JOURNAL OF CHEMICAL PHYSICS
VOLUME 119, NUMBER 10
8 SEPTEMBER 2003
Characterization of dihydrogen-bonded D–H¯H–A complexes on the basis
of infrared and magnetic resonance spectroscopic parameters
Hubert Cybulski, Magdalena Pecul, and Joanna Sadleja)
Department of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland
Trygve Helgaker
Department of Chemistry, University of Oslo, Box 1033 Blindern, N-0315 Oslo, Norway
共Received 14 March 2003; accepted 11 June 2003兲
The structural, energetic, and spectroscopic properties of the dihydrogen-bonded complexes
LiH¯H2 , LiH¯CH4 , LiH¯C2 H6 , and LiH¯C2 H2 are investigated. In particular, the interaction
energy is decomposed into physically meaningful contributions, and the calculated vibrational
frequencies, the magnetic resonance shielding constants, and inter- and intramolecular spin–spin
coupling constants are analyzed in terms of their correlation with the interaction energy. Unlike the
other three complexes, which can be classified as weak van der Waals complexes, the LiH¯C2 H2
complex resembles a conventional hydrogen-bonded system. The complexation-induced changes in
the vibrational frequencies and in the magnetic resonance shielding constants correlate with the
interaction energy, as does the reduced coupling 2h J HX between the proton of LiH and hydrogen or
carbon nucleus of the proton donor, while 1h J HH do not correlate with the interaction energy. The
calculations have been carried out using Møller–Plesset perturbation theory, coupled-cluster theory,
and density-functional theory. © 2003 American Institute of Physics. 关DOI: 10.1063/1.1597633兴
I. INTRODUCTION
van der Waal systems without hydrogen bonds such as
CH4 ¯HF18 and He¯He26 show that the transmission of
spin–spin couplings cannot necessarily be taken as evidence
for covalency, as sometimes maintained.10,29
Hydrogen bonds are usually formed between the positively charged hydrogen of an A–H proton donor 共a weak
acid兲 and an electronegative atom B, representing the proton
acceptor 共a weak base兲. Recently, however, proton–hydride
D–H␦ ⫹ ¯ ␦ ⫺ H–A interactions have attracted some attention.
Such dihydrogen bonds 共DHBs兲, where D–H acts as a proton
donor and H–A as an acceptor, have been the subject of
many investigations.30– 42 Typical elements A that can accommodate this hydridic hydrogen, acting as proton acceptors, are the transition metals and boron.32,33,36,37 From x-ray
and neutron diffraction, it is known that the H¯H distances
are usually shorter than 2 Å and significantly smaller than
the sum of the van der Waals radii of the hydrogens in the
N–H¯H–Ir complex—for example, the H¯H distance has
been reported as 1.8 Å.33
Like conventional hydrogen bonds, dihydrogen bonds
may find an application in supramolecular syntheses and in
crystal engineering; they may also play an important role in
catalytic processes.37 Because of the unusual character of the
weak interaction, these complexes are interesting also from a
theoretical point of view. So, even though the small
dihydrogen-bonded systems have not been much studied experimentally, they are ideal for theoretical investigations,
which may provide not only useful information on the structure and bonding of these complexes but also suggest future
experiments.
The question we address in this paper is the spectroscopic characterization of dihydrogen bonds and the possibility of their detection and characterization by optical and
Molecular spectroscopy represents an important 共and
sometimes the only兲 method for the detection and characterization of hydrogen bonds and other intermolecular interactions. Infrared spectra 共IR兲 and nuclear magnetic-resonance
共NMR兲 iso- and anisotropic chemical shifts, in particular,
have for a long time provided indirect evidence for
hydrogen-bond formation through the changes that are measured in the parameters relative to the monomers.1–5 Numerous experimental and theoretical studies have been carried
out to correlate these changes with the hydrogen-bond geometry 共bond lengths and bond angles兲6 as well as with the
hydrogen-bond type.7 Moreover, progress in NMR spectroscopy has made it possible to use the nuclear spin–spin coupling constants not only as indirect evidence of hydrogen
bonds8 but also as direct evidence, following the recent discovery of intermolecular hydrogen-bond-transmitted spin–
spin coupling constants. Such couplings have been observed
in biomacromolecules 共i.e., proteins9–11 and nucleic
acids12,13兲 and in fluorine-containing clusters.14,15
Simultaneously with this experimental work, many theoretical studies have been carried out. The coupling constants transmitted through hydrogen bonds have been calculated for many complexes,6,7,14,16 –24 including neutral dimers
of simple organic and inorganic molecules,16,17,19,20 fluorinecontaining clusters,14,18,22 and low-barrier hydrogen-bond
complexes.7,20,22,23 Some effort has also been aimed at predicting the coupling constants transmitted through bonds
weaker than hydrogen bonds.18,25–28 In particular, the observation of non-negligible intermolecular coupling constants in
a兲
Author to whom correspondence should be addressed. Electronic mail:
[email protected]
0021-9606/2003/119(10)/5094/11/$20.00
5094
© 2003 American Institute of Physics
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J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
NMR spectroscopy. To answer this question, the IR frequencies and NMR parameters are evaluated for dihydrogenbonded complexes and analyzed as potential parameters for
the characterization of dihydrogen bonds by correlating them
with interaction energies and intermolecular distances.
As DHB models, we have chosen the complexes
LiH¯H2 , LiH¯C2 H6 , LiH¯CH4 , and LiH¯C2 H2 , all
with LiH as the proton acceptor. The proton donors include
H2 and the C–H group from the hydrocarbons CH4 , C2 H6 ,
and C2 H2 . These molecules differ by the quadrupole moment. Preliminary calculations have also been carried out for
some other complexes such as LiH¯H2 O, LiH¯H2 CO,
LiH¯HF, BH3 ¯NH3 , and BH3 ¯H2 O. However, since
their DHB structures turned out not to be minima on the
potential energy surface, these systems were not pursued further. On the other hand, calculations of the properties of the
true DHB systems LiH¯HCN, LiH¯HNC, NaH¯HCN,
NaH¯HNC, LiH¯HOH, NaH¯HOH, LiH¯C2 H2 have
been published.41,42 For these systems, the intermolecular
coupling constant 1h J HH depends on the nature of the
proton–donor group and the proton–acceptor metal hydride,
as well as on the intermolecular distances H¯H. 42 Their IR
data were also reported, although the NMR shielding constants were not.41 The present work, which extends the range
of molecules studied to include van der Waals complexes
with a weak H¯H interaction, can provide valuable insight
about DHBs, as contrasted with conventional hydrogen
bonds and weak van der Waals forces.
In the present paper, we examine whether there is a fundamental difference between DHB and other van der Waals
systems. To explore this issue, we have examined the spectroscopic properties of the DHB complexes under study and
their interaction energy, including its decomposition into individual contributions. This decomposition is carried out
within the framework of intermolecular perturbation theory,
combined with the supermolecular scheme.43– 45 In this manner, we would like to establish whether DHBs share the
properties of conventional hydrogen bonds such as electrostatic stabilization46 and to see how they may differ from
weaker van der Waals interactions through H¯H contacts.
To elucidate the role of the individual contributions to the
interaction energy such as the electrostatic, exchange, induction, and dispersion components, we employ intermolecular
Møller–Plesset perturbation theory 共IMPPT兲.43– 45 The resulting decomposition is unambigous, offering an opportunity to investigate the physical origin of the bonding effects.
In Sec. II of this paper, the methods employed for the
optimization of the geometry, the calculation of the interaction energy and its decomposition, and the calculation of
molecular properties are described. Next, in Sec. III, the results of these calculations are discussed—in particular, the
optimized structures, the interaction energies, the infrared
spectra, and the NMR shielding constants and indirect spin–
spin coupling constants. A summary and main conclusions
are presented in Sec. IV.
Dihydrogen-bonded complexes
5095
II. COMPUTATIONAL DETAILS
A. Calculation of equilibrium structure
and interaction energy
1. Geometry optimization and vibrational frequencies
The structures of all monomers and complexes were optimized by means of frozen-core second-order Møller–
Plesset 共MP2兲 perturbation theory. Except for the large
LiH¯C2 H6 complex, the structures were optimized using
frozen-core fourth-order Møller–Plesset 共MP4兲 theory and
coupled-cluster single-and-double 共CCSD兲 theory as well.
For the small LiH¯H2 complex, a frozen-core optimization
was also carried out using CCSD theory with a perturbative
triples corrections 关CCSD共T兲兴.46 For comparison, geometry
optimizations were carried out using density-functional
theory 共DFT兲, used with the hybrid three-parameter Becke–
Lee–Yang–Parr 共B3LYP兲 functional, as implemented in the
47
GAUSSIAN98 program. In the geometry optimizations, no
counterpoise corrections were made for the basis-set superposition error. The vibrational frequencies were computed
within the harmonic approximation, at the respective level of
theory.
For the geometry optimizations, the frequency calculations, and the calculations of the interaction energy, we used
the aug-cc-pVTZ basis.48,49 As shown,50,51 this basis accurately reproduces geometries, frequencies, and electric properties of the isolated molecules and their complexes.
2. The total interaction energy
The supermolecular interaction energy was obtained by
substracting the energies of the monomers from those of the
complex for each complex. The computed interaction energies were corrected for basis-set superposition error following the prescription of Boys and Bernardi,52 and for the relaxation of the monomer geometry during complex
formation.51 To relate the calculated interaction energy to the
observed dissociation energy D 0 , a correction for the difference in the zero-point vibrational 共ZPV兲 energies of the complex and the monomers was added. The ZPV correction was
calculated in the harmonic approximation at the respective
level of theory. The geometry optimizations as well as the
calculation of vibrational frequencies and interaction energies were carried out using the GAUSSIAN 98 program.47
3. The partitioning of the interaction energy
For more insight into the nature of the H¯H interaction,
we have partitioned the interaction energy using
IMPPT.43– 45,53 The IMPPT interaction-energy corrections are
denoted by ⑀ (i j) , where i and j are the orders of the intermolecular interaction operator and the intramolecular correction operator, respectively.43– 45
At the all-electron MP2 level, the total interaction energy
is decomposed into a Hartree–Fock self-consistent field
共SCF兲 contribution and a correlation contribution:
⌬E MP2⫽⌬E SCF⫹⌬E (2) .
共1兲
The SCF contribution is further decomposed into deformation and Heilter–London parts:
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Cybulski et al.
J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
SCF
⌬E SCF⫽⌬E def
⫹⌬E HL.
共2兲
SCF
⌬E def
The deformation energy
is interpreted as an effect due
to relaxation of orbitals in the Coulomb field of the partner
under the restriction imposed by Pauli principle. We also
SCF
.
consider the second-order IMPPT approximation to ⌬E def
It can be approximated as the induction response terms
(n,0)
(20)
⑀ ind,r
, where the term ⑀ ind,r
is calculated by coupledperturbed Hartee–Fock theory. The Heilter–London contribution to the SCF interaction energy, Eq. 共2兲 is next decomposed as
(10)
HL
⌬E HL⫽ ⑀ els
⫹ ⑀ exch
,
(10)
⑀ els
共3兲
HL
⑀ exch
and
are electrostatic and exchange energies,
where
respectively. Finally, the correlation correction to the MP2
interaction energy in Eq. 共1兲 is represented as
(2)
(20)
(12)
⫹ ⑀ disp
⫹ ⑀ els,r
,
⌬E (2) ⫽⌬E exch
共4兲
(2)
is the second-order exchange correlation corwhere ⌬E exch
(20)
(12)
rection, ⑀ disp the dispersion correlation correction, and ⑀ es,r
the second-order electrostatic correlation correction.
In the interpretation of our results, we shall focus on
(10)
HL
SCF
(20)
⑀ els
, ⑀ exch
, ⌬E def
, and ⑀ disp
. All terms ⑀ (i j) were calculated in the basis of the full complex. The IMPPT calculations were carried out in aug-cc-pVDZ basis, and, for the
smaller complexes, in the aug-cc-pVTZ basis, using the
54
TRURL 94 package of Cybulski.
B. The calculation of NMR parameters
1. NMR shielding constants
The calculations of the NMR shielding constants
were carried out at the all-electron MP2 level, using London
orbitals.55–57 The basis-set superposition error for the
complexation-induced changes in the shielding constants
was estimated using the counterpoise correction method.52
The shielding constants were calculated with the
47
GAUSSIAN 98 program, using the aug-cc-pCVTZ basis except for the Li atom, for which no core–valence functions
are available and the aug-cc-pVTZ-su1 共see later兲 basis was
used instead.
2. Nuclear spin – spin coupling constants
The indirect nuclear spin–spin coupling constants were
calculated using CCSD theory and DFT. Unless otherwise
indicated, all four nonrelativistic contributions to the spin–
spin coupling constants were calculated: the Fermi-contact
共FC兲 term, the spin–dipole 共SD兲 term, the paramagnetic
spin–orbit 共PSO兲 term, and the diamagnetic spin–orbit
共DSO兲 term. The lithium coupling constants are given for the
7
Li isotope. All NMR properties were calculated at the MP2/
aug-cc-pVTZ geometries.
The CCSD nuclear spin–spin coupling constants were
calculated as unrelaxed second derivatives of the electronic
energy, using a version of ACES II58—see Ref. 59 and references therein. The B3LYP spin–spin calculations were carried out with a development version of the DALTON
program.60 The use of the inexpensive B3LYP model made it
possible to carry out calculations at several different inter-
FIG. 1. The structures of LiH¯H2 , LiH¯CH4 , LiH¯C2 H6 , and
LiH¯C2 H2 .
molecular distances, which would have been too expensive
at the CCSD level. In addition, these calculations give us an
opportunity to examine the performance of DFT for atypical
systems such as DHB complexes.
The spin–spin coupling constants were calculated by
means of aug-cc-pVDZ-su1共11s5p2d/11s3p2d for C and Li,
6s2p/6s2p for H兲 and aug-cc-pVTZ-su1 共12s6p3d2f/
12s4p3d2f for C, 13s6p3d2f/13s4p3d2f for Li, 7s3p2d/
7s3p2d for H兲 basis sets. They are obtained from the standard augmented correlation-consistent aug-cc-pVTZ basis
sets of Dunning and co-workers48,49 by decontracting the s
functions and by adding one tight s orbital.61 Their suitability
for the calculations presented here has been established in
Refs. 16, 17, and 62.
III. RESULTS AND DISCUSSION
A. Geometry and energetic of the complexes
Figure 1 presents the optimized structures of the DHB
complexes investigated in this study: LiH¯H2 , LiH¯CH4 ,
LiH¯C2 H6 , and LiH¯C2 H2 . Since these calculations were
performed on model complexes for which the geometries
and binding energies are experimentally unknown, no verification is possible. We also note that the optimized H¯H
structures represent local minima of the potential energy surfaces.
The geometrical parameters of the optimized structures
are listed in Table I, while Table II contains the corresponding interaction energies D e , the harmonic ZPV energies
⌬E ZPV , and the dissociation energies D 0 . In the following,
we base our discussion on the CCSD results or, when these
are unavailable 共for LiH¯C2 H6 ), on the MP2 results, as the
most accurate ones.
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J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
Dihydrogen-bonded complexes
5097
TABLE I. Selected calculated geometrical parameters 共in Å兲 and their complexation-induced changes 共in parentheses兲 of the LiH¯H2 , LiH¯CH4 ,
LiH¯C2 H6 , LiH¯C2 H2 complexes. All calculations are in the aug-cc-pVTZ basis set.
Parameter
Model
LiH¯H2
LiH¯CH4
LiH¯C2 H6
LiH¯C2 H2
r(H¯H)
MP2
MP4
CCSD
CCSD共T兲
B3LYP
MP2
MP4
CCSD
CCSD共T兲
B3LYP
MP2
MP4
CCSD
CCSD共T兲
B3LYP
2.6016
2.5739
2.6388
2.5901
2.5733
1.6047 (⫺0.0002)
1.6082 (⫺0.0003)
1.6101 (⫺0.0004)
1.6101 (⫺0.0004)
1.5893 (⫺0.0006)
0.7403 (⫹0.0029)
0.7445 (⫹0.0029)
0.7455 (⫹0.0025)
0.7458 (⫹0.0028)
0.7459 (⫹0.0030)
2.5093
2.4936
2.5794
...
2.6287
1.6052 (⫹0.0003)
1.6088 (⫹0.0003)
1.6104 (⫺0.0001)
...
1.5894 (⫺0.0005)
1.0872 (⫹0.0010)
1.0905 (⫹0.0008)
1.0888 (⫹0.0003)
...
1.0886 (⫹0.0003)
2.5001
...
...
...
2.6213a
1.6060 (⫹0.0011)
...
...
...
1.5896 (⫺0.0003) a
1.0888 (⫺0.0003)
...
...
...
1.0905 (⫺0.0005) a
1.9721
1.9758
2.0370
...
2.0040
1.6017 (⫺0.0032)
1.6047 (⫺0.0037)
1.6060 (⫺0.0045)
...
1.5848 (⫺0.0051)
1.0733 (⫹0.0116)
1.0752 (⫹0.0113)
1.0715 (⫹0.0094)
...
1.0734 (⫹0.0118)
r(Li–H)
r(H–X)
a
Saddle point.
Except for LiH¯C2 H6 , all complexes where a H–C
bond donates a proton to the hydridic hydrogen of LiH have
a colinear Li–H¯H–C arrangement. In addition, LiH¯H2
is linear. Based on the H¯H separation, the complexes can
be divided into two groups: LiH¯H2 , LiH¯CH4 , and
LiH¯C2 H6 have a long H¯H separation and can be classified as weak van der Waals complexes, whereas
LiH¯C2 H2 , with an intermolecular separation of 2 Å, has a
dihydrogen bond strength comparable with that of conventional hydrogen bonds. As we shall see, this difference between the three weak van der Waals complexes on the one
hand and LiH¯C2 H2 on the other hand is found in all the
properties studied.
The Li–H distance of the proton acceptor is constant in
the weak van der Waals complexes but shortened in
LiH¯C2 H2 . The shifts in the proton–donor bond distance,
however, are less systematic. As expected, the largest shift in
the proton–donor CH bond length occurs for LiH¯C2 H2 .
More surprisingly, the CH bond in LiH¯CH4 changes in the
opposite direction of the bond in LiH¯C2 H6 . We recall,
however, that LiH¯C2 H6 has a nonlinear DHB bond, which
may account for this difference.
The interaction energy in Table II follows the same trend
as the interatomic distances, increasing in the sequence
LiH¯H2 ⬍LiH¯CH4 ⬍LiH¯C2 H6 ⬍LiH¯C2 H2 , which
correlate with the quadrupole moment of the proton donors
molecules. As for the bond distance, there is a difference
between LiH¯C2 H2 and the weak van der Waals complexes. In the van der Waals complexes, the energy minimum
is very shallow—in fact, LiH¯H2 is unstable in the sense
that the minimum is not sufficiently deep to accomodate one
vibrational energy level. By contrast, the interaction energy
of LiH¯C2 H2 is similar to those of neutral complexes with
a single hydrogen bond such as in the water dimer.63,64
The inclusion of the harmonic ZPV correction changes
TABLE II. Calculated interaction energy D e , vibrational contribution to the interaction energy ⌬E ZPV , and the
dissociation energy D 0 共in kJ/mol兲 of the LiH¯H2 , LiH¯CH4 , LiH¯C2 H6 , LiH¯C2 H2 complexes. All
calculations are in the aug-cc-pVTZ basis.
Parameter
De
⌬E ZPV
D0
Level
MP2
MP4
CCSD
CCSD共T兲
B3LYP
MP2
MP4
CCSD
CCSD共T兲
B3LYP
MP2
MP4
CCSD
CCSD共T兲
B3LYP
LiH¯H2
LiH¯CH4
LiH¯C2 H6
LiH¯C2 H2
⫺2.98
⫺3.20
⫺2.80
⫺2.78
⫺2.10
5.17
5.22
5.00
5.15
5.49
⫹2.19
⫹2.03
⫹2.20
⫹2.37
⫹3.40
⫺3.20
⫺3.48
⫺2.84
⫺3.38a
⫺1.48
2.37
2.23
2.26
...
2.29
⫺0.83
⫺1.25
⫺0.58
...
⫹0.81
⫺3.93
...
...
⫺4.11a
⫺1.39b
1.49
...
...
...
⫺2.44
...
...
...
-
⫺17.78
⫺17.82
⫺16.04
⫺17.22a
⫺15.27
4.61
4.67
4.54
...
4.24
⫺13.17
⫺13.16
⫺11.50
...
⫺11.03
a
Geometry optimized at the MP2 level.
Saddle point.
b
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Cybulski et al.
J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
TABLE III. Decomposition of the MP2 interaction energy 共in kJ/mol兲 of the LiH¯H2 , LiH¯CH4 , LiH¯C2 H6 , LiH¯C2 H2 complexes in the aug-ccpVDZ 共aD兲 and aug-cc-pVTZ 共aT兲 basis sets 共without monomer relaxation effects兲. Geometry optimized with a respective basis set.
LiH¯H2
MP2
⌬E all
el.
MP2
⌬E
⌬E HL
HL
⑀ exch
(10)
⑀ els
SCF
⌬E def
(20)
⑀ ind,r
(20)
⑀ disp
(21)
⑀ disp
(12)
⑀ els,r
LiH¯CH4
LiH¯C2 H6
LiH¯C2 H2
H2 O¯H2 O
aD
aT
aD
aT
aD
aT
aD
aT
aD
aT
⫺2.57
⫺2.56
1.64
6.23
⫺4.58
⫺2.45
⫺1.81
⫺2.74
⫺0.46
0.23
⫺3.00
⫺3.00
1.12
5.48
⫺4.36
⫺2.22
⫺1.66
⫺2.79
⫺0.48
0.24
⫺2.88
⫺2.86
3.35
8.01
⫺4.66
⫺2.91
⫺3.41
⫺4.41
⫺0.50
⫺0.08
⫺3.25
⫺3.23
2.80
6.88
⫺4.08
⫺2.60
⫺3.11
⫺4.34
⫺0.51
⫺0.07
⫺3.58
⫺3.56
4.48
9.41
⫺4.94
⫺3.35
⫺4.78
⫺6.11
⫺0.45
⫺0.15
⫺4.06
...
...
...
...
...
...
...
...
⫺17.88
⫺17.88
⫺2.41
27.52
⫺29.93
⫺11.39
⫺13.80
⫺9.51
⫺0.24
2.48
⫺18.07
...
...
...
...
...
...
...
...
⫺18.69
⫺18.67
⫺5.69
29.42
⫺35.11
⫺9.67
⫺11.92
⫺9.31
⫺0.46
0.25
⫺19.97
⫺19.87
⫺5.20
29.91
⫺35.10
⫺9.90
⫺12.69
⫺10.74
⫺0.48
0.39
the interaction energy substantially—not only for LiH¯H2 ,
but for the other complexes as well. For example, judging
from D e , LiH¯CH4 and LiH¯C2 H6 have similar interaction energies, whereas the D 0 values indicate that the
LiH¯C2 H6 complex is significantly more stable. To understand this behavior, we recall that the minima of the three
weak van der Waals complexes are very shallow, but ZPV
corrections are calculated at the harmonic approximation.
For LiH¯H2 system the potential could be very anharmonic
one and that is why this system is unstable in this approximation.
The geometry optimization was carried out at different
ab initio levels. Usually, the accuracy of the results increases
in the order MP2, CCSD, and CCSD共T兲, with the performance of MP4 being slightly unpredictable 共due to the frequent nonconvergence of the Møller–Plesset series65兲. Indeed, from Tables I and II, we see that the MP2 results are
closer to CCSD than are the MP4 results—MP4 overestimates the binding energy and underesimates the intermolecular distance. On the other hand, for the dipole moment and
polarizability of LiH, the convergence of the MP2, MP4,
CCSD series is smooth. For LiH¯H2 , there is essentially no
difference between D e calculated at the CCSD and CCSD共T兲
levels but the interatomic distances are different.
Since DFT has previously been used in studies of
DHBs,38,66 it is of some interest to compare its performance
relative to MP2 and CCSD. Concerning the intermolecular
H¯H distance, we note that DFT performs well for the
strong LiH¯C2 H2 complex, just as for conventional hydrogen bonds.67,68 For the three weak DHB complexes, the quality of the DFT H¯H distances is poorer, although it should
be pointed out that, in this case, the differences between MP2
共and MP4兲 results and the CCSD results are also substantial.
However, while MP2 consistently underestimates the bond
distance relative to CCSD, DFT underestimates it for
LiH¯H2 but overestimates for LiH¯CH4 , suggesting a
less predictable performance. We also note that the intramolecular LiH distance is significantly underestimated at the
DFT level.
The inadequacy of DFT for the weakly bound complexes
is more clearly noticeable from the interaction energies in
Table II. While DFT is reasonably accurate for LiH¯C2 H2 ,
there are significant discrepancies between DFT and MP2/
MP4 for LiH¯H2 , LiH¯CH4 , and LiH¯C2 H6 . For example, with ⌬E ZPV included, LiH¯CH4 is bound at the
MP2 and MP4 levels but not at the DFT level. For
LiH¯C2 H6 , on the other hand, the DHB structure optimized at the DFT level does not remain a minimum on the
potential energy surface.
The reason for the failure of DFT to reproduce the structure and energetics of the weak DHB complexes is probably
the same as for other weakly interacting van der Waals
complexes—in its present incarnation, DFT is incapable of a
correct description of dispersion, which plays a crucial role
in stabilizing these complexes.69
B. The decomposition of the interaction energies
The components of the interaction energy calculated by
means of IMPPT to second order are presented in Table III.
For comparison with a conventional hydrogen-bonded system, we have included the results for the water dimer, calculated in the same basis. An inspection of Table III shows that
the classification of the complexes in two groups 共the strong
LiH¯C2 H2 complex and the weak van der Waals complexes兲 is valid also for the individual contributions to the
interaction energy.
The decomposition of the interaction energy of
LiH¯C2 H2 in Table III is very similar to that of the water
dimer53—the main binding contributions come from the
(10)
, followed by the induction energy
electrostatic energy ⑀ els
SCF
(20)
or ⑀ ind,r
) and the dispersion en共expressed as either ⌬E def
(20)
ergy ⑀ disp . In both LiH¯C2 H2 and H2 O¯H2 O, the weights
of the electrostatic and exchange energies calculated with the
Hartree–Fock monomer wave functions are such that their
(20)
provides a good approxisum ⌬E HL is negative. Since ⑀ ind,r
SCF
mation to ⌬E def for the complexes in this group, the SCF
SCF
(20)
⫺ ⑀ ind,r
)
exchange-deformation effects 共estimated as ⌬E def
are small for these systems. The results in Table III thus
suggest that there is no fundamental difference in the energy
decomposition of DHB complexes and hydrogen-bond complexes of comparable strength.
For the three weak complexes LiH¯H2 , LiH¯CH4 ,
and LiH¯C2 H6 , the decomposition of the interaction energy presents a different picture. Here, the large repulsive
exchange term outweighs the attractive electrostatic term
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J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
Dihydrogen-bonded complexes
5099
TABLE IV. Selected calculated harmonic vibrational frequencies 共in cm⫺1 ) for the complexes and their shifts
upon complexation at the MP2, MP4, CCSD, CCSD共T兲, and B3LYP levels of theory in the aug-cc-pVTZ basis.
Complex
Level
␯共LiH兲
␯共donor兲
␯ dim.
⌬␯
␯ dim.
⌬␯
1424
1406
1396
1396
1430
8
9
9
10
10
␯共HH兲
␯共HH兲
␯共HH兲
␯共HH兲
␯共HH兲
4466
4382
4361
4354
4359
⫺51
⫺51
⫺41
⫺47
⫺58
1424
8
␯ s (CH)
␯ as (CH)
␯ as (CH)
␯ s (CH)
␯ as (CH)
␯ as (CH)
␯ s (CH)
␯ as (CH)
␯ as (CH)
␯ s (CH)
␯ as (CH)
␯ as (CH)
3057
3192
3195
3018
3141
3149
3036
3150
3162
3019
3118
3127
⫺12
⫺12
⫺9
⫺12
⫺13
⫺6
⫺10
⫺13
0
⫺10
⫺12
⫺3
MP4
1406
9
CCSD
1396
9
B3LYP
1429
9
LiH¯C2H6a
MP2
1429
13
␯ (CuH)
␯共CH兲
␯共CH兲
␯共CH兲
␯共CH兲
␯共CH兲
3066
3069
3139
3143
3163
3168
⫺7
⫺6
⫺8
⫺4
⫺6
⫺1
LiH¯C2H2
MP2
1465
49
MP4
1450
53
CCSD
1440
53
B3LYP
1468
48
␯ (CwC)
␯ as (CH)
␯ s (CH)
␯ (CwC)
␯ as (CH)
␯ s (CH)
␯共CC兲
␯ as (CH)
␯ s (CH)
␯共CC兲
␯ as (CH)
␯ s (CH)
1945
3303
3494
1931
3278
3462
2025
3325
3492
2043
3275
3479
⫺23
⫺129
⫺40
⫺24
⫺120
⫺40
⫺19
⫺92
⫺38
⫺25
⫺137
⫺37
LiH¯H2
MP2
MP4
CCSD
CCSD共T兲
B3LYP
LiH¯CH4
MP2
a
Saddle point at the B3LYP level.
(10)
⑀ els
, making the Heitler–London interaction energy ⌬E HL
positive. Among the remaining terms, the main attractive
(20)
, although
contribution comes from the dispersion term ⑀ disp
induction is also substantial. Moreover, the first-order corre(21)
constitutes
lation correction to the dispersion energy ⑀ disp
(20)
about 10% of ⑀ disp , much more than in LiH¯C2 H2 . In
LiH¯C2 H6 and LiH¯CH4 , the dispersion contribution is
larger than the electrostatic contribution, at least in the aug(20)
is smaller
cc-pVTZ basis. By contrast, in LiH¯H2 , ⑀ disp
(10)
than ⑀ els , which may be rationalized in terms of the small
polarizability of H2 .
In short, the decomposition of the interaction energy of
LiH¯C2 H2 does not differ from that in the hydrogen
bonded H2 O¯H2 O complex: the leading attractive term is
the electrostatic energy, which outweighs the exchange–
repulsion term. By contrast, for LiH¯H2 , LiH¯CH4 , and
LiH¯C2 H6 —already classified as weak van der Waals complexes on the basis of their total interaction energy—the en-
ergy decomposition confirms that they are indeed bound by
dispersion, the electrostatic term being too small to compensate for the large exchange-repulsion term.
C. The vibrational harmonic frequencies
The vibrational harmonic frequencies of the DHB complexes were calculated at the MP2, MP4, CCSD, and B3LYP
levels of theory, at their respective optimized geometries—
see Table IV. In the following, we discuss only the intramolecular complex modes—that is, the vibrational modes localized in one of the monomers. To facilitate this discussion,
Table IV also contains the changes in the monomer parameters induced by the formation of the DHB complex.
Concerning ␯共LiH兲 stretching vibration, we note that
complexation causes a large blueshift of about 50 cm⫺1 in
C2 H2 . In the weaker complexes, this mode is still blueshifted but only by about 10 cm⫺1 and correlated with the
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5100
Cybulski et al.
J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
TABLE V. Calculated isotropic and anisotropic shielding constants 共in ppm兲 in the complexes and their shifts upon complex formation at the MP2 and B3LYP
level of theory. All calculations in the aug-cc-pCVTZ basis for H and C, and in the aug-cc-pVTZ-su1 basis for Li.
Li–H
Complex
␴
␴ Li– H
␴ H– X
LiH¯H2
iso
aniso
iso
aniso
iso
aniso
26.59
3.25
26.53
4.62
26.85
5.82
25.75
4.41
30.11
13.45
27.09
21.83
iso
aniso
iso
aniso
iso
aniso
iso
aniso
26.45
3.34
26.40
4.67
26.44
4.65
26.76
5.86
25.73
4.44
30.25
12.48
29.68
10.05
27.28
21.66
H–X
⌬ ␴ CC
⌬ ␴ relax
⌬ ␴ CC
⌬ ␴ relax
⫺0.01
0.83
⫺0.09
2.21
0.23
3.40
0.00
0.00
⫺0.00
⫺0.00
0.01
0.02
⫺0.93
2.63
⫺1.23
3.18
⫺2.61
6.29
⫺0.06
⫺0.01
⫺0.05
⫺0.01
⫺0.39
⫺0.22
⫺0.04
0.85
⫺0.10
2.19
⫺0.05
2.18
0.26
3.35
0.00
0.00
0.00
0.00
0.00
⫺0.01
0.01
0.02
⫺1.03
2.83
⫺1.29
3.28
⫺1.14
1.16
⫺2.79
6.57
⫺0.06
⫺0.01
⫺0.05
⫺0.01
⫺0.03
⫺0.03
⫺0.39
⫺0.23
MP2
LiH¯CH4
LiH¯C2 H2
B3LYP
LiH¯H2
LiH¯CH4
LiH¯C2H6
LiH¯C2H2
interaction energy. The large blueshift in LiH¯C2 H2 can be
traced to the significant bond shortening of LiH—see Table I.
In the weaker complexes, the effect of complexation on the
LiH bond length is very small, explaining the small change
in the ␯共LiH兲 frequency.
In the proton donors, the stretching frequencies—that is,
␯共HH兲 in H2 , ␯ s(CH) and ␯ as(CH) in C2 H2 , ␯共CH兲 in CH4
and C2 H6 —are redshifted. As for ␯共LiH兲, these shifts correlate to some extent with the interaction energies. In C2 H2 ,
the asymmetric CH stretching band is shifted by about
⫺120 cm⫺1 and the symmetric band by about ⫺40 cm⫺1 ;
in the weak complexes, ␯共CH兲 changes of only about
⫺10 cm⫺1 are observed. Clearly, these shifts reflect the
changes in the CH bond lengths upon DHB formation—see
Table I. The shift in the vibrational mode of H2 is substantial,
in spite of the very small interaction energy in LiH¯H2 .
This is understandable, considering the small reduced mass
of H2 .
The DFT/B3LYP functional reproduces the stretching
frequencies and their complexation shifts with an accuracy
comparable with the MP2 method. The differences between
MP2 frequencies and the MP4 or CCSD frequencies are also
small.
D. The NMR shielding constants
The isotropic and anisotropic proton shielding constants
and their counterpoise-corrected shifts upon complexation
⌬ ␴ cc , calculated at the MP2 and DFT/B3LYP levels of
theory, are collected in Table V. The monomer-relaxation
corrections ⌬ ␴ relax are listed separately. For LiH¯C2 H6 ,
only DFT calculations were carried out, the all-electron MP2
calculations being too expensive.
The shifts in the isotropic shielding constant of the acceptor hydrogen in LiH are small. However, there is a difference between LiH¯C2 H2 and the weak van der Waals
complexes. Whereas the LiH isotropic proton shielding in-
creases upon the formation of LiH¯C2 H2 , it decreases for
the weaker complexes. The corresponding shift in the LiH
proton shielding anisotropy is in the same direction and exhibits an inverse correlation with the intermolecular distance,
although not with the interaction energy 共the shift of 3.42
ppm in the shielding anisotropy of LiH¯C2 H2 is relatively
too small兲. For all complexes, the monomer relaxation contribution to the proton shift in LiH is negligible.
The shifts in the proton shielding constants in the proton
donors are more substantial. Predictably, the largest shifts in
the isotropic (⫺3.00 ppm) and anisotropic 共6.07 ppm兲 proton shieldings occur in the strongest complex LiH¯C2 H2 ,
and they are similar to those previously calculated for
H2 O¯C2 H2 . 70 For the other complexes, the shifts in the isoand anisotropic shielding constants are much smaller but in
the same direction. The shift in the isotropic shielding correlates with the inverse of the intermolecular distance; for the
anisotropy, the correlation is weaker. For example, in spite of
similar intermolecular distances and interaction energies, the
shift is much larger in LiH¯CH4 than in LiH¯C2 H6 . This
difference probably arises since LiH¯CH4 , unlike
LiH¯C2 H6 , has a colinear DHB structure, making the
shielding tensor more anisotropic. Although the effect of
monomer relaxation is more substantial for the donor proton
than for the acceptor proton, it is significant only in
LiH¯C2 H2 .
The proton shielding constants and their shifts calculated
at the DFT level are very close to those at the MP2 level,
probably because proton shielding shifts are mostly influenced by the magnetizability tensor of the neighboring
molecule,71 which is rather insensitive to electron
correlation.72 For the remaining shieldings such as those of
13
C, the complexation-induced shifts calculated at the DFT
and MP2 levels 共not shown in Table V兲 differ more since the
electrostatic and dispersion effects are larger than the purely
magnetic ones.71
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J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
Dihydrogen-bonded complexes
5101
TABLE VI. Intermolecular indirect spin–spin coupling constants J 共in Hz兲 calculated at CCSD and B3LYP levels of theory in the aug-cc-pVTZ-su1 共aT-su1兲
basis and the aug-cc-pVDZ-su1 共aD-su1兲 basis.
Term
level/basis
1h
JHH
FC
DSO
PSO
SD
CCSDÕaDsu1
FC
DSO
PSO
SD
CCSDÕaTsu1
FC
DSO
PSO
SD
B3LYPÕaTsu1
⫺1.10
0.71
⫺0.58
0.01
À0.95
⫺1.15
0.74
⫺0.66
0.00
À1.07
⫺1.33
0.74
⫺0.66
0.00
À1.25
FC
DSO
PSO
SD
CCSDÕaDsu1
FC
DSO
PSO
SD
CCSDÕaTsu1
FC
DSO
PSO
SD
B3LYPÕaTsu1
⫺0.79
1.62
⫺1.18
...
À0.35
...
...
...
...
...
⫺0.94
⫺0.02
⫺1.43
1.65
À0.74
2h
JLiH
LiH¯H2
⫺0.34
0.03
0.00
0.01
À0.30
⫺0.35
0.03
0.00
0.01
À0.30
⫺0.58
0.03
0.00
0.01
À0.54
LiH¯C2H6
⫺0.03
0.17
⫺0.04
...
0.10
...
...
...
...
...
0.01
0.01
⫺0.12
0.18
0.07
2h
JHX
3h
JLiX
1h
JHH
3.64
⫺0.27
0.32
⫺0.02
3.67
3.87
⫺0.28
0.32
⫺0.03
3.88
5.89
⫺0.82
0.32
⫺0.03
5.89
1.89
⫺0.10
0.05
0.00
1.84
1.93
⫺0.10
0.05
0.00
1.89
3.72
⫺0.10
0.12
0.00
3.73
⫺0.57
1.55
⫺1.33
0.01
À0.35
⫺0.62
1.55
⫺1.33
...
À0.40
⫺0.61
1.55
⫺1.34
0.00
À0.41
2.31
0.06
⫺0.06
...
2.32
...
...
...
...
...
3.50
0.04
⫺0.06
0.06
3.53
0.93
0.00
0.00
...
0.93
...
...
...
...
...
1.49
0.00
0.01
0.00
1.50
⫺0.99
2.28
⫺1.63
⫺0.02
À0.37
⫺1.06
2.32
⫺2.01
⫺0.06
À0.81
0.05
2.31
⫺2.04
⫺0.06
0.26
E. The intermolecular indirect nuclear spin–spin
coupling constants
1. The spin – spin coupling constants
at the equilibrium geometry
The intermolecular indirect nuclear spin–spin coupling
constants of the complexes under investigation nh J, calculated at the CCSD and DFT levels in the aug-cc-pVDZ-su1or
aug-cc-pVTZ-su1 basis sets, are tabulated in Table VI. Since
coupling constants transmitted through strong dihydrogen
bonds have already been discussed elsewhere,42 we focus
here on the comparison of these parameters in strong complex LiH¯C2 H2 and in the weak van der Waals complexes.
The initial discussion in this subsection is based on the
CCSD results.
The most interesting coupling constants transmitted
through Li–H¯H–X–W are probably the short-range intermolecular proton–proton coupling constants 1h J HH . These
constants are relatively small and negative; they do not correlate with the interaction energy—at least not when the
whole set of complexes is considered, since the largest coupling of ⫺0.95 Hz is observed for the weakest complex
LiH¯H2 . However, when only complexes containing the
Li–H¯H–C–W dihydrogen bond are compared, a qualitative correlation with the intermolecular distance is observed.
Except for 1h J HH in LiH¯H2 , the largest contribution to the
2h
JLiH
2h
JHX
LiH¯CH4
⫺0.06
2.90
0.17
0.02
⫺0.05
⫺0.04
0.01
0.06
0.05
2.88
⫺0.09
2.94
0.17
0.02
⫺0.05
⫺0.04
...
...
0.03
2.92
⫺0.05
4.57
0.17
0.02
⫺0.12
⫺0.04
0.01
0.07
0.02
4.62
LiH¯C2H2
⫺1.22
9.05
0.21
0.11
⫺0.04
⫺0.09
0.03
0.11
9.18
À1.02
⫺1.24
9.43
0.22
0.11
⫺0.06
⫺0.14
0.03
0.11
9.51
À1.06
⫺1.59
11.64
0.22
0.11
⫺0.13
⫺0.15
0.02
0.13
11.72
À1.48
3h
JLiX
0.99
⫺0.01
0.00
0.01
0.99
0.98
⫺0.01
0.00
...
0.98
1.63
⫺0.01
0.01
0.01
1.65
5.80
0.01
0.00
0.01
5.83
5.73
0.01
0.00
0.02
5.76
8.68
0.01
0.00
0.02
8.70
short-range intermolecular proton–proton couplings originate from spin–orbit terms; in this respect, the short-range
proton–proton intermolecular couplings resemble the longrange ones.16,17
The 2h J LiH couplings in LiH¯CH4 and LiH¯C2 H6 are
negligible and dominated by the spin–orbit interactions. The
corresponding couplings in LiH¯H2 and LiH¯C2 H2 are
different in character, being larger (⫺0.30 Hz and
⫺1.02 Hz, respectively兲 and dominated by the FC interaction. Clearly, no correlation with the interaction energy is
observed for these coupling constants.
The intermolecular coupling constant 2h J HX between the
hydrogen atom of LiH and the hydrogen or carbon atoms of
the proton donor are positive and much larger than 1h J HH , in
spite of the longer separation. The largest reduced coupling
is observed for LiH¯C2 H2 and the smallest for LiH¯H2 ,
so in this sense 2h J HX correlates 共qualitatively兲 with the intermolecular distance. However, the 2h J HC coupling is larger
for LiH¯CH4 than for LiH¯C2 H6 , which is the opposite
of the relation for the interaction energies 共see Table II兲. This
is probably caused by nonlinearity of dihydrogen bond in
LiH¯C2 H6 .
The 3h J LiX coupling constants are all positive. The
smallest reduced coupling is observed in LiH¯H2 and the
largest in LiH¯C2 H2 . While 3h J LiC correlates well with the
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5102
J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
interaction energy, 3h J LiH in LiH¯H2 is too large in relative
terms, although 共as noted above兲 it has the smallest reduced
value of all 3h J LiX coupling constants studied. Unlike 1h J HH ,
most of the longer-range coupling constants in Table VI—
that is, 2h J LiH , 2h J HX 共including 2h J HH in LiH¯H2 ), and
3h
J LiX—are dominated by the FC interaction.
In short, the intermolecular indirect spin–spin coupling
constants do not discriminate between the strong dihydrogen
bond in LiH¯C2 H2 and the weaker interactions in
LiH¯H2 , LiH¯CH4 , and LiH¯C2 H6 . The coupling constants have the same sign in all complexes but differ in magnitude, the reduced 2h J HX and 3h J LiX couplings being correlated with the intermolecular distance.
Now, let us discuss briefly the methodological aspects.
Except for 1h J HH in LiH¯C2 H2 , the effects of extending the
basis from aug-cc-pVDZ-su1 to aug-cc-pVTZ-su1 are not
large. Thus, although we cannot claim to have reached basisset convergence, the basis sets employed seem sufficiently
large for the semiquantitative analysis carried out in the
present paper.
Compared with CCSD, the accuracy of the intermolecular coupling constants calculated by DFT/B3LYP is unsatisfactory, the results in some cases differing by as much as
100%. In general, DFT and CCSD agree for the spin–orbit
terms 共PSO and DSO兲 and for the small spin–dipole term.
However, for the usually dominant FC term, the CCSD and
DFT results differ, explaining why CCSD and DFT agree for
1h
J HH 共dominated by PSO兲 in LiH¯CH4 but disagree for
2h
J HC 共dominated by FC兲. Still, DFT may serve as a useful
computational tool for DHB-transmitted coupling constants
since the sign of the coupling 共except for 1h J HH in
LiH¯C2 H2 ) and its order of magnitude are correct. We thus
decided to use DFT to calculate the distance dependence of
the intermolecular couplings, the calculation of which would
otherwise be too expensive.
2. The distance dependence of the intermolecular
spin – spin coupling constants
While vibrational frequencies and NMR shielding constants have for a long time been used as probes of hydrogen
bond and other intermolecular interactions,1–5 the intermolecular indirect nuclear spin–spin coupling constants have
only recently been employed for this purpose. Hence, their
use as probes of intermolecular interactions is much less well
investigated. We therefore decided to pursue the study of the
intermolecular coupling constants in the DHB complexes
further, calculating the dependence of these parameters on
the intermolecular distance. Since such calculations are
much more time-consuming than single-point calculations,
we used DFT rather than CCSD for this purpose. However,
for the smallest system LiH¯H2 , we used CCSD as well as
DFT, to check whether the overall dependence of the coupling constants on the intermolecular distance is the same at
the two levels.
To answer the last question, we have plotted the intermolecular couplings constants 1h J HH and 3h J LiH in LiH¯H2
as functions of the internuclear distance, calculated in the
aug-cc-pVTZ-su1 basis at the DFT and CCSD levels of
theory—see Fig. 2. The DFT and CCSD curves are similar
Cybulski et al.
FIG. 2. The dependence of the CCSD and DFT intermolecular coupling
constants 共Hz兲 in LiH¯H2 on the intermolecular distance 共Å兲.
but vertically displaced, the DFT constants being larger than
the CCSD constants in absolute value.
The distance dependence of the B3LYP/aug-cc-pVTZsu1 intermolecular coupling constants in the three larger
complexes LiH¯CH4 , LiH¯C2 H6 , and LiH¯C2 H2 is
presented in Fig. 3. The behavior of the 1h J HH coupling constants in LiH¯CH4 and LiH¯C2 H6 is similar to that observed in LiH¯H2 : the coupling is small and negative, decaying slowly to zero with the intermolecular distance.
The 1h J HH coupling constant in LiH¯C2 H2 has a distance dependence different from that in the three weak
complexes—it is negative for larger distances and positive
for short ones. This behavior may be understood from the
fact that proton–proton coupling constants transmitted
through one covalent bond 共such as in the hydrogen molecule兲 are positive.73 For larger intermolecular distances, the
1h
J HH coupling will probably decay to zero again. Similar
sign changes have been observed for the NH¯N, OH¯O,
and FH¯F hydrogen bonds.18,20 The sign changes of 1h J HH
in LiH¯C2 H2 may also explain why, for this particular coupling, the DFT and CCSD calculations give opposite signs,
something that does not happen for any of the other coupling
constants studied by us.
Another difference in the distance dependence of 1h J HH
in LiH¯C2 H2 is that, unlike in the other DHB complexes, it
decays in a steep, exponential manner with intermolecular
distance, resembling the behavior observed for conventional
hydrogen-bonded complexes.17,19,21 However, this behavior
should not be taken as evidence of some unique character of
FIG. 3. The dependence of the DFT intermolecular coupling constants 共Hz兲
in LiH¯CH4 , LiH¯C2 H6 , and LiH¯C2 H2 on the intermolecular distance
共Å兲.
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J. Chem. Phys., Vol. 119, No. 10, 8 September 2003
Dihydrogen-bonded complexes
TABLE VII. Shifts in the intramolecular indirect nuclear spin–spin coupling constants J 共Hz兲 of the monomers due to the complex formation calculated at the CCSD and B3LYP levels of theory in the aug-cc-pVTZ-su1
共aT-su1兲 and aug-cc-pVDZ-su1 共aD-su1兲 basis sets.
Relax.
Level/Basis
LiH¯H2
CCSD/aDsu1
CCSD/aTsu1
B3LYP/aTsu1
LiH¯CH4
CCSD/aDsu1
CCSD/aTsu1
B3LYP/aTsu1
LiH¯C2H6
CCSD/aDsu1
CCSD/aTsu1
B3LYP/aTsu1
LiH¯C2H2
CCSD/aDsu1
CCSD/aTsu1
B3LYP/aTsu1
a
⌬ JLiH
1
As expected, the shifts in the intramolecular coupling
constants due to the complex formation are dominated by the
FC interaction, the other interactions contributing less than
10%.
Dimer.
⌬ JXH
1
⌬ JLiH
1
⌬ 1 JXH
⫺0.01
⫺0.01
⫺0.03
1.62
1.71
2.22
⫺1.95
⫺2.10
⫺4.62
0.03
0.03
0.06
1.04
1.08
1.21
⫺1.71a
⫺1.98a
⫺4.37
6.24a
5.78a
6.27
0.09a
...
0.18
0.70a
...
0.81
⫺1.50a
...
⫺4.29
5.49a
...
5.84
⫺0.26
⫺0.25
⫺0.53
5103
2.59
2.68
3.45
⫺15.80
⫺15.91
⫺26.65
⫺3.91
⫺4.31
⫺5.60
3.07
2.86
1.25
No SD term.
the hydrogen-bond-transmitted couplings since the same pattern has been observed for the 3He coupling constant in the
very weakly bound helium dimer.26
Finally, we note that the distance dependence of the
3h
J LiX coupling constant is essentially the same in all four
complexes studied here. The coupling constants are positive
at all intermolecular separations and decay rapidly with increasing separation, in an exponential manner.
3. Complexation-induced shifts in the intramolecular
coupling constants
The complexation-induces shifts in the intramolecular
coupling constants are listed in Table VII. As for the shielding constants, they are decomposed into the effects arising
from the deformation of the electronic cloud 共without taking
into account geometry changes兲 and from the monomer relaxation.
The changes of 1 J LiH in the proton acceptor are substantial and determined mostly by the electron-cloud deformation. However, they do not correlate with the hydrogen-bond
strength. The LiH¯H2 complex formation causes a change
as large as ⫺2.1 Hz 共CCSD/aug-cc-pVTZ-su1兲 in 1 J LiH ,
while for LiH¯CH4 1 J LiH changes by only ⫺1.95 Hz
共CCSD/aug-cc-pVTZ-su1兲, although the relation for the interaction energies is opposite. As expected, the change in
1
J LiH in LiH¯C2 H2 is by far the largest.
The changes in 1 J XH in the proton donor are also significant but do not follow any consistent pattern. They are positive for the 1 J CH coupling constants and do not correlate with
the interaction energy since the largest effect is observed for
LiH¯CH4 rather than for LiH¯C2 H2 . Moreover, the
change in 1 J XH has a different sign in LiH¯H2 than in the
other complexes. In this case, monomer relaxation contributes significantly to the shift, although the electronic effect is
larger.
IV. SUMMARY AND CONCLUSIONS
In the present study, we have investigated the structural,
energetic, and spectroscopic properties of the four
dihydrogen-bonded complexes LiH¯H2 , LiH¯CH4 ,
LiH¯C2 H6 , and LiH¯C2 H2 . We have paid special attention to the decomposition of the interaction energy into
physically meaningful contributions and have attempted to
uncover the correlation between the calculated interaction
energies and molecular properties—in particular, the intermolecular indirect nuclear spin–spin coupling constants. Our
results can be summarized as follows:
共1兲 The complexes can be divided into two groups, based
on the calculated intermolecular distances and interaction energies. The first group consists of LiH¯H2 , LiH¯CH4 ,
and LiH¯C2 H6 complexes, which can be classified as weak
van der Waals complexes. The LiH¯C2 H2 complex, whose
interaction energy is comparable to that of conventional hydrogen bonds, belongs to the second group. The weakest
complex LiH¯H2 is not bound since the ZPV energy exceeds the electronic binding energy. Except for LiH¯C2 H6 ,
the equilibrium structures of the complexes have a linear
dihydrogen bond.
共2兲 The IMPPT decomposition of the interaction energy
indicates that LiH¯C2 H2 is bound mainly by strong electrostatic and induction interactions, just like a conventional
hydrogen-bonded complex such as (H2 O) 2 . By contrast, in
LiH¯H2 , LiH¯CH4 , and LiH¯C2 H6 , the repulsive exchange interaction outweighs the attractive electrostatic and
induction interactions. These three complexes are bound predominantly by dispersion.
共3兲 The vibrational frequencies of C2 H2 undergo substantial changes when the complex with LiH is formed.
When all complexes are considered, the shifts of the stretching vibrations in the proton donors and acceptors correlate
approximately with the interaction energy.
共4兲 An inverse correlation with the intermolecular distance is observed for the complexation shifts of the LiH proton shielding anisotropy. The shifts of the isotropic LiH proton shielding are in opposite directions for LiH¯C2 H2
共deshielding兲 and for the van der Waals complexes 共shielding兲. The complexation shifts of the proton shielding constants of the proton donors exhibit an inverse correlation
with the intermolecular distance.
共5兲 The short-range intermolecular indirect nuclear spin–
spin coupling constants 1h J HH are small and negative. They
do not correlate with the interaction energy. For the longrange intermolecular coupling constants, correlation with the
interaction energy is observed only for the reduced intermolecular coupling 2h J HX between the LiH proton and the hydrogen or carbon nucleus of the proton donor; although
3h
J LiC correlates with the interaction energy, the reduced
3h
J LiH coupling in LiH¯H2 does not fit this pattern. The
intermolecular coupling constants do not discriminate visibly
between strong and weak complexes. The dependence of the
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5104
coupling constants on the intermolecular distance is determined by the coupling mechanism: they decay steeply with
the distance when FC dominates 共e.g., 3h J LiX), more slowly
when the DSO and PSO interactions dominate the coupling
共e.g., 1h J HH in LiH¯CH4 ). The complexation-induced shifts
in the intramolecular coupling constants are substantial 共up
to several Hertz兲 but do not correlate with the interaction
energy.
共6兲 DFT/B3LYP gives an accurate description of the interaction energy in LiH¯C2 H2 , which is dominated by electrostatics and induction. By contrast, for the weak LiH¯H2 ,
LiH¯CH4 , and LiH¯C2 H6 complexes, DFT is inadequate,
providing an incorrect description of dispersion. The
interaction-induced shifts of the proton shielding constants
calculated at the DFT level are very close to those obtained
at the MP2 level. However, the intermolecular spin–spin
coupling constants calculated at the DFT level are only of
qualitative accuracy, as compared with the CCSD results.
ACKNOWLEDGMENTS
We would like to express our gratitude to O. Christiansen, J. Gauss, and J. Stanton for allowing us to use their
development version of the ACES II code. This work was
supported by the 3 TO9A 121 16 KBN Grant.
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