Hydrogen bonds, improper hydrogen bonds and dihydrogen bonds

Maganthran G. Govender1, Thomas A. Ford*

Centre for Theoretical and Computational Chemistry, School of Pure and Applied Chemistry, University of Natal, Durban 4041, South Africa

Received 7 August 2002; accepted 29 November 2002

Abstract

The structures, interaction energies and vibrational spectra of a large number of molecular complexes, formed by binary

combination of the covalent hydrides of some of the elements of the first two rows of the periodic table, have been determined

by means of ab initio molecular orbital theory at the MP2 level, using the 6-311þþG(d,p) basis set. The results are discussed in

terms of a variety of different types of interaction experienced by the monomer species as they undergo association, namely

conventional hydrogen bonding, improper hydrogen bonding, dihydrogen bonding and electron donor–acceptor interaction.

q 2003 Elsevier Science B.V. All rights reserved.

Keywords: Ab initio; Molecular orbital theory; Binary complexes; Covalent hydrides; Hydrogen bonding; Electron donor–acceptor interaction

1. Introduction

As part of our ongoing studies of the properties of a

variety of types of molecular association, we have

examined the range of interactions experienced by the

hydrides of the elements of groups 14–17 and the first

two rows of the periodic table [1]. Binary complexes

formed from this sample of hydrides exhibit a range of

different forms of association. Among these are

hydrogen bonding, exemplified by the hydrogen

fluoride dimer and the hydrogen chloride–water

complex; improper hydrogen bonding, of which the

complexes of methane with water or phosphine are

examples; dihydrogen bonding, found in the adducts of

silane with hydrogen fluoride or hydrogen chloride;

and electron donor–acceptor interaction, which is

responsible for the stability of the aggregates formed

between silane and ammonia or hydrogen sulphide.

The structures, energetics and vibrational spectra of the

pairwise combinations of the hydride monomers of this

set have been computed, using ab initio molecular

orbital theory, and the various types of association

have been identified. Table 1 shows the distribution of

these four kinds of association among the binary

complexes investigated. The results indicate the rich

variety of structural and vibrational properties exhib-

ited by the adducts formed from among this set of

simple covalently bonded monomeric species, and

these results are discussed in this contribution.

2. Computational details

The calculations were carried out using the GAUS-

SIAN-98 program [2], at the MP2 level of theory [3], and

with the 6-311þþG(d,p) basis set [4,5]. The program

0166-1280/03/$ - see front matter q 2003 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0166-1280(03)00145-3

Journal of Molecular Structure (Theochem) 630 (2003) 11–16

www.elsevier.com/locate/theochem

1 Sasol Synfuels, Private Bag X1000, Secunda 2302, South

Africa.

* Corresponding author.

E-mail address: ford@nu.ac.za (T.A. Ford).

was run on Silicon Graphics Indy and Compaq DS20

workstations. Full geometry optimizations were car-

ried out, with the VERYTIGHT convergence criterion,

usually using the Berny algorithm [6], except for those

cases of slow convergence when large atomic dis-

placements were encountered, in which case the

Murtaugh–Sargent option was employed [7].

3. Results and discussion

3.1. The HF/HCl/H2O/H2S/NH3/PH3 series

The series of complexes featuring HF, HCl, H2O

and H2S as proton donors, and the same four monomers

with the addition of NH3 and PH3 as proton acceptors,

were found to exhibit classical AH· · ·B hydrogen

bonded interactions. Such interactions are associated

with a lengthening of the bonded AH bond and a

decrease in the bonded AH stretching wavenumber,

measured relative to their values in the AH monomers

[8]. For some pairwise combinations two minimum

energy structures were identified, one being the global

minimum and the other, a ‘reverse’ structure derived

from the first by the interchange of proton donor and

acceptor, representing a local minimum, e.g. H2O·HCl,

H2O·H2S, H2S·HF, H2S·HCl and HCl·HF.

The interaction energies, the lengthening of the AH

bonds and the AH stretching wavenumber shifts of

each of the binary complexes in this series are

presented in Table 2. Table 3 shows the energy

Table 1

Binary complexes studied in this work

Electron acceptor Electron donor

HF H2O NH3 CH4 HCl H2S PH3 SiH4

HF (HF)2 HF·H2O HF·NH3 HF·CH4 HF·HCl HF·H2S HF·PH3

H2O (H2O)2 H2O·NH3 H2O·HCl H2O·H2S H2O·PH3

NH3 (NH3)2CH4 CH4·H2O CH4·NH3 (CH4)2 CH4·PH3

HCl HCl·HF HCl·H2O HCl·NH3 HCl·CH4 (HCl)2 HCl·H2S HCl·PH3

H2S H2S·HF H2S·H2O H2S·NH3 H2S·CH4 H2S·HCl (H2S)2 H2S·PH3

PH3 (PH3)2

SiH4 SiH4·HFa SiH4·H2Ob SiH4·NH3b SiH4·HCla SiH4·H2Sb SiH4·PH3

b (SiH4)2

Conventional hydrogen bonds in bold; improper hydrogen bonds in italics.a Dihydrogen bond.b Electron donor–acceptor interaction.

Table 2

Interaction energies, AH bond length changes and AH stretching

wavenumber shifts of the HF, HCl, H2O, H2S, NH3 and PH3

complexes

Complex Interaction energy

(kJ mol21)

AH bond length

change (pm)

AH stretching

wavenumber

shift (cm21)

(HF)2 219.863 0.46 294.5

HF·H2O 240.720 1.50 2347.5

HF·NH3 255.953 3.12 2716.0

HF·HCl 213.193 0.34 283.1

HF·H2S 223.231 0.90 2218.1

HF·PH3 224.186 1.02 2247.6

HCl·HF 212.889 0.30 228.4

HCl·H2O 227.213 1.36 2185.5

HCl·NH3 238.751 3.86 2561.8

(HCl)2 28.819 0.22 227.8

HCl·H2S 215.170 0.74 2110.9

HCl·PH3 215.591 0.87 2131.9

H2O·HFa

(H2O)2 225.425 0.60 277.2

H2O·NH3 230.751 1.21 2204.4

H2O·HCl 26.974 0.09 23.6

H2O·H2S 213.955 0.32 238.2

H2O·PH3 213.863 0.35 244.7

H2S·HF 27.440 0.03 3.3

H2S·H2O 215.345 0.33 226.9

H2S·NH3 217.959 0.91 2110.4

H2S·HCl 25.623 0.03 0.9

(H2S)2 29.298 0.14 210.5

H2S·PH3 28.766 0.18 215.7

(NH3)2 215.892 0.46 244.9

(PH3)2 24.334 20.12 6.8

a Relaxed to HF·H2O on optimization.

M.G. Govender, T.A. Ford / Journal of Molecular Structure (Theochem) 630 (2003) 11–1612

barriers to interconversion of the proton donor and

acceptor for those complexes for which alternative

reverse structures were observed. The structures of a

number of the complexes having HF as the proton

donor are shown as examples in Fig. 1.

The interaction energies were found to vary

directly with the proton affinity [9], and inversely

with the hardness [10] of the base, as indicated in

Fig. 2. The AH bond lengthening and the AH

stretching wavenumber shifts depend monotonically

on the interaction energies, as expected [8]; these

relationships are shown in Fig. 3.

All the complexes in this series feature conven-

tional (red-shifting) hydrogen bonds, with the excep-

tions of H2S·HF and H2S·HCl, where the bonded SH

stretching wavenumber shifts are very slightly to the

blue.

3.2. The HF/HCl/H2O/H2S/CH4/SiH4 series

The interaction energies, AH bond length changes

and AH stretching wavenumber shifts of the com-

plexes in this series are listed in Table 4 and the

structures of some of these species are shown in Fig. 4.

The structures of HF·CH4 and SiH4·HF are qualitat-

ively similar to those of HCl·CH4 and SiH4·HCl,

respectively.

The increases of the HF and HCl bond lengths and

the red HF and HCl stretching wavenumber shifts of

HF·CH4 and HCl·CH4 classify them as conventionally

FH· · ·C (ClH· · ·C) hydrogen bonded adducts.

Table 3

Energy barriers to interconversion of proton donors and acceptors

Global minimum Local minimum Energy barrier (kJ mol21)

HF·HCl HCl·HF 20.304

HF·H2S H2S·HF 215.791

HCl·H2O H2O·HCl 220.239

HCl·H2S H2S·HCl 29.547

H2S·H2O H2O·H2S 21.390

Fig. 1. Optimized structures of the (HF)2, HF·HCl, HF·H2O, HF·H2S, HF·NH3 and HF·PH3 complexes.

M.G. Govender, T.A. Ford / Journal of Molecular Structure (Theochem) 630 (2003) 11–16 13

SiH4·HF and SiH4·HCl have positive HF and HCl

bond length changes and red HF and HCl stretching

wavenumber shifts; here the interactions are of the

FH· · ·H and ClH· · ·H types, therefore these complexes

are classified as dihydrogen bonded [11]. The

negative bond length changes and positive AH

stretching wavenumber shifts of CH4·H2O and

H2S·CH4 confirm their description as improper

(blue-shifting) hydrogen bonded species [12], con-

taining CH· · ·O and SH· · ·C interactions.

SiH4·H2O and SiH4·H2S are found to be electron

donor–acceptor complexes, with Si· · ·O and Si· · ·S

interactions, resulting from donation of charge from

the orbitals dominated by the O or S lone pairs into the

orbitals of SiH4 correlating with the low-lying Si d

atomic orbitals. Their interaction energies, and the

separations of their heavy atoms, after subtracting

Fig. 2. Plots of the interaction energy versus (a) the proton affinity

and (b) the hardness of the base for the HF complexes.

Fig. 3. Plots of (a) the change of the HF bond length and (b) the HF

stretching wavenumber shift versus the interaction energy for the

HF complexes.

Table 4

Interaction energies, changes of the AH bond lengths and AH

stretching wavenumber shifts of some binary complexes formed

from HF, HCl, H2O, H2S, CH4 and SiH4

Complex Interaction energy

(kJ mol21)

AH bond

length change

AH stretching

wavenumber

shift

Bond Change

(pm)

Bond Shift

(cm21)

HF·CH4 25.887 HF 0.15 HF 235.1

HCl·CH4 24.985 HCl 0.10 HCl 27.9

SiH4·HF 25.178 HF 0.20 HF 247.9

SiH4·HCl 24.130 HCl 0.16 HCl 222.7

CH4·H2O 24.335 CH 20.04 CH 8.2

H2S·CH4 23.977 SH 20.01 SH 2.0

M.G. Govender, T.A. Ford / Journal of Molecular Structure (Theochem) 630 (2003) 11–1614

the sum of their single bond covalent radii [13], are

given in Table 5. The correction for the single bond

covalent radii of Si, O and S allows a more

appropriate comparison of the intermonomer separ-

ations of hydrides having heavy atoms

belonging to different periods than the pure Si· · ·O

or Si· · ·S distances. The heavy atom separations are

observed to be inversely dependent on the interaction

energies.

3.3. The NH3/PH3/CH4/SiH4 series

The complexes in this series containing CH4 are

characterized by the presence of CH· · ·N or CH· · ·P

bonds. The interaction energies, CH bond length

changes and CH stretching wavenumber shifts are

presented in Table 6. CH4·NH3 is stabilized by a very

weak conventional hydrogen bond. By contrast,

CH4·PH3 contains a weak improper hydrogen bond,

as evidenced by the marginal CH bond shortening and

the small blue CH stretching wavenumber shift.

The corresponding complexes containing SiH4 are

electron donor-acceptor complexes, with Si· · ·N or

Si· · ·P interactions. The properties of these species are

listed in Table 7. The Si· · ·N bond is stronger, as

confirmed by the shorter heavy atom separation in

SiH4·NH3, compared with that in SiH4·PH3. In the

cases of CH4·NH3, CH4·PH3, SiH4·NH3 and SiH4·PH3,

two conformers, eclipsed and staggered, were

Fig. 4. Optimized structures of the HCl·CH4, CH4·H2O, H2S·CH4 and SiH4·HCl complexes.

Table 7

Interaction energies and heavy atom separations (corrected for the

sum of the heavy atom single bond covalent radii) of some binary

complexes formed from NH3, PH3 and SiH4

Complex Interaction energy

(kJ mol21)

Heavy atom separation

(pm)

SiH4·NH3 (staggered) 29.462 131.10

SiH4·NH3 (eclipsed) 29.403 132.47

SiH4·PH3 (eclipsed) 25.453 174.45

SiH4·PH3 (staggered) 25.448 173.71

Table 6

Interaction energies, changes of the CH bond lengths and CH

stretching wavenumber shifts of some binary complexes formed

from NH3, PH3 and CH4

Complex Interaction

energy

(kJ mol21)

CH bond

length

change (pm)

CH stretching

wavenumber

shift (cm21)

CH4·NH3 (staggered) 24.278 0.017 20.005

CH4·NH3 (eclipsed) 24.223 0.019 20.7

CH4·PH3 (staggered) 23.312 20.027 4.3

CH4·PH3 (eclipsed) 23.290 20.026 4.2

Table 5

Interaction energies and heavy atom separations (corrected for the

sum of the heavy atom single bond covalent radii) of some binary

complexes formed from H2O, H2S and SiH4

Complex Interaction energy

(kJ mol21)

Heavy atom separation

(pm)

SiH4·H2O 28.214 130.85

SiH4·H2S 25.860 168.26

M.G. Govender, T.A. Ford / Journal of Molecular Structure (Theochem) 630 (2003) 11–16 15

examined. The structures of the more stable con-

former of each pair are shown in Fig. 5.

4. Summary

Those complexes containing HF, HCl, H2O and

H2S as proton donors are all conventionally hydrogen

bonded, except for the SiH4·HF and SiH4·HCl species,

where the interaction is a dihydrogen bond. CH4 acts

as a proton donor in CH4·H2O, CH4·NH3 and

CH4·PH3; in CH4·NH3 the hydrogen bond is of

the red-shifted variety, while for CH4·H2O and

CH4·PH3 it is of the improper blue-shifted type. In

H2S·CH4 the SH· · ·C bond is a blue-shifted hydrogen

bond. The complexes of SiH4 with H2O, H2S, NH3

and PH3 are all of the electron donor–acceptor type,

in which the heavy atom separations are uniformly

inversely proportional to the interaction energies. The

properties of these various classes of molecular

complexes will be discussed in more detail in a

forthcoming series of papers.

Acknowledgements

The authors acknowledge the financial support of

the National Research Foundation and the University

of Natal Research Fund, and the highly competent

technical assistance of Mr Kishore Singh.

References

[1] M.G. Govender, PhD Thesis, University of Natal, 2001

[2] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A.

Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery

Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam,

A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi,

V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.

Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala,

Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck,

K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz,

A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz,

I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith,

M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez,

M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W.

Wong, J.L. Andres, M. Head-Gordon, E.S. Replogle, J.A.

Pople, GAUSSIAN-98, Rev. A.7, Gaussian Inc., Pittsburgh, PA,

1998

[3] C. Møller, M.S. Plesset, Phys. Rev. 46 (1934) 618.

[4] R. Krishnan, J.S. Binkley, R. Seeger, J.A. Pople, J. Chem.

Phys. 72 (1980) 650.

[5] T. Clark, J. Chandrasekhar, G.W. Spitznagel, P.v.R. Schleyer,

J. Comput. Chem. 4 (1983) 294.

[6] H.B. Schlegel, J. Comput. Chem. 3 (1982) 214.

[7] B.A. Murtaugh, R.W.H. Sargent, Comput. J. 13 (1970) 185.

[8] G.C. Pimentel, A.L. McClellan, The Hydrogen Bond, Free-

man, San Francisco, CA, 1960, pp. 68–71.

[9] E.P.L. Hunter, S.G. Lias, J. Phys. Chem. Ref. Data 27 (1998)

413.

[10] R.G. Pearson, J. Org. Chem. 54 (1989) 1424.

[11] R.H. Crabtree, P.E.M. Siegbahn, O. Eisenstein, A.L. Rhein-

gold, T.F. Koetzle, Acc. Chem. Res. 29 (1996) 348.

[12] P. Hobza, Z. Havlas, Chem. Rev. 100 (2000) 4253.

[13] G.E. Rodgers, Introduction to Coordination, Solid State and

Descriptive Inorganic Chemistry, McGraw-Hill, New York,

NY, 1994, p. 164.

Fig. 5. Optimized structures of the stable conformers of the CH4·NH3, CH4·PH3, SiH4·NH3 and SiH4·PH3 complexes.

M.G. Govender, T.A. Ford / Journal of Molecular Structure (Theochem) 630 (2003) 11–1616