AN AB INITIO STUDY OF THE PROPERTIES OF
SOME LITHIUM-BONDED COMPLEXES
– COMPARISON WITH THEIR
HYDROGEN-BONDED ANALOGUES
Tony Ford
School of Chemistry and Physics,
University of KwaZulu-Natal,
Durban
INTRODUCTION
The hydrogen bond is the most ubiquitous of all non-covalent
interactions, and was first named by Latimer and Rodebush in
1920.
The analogous lithium bond was first observed experimentally
by Shigorin in 1959, and is known to have many similarities
with the more conventional hydrogen bond.
In this paper we explore the properties of a series of simple
lithium-bonded complexes and compare them with those of their
corresponding hydrogen-bonded counterparts.
COMPUTATIONAL DETAILS
Program used: Gaussian-09 (Frisch et al.).
Level of theory: second order Møller-Plesset perturbation
theory (MP2).
Basis set: augmented correlation-consistent polarized valence
triple-zeta (aug-cc-pVTZ) (Dunning et al.).
COMPLEXES STUDIED IN THIS WORK
Base
Lithium-bonded complexes
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3






H2O






PH3






H2S






OPTIMIZED GEOMETRIES
The complexes with NH3 and PH3 optimized in C3v symmetry,
with a single Li…N or Li…P lithium bond.
Those with H2O and H2S were found to be cyclic, with C1
symmetry, and with both a Li…O or Li…S lithium bond and a
H…X hydrogen bond (X = F, Cl, Br), with the heavy atoms and
one of the hydrogens virtually coplanar.
LiCl.NH3
LiCl.H2O
LiBr.PH3
LiF.H2S
INTERACTION ENERGIES
The interaction energies were computed from those of the
optimized complexes and the relaxed monomers.
They were corrected for basis set superposition error (BSSE)
and for vibrational zero-point energy differences.
INTERACTION ENERGIES, CORRECTED FOR BASIS SET
SUPERPOSITION ERROR AND VIBRATIONAL ZERO-POINT
ENERGY DIFFERENCES, OF THE LITHIUM-BONDED
COMPLEXES AND THEIR HYDROGEN-BONDED ANALOGUES
Interaction energy/kJ mol-1
Base
Lithium-bonded complexes
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
-72.02
-82.28
-84.55
-43.32
-31.41
-29.77
H 2O
-77.31
-74.79
-75.33
-25.51
-15.97
-13.20
PH3
-34.41
-41.75
-43.52
-14.44
-9.90
-8.82
H 2S
-43.74
-43.18
-44.08
-13.45
-9.29
-8.18
INTERACTION ENERGIES
The interaction energies of the lithium-bonded complexes fall
into two groups, those with NH3 and H2O, with energies in the
range -70 to -90 kJ mol-1, and those with PH3 and H2S, which
are more weakly bound (-30 to -50 kJ mol-1).
The hydrogen-bonded complexes are less strongly bound than
their lithium-bonded counterparts, and the energies vary more
systematically.
100
LiF complexes
LiCl complexes
LiBr complexes
-E/kJ mol-1
80
60
40
20
0
NH3
H2O
PH3
H2S
Base
Lithium-bonded complexes
Hydrogen-bonded complexes
In both cases the interaction energies correlate with the
dipole moments of the acids.
For the NH3 and PH3 complexes the interaction energies vary
directly with the gas phase basicities of the bases, while the
reverse is true for the H2O and H2S complexes.
The reason for the reversal of the interaction energies for
the H2O and H2S complexes is that in the H2O case the
interactions involve the a1 (sp3 hybridized) oxygen lone pairs, in
an approximately axial fashion, while in that of H2S they
involve the b1 (pure 3p) sulphur lone pairs, in more or less
perpendicular coordination, which is less favourable for strong
bonding.
COMPUTED Li…Y AND H…Y DISTANCES OF THE
LITHIUM-BONDED COMPLEXES AND THEIR
HYDROGEN-BONDED ANALOGUES (Y = N, O, P, S)
Base
Li…Y or H…Y distance/pm
Lithium-bonded complexes
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
208.02
205.48
204.42
167.90
173.88
167.70
H2O
195.04
192.22
191.47
170.38
186.35
189.30
PH3
265.47
261.75
260.23
233.55
250.50
251.90
H2S
254.52
251.68
250.89
226.80
241.61
243.41
Li…Y AND H…Y BOND DISTANCES
The Li…Y bond distances are significantly greater than the
H…Y separations, due to the presence of the filled lithium 1s
core orbital.
Thetrends are in inverse proportion to the interaction
energies, in the order PH3 > H2S > NH3  H2O in each case.
LiX AND HX BOND LENGTH CHANGES OF THE
LITHIUM-BONDED COMPLEXES AND THEIR
HYDROGEN-BONDED ANALOGUES (X = F, Cl, Br)
Base
Bond length change/pm
Lithium-bonded complexes
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
2.61
3.14
3.15
3.53
5.28
6.91
H2O
7.79
7.51
7.82
1.79
1.82
1.77
PH3
1.52
1.85
1.87
1.23
1.29
1.32
H2S
5.61
4.27
4.63
1.21
1.36
1.39
LiX AND HX BOND LENGTH CHANGES
For the lithium-bonded complexes the LiX bond length
changes for the H2O and H2S adducts are substantially greater
than for the NH3 and PH3 series, on account of the cyclic
nature of the first set.
Thechanges correlate broadly with the interaction energies,
with the four families grouped in the order
H2O > H2S > NH3 > PH3.
For thehydrogen-bonded complexes those with NH3 show the
largest changes in the HX bond lengths, with the other three
series being relatively unaffected, while the distortions fall off
in the order HBr > HCl > HF.
Lithium-bonded complexes
Hydrogen-bonded complexes
COMPUTED AND EXPERIMENTAL LiX STRETCHING WAVENUMBERS
OF THE LITHIUM-BONDED COMPLEXES (X = F, Cl, Br)
LiX stretching wavenumber/cm-1
Base
LiF
Calc.
LiCl
Calc.
Expt.a
LiBr
Calc./
Calc.
Expt.a
Expt.
NH3
875.6
686.8
538 (6LiCl)
497 (7LiCl)
H2O
718.3
527.2
a
Expt.
649.2
584 (7LiBr)
1.112
483.4
460 (7LiBr)
1.051
1.382
553 (6LiCl)
518 (7LiCl)
Calc./
1.018
PH3
862.2
645.3
591.3
H2S
781.7
580.3
521.3
Ref: B. S. Ault and G. C. Pimentel, J. Phys. Chem., 79 (1975) 621.
Isotopic ratios: LiCl.NH3 1.082, LiCl.H2O 1.068; (7Li/6Li)1/2 = 1.080.
LiX STRETCHING WAVENUMBERS
The computed wavenumbers of the LiX complexes correlate
fairly well with the experimental values for the complexes of
7
LiCl and 7LiBr with NH3 and H2O reported by Ault and
Pimentel, with calculated/experimental ratios from 1.018 to
1.382.
The theoretical isotopic ratio, (7Li/6Li)1/2, is 1.080,
suggesting that the experimental assignments for the LiCl.NH3
complex may be in error, explaining the unusually high
calculated/experimental wavenumber ratio of 1.382 for this
complex.
LiX AND HX STRETCHING WAVENUMBER SHIFTS OF
THE LITHIUM-BONDED COMPLEXES AND THEIR
HYDROGEN-BONDED ANALOGUES (X = F, Cl, Br)
Wavenumber shift/cm-1
Base
Lithium-bonded complexes
LiF
LiCl
Hydrogen-bonded complexes
LiBr
HF
HCl
HBr
NH3
-0.7
58.8
92.0
-785.0
-744.3
-861.4
H2O
-158.0
-100.8
-73.8
-406.3
-253.3
-224.2
PH3
-14.1
17.3
34.1
-290.1
-190.7
-175.0
H2S
-94.6
-47.7
-35.9
-282.1
-197.2
-183.2
LiX STRETCHING WAVENUMBER SHIFTS
Four of the LiX stretching wavenumber shifts are to the blue.

Therelative wavenumber shifts Δν/ν correlate with the gas
phase basicities of the bases according to a vibrational
correlation diagram, with the Δν/ν values in the order
LiBr > LiCl > LiF.
The blue-shifting LiX stretching wavenumber shifts values are
part of the same continua with the red-shifting counterparts.
Lithium-bonded complexes
Hydrogen-bonded complexes
WAVENUMBERS OF THE INTERMONOMER STRETCHING
VIBRATIONS OF THE LITHIUM-BONDED COMPLEXES AND
THEIR HYDROGEN-BONDED ANALOGUES
Wavenumber/cm-1
Base
Lithium-bonded complexes
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
271.0
238.8
211.4
276.0
188.4
154.7
H 2O
410.2
453.2
455.5
226.7
150.5
126.5
PH3
158.4
144.6
125.8
140.5
95.0
79.0
H 2S
266.0
278.4
280.5
146.1
100.9
83.5
INTERMONOMER STRETCHING WAVENUMBERS
The intermonomer stretching wavenumbers of the lithiumbonded complexes show a consistent trend of increasing with
increasing interaction energy, indicating separate relationships
for each family of complexes, with H2O > H2S > NH3 > PH3.
The higher values for the H2O, H2S series are due to the
presence of the second site of interaction, H…X.
For the hydrogen-bonded complexes the wavenumbers are
generally lower, but they still exhibit a systematic trend,
NH3 > H2O > H2S > PH3.
In each case the wavenumbers correlate well with the
interaction energies.
Lithium-bonded complexes
Hydrogen-bonded complexes
MAJOR MOLECULAR ORBITAL INTERACTIONS OF THE LITHIUM-BONDED COMPLEXES
AND THEIR HYDROGEN-BONDED ANALOGUES
Lithium-bonded complexes
Hydrogen-bonded complexes
Complex
Orbital interactiona
Complex
Orbital interactiona
LiF.NH3
n(N)(2sp3) ? Li(2sp)
HF.NH3
n(N)(2sp3) ? σ*(HF)
LiF.H2O
n(O)(2sp3) ? Li(2p)
HF.H2O
n(O)(2sp3) ? σ*(HF)
n(F)(2p) ? σ*(OH)
LiF.PH3
n(P)(3sp3) ? Li(2sp)
HF.PH3
n(P)(3sp3) ? σ*(HF)
LiF.H2S
n(S)(3p) ? Li(2p)
HF.H2S
n(S)(3p) ? σ*(HF)
n(F)(2p) ? σ*(SH)
LiCl.NH3
n(N)(2sp3) ? Li(2sp)
HCl.NH3
n(N)(2sp3) ? σ*(HCl)
LiCl.H2O
n(O)(2sp3) ? Li(2p)
HCl.H2O
n(O)(2sp3) ? σ*(HCl)
LiCl.PH3
n(P)(3sp3) ? Li(2sp)
HCl.PH3
n(P)(3sp3) ? σ*(HCl)
LiCl.H2S
n(S)(3p) ? Li(2p)
HCl.H2S
n(S)(3p) ? σ*(HCl)
LiBr.NH3
n(N)(2sp3) ? Li(2sp)
HBr.NH3
n(N)(2sp3) ? σ*(HBr)
LiBr.H2O
n(O)(2sp3) ? Li(2p)
HBr.H2O
n(O)(2sp3) ? σ*(HBr)
LiBr.PH3
-b
HBr.PH3
n(P)(3sp3) ? σ*(HBr)
LiBr.H2S
n(S)(3p) ? Li(2p)
HBr.H2S
n(S)(3p) ? σ*(HBr)
a
Only those orbital interaction energies exceeding an arbitrary threshold of 50 kJ mol -1 are
included.
b
NBO analysis indicates that BrLiPH3 is a single molecule, with a LiP σ bond.
MAJOR NATURAL BOND ORBITAL INTERACTIONS
The chief interactions among the lithium-bonded complexes
are donation from a N (O, P, S) lone pair orbital to an empty
Li 2sp (NH3 and PH3 complexes) or Li 2p (H2O and H2S
complexes) orbital.
For the complexes with H2O and H2S there is an additional
donation from an F (Cl, Br) lone pair to a σ*(OH, SH) orbital.
Only for LiF.H2O and LiF.H2S are these secondary orbital
interaction energies comparable with those of the major
attraction.
For the hydrogen-bonded complexes the only interactions are
n(N, O, P, S)  σ*(HF, HCl, HBr) donations.
NATURAL BOND ORBITAL TOTAL CHARGE TRANSFERS
OF THE LITHIUM-BONDED COMPLEXES AND THEIR
HYDROGEN-BONDED ANALOGUES
Charge transfer/me
Base
Lithium-bonded complexes
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
32.9
49.1
52.2
57.1
70.7
91.1
H 2O
13.1
15.9
16.7
26.4
22.2
23.4
PH3
63.6
98.4
106.6
30.6
30.7
35.7
H 2S
14.5
68.1
70.3
29.1
31.4
36.0
NATURAL BOND ORBITAL TOTAL CHARGE TRANSFERS
For the lithium-bonded complexes the total amounts of charge
transferred decrease consistently in the orders
LiBr > LiCl > LiF and PH3 > H2S > NH3 > H2O.
For the hydrogen-bonded complexes the same sequence is
observed as for the lithium halides, although the charge
transfers for the NH3 complexes are substantially larger than
for the H2O, PH3 and H2S series, which are clustered much
more closely together.
NATURAL BOND ORBITAL CHARGE TRANSFERS OF THE
LITHIUM AND HALOGEN ATOMS OF THE
LITHIUM-BONDED COMPLEXES
Charge transfer/me
Base
LiF
LiCl
LiBr
Li
F
Li
Cl
Li
Br
NH3
-53.9
21.0
-97.1
48.0
-107.4
55.2
H 2O
-22.5
35.6
-43.7
27.8
-44.4
27.7
PH3
-81.6
18.0
-153.0
54.7
-173.1
66.4
H 2S
-54.2
39.7
-112.3
44.2
-123.4
53.1
NATURAL BOND ORBITAL LITHIUM AND HALOGEN ATOM
CHARGE TRANSFERS OF THE LITHIUM-BONDED COMPLEXES
For the lithium-bonded complexes the lithium atoms are net
acceptors of charge and the halogen atoms net donors.
For both the lithium and halogen atoms the order is
LiF < LiCl < LiBr, tracking with the lithium halide dipole
moments.
The charge transfers are regularly greater for the NH3 and
PH3 series than for the H2O and H2S complexes, which are
much more constant, reflecting the order of interaction
energies.
NATURAL BOND ORBITAL CHARGE TRANSFERS OF THE
HYDROGEN AND HALOGEN ATOMS OF THE
HYDROGEN-BONDED COMPLEXES
Charge transfer/me
Base
HF
HCl
HBr
H
F
H
Cl
H
Br
NH3
21.9
-79.0
61.3
-132.0
77.2
-168.3
H 2O
26.0
-52.4
48.5
-70.7
52.5
-75.9
PH3
11.4
-42.0
16.7
-47.4
12.5
-48.2
H 2S
8.8
-37.9
14.1
-45.5
10.4
-46.4
NATURAL BOND ORBITAL HYDROGEN AND HALOGEN ATOM
CHARGE TRANSFERS OF THE
HYDROGEN-BONDED COMPLEXES
By contrast, for the hydrogen-bonded complexes the
hydrogen atoms are net donors of charge and the halogen
atoms net acceptors.
For the hydrogen atoms the order is HF < HCl < HBr, in
inverse relationship with the hydrogen halide dipole moments.
For the halogen atoms, the order is reversed,
HF > HCl > HBr.
 In both cases the charge transfers reproduce the order of
interaction energies.
Lithium-bonded complexes
Hydrogen-bonded complexes
LiCl.NH3
LiBr.PH3
LiCl.H2O
LiF.H2S
ATOMS-IN-MOLECULES MOLECULAR GRAPHS OF THE
LiCl.NH3, LiBr.PH3, LiCl.H2O AND LiF.H2S COMPLEXES
For all the NH3 and PH3 complexes bond critical points are
observed for all the covalent bonds, and in the intermolecular
Li…Y regions.
For the H2O and H2S complexes an additional bond critical
point is detected in the H…X region, and a ring critical point is
found in the space enclosed by the Li, X, H and Y atoms.
The exception is the case of LiF.H2S, where no Li…S
interaction is found, even though the NBO n(S)  Li(2p) orbital
interaction energy is comparable with that for the
F(2p)  σ*(SH) interaction.
LiCl.NH3
LiBr.PH3
LiCl.H2O
LiF.H2S
ATOMS-IN-MOLECULES CHARGE DENSITY CONTOUR PLOTS
OF THE LiCl.NH3, LiBr.PH3, LiCl.H2O AND LiF.H2S COMPLEXES
The charge density contour graphs are plotted in the plane of
the heavy atoms.
They show the accumulation of charge around the atomic
nuclei and in the vicinities of the bond critical points.
CHARGE DENSITIES AT THE Li…Y and H…Y BOND CRITICAL
POINTS OF THE LITHIUM-BONDED COMPLEXES AND THEIR
HYDROGEN-BONDED ANALOGUES (Y = N, O, P, S)
Charge density, ρc/a.u.a
Base
Lithium-bonded complexes
a
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
0.0256
0.0273
0.0281
0.0556
0.0522
0.0604
H 2O
0.0261
0.0281
0.0288
0.0426
0.0311
0.0300
PH3
0.0136
0.0148
0.0154
0.0235
0.0182
0.0183
H 2S
-
0.0154
0.0158
0.0245
0.0198
0.0197
1 a.u. of charge density = 1.0812 x 1012 C m-3.
CHARGE DENSITIES AT THE Li…Y AND H…Y BOND CRITICAL
POINTS OF THE LITHIUM-BONDED AND
HYDROGEN-BONDED COMPLEXES
The charge densities at the bond critical points for both the
NH3 and H2O complexes are significantly larger than those for
the PH3 and H2S counterparts.
This is more noticeable for the lithium-bonded complexes, but
is also true for the hydrogen-bonded series. For each base the
hydrogen-bonded complexes have consistently larger values than
the lithium-bonded adducts.
In each case the charge densities correlate fairly well with
the complex interaction energies.
Lithium-bonded complexes
Hydrogen-bonded complexes
LAPLACIANS OF THE CHARGE DENSITIES AT THE Li…Y and
H…Y BOND CRITICAL POINTS OF THE LITHIUM-BONDED
COMPLEXES AND THEIR HYDROGEN-BONDED ANALOGUES
(Y = N, O, P, S)
Laplacian of charge density, 2ρc/a.u.a
Base
Lithium-bonded complexes
a
Hydrogen-bonded complexes
LiF
LiCl
LiBr
HF
HCl
HBr
NH3
0.1566
0.1698
0.1751
0.0674
0.0597
0.0471
H 2O
0.2180
0.2308
0.2359
0.1030
0.0899
0.0881
PH3
0.0588
0.0655
0.0681
0.0366
0.0338
0.0340
H 2S
-
0.0804
0.0820
0.0441
0.0404
0.0404
1 a.u. of Laplacian of charge density = 3.8611 x 1032 C m-5.
LAPLACIANS OF THE CHARGE DENSITIES AT THE Li…Y AND
H…Y BOND CRITICAL POINTS OF THE LITHIUM-BONDED
AND HYDROGEN-BONDED COMPLEXES
The same generalizations regarding the charge densities at
the bond critical points also hold for their Laplacians, as those
for both the NH3 and H2O complexes are larger than those for
the PH3 and H2S counterparts.
 For the lithium-bonded complexes the Laplacians of the
charge densities correlate sensibly with the complex interaction
energies, with separate regions for each base.
For the hydrogen-bonded complexes, the dependence on
interaction energy is much less pronounced, although similar
clustering of the points for the separate bases is observed.
Lithium-bonded complexes
Hydrogen-bonded complexes
CONCLUSIONS
While the structures of the hydrogen-bonded complexes are
all similar to one another, those of the lithium-bonded adducts
fall into two groups, the NH3 and PH3 series, which feature a
XLi…N or P lithium bond only, and the H2O and H2S series
where, in addition to a XLi…O or S lithium bond there is also a
conventional H…X hydrogen bond.
This feature dominates the sharp distinction between the
XLi…N and XLi…P bonded complexes and the XLi…O and XLi…S
set.
In each case there are systematic differences, which can
usually be traced to the substantially higher polarities of the
lithium halides than the hydrogen halides.
Properties such as the elongation of the LiX and HX bonds,
the intermonomer stretching mode wavenumber, the total
intermolecular charge transfer and the charge density at the
Li…Y or H…Y bond critical point vary directly with the
interaction energy.
The Li…Y and H…Y distances, on the other hand, vary
inversely with the strength of interaction.
ACKNOWLEDGEMENTS
The National Research Foundation.
The University of KwaZulu-Natal Research Fund.
The Centre for High Performance Computing.