532
Journal of the Chinese Chemical Society, 2009, 56, 532-538
Computational Study on the Unconventional Hydrogen-Bonded F–H···C
Systems
Hsin-Yi Liao (
)
Department of Science Education, National Taipei University of Education, Taipei 10659, Taiwan, R.O.C.
The F–H···YZ2 (Y = C, Si, BH, AlH; Z = H, PH3) systems were examined using density functional theory calculations. The main focus of this work is to demonstrate that the chemistry of Y(PH3)2 exhibits a
novel feature which is a central Y atom with unexpected high basicity. Further, the hydrogen bond strength
can be adjusted by the substitution of H atoms of YH2 by PH3 groups. The FH···C(PH3)2 system has the
strongest hydrogen bond interaction, which is larger than a conventional hydrogen bond. In addition to
electrostatic interaction, donor-acceptor interaction also plays an important role in determining the hydrogen bond strength. Therefore, a carbon atom can not only be the hydrogen bond acceptor but also can create an unusual stabilized hydrogen bond complex. Also, X3B–YZ2 (X = H, F; Y = C, Si, BH, AlH; Z = PH3,
NH3) systems were examined, and it was found that the bond strength is controlled predominately by the
HOMO-LUMO gap (DIP). The smaller the DIP, the larger the bond dissociation energy of the B–Y bond.
In addition, NH3 is a better electron-donating group than PH3, and thus forms the strongest donor-acceptor
interaction between X3B and Y(NH3)2.
Keywords: Unconventional hydrogen bonds; Density functional theory; HOMO-LUMO gap;
Donor-acceptor interaction.
INTRODUCTION
Hydrogen bonds are one of the most often investigated topics in chemistry since they are involved in numerous processes.1 There are different types of hydrogen bond
interactions. 2,3 The so-called unconventional hydrogen
bonds have been studied recently. One kind of unconventional hydrogen bond is the hydrogen bond with unconventional acceptors such as X–H···C. 4-7 It refers to the
X–H +d ··· –d C system in which X–H is usually the typical
proton donating bond with an electronegative X atom, and
the carbon atom possesses an excess negative charge behaving as an acceptor.
While C–H···O hydrogen bonds are widespread, the
complementary O–H···C interaction is rare because C is not
as electronegative as O. A striking example of such an
O–H···C hydrogen bond has been reported by Desiraju et
al.7 They found that the O–H···C interaction existed in the
crystal structure of 17a-ethynylandrosta-2,4-dieno[2,3d]dihydroxazol-17b-ol.7
Since C–H moieties have lower acidity, C–H···C
bonds are anticipated to be weak. However, Woïniak et al.
utilized MP2/6-311++G(d,p) calculations to indicate that
C–H···C hydrogen bonds with strengths of up to 35 kJ/mol
in H 3N–CH 2···H–CCH complexes. 4 Woïniak et al. suggested that a “closed-shell” hydrogen-bond critical point
existed in the complexes from the topology of the charge
density.4 That is, the hydrogen-bonded interaction may be
enhanced by the use of more acidic proton donor fragments
(H–CCH) or by increasing the basicity of the acceptor
(ylides).
Thus, the X–H···C hydrogen bond strength may be increased by maximizing the basicity of carbon atoms. A sufficiently electron-rich C atom could be a potential candidate to form an unconventional hydrogen bond with X–H
groups (X = O, N, F). A recent publication by Frenking et
al. introduced theoretical and experimental evidence suggesting that C(PR3)2 are carbon-containing compounds in
which the atomic charge at the central carbon atom of
C(PR3)2 calculated by the NBO method has a large negative
value, –1.43e at a BP86/TZVPP2//RI-BP86/SVP level of
theory.8 The theoretical result is supported by experimental
observations and the C(PR3)2 compounds serve as a fourelectron donor so that the salt compound [(PPh 3) 2CH 2][FeCl4]2 can be prepared.9
* Corresponding author. Tel: +886-2-2732-1104 ext. 3309; Fax: +886-2-2735-2784; E-mail: [email protected]
Study on the Unconventional Hydrogen-Bonded Systems
J. Chin. Chem. Soc., Vol. 56, No. 3, 2009
The first C(PR3)2 compounds, C(PPh3)2, were synthesized in 1961 by Ramirez et al.10,11 The chemistry of C(PR3)2
compounds was studied experimentally in the following
years and numerous compounds containing the C(PR3) 2
moieties were isolated.12 The bonding in C(PR3) 2 compounds has been described either in terms of two electron
pairs at the central carbon atom,13 or in the notation of
R3P=C=PR3.12,14
Hence the aim of this study is to propose an unconventional hydrogen-bonding complex F–H···YZ2 (Y = C,
Si, BH, AlH; Z = H, PH3) in order to examine its interaction
between the hydrogen bonded acceptor and the hydrogen
bonded donors. Some rationalization was provided to
identify the key factors that control the hydrogen bonded
strength of this kind of system. Thereafter, we can choose
suitable substituents to maximize the hydrogen bond energies in the unconventional F–H···YZ2 complex. In addition,
the acid-case complex X3B–YZ2 (X = H, F; Y = C, Si, BH,
AlH; Z = H, PH 3, NH 3) is investigated to see how good
C(PR3)2 compounds can be as electron-pair donors.
METHODOLOGY
The geometries of these hydrogen bonded structures
have been fully optimized and vibrational frequencies
were calculated using the B3LYP method with the 6311++G** basis set.15-18 True minima were confirmed by
frequency analysis. All calculations were performed with
the GAUSSIAN 03 package.19 Zero-point vibrational energies (ZPE) were included in the reported energies. Since
the relative energies are of our concern, the BSSE correction was not considered explicitly. Orbital energies were
determined at the HF/6-311++G** level of theory. It is
known that the HF results are a useful reference for comparson with experimental results according to Koopmans’
theorem, and the B3LYP results should be adjusted through
a scaling scheme.20,21 In addition, the orbitals and charges
were analyzed by means of the natural bond orbital (NBO)
scheme.22
RESULTS AND DISCUSSION
The molecules studied are calculated as singlets. As
can be seen in Table 1, the B3LYP/6-311++G** results
agree quite well with previously reported theoretical data.23
Thus, B3LYP/6-311++G** can be viewed as an effective
method for calculating this hydrogen bond system. Fully
optimized B3LYP/6-311++G** structures of HF, CH 2,
C(PH3)2, FH···CH2 and FH···C(PH3)2 are shown in Fig. 1.
As can be seen in Fig. 1, after forming the FH···CH2 hydrogen-bonded complex, d(H–F) elongated, whereas d(C–H)
is shortened. When the hydrogen bond is formed, the intramolecular interaction in the proton donor HF weakens and
thus d(H–F) extends. This effect is similar to what happens
in conventional hydrogen bond systems.24 On the contrary,
when the hydrogen bond is formed, the charge separation
in CH2 increases and the electrostatic interaction increases.
Thus, a shorter C–H bond length is obtained.
However, the FH···C(PH 3) 2 complex shows an increase of the C–P bond length which is opposite of what is
observed in the FH···CH2 complex. We suggest that the carbon-phosphorous bonds in C(PH3)2 come from P ® C donor-acceptor interactions rather than electron-sharing C–H
covalent bonds in carbenes. Therefore, when the hydrogen
bond is formed, the donor-acceptor interactions in C(PH3)2
weakens and d(C–P) extends. As can be seen in Table 2,
these geometrical characteristics also exist in the silylene
systems.
The H···C distance of FH···CH2 is found to be 1.772
Å, which is between the covalent bond length of C–H
(~1.08 Å) and the sum of two radii of C and H atoms (~2.90
Å). The interaction energy of CH2 and HF is 10.28 kcal/
mol, which is in the energy range of a conventional hydrogen bond (2~10 kcal/mol).25 Therefore, the FH···CH2 system conforms to the definition of hydrogen-bonded interaction. In addition, the existence of hydrogen-bonded in-
Table 1. B3LYP/6-311++G** optimized hydrogen bond lengths (d(H···Y), Å) and hydrogen
bond energies (EHB, kcal/mol) of the F–H···YH2 complexes (Y = C, Si)
System
F–H···CH2
F–H···SiH2
a
B3LYP/6-311++G**a
d(H···Y)
EHBc
1.772
2.415
–10.28
0–3.68
533
MP2/6-311++G**b
MP2/6-31G**b
d(H···Y)
EHBc
d(H···Y)
EHBc
1.831
2.488
–10.73
0–4.32
1.870
2.599
–10.64
0–3.35
This study. b Reference 23. c EHB = E[F–H···YH2] – E[HF] – E[YH2].
534
J. Chin. Chem. Soc., Vol. 56, No. 3, 2009
teraction in the FH···SiH 2 system is also verified by the
H···Si distance and the hydrogen bond strength. That is, the
group 14 elements could be the hydrogen bond acceptors in
some certain conditions.
Notably, we can compare FH···CH2 with the familiar
hydrogen bond complex FH···OH 2 because CH 2 has the
same structure as H2O. We found that EHB = –7.35 kcal/mol
for FH···OH2 at the B3LYP/6-311++G** level of theory
and is less in magnitude than that of FH···CH2. Similarly,
the hydrogen bond interaction in conventional FH···SH 2
complex (EHB = –3.64 kcal/mol) is also weaker than the un-
Fig. 1. B3LYP/6-311++G** optimized geometries (in
Å), natural charges for (a) HF, CH2, and FHCH2
systems; (b) HF, C(PH3)2, and FHC(PH3)2 systems. Dashed lines indicate hydrogen bonds.
Liao
conventional FH···SiH2 complex at the B3LYP/6-311++G**
level of theory.
As can be seen in Table 2, the substitution of H atoms
of YH2 (Y = C, Si) by PH3 groups increase significantly the
strength of the hydrogen-bonded interaction and decrease
the H···Y bond length. Further, the Y atom participating in
the hydrogen bond is much more negative in its natural
charge. However, the larger charge separation at FHd+ and
d–
Y does not always induce larger hydrogen-bonded interaction energy. For example, the FH···CH 2 system has a
larger EHB (–10.28 vs. –7.35 kcal/mol) but has a smaller
negative q(Y) (–0.08 vs. –0.93) than the FH···OH 2 complex. Therefore, it appears that there are two kinds of interactions operational in the F–H···YZ2 system (Y = C, Si; Z =
H, PH3). One is electrostatic contributions as expected for
the conventional hydrogen bond. The second is the covalent character of the hydrogen bond.3
The covalency can be correlated to the energy gap between the HOMO of an electron-pair donor (n orbital of
YZ2) and the LUMO of an electron-pair acceptor (s* orbital of HF). HOMO energy of YZ2 and LUMO energies of
HF are calculated at the RHF/6-311++G** level of theory
and are shown in Fig. 2. It is known that the Hartree-Fock
orbital energies are a useful reference for experimental results according to Koopmans’ theorem; thus, we utilize HF
results to estimate the HOMO-LUMO energy gap.26,27
The substitution of H atoms of YH2 by PH3 groups
raises the HOMO orbital (Fig. 2(a)). Then, the energy gap
between the HOMO and LUMO is decreased and the interaction between the hydrogen-bonded donor and hydrogen-bonded acceptor is strengthened. When Y = C, their
HOMO energies are higher than those of H2O. Therefore,
the F–H···CZ2 series has much larger interaction energies
than FH···OH2. The interaction of HF and C(PH3)2 results
in a short and strong hydrogen bond (HOMO-LUMO gap =
8.82 eV). Similarly, the series of Y = Si shows the same relationship between the EHB and HOMO-LUMO gap as
shown in Table 2 and Fig. 2(b).
The rising of HOMO in the C(PH3)2 system can also
reflect the conversion of C0+ (CH 2) into C1.5– (C(PH 3) 2)
with increasing nucleophilicity of the electronic pair on the
carbon atom. That is, the electrostatic interaction plays a
major role in the formation of the F–H···YZ2 system at first.
Then, utilizing the electron donating ability of P ® C can
adjust the basicity of the electron-pair donor (YZ2). When
the HOMO-LUMO gap is lowered to a threshold value, the
donor-acceptor interaction dominates and a strong uncon-
Study on the Unconventional Hydrogen-Bonded Systems
J. Chin. Chem. Soc., Vol. 56, No. 3, 2009
535
Table 2. B3LYP/6-311++G** optimized bond lengths (Å), natural charges (q) and hydrogen
bond energies (EHB, kcal/mol) of the isolated monomers and the F–H···YZ2 (Y = C,
Si, BH, AlH, O, S, NH, PH; Z = H, PH3) complexes
d(F–H)
d(Y–Z)
d(H···Y)
q(F, H, Y)
EHBa
HF
H2O
CH2
C(PH3)2
H2S
SiH2
Si(PH3)2
NH3
BH(PH3)2
PH3
AlH(PH3)2
0.922
—
—
—
—
—
—
—
—
—
—
—
0.962
1.113
1.635
1.348
1.527
2.286
1.014
1.822
1.423
2.692
—
—
—
—
—
—
—
—
—
—
—
(-0.55, 0.55, —)
(—, —, –0.92)
(—, —, –0.11)
(—, —, –1.48)
(—, —, –0.26)
(—, —, +0.59)
(—, —, –0.33)
(—, —, –1.05)
(—, —, –0.98)
(—, —, +0.05)
(—, —, +0.25)
—
—
—
—
—
—
—
—
—
—
—
FH···OH2
FH···CH2
FH···C(PH3)2
FH···SH2
FH···SiH2
FH···Si(PH3)2
FH···NH3
FH···BH(PH3)2
FH···PH3
FH···AlH(PH3)2
0.942
0.961
0.979
0.936
0.939
0.961
0.962
0.979
0.937
0.951
0.963
1.105
1.657
1.349
1.516
2.305
1.016
1.848
1.417
2.661
1.701
1.772
1.693
2.272
2.415
2.346
1.673
1.932
2.322
2.435
(–0.59, 0.56, –0.93)
(–0.62, 0.51, –0.08)
(–0.63, 0.55, –1.56)
(–0.58, 0.54, –0.26)
(–0.59, 0.53, 0.59)
(–0.63, 0.51, –0.33)
(–0.62, 0.55, –1.05)
(–0.65, 0.52, –1.03)
(–0.58, 0.55, 0.02)
(–0.61, 0.52, 0.20)
–7.35
–10.28
–15.22
–3.64
–3.68
–9.79
–11.25
–12.57
–3.67
–7.55
a
EHB = E[F–H···Y(PH3)2] ?– E[HF] – E[Y(PH3)2].
ventional hydrogen bond forms.
For increasing the hydrogen bond strength further,
we utilize NH3 as the substituent because Y(NH3)2 has a
higher HOMO energy than the corresponding Y(PH3)2 as
shown in Fig. 2. However, the HOMO-LUMO gap of
F–H···Y(NH3)2 is too small so that the interaction is strong
enough to break the H–F bond and F –···HY(NH 3) 2+ is
formed (Scheme I). That is, we can gradually reduce the
HOMO-LUMO gap between the electron donor and acceptor by different substituents and then gradually strengthen
the hydrogen bond interaction. Finally, the conversion of
Scheme I
the hydrogen bond interaction into a covalent bond occurs
(H···Y ® H–Y).
Next, we tried to use atoms of group 13 whose electronegativity is smaller than C or Si atoms to form the unconventional hydrogen bond complex with an HF molecule. Because a B atom has low electronegativity: EN =
3.98 (F) > 2.20 (H) > 2.04 (B), 28 a dihydrogen bond
F–Hd+···–dH–BH2 is formed. That is, the boron atom in BH3
cannot be the hydrogen bond acceptor. When we utilize the
PH3 group to substitute two H atoms in BH3 (to resemble
C(PH 3) 2), F–H···BH(PH 3) 2 is obtained and its hydrogen
bond strength is stronger than the conventional hydrogen
bond complex F–H···NH 3 (–12.57 vs. –11.25 kcal/mol).
Likewise, AlH3 also forms a dihydrogen bond with HF but
F–H···AlH(PH3)2 can have a much stronger hydrogen bond
interaction than F–H···PH 3 (–7.55 vs. –3.67 kcal/mol).
Also, when Z = NH3, the HF molecule is dissociated. The
abovementioned phenomena agrees well with the order of
the HOMO energies for NH3 (–11.53 eV), BH(PH3)2 (–5.67
eV), BH(NH3)2 (–4.67 eV), and PH3 (–10.38 eV), AlH(PH3)2
(–6.78 eV), AlH(NH3)2 (–5.47 eV).
To examine the electron-donating ability of Y(NH3)2
536
J. Chin. Chem. Soc., Vol. 56, No. 3, 2009
Liao
B–Y bond is weakened and BDE is decreased. That is,
BDE(X = H) > BDE(X = F) because BF 3 has a higher
LUMO energy and thus a larger DIP and a weaker donoracceptor interaction. Also, in the series of Y, the smaller the
DIP, the larger the BDE. For example, DIP = 6.09 < 6.96 <
8.66 < 9.53 < 14.92 < 15.79 eV and BDE = 72.02 > 68.35 >
35.24 > 31.12 > 8.06 > 5.88 kcal/mol for the Y = C series as
shown in Table 3. One exception occurs in the Y = AlH series beacause a strong electrostatic attraction exists in
H3B–PH3 (q(B) = –0.59; q(P) = 0.57), whereas a large electrostatic repulsion exists in F3B–AlH(PH3)2 (q(B) = 0.95;
q(Al) = 0.60). Notably, because the electron-deficient
property of BH3, B2H6 can only have a bridging structure.
However, when utilizing an NH3 or PH3 group to substitute
H atoms in BH 3, BH(NH 3) 2 can complex with BH 3 and
form a strong B–B bond.
Fig. 2. The HOMO and LUMO energies (in eV) of YZ2
and HF calculated at the RHF/6-311++G**
level of theory. (a) Y = O, C; Z = H, PH3, NH3;
(b) Y = S, Si; Z = H, PH3, NH3.
quantitatively, the Lewis acid-base complexes X3B–YZ2
(X = H, F; Y = C, Si, BH, AlH; Z = PH3, NH3) were investigated. According to our previous results,29 the donor-acceptor interaction is a key factor controlling the bond
strength of acid-base complexes. As shown in Table 3,
BDE for X 3B–Y(NH 3) 2 is larger than that of the corresponding X 3B–Y(PH 3) 2 because Y(NH 3) 2 has a higher
HOMO energy and thus a smaller DIP and a stronger donor-acceptor interaction. In addition, the complexes using
YZ2 as electron donors are much more stable than those using water or ammonia as electron donors. For example,
BDE(H 3B–C(NH 3) 2) = 72.02 > BDE(H 3B–C(PH 3) 2) =
35.24 > BDE(H3B–OH2) = 8.06 kcal/mol.
When we replace BH 3 with a weaker acid BF 3, the
CONCLUSIONS
We found that the chemistry of C(PH3)2 and Si(PH3)2
exhibits novel features which has a central C or Si atom
with unexpected high basicity. The hydrogen bond strength
can be adjusted by the substitution of H atoms of YH2 (Y =
C, Si) by PH3 groups because the HOMO energy of Y(PH3)2
is higher than that of YH2. Thus, Y(PH3)2 has a much more
negative charge on Y and the carbon and silicon atoms can
be a hydrogen bond acceptor. In this study, the HF···C(PH3)2
system has the strongest hydrogen bond interaction at the
B3LYP/6-311++G** level of theory and even its EHB is
larger than a conventional hydrogen bond, e.g. HF···OH2.
That is, the electrostatic interaction plays a major role in the
formation of the F–H···Y(PH3)2 system at first. Then, utilizing the electron donating ability of P ® C can adjust the
basicity of the electron-pair donor. When the HOMOLUMO gap is lowered to a threshold value, the donor-acceptor interaction dominates and a strong unconventional
hydrogen bond forms. Therefore, a carbon atom cannot
only be the hydrogen bond acceptor but also can create an
unusual stabilized hydrogen bond complex.
Further, X3B–YZ2 (X = H, F; Y = C, Si, BH, AlH; Z =
PH3, NH3) was examined, and it was found that its bond
strength is also controlled predominately by the HOMOLUMO gap (DIP). The smaller the DIP, the larger the bond
dissociation energy of the B–Y bond. In addition, NH3 is a
better electron-donating group than PH3 and thus forms the
strongest donor-acceptor interaction between X 3B and
Y(NH3)2.
Study on the Unconventional Hydrogen-Bonded Systems
J. Chin. Chem. Soc., Vol. 56, No. 3, 2009
537
Table 3. B3LYP/6-311++G** optimized bond lengths (Å), natural charges (q), HOMOLUMO gap (DIP, eV) and bond dissociation energies (BDE, kcal/mol) of the X3B–
YZ2 (X = H, F; Y = C, Si, O, S, BH, AlH, NH, PH; Z = H, PH3, NH3) complexes
DIPa
BDEb
(–0.43, –0.26)
(1.11, –0.38)
(–0.33, –1.35)
(1.23, –1.44)
(0.02, –0.77)
(1.38, –0.85)
6.09
6.96
8.66
9.53
14.92
15.79
72.02
68.35
35.24
31.12
8.06
5.88
2.021
2.111
2.071
2.204
2.083
3.088
(–0.92, 0.64)
(0.83, 0.49)
(–0.84, 0.26)
(0.96, 0.05)
(–0.29, 0.13)
(1.41, –0.26)
5.43
6.30
6.59
7.46
11.49
12.36
59.59
47.81
31.44
16.64
7.38
–1.77
H3B–BH(NH3)2
F3B–BH(NH3)2
H3B–BH(PH3)2
F3B–BH(PH3)2
H3B–NH3
F3B–NH3
1.707
1.731
1.790
1.815
1.665
1.679
(–0.70, 0.25)
(0.98, 0.10)
(–0.58, –0.69)
(1.09, –0.83)
(–0.15, –0.84)
(1.28, –0.92)
5.69
6.56
6.69
7.56
12.55
13.42
71.85
67.26
38.20
29.24
23.22
18.08
H3B–AlH(NH3)2
F3B–AlH(NH3)2
H3B–AlH(PH3)2
F3B–AlH(PH3)2
H3B–PH3
F3B–PH3
2.081
2.171
2.107
2.250
1.954
3.213
(–1.02, 1.18)
(0.83, 0.96)
(–0.94, 0.91)
(0.95, 0.60)
(–0.59, 0.57)
(1.42, 0.03)
6.49
7.36
7.80
8.67
11.40
12.27
41.79
28.98
28.43
10.90
16.86
01.62
d(B–Y)
q(B, Y)
H3B–C(NH3)2
F3B–C(NH3)2
H3B–C(PH3)2
F3B–C(PH3)2
H3B–OH2
F3B–OH2
1.608
1.621
1.680
1.671
1.757
1.843
H3B–Si(NH3)2
F3B–Si(NH3)2
H3B–Si(PH3)2
F3B–Si(PH3)2
H3B–SH2
F3B–SH2
DIP = E(LUMO) – E(HOMO). E(LUMO) = +1.02 eV for BH3 and E(LUMO) = +1.89 eV
for BF3. b BDE is defined as DE for X3B–YZ2 ® X3B + YZ2.
a
ACKNOWLEDGMENT
The author is grateful to the National Center for
High-Performance Computing for computer time and facilities. The author thanks the National Science Council of
Taiwan for their financial support (NSC 97-2113-M-152001-MY2). The author also thanks Prof. Dr. San-Yan Chu
for his helpful and generous suggestions.
Received December 31, 2008.
REFERENCES
1. Grabowski, S. J. Hydrogen Bonding – New Insights;
Springer: New York, 2006.
2. Alkorta, I.; Rozas, I.; Elguero, J. Chem. Soc. Rev. 1998, 27,
163-170.
3. Liao, H.-Y. Chem. Phys. Lett. 2006, 424, 28-33.
4. Platts, J. A.; Howard, S. T.; Woïniak, K. Chem. Commum.
1996, 63-64.
5. Ahlberg, P.; Davidsson, Ö.; Löwendahl, M.; Hilmersson, G.;
Karlsson, A.; Håkansson, M. J. Am. Chem. Soc. 1997, 119,
1745-1750.
6. Steiner, T. J. Chem. Soc., Chem. Commun. 1995, 95-96.
7. Viswamitra, M. A.; Radhakrishnan, R.; Bandekar, J.;
Desiraju, G. R. J. Am. Chem. Soc. 1993, 115, 4868-4869.
8. Tonner, R.; Öxler, F.; Neumüller, B.; Petz, W.; Frenking, G.
Angew. Chem. Int. Ed. 2006, 45, 8038-8042.
9. Walker, J. D.; Poli, R. Polyhedron 1989, 8, 1293-1297.
10. Ramirez, F.; Desai, N. B.; Hansen, B.; McKelvie, N. J. Am.
Chem. Soc. 1961, 83, 3539-3540.
11. Handy, G. E.; Zink, J. I.; Kaska, W. C.; Baldwin, J. C. J. Am.
Chem. Soc. 1978, 100, 8002-8004.
12. Jones, N. D.; Cavell, R. G. J. Organomet. Chem. 2005, 690,
5485-5496.
13. Kaska, W. C.; Mitchell, D. K.; Reichelderfer, R. F. J.
Organomet. Chem. 1973, 47, 391-402.
14. Marrot, S.; Kato, T.; Gornitzka, H.; Baceiredo, A. Angew.
Chem. Int. Ed. 2006, 45, 2598-2601.
15. Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652.
16. Becke, A. D. J. Chem. Phys. 1992, 97, 9173-9177.
17. Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. 1988, B37, 785789.
538
J. Chin. Chem. Soc., Vol. 56, No. 3, 2009
18. Krishnan, R.; Binkley, J. S.; Seger, R.; Pople, J. A. J. Chem.
Phys. 1980, 72, 650-654.
19. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A.; Vreven,
Jr., T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S.
S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.;
Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;
Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.;
Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.;
Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.;
Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C. J.;
Ochterski, W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.;
Daniels, A. D.; Strain, M. C.; Farkas, O. D.; Malick, K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J.
V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.;
Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;
Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham,
M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill,
P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.;
Pople, J. A. Gaussian 03, Revision A1; Gaussian, Inc.: Pittsburgh, PA, 2003.
Liao
20. Baerends, E. J.; Gritsenko, O. V.; van Leeuwen, R. Chemical
Application of Density-Functional Theory; Laird, B. B.;
Ross, B.; Zeigler, T. Eds.; American Chemical Society:
Washington D.C., 1996.
21. Baerends, E. J.; Gritsenko, O. V.; van Leeuwen, R. J. Phys.
Chem. A 1997, 101, 5383-5403.
22. Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold,
F. NBO 4.0; Theoretical Chemistry Institute, University of
Wisconsin: Madison, WI, 1996.
23. Alkorta, I.; Elguero, J. J. Phys. Chem. 1996, 100, 1936719370.
24. Audier, H. E.; Koyanagi, G. K.; McMahon, T. B.; Tholmann,
D. J. Phys. Chem. 1996, 100, 8220-8223.
25. Grabowski, S. J.; Sokalski, W. A.; Leszczynski, J. J. Phys.
Chem. A 2005, 109, 4331-4341.
26. Stowasser, R.; Hoffmann, R. J. Am. Chem. Soc. 1999, 121,
3414-3420.
27. Vlcek, Jr. A. Chemtracts-Inorg. Chem. 1999, 12, 899.
28. Huheey, J. E.; Keiter, E. A.; Keiter, R. L. Inorganic Chemistry: Principle of Structure and Reactivity; Harper Collins
College Publishers: New York, 1993.
29. Liao, H.-Y. Int. J. Quant Chem. 2007, 108, 84.