonance” structures) and their super-
a
e
ocI/
’
oc
0
c
oc 0
co co
TIC
CO
(b)
c; c\ /= oc-co-co-co
“ooc I I\
Jn
0”
(a) 0
u0 \
a
Je
% (cl
co
“, c”
:
position is necessary to obtain a proper wavefimction. However, in order to understand the bonding requirements and predict the proper geometry it is only necessary to consider one of them. For Mn( 7A), five dative bonds and one covalent bond with octahedral hybrids are to be expected, leading to the geometry of the molecule in fig. 2b. The case of Ti(Cp),(CO), with Ti(4B) introduces a new hybridization, square antiprismatic (fig. 1e), with two covalent bonds and six dative bonds. Each Cp is bonded to a set of three hybrids pointing to the shaded faces of fig. 1e; the CO molecules form dative bonds to the shaded orbitals. The resulting geometry is that of fig. 2c. The bonding of three binuclear metal carbonyls is investigated next. The molecule of fig. 2d is derived from two Co (9A) atoms, each of which forms one covalent bond and four dative bonds with a local trigonal bipyramidal geometry. There is one Co-Co covalent bond and eight Co-CO dative bonds. In fig. 2e the molecule is derived from two Co( 9B) atoms each of which forms three covalent bonds and three dative bonds and has a local octahedral geometry. This molecule is formed by bringing the triangular faces of the octahedra together and allowing five covalent bonds to form. Four of these are used by the bridging CO ligands and one is a “bent” Co-Co bond. The Mn, (CO) ,,-,molecule (fig. 2f) derives from two Mn ( 7A) atoms (octahedral hybrids/five dative/one covalent) and corresponds to two octahedra sharing a’vertex. Some multinuclear metal carbonyls are the next examples for discussion. The Fe3 ( CO), z molecule (fig. 2g) is composed of one Fe( 8B) atom and two Fe( 8C) atoms. The hybrids of the 8C configuration point toward the vertices of a capped octahedron forming three dative and four covalent bonds. The caps are oriented toward one another along the Fe(K)-Fe(8C) covalent bond axis. This axis is bridged by two carbonyls making four covalent bonds. The Fe( 8B) atom (octahedral/two covalent/ four dative) forms two covalent (bent) Fe-Fe bonds, one each with the two Fe( 8C) atoms. The structure of Os,( CO) r2 (fig. 2h) is much simpler, being composed of three Os( 8B) atoms (octahedral/two covalent/four dative). Each OS atom forms two covalent bonds, one each to the other two OS atoms; all these bonds are bent. The three octahedra are “packed” so
\,:25$4 o.-~~~~n-co
0
tco O,/? 1 ‘co
0”;’c
0
0
Cd)
(9)
5 December 1986
(h)
(i)
Fig. 2. Structures of some molecular examples: (a) ferrocene; (b) MnCp(CO)S; (c) Ti(CPMCOh; (4 CMCOh; (e) CodCOh; (f) Mn,(CO),o; (g) Fe3(CO)12; (h) OSACO)~~; (9 Ir4(CO)12.
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CHEMICAL PHYSICS LETTERS
to achieve the best overlap of the hybrid orbitals forming the OS-OS bonds. Note that trinuclear Fe complex prefers two 8C atoms, while the corresponding OS complex prefers all 8B atoms. This can be understood on the basis of the atomic structure of the atoms. The Ir,(CO) ,2 cluster (fig. 2i) is composed of four Ir( 9B) atoms (octahedral/three covalent/three dative), the octahedra are packed to achieve optimal overlap of the hybrids forming the six Ir-Ir covalent bonds; all the Ir-Ir bonds are “bent”. It has been possible to discuss only a few examples in this note, and in attempting to clearly present the basic ideas, only the simplest applications have been considered. Some of the more interesting applications, to be treated in future work, include discussions of: (1) the effect of the doubly occupied metal orbitals; (2) alternative sets of hybrids for a given number of empty and singly occupied orbitals; (3) estimates of the relative energetics of the various possible configurations; (4) the distribution of empty and singly occupied hybrids and its effect on isomers; and (5) situations where more than one metal atom configuration is necessary. However, as presented here, the polyhedral hybrid approach should provide a useful framework for understanding and interpreting not only experimental information but also future GVB calculations. Although the latter will undoubtedly help to refine and make more quantias
164
5 December 1986
tative the present theory, which is essentially qualitative, it is not to be expected that such calculations will seriously challenge the simple underlying physical principles from which this approach is derived.
References [ 11 J.J. Low and W.A. Goddard III, J. Am. Chem. Sot. 106 (1984) 6928. [ 21 M. Steigerwald and W.A. Goddard III, J. Am. Chem. Sot. 107 (1985) 5027. [3] M.H. McAdon and W.A. Goddard III, Phys. Rev. Letters 55 (1985) 2563. [4] R.P. Messmer, P.A. Schultz, R.C. Tatar and H.-J. Freund, Chem. Phys. Letters 126 (1986) 176. [ 51 R.P. Messmer and P.A. Schultz, Phys. Rev. Letters, submitted for publication. [6] P.A. Schultz and R.P. Messmer, unpublished results. [7] R.E. Williams, Inorg. Chem. 10 (1971) 210. [ 8 ] K. Wade, Advan. Inorg. Chem. Radiochem. 18 ( 1976) 1. [ 91 D.M.P. Mingos, Nature 99 (1972) 236. [lo] J.W. Lauher, J. Am. Chem. Sot. 100 (1978) 5305. [ I1 ] R. Hoffmann, Angew. Chem. Intern. Ed. En& 21 (1982) 2297. [ 121 A.J. Stone, Mol. Phys. 41 (1980) 1339. [ 131 P.J. Hunt, P.J. Hay and W.A. Goddard III, J. Chem. Phys. 57 (1972) 738. [ 141 R.C. Ladner and W.A. Goddard III, J. Chem. Phys. 51 (1969) 1073; F.W. Bobrowicz and W.A. Goddard III, in: Modem thew retical chemistry, Vol. 3. Methods of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 79.
CHEMICAL PHYSICS LETTERS
5 December 1986
POLYHEDRAL HYBRID APPROACH TO BONDING IN MOLECULES CONTAINING TRANSITION METALS Richard P. MESSMER General Electric Corporate Research and Development, Schenectady, NY 12301, USA and Department of Physics, University ofPennsylvania, Philadelphia, PA 19104, USA
Received 1 July 1986; in final form IO September 1986
A polyhedral hybrid approach, based on generalized valence bond theory, is proposed to treat the electronic structure and bonding in transition metal molecules. A key feature of the approach is the ubiquity of “bent bonds” formed from overlapping hybrid orbitals.
On the basis of inductive reasoning from the results of recent generalized valence bond (GVB) calculations [ l-61, a set of postulates (referred to collectively as the polyhedral hybrid approach) are proposed regarding the bonding in transition metal molecules. This approach should prove to be not only a useful conceptual device in interpreting experimental situations, but also a vehicle to relate various future GVB calculations to a common theoretical structure. The basic tenets of the theory are outlined here and a few representative examples of applications to molecules are presented. A more comprehensive discussion of the theory, together with its application to many transition metal complexes, organometallic molecules, and transition metal clusters will be presented elsewhere. Over the last 12-l 5 years, a number of highly instructive and useful approaches to the understanding of bonding in molecules containing transition metal atoms have been developed [ 7- 121. The theoretical foundations of these approaches derive from molecular orbital (MO) theory, and thus ignore the physical consequences of potentially important electronic correlation effects. Hence, it is of some considerable interest to understand how electronic correlation effects might alter one’s view of bonding. The generalized valence bond (GVB) theory [ 13,141 offers the opportunity to study this situation as it treats some of the dominant electronic correlation
effects neglected in the MO theory. GVB calculations have recently led to three important findings regarding the effects of correlation on bonding: (1) well-defined covalent and dative bonds exist simultaneously in transition metal complexes [ 1,2]; (2) multicenter one-electron bonds exist in metal clusters and are likely the origin of “metallic bonding” [ 33; ( 3) equivalent multiple “bent bonds” ( R bonds) composed of overlapping atomic hybrid orbitals have been found to be more energetically favorable than the traditional o and rr bonds for cases of double [ 41, triple [ 51, and conjugated bonds [ 61. Given the above developments, particularly that regarding Q bonds, one is led to consider the consequences for describing bonding in transition metal molecules. These considerations lead to the polyhedral hybrid approach to bonding, whose basic postulates are now briefly outlined: (1) In transition metal molecules there are four limiting types of non-classical bonds of principal concern: (a) covalent, (b) dative, (c) metallic and (d) three-electron bonds. (2) Covalent bonds are composed of overlapping atomic hybrids on each of two sites having one electron per orbital; the two hybrids of a bond need not be directed along the internuclear axis. Dative bonds are also composed of overlapping atomic hybrids, however one hybrid contains two electrons and the other is empty (in a somewhat idealized descrip-
0 009-26 14/86/$ 03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
161
Volume 132, number 2
CHEMICAL PHYSICS LETTERS
5 December 1986
formed in addition to the three dative bonds it the hybrids above and below the trigonal plane are used for bonding. A trigonal bipyramidal geometry is obtained thereby, as in Ni( CN)2(PR3)3. For the ( 1OC) configuration, d2sp3hybrids (fig. 1c) suggest an octahedral coordination. As in the (1 OB) case, however, the hybrids above and below the plane each can be occupied by a single electron and these electrons can be singlet coupled into an angularly correlated pair. Then two covalent and two dative bonds can be formed with the remaining orbitals, leading to a square-planar molecular geometry. An example of such a molecule is Pt (NH3)*C12. If the electrons in the axial hybrids are uncoupled then two new covalent bonds can be formed as in Pt(NH3)2Cl, which has the octahedral geometry. In the Pt(lOD) configuration, d3sp3 pentagonal bipyramidal hybrids (fig. 1d) are formed which can accommodate six covalent bonds and one dative bond. The PtF6 molecule is an example; however, one of the fluorine ligands uses two coordination sites (one covalent and one dative) *. Note that the coordination number here is not the same as the ligancy. Some applications to transition metals in other columns of the periodic table are now considered. Three organometallic molecules are discussed first. The ferrocene molecule (fig. 2a) is derived from the Fe( 8B) configuration a with octahedral hybrids which can form two covalent bonds and four dative bonds. Each cyclopentadienyl (Cp) ring may be thought of as containing two sets of double Q bonds [4] and a radical orbital. One L-Jbond in each set makes a dative bond to the Fe and the radical orbital
tion); the hybrids again need not be along the internuclear axis, i.e. “bent bonds” can be formed. (3) The possible electronic configurations of a transition metal atom are described schematically in table 1 (using the Ni, Pd, Pt group as an example), where the nature of the polyhedral hybrids is determined by the singly occupied and empty orbitals. The A configuration for any atom always has the maximum number of doubly occupied orbitals; each succeeding configuration has one less doubly occupied orbital. The numerical prefix in the configuration designation corresponds to the number of valence electrons. (4) The number of dative bonds which can be formed is equal to the number of empty orbitals; the number of covalent bonds which can be formed is equal to the number of singly occupied orbitals. Each transition metal atom wants to share 18 valence electrons. (5) The geometry of a molecule is determined by the bonding characteristics of the individual atoms. These characteristics, in turn, are dictated by the possible polyhedral hybrids arising from the given electronic configuration. The application of these postulates is illustrated now for the Ni, Pd, Pt group. For the (10A) configuration, sp3 hybrids (fig. 1a) arise because of the formation of four equivalent orbitals from the empty s and three empty p orbitals, and thus a tetrahedral geometry with four dative bonds is expected as in Pd(PF3)4. The (10B) configuration results in dsp3 hybrids (fig. lb) giving a trigonal bipyramidal geometry. Two of the hybrids, one above and the other below the trigonal plane, can contain an electron each. They will slightly re-hybridize in order to overlap and form an angularly correlated electron pair, leaving three empty hybrids in the plane at 120” to each other. These orbitals can form three dative bonds as in Pd ( PPh3) 3. Two covalent bonds can be
t As there are clearly a number of symmetry-related structures in this case, the total wavefunction must be made up of a coherent superposition of all such possible (classically independent) structures, i.e. one must consider “resonance”. ff For Fe(8A), five dative bonds and a trigonal bipyramidal geometry would be expected as in Fe( CO) 5.
Table 1
162
Configuration
d,
d2
d3
d,
d5
s
p,
pz
p3
IOA 10B 1oc 10D 10E
2 2 2 2 2
2 2 2 2 I
2 2 2 1 1
2 2 1 1 1
2 1 1 1 1
00 1 1 1 1
0 1 1 1
0 0 0 1 1
0 0 0 0 1
Volume 132, number 2
CHEMICAL PHYSICS LETTERS
. +ib . (a)
0
(b)
& l
0
.
.’
.
(e)
Cd)
Fig. 1. Geometries of various sets of polyhedral hybrids: (a) tetrahedron; (b) trigonal bipyramid; (c) octahedron; (d) pentagonal bipyramid, (e) square antiprism.
makes a covalent bond, which leads to the observed geometry. There are several equivalent classical structures (“resonance” structures) and their super-
a
e
ocI/
’
oc
0
c
oc 0
co co
TIC
CO
(b)
c; c\ /= oc-co-co-co
“ooc I I\
Jn
0”
(a) 0
u0 \
a
Je
% (cl
co
“, c”
:
position is necessary to obtain a proper wavefimction. However, in order to understand the bonding requirements and predict the proper geometry it is only necessary to consider one of them. For Mn( 7A), five dative bonds and one covalent bond with octahedral hybrids are to be expected, leading to the geometry of the molecule in fig. 2b. The case of Ti(Cp),(CO), with Ti(4B) introduces a new hybridization, square antiprismatic (fig. 1e), with two covalent bonds and six dative bonds. Each Cp is bonded to a set of three hybrids pointing to the shaded faces of fig. 1e; the CO molecules form dative bonds to the shaded orbitals. The resulting geometry is that of fig. 2c. The bonding of three binuclear metal carbonyls is investigated next. The molecule of fig. 2d is derived from two Co (9A) atoms, each of which forms one covalent bond and four dative bonds with a local trigonal bipyramidal geometry. There is one Co-Co covalent bond and eight Co-CO dative bonds. In fig. 2e the molecule is derived from two Co( 9B) atoms each of which forms three covalent bonds and three dative bonds and has a local octahedral geometry. This molecule is formed by bringing the triangular faces of the octahedra together and allowing five covalent bonds to form. Four of these are used by the bridging CO ligands and one is a “bent” Co-Co bond. The Mn, (CO) ,,-,molecule (fig. 2f) derives from two Mn ( 7A) atoms (octahedral hybrids/five dative/one covalent) and corresponds to two octahedra sharing a’vertex. Some multinuclear metal carbonyls are the next examples for discussion. The Fe3 ( CO), z molecule (fig. 2g) is composed of one Fe( 8B) atom and two Fe( 8C) atoms. The hybrids of the 8C configuration point toward the vertices of a capped octahedron forming three dative and four covalent bonds. The caps are oriented toward one another along the Fe(K)-Fe(8C) covalent bond axis. This axis is bridged by two carbonyls making four covalent bonds. The Fe( 8B) atom (octahedral/two covalent/ four dative) forms two covalent (bent) Fe-Fe bonds, one each with the two Fe( 8C) atoms. The structure of Os,( CO) r2 (fig. 2h) is much simpler, being composed of three Os( 8B) atoms (octahedral/two covalent/four dative). Each OS atom forms two covalent bonds, one each to the other two OS atoms; all these bonds are bent. The three octahedra are “packed” so
\,:25$4 o.-~~~~n-co
0
tco O,/? 1 ‘co
0”;’c
0
0
Cd)
(9)
5 December 1986
(h)
(i)
Fig. 2. Structures of some molecular examples: (a) ferrocene; (b) MnCp(CO)S; (c) Ti(CPMCOh; (4 CMCOh; (e) CodCOh; (f) Mn,(CO),o; (g) Fe3(CO)12; (h) OSACO)~~; (9 Ir4(CO)12.
163
Volume132,number 2
CHEMICAL PHYSICS LETTERS
to achieve the best overlap of the hybrid orbitals forming the OS-OS bonds. Note that trinuclear Fe complex prefers two 8C atoms, while the corresponding OS complex prefers all 8B atoms. This can be understood on the basis of the atomic structure of the atoms. The Ir,(CO) ,2 cluster (fig. 2i) is composed of four Ir( 9B) atoms (octahedral/three covalent/three dative), the octahedra are packed to achieve optimal overlap of the hybrids forming the six Ir-Ir covalent bonds; all the Ir-Ir bonds are “bent”. It has been possible to discuss only a few examples in this note, and in attempting to clearly present the basic ideas, only the simplest applications have been considered. Some of the more interesting applications, to be treated in future work, include discussions of: (1) the effect of the doubly occupied metal orbitals; (2) alternative sets of hybrids for a given number of empty and singly occupied orbitals; (3) estimates of the relative energetics of the various possible configurations; (4) the distribution of empty and singly occupied hybrids and its effect on isomers; and (5) situations where more than one metal atom configuration is necessary. However, as presented here, the polyhedral hybrid approach should provide a useful framework for understanding and interpreting not only experimental information but also future GVB calculations. Although the latter will undoubtedly help to refine and make more quantias
164
5 December 1986
tative the present theory, which is essentially qualitative, it is not to be expected that such calculations will seriously challenge the simple underlying physical principles from which this approach is derived.
References [ 11 J.J. Low and W.A. Goddard III, J. Am. Chem. Sot. 106 (1984) 6928. [ 21 M. Steigerwald and W.A. Goddard III, J. Am. Chem. Sot. 107 (1985) 5027. [3] M.H. McAdon and W.A. Goddard III, Phys. Rev. Letters 55 (1985) 2563. [4] R.P. Messmer, P.A. Schultz, R.C. Tatar and H.-J. Freund, Chem. Phys. Letters 126 (1986) 176. [ 51 R.P. Messmer and P.A. Schultz, Phys. Rev. Letters, submitted for publication. [6] P.A. Schultz and R.P. Messmer, unpublished results. [7] R.E. Williams, Inorg. Chem. 10 (1971) 210. [ 8 ] K. Wade, Advan. Inorg. Chem. Radiochem. 18 ( 1976) 1. [ 91 D.M.P. Mingos, Nature 99 (1972) 236. [lo] J.W. Lauher, J. Am. Chem. Sot. 100 (1978) 5305. [ I1 ] R. Hoffmann, Angew. Chem. Intern. Ed. En& 21 (1982) 2297. [ 121 A.J. Stone, Mol. Phys. 41 (1980) 1339. [ 131 P.J. Hunt, P.J. Hay and W.A. Goddard III, J. Chem. Phys. 57 (1972) 738. [ 141 R.C. Ladner and W.A. Goddard III, J. Chem. Phys. 51 (1969) 1073; F.W. Bobrowicz and W.A. Goddard III, in: Modem thew retical chemistry, Vol. 3. Methods of electronic structure theory, ed. H.F. Schaefer III (Plenum Press, New York, 1977) p. 79.