Science in China Series B: Chemistry
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Boron rings containing planar octa- and
enneacoordinate cobalt, iron and nickel metal
elements
LUO Qiong
School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China (email: [email protected])
For a series of boron rings with planar hyper-coordinate 8th group transition metal atoms, singlet
1
FeB8−2, multiplet kFeB9n (n = −1, k = 1; n = 0, k = 2), singlet 1CoB8n(n = −1, +1, +3), multiplet kCoB9n (n = +1, k
= 2; n = 0, k = 1) and singlet 1NiB9+, the geometry structures have been optimized to be local minima on
corresponding potential hyper-surfaces. The electron structures are discussed by orbital analysis and
the aromaticity is predicted by nucleus-independent chemical shifts calculation at both the
B3LYP/6-311+G* and BP86/6-311+G* levels of theory, respectively. The results suggest that all these
structures with high symmetry planar geometries are stable and have aromatic properties with six π
valence electrons.
planar hyper-coordinate, transition metal, DFT
1 Introduction
Since the possibility of existence of tetracoordinate planar carbon (TPC) was first proposed by Hoffmann and
co-workers[1] in planar methane, a great deal of studies
on planar tetracoordinate carbon structures have been
－
made both theoretically and experimentally[2 24]. Considerable progress has been achieved on the theoretical
prediction and experimental realization of these species
－
with tetracoordinate planar carbons[25 27]. The recent
theoretical and experimental confirmations of tetracoordinate planar carbons, in D4h symmetry Al4C− [6], C2v
symmetry Al 3 XC and Al 3 XC − (X=Si, Ge) [9] , and
CAl42−[8], have stimulated extensive interest in searching
for new tetracoordinate and other hyper-coordinate planar carbon species. In particular, a series of hyper-coordinate planar carbons with boron ligands rings have
been theoretically predicted[27]. Following the study of
Exner and Schleyer on the stability of planar hexacoordinate carbon in 2000 [28] , planar penta- [29,30] , planar
－
hexa- [31 34] , and planar heptacoordinate [29,35] carbons
have been extensively investigated in the past 30 years.
For instance, the simplest tetra-, hexa- and hepta-coordinate planar carbon species with high symmetry of D4h,
D6h and D7h, respectively, Al4C− [5], CB62− [9] and CB7−[4],
have all been found theoretically, which achieve their
planarity by means of forming electron-deficient
in-plane bonding with the σ donation from the p-block
ligands.
Up to date, many boron rings containing planar
－
tetra-,[36 38] planar penta-,[39,40] planar hexa-,[41,42] planar
hepta- and planar octa-coordinate atoms[43,44] have been
studied. Some species with other planar hyper-coordinate main group atoms, such as planar hyper-coor－
dinate silicon[46,47], have also been reported[30,35,45 50].
Even boron rings with higher planar octa-, planar ennea-,
and planar deca-coordinate atoms, such as Si, Ge, Sn,
and Pb, have also been investigated computationally[27].
Recently, the studies of planar hyper-coordinate atB
Received April 14, 2008; accepted April 18, 2008
doi: 10.1007/s11426-008-0073-9
Supported by the Research Fund for the Doctoral Program of Higher Education
(Grant No. 20070533142) and the China Postdoctoral Science Foundation (Grant No.
20070410139)
Sci China Ser B-Chem | Jul. 2008 | vol. 51 | no. 7 | 607-613
oms are extended to planar hyper-coordinate transition
metals (PHTMs). For example, singlet D5h FeBi5– and
FeSb5– have been predicted[51]; hexagonal planar hyper-coordinate gold has also been investigated[52].
In the present work, a series of octa- and enneagon
boron rings with planar hyper-coordinate 8th group transition metals Fe, Co and Ni were theoretically synthesized and their properties are predicted.
2 Theoretical methods
In the present study, the density functional methods
B3LYP/6-311+G* and BP86/6-311+G* were applied to
optimize all stable configurations. B3LYP is the combination of the three-parameter Becke functional (B3) with
the Lee-Yang-Parr (LYP) correlation functional[53,54]
while BP86 is the combination of Becke’s 1988 exchange functional (B) with Perdew’s 1986 gradient corrected correlation functional (P86)[55,56]. The 6-311+
G*[57] basis set is a polarized and diffused split-valence
basis set. Stationary points were characterized by harmonic frequency computations, and the zero-point energy (ZPE) of each species was evaluated to correct its
total energy; the Kohn-Sham orbitals were examined to
be stable at the B3LYP/6-311+G* level of theory.
To assess the aromatic character of these species, the
nucleus independent chemical shifts (NICS) [58] were
also determined by applying the gauge-independent
atomic orbital (GIAO)[59,60] procedure at the B3LYP/
6-311+G* level of theory. All the calculations in the
present paper were performed by using the Gaussian 03
program[61].
3 Results and discussion
The optimized geometric structures for the title species
are shown in Figure 1 and the corresponding computational results, including total energies (Etot, in hartree,
1 hartree = 4.36×10−18 J), zero-point energies (ZPE, in
kcal/mol, 1 cal = 4.184 J), geometry parameters M-B and
B-B bond distances (rM-B and rB-B in Å), the values of
the HOMO-LUMO gap (Gap, in kcal/mol), the lowest
vibrational frequencies (νmin, in cm−1) and both values of
NICS(0) and NICS(1) (in ppm) are summarized in Table
1 at both B3LYP/6-311+G* and BP86/6-311+G* levels
of theory; the occupied valence orbitals of FeB82− and
FeB9− are shown in Figure 2.
3.1 Comparison between results from B3LYP and
BP86
As shown in table 1, the results from both functionals,
including total energies, zero-point energies, geometry
parameters M-B and B-B bond distances, the values of
the HOMO-LUMO gap, the lowest vibrational frequencies, and both values of NICS(0) and NICS(1) are similar to each other for singlet 1FeB8−2, multiplet kFeB9n (n
= −1, k = 1; n = 0, k = 2), singlet 1CoB8n(n = −1, +3),
singlet 1CoB9 and singlet 1NiB9+1 . The predicted energy
Table 1 Total energies (Etot, in hartree), zero-point energies (ZPE, kcal/mol), M—B and B—B bond distances (rM-B and rB-B, in Å), the values of the
HOMO-LUMO gap (Gap, in kcal/mol), the lowest vibrational frequencies (νmin, in cm−1) and both values of NICS(0) and NICS(1) (in ppm) for MB8
(M=Fe2−, Co1−,1+,3+) and MB9 (M= Fe1−,0, Co0,1+, Ni1+) at the B3LYP/6-311+G* and BP86/6-311+G* levels of theory
B
B
B
Species
1
FeB8
1
FeB91−
2
2−
FeB9
1
CoB81−
1
CoB81+
(D2h)
1
CoB83+
1
2
CoB9
CoB91+
NiB91+
1
608
νmin
DFT
B3LYP
BP86
B3LYP
BP86
B3LYP
BP86
B3LYP
BP86
Etot
−1462.39229
−1462.59567
−1487.28935
−1487.47721
−1487.17992
−1487.34861
−1581.51132
−1581.72565
ZPE
20.3
19.6
22.4
21.5
22.1
21.5
20.4
19.7
Gap
2.51
1.29
3.08
0.97
1.88
0.84
2.73
1.27
90.7
91.5
110.5
20.5
109.5
106.0
59.2
54.9
B3LYP
−1581.08295
18.8
0.79
105.2
r M —B
2.043
2.057
2.220
2.236
2.244
2.247
2.036
2.051
2.009
2.092
B3LYP
BP86
B3LYP
BP86
B3LYP
B3LYP
BP86
−1579.88816
−1580.09617
−1606.22716
−1606.42895
−1605.92264
−1731.47580
−1731.67626
17.9
16.7
22.0
21.2
21.5
21.4
20.7
1.78
0.12
2.47
1.04
1.76
1.99
0.69
176.9
−129.5
96.7
41.4
75.2
110.5
79.0
2.093
2.106
2.226
2.241
2.255
2.251
2.265
LUO Qiong Sci China Ser B-Chem | Jul. 2008 | vol. 51 | no. 7 | 607-613
r B —B
1.563
1.574
1.519
1.529
1.535
1.537
1.559
1.570
1.616
1.564
1.533
1.602
1.612
1.522
1.533
1.543
1.540
1.549
NICS(1)
−182.7
−134.4
−293.3
−198.1
−115.1
−132.5
−130.5
−105.7
−101.4
−138.7
−106.3
−194.2
−145.5
−187.7
−96.6
−87.5
Figure 1 The optimized geometry structures of MB8 (M=Fe2−, Co1−,1+,3+) and MB9 (M= Fe1−,0, Co0,1+, Ni+), bond distances in Å.
B
values from BP86 are smaller than those from B3LYP
with differences in ranges of 0.168－0.214 hartrees
for total energies, 0.6－1.2 kcal/mol for zero point energy, and 1.04－2.11 eV for the HOMO-LUMO gap.
The predicted geometric and NICS values from BP86
are larger than those from B3LYP for M—B bond distances ( with a difference in a range of 0.016－0.03 Å),
B—B bond distances (with a difference in a range of
0.002－0.011 Å), and NICS(1) (with a difference in a
range of 9－95.2 ppm). However, for the lowest vibrational frequencies, the differences between the two functionals have no consistency for all species. Therefore,
the differences between both functionals are small for
molecular structure calculations, which is why only the
B3LYP results are discussed in text. It should be men-
tioned that the structure of CoB8+1 and 2CoB9+1 cannot
be obtained by using BP86/6-311+G*.
3.2 Geometric structures
Except for CoB81+, optimized structures of all these species have the highest symmetry, D8h or D9h. There are
only two different bond distances in these species: B—B
bond distances and M-B bond distances.
For B—B bonds, the distances are 1.559－1.602 Å
with the average of 1.575 Å for eight-membered ring
species and 1.519－1.543 Å with the average of 1.532 Å
for nine-membered ring species. All these B—B bond
distances are shorter than 1.76 Å, twice of boron atom’s
covalence radius, indicating all B—B bonds in these species are covalent single bond. The B—B bond distances
in nine-membered ring species are smaller than those in
LUO Qiong Sci China Ser B-Chem | Jul. 2008 | vol. 51 | no. 7 | 607-613
609
Figure 2 The occupied valence orbitals of (a) FeB82− and (b) FeB9−.
eight-membered ring species, indicating that there is a
stronger interaction between two boron atoms in
nine-membered ring species than that in eight-mem610
bered ring species.
For M—B bonds, because the atomic radii, 1.24, 1.25
and 1.24 Å, and covalent radii, 1.16, 1.16 and 1.15 Å,
LUO Qiong Sci China Ser B-Chem | Jul. 2008 | vol. 51 | no. 7 | 607-613
for iron, cobalt and nickel atom, respectively, are almost
the same, the differences among radii for these metal
atoms are not distinguishable. As shown in Table 1, the
M-B bond distances are 2.036－2.093 Å with the average of 2.057 Å for eight-membered ring species and
2.220－2.255 Å with the average of 2.239 Å for ninemembered ring species. All these B—M bond distances
in eight-membered ring species are very close to the sum,
2.04 Å, of the covalence radius of boron atoms, 0.88 Å,
and the average covalence radius of metal atoms, 1.16 Å,
suggesting that there exists a strong bonding interaction
between M and B atoms in these structures. All these
B—M bond distances in nine-membered ring species are
larger than the sum of the covalence radius of boron
atoms and the average covalence radius of metal atoms,
indicating that there exists a comparably weak bonding
interaction in these structures. These data mean that the
species with eight-membered rings are more stable than
those with nine-membered rings. The sum of all these
interactions between the metal atom and each boron
atom makes the metal atom more stable in the center of
a boron ligand ring. It is suggestive that there exist
multi-center bonds among the metal atom and the boron
atoms.
For the CoB8+1 structure, the optimized geometry
does not have D8h symmetry, but has D2h symmetry. B—B
bond distances are 1.616, 1.564 and 1.533 Å with the
average of 1.569 Å, which are all smaller than 1.76 Å,
twice of boron atom’s covalence radius, indicating that
all B—B bonds in these species are also covalent single
bonds. M—B bond distances are 2.009 and 2.092 Å with
the average of 2.051 Å, exhibiting the similarity to those
of FeB82−, CoB8− and CoB83+; there exist strong interactions between the metal atom and the boron atoms in
this structure.
3.3 Electron structure
To understand the nature of structural integrity and planarity of the species studied here, valence Kohn- Sham
orbitals were analyzed. As species containing an
eight-membered boron ring, both FeB8−2 and CoB8−1
have 17 occupied valent orbitals, in which there exist
eight orbitals forming eight B-B bonds along the edge of
the boron ring, three delocalized π orbitals leading to
aromaticity of the species, five metal-B8 ring interaction
orbitals making the structure more stable, and one
lone-pair electron orbital. As an example, FeB82− vaB
lence Kohn-Sham orbitals are shown in Figure 2. It can
be seen from Figure 2 that HOMO-8 and HOMO-10－
HOMO-16 are eight B—B bond orbitals; HOMO-5－
HOMO-7 are three delocalized π orbitals; HOMO－
HOMO-4 are five metal-B8 ring interaction orbitals
while HOMO-9 is a lone-pair electron orbital. The electron structures in both CoB8+3 and CoB8+1 are similar to
that of CoB8−1 with the only difference between them to
be that the numbers of metal-B8 ring interaction orbitals
in CoB8+3 and CoB8+1 are three and four (but five in
CoB8−1) due to the 30 or 32 valent electrons occupying
15 or 16 valent orbitals, respectively.
As species containing a nine-membered boron ring,
singlet FeB9−1, CoB9 and NiB9+1 all have 18 occupied
valent orbitals, in which there exist nine orbitals forming
nine B-B bonds along the edge of the boron ring, three
delocalized π orbitals leading to aromaticity of the species, five metal-B9 ring interaction orbitals making the
structure more stable, one lone-pair electron orbital. In
the valence Kohn-Sham orbitals of FeB9− shown in Figure 3, one can easily find that the HOMO-9－HOMO-17
are nine B—B bond orbitals; HOMO-5－HOMO-7 are
B
B
B
B
B
B
B
three delocalized π orbitals; HOMO, HOMO-1,
HOMO-3, HOMO-4 and HOMO-8 are five metal-B9
ring interaction orbitals while HOMO-2 is a lone-pair
electron orbital. The electron structures in 2FeB9 and
2
CoB9+1 are similar to that of 1FeB9−1 with the only difference between them to be that the number of electrons
occupying the lone-pair electron orbital in 2FeB9 or
2
CoB9+1 is one (but two in 1FeB9−1) due to the 35
electrons occupying 18 valent orbitals.
3.4 Aromatic properties
From the electron structures discussed above, one can
expect that there might exist aromaticity in all these species due to the six π electrons. To confirm this expectation, the NICS(0) and NICS(1) were evaluated with the
ghost atom located on the center metal atom and above
the center metal atom by 1.0 Å along the main symmetric axis, respectively. The results of all these structures
are listed in Table 1. Both the species containing an
eight-membered boron ring and a nine-membered boron
ring have large positive NICS(0) values, 1779－22517
ppm, indicating that σ delocalization does not occur. The
NICS(1) values, from −293 to −96 ppm, denote significant π electrons delocalization. Therefore, only π aro-
LUO Qiong Sci China Ser B-Chem | Jul. 2008 | vol. 51 | no. 7 | 607-613
611
maticity but no σ aromaticity exists in both the species
containing an eight-membered and a nine-membered boron ring. For the species containing an eightmembered boron ring, the range of NICS(1) values is
from −183 (1FeB8−2) to −101(1CoB8+1) ppm, while for
the species containing a nine-membered boron ring the
range of NICS(1) values is from −97 (1NiB9+1) to
−293(1FeB9−1) ppm. This indicates that the species containing an eight-membered boron ring have similar aromaticity, but the aromaticity in species containing a
nine-membered boron ring. are of extension. It should
be noticed that the NICS(1) values of doublet species
(−115 ppm, for 2FeB9 and −187 ppm for 2CoB9+1 ) fall in
the range of singlet species containing a nine-membered
boron ring, −97 (1NiB9+1)－−293(1FeB9−1) ppm, suggesting that the existence of an unpaired electron does
not affect the aromatic property.
4 Summary
In the present work, a series of potential boron rings
with planar hyper-coordinate 8th group transition metal
1
2
3
4
5
6
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8
9
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