1. Jan Lundell Department of Chemistry, University of Jyväskylä
The Hydrogen Bond
Jan Lundell Department of Chemistry, University of Jyväskylä

2. The Hydrogen Bond

3. The Hydrogen Bond
Adenine
Thymine
Cytosine
Guanine
Peter Agre (Nobel Prize, 2003): The purest form of hydrogen bond there is…

4. The Hydrogen Bond
”The hydrogen nucleus held by two octets constitutes a weak bond”
W.M.Latimer and W.H.Rodebush, JACS 42, 1920, 1419
”Under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms instead of only one, so that it may be considered to be acting as a bond between them. This is called a hydrogen bond.”
L. Pauling, Nature of Chemical Bond, 1939

5. The Hydrogen Bond
HCOOH in the gas phase – IR ( from webbook.nist.gov )
Absorbance
Wavenumber

6. The Hydrogen Bond
”A hydrogen bond exists between the functional group, A-H, and an atom or a group of atoms, B, in the same or different molecules when
(a) there is evidence of bond formation (association or chelation)
(b) there is evidence that this new bond linking A-H and B specifically involves a hydrogen atom already bonded to A”
G.C.Pimentel, A.L.McClellan, The Hydrogen Bond, 1960

7. The Hydrogen Bond bond distance A-H  H...B A-H < H...B
Strong
Medium
Weak
bond distance
A-H  H...B
A-H < H...B
A-H << H...B
H...B (Å)  
A...B (Å)
bond angle (º)
binding energy (kJ/mol)
< 15

8. The Hydrogen Bond dimers of strong acids and bases in the gas phase
Medium
Weak
dimers of strong acids and bases in the gas phase
acids
dimers of weak acids and bases in the gas phase
Acid salts
alcohols, phenols
C-H...O/N
Proton sponges
hydrates
O/N-H...
HF complexes
all biological molecules
dihydrogen bonds

9. The Hydrogen Bond
”A hydrogen atom with only one stable orbital cannot form more than one pure covalent bond and the attraction of the two atoms observed in hydrogen bond formation must be due largely to ionic forces””
L.Pauling, The Nature of Chemical Bond, 1939 d+ d-

10. The Hydrogen Bond YHB = aYa + bYb + cYc + dYd + eYe
Ya A-H…B covalent A-H bond
Yb A- -H+ …B ionic A-H bond
Yc A- -H…B+ charge transfer , A…B bond
Yd A+ -H- …B ionic A-H bond
Ya A-H- …B+ charge transfer, H…B bond
C.A.Coulson, In Hydrogen Bonding, D.Hadzi (Ed.) 1959, pp
O-H … O with O … O = 2.8 Å
Yb + Yd contribute 65 % of the hydrogen bond energy

11. Interaction energy of a H-bond
Supermolecular approach
Eint = EAB – (EA + EB)

12. Interaction energy decomposition scheme

13. HCN…HCN ( MP2 )
A.Heikkilä, J.Lundell, J.Phys.Chem. A 104, 2000,

14. Symmetry-Adapted Perturbation Theory (SAPT)
K.Szalewicz, K.Patkowski, B.Jeziorski ,Struct.Chem. 116, 2005,

15. R.A.Christie, K.D.Jordan, Struct.Chem. 116, 2005, 27-41

16. Having more than two molecules?
S.S.Xantheas Struct.Chem. 116, 2005,

19. S.S.Xantheas Struct.Chem. 116, 2005, 119-148

20. Non-additive (cooperative) effects

21. S.S.Xantheas Struct.Chem. 116, 2005, 119-148

22. Basis set superposition error (BSSE)
Not perfect basis sets, so needs to borrow from the neighbour…
HNC…HCN
The ”cure”: Counterpoise correction (Boys-Bernardi )

25. S.S.Xantheas Struct.Chem. 116, 2005, 119-148

26. J.R.Lane, H.G.Kjaergaard, J.Phys.Chem. 131, 2009, 034307

27. Changes upon hydrogen bonding…
G.A.Jeffrey, An Introduction to Hydrogen Bonding, 1997

28. HCOOH photochemistry in matrices
H2O + CO vs
CO2 + H2
t-HCOOH hn
J.Lundell, M.Räsänen, J.Phys.Chem. 99, 1995,

29. H2O...CO : Two stable complex structures
2.323
2.365
CCSD(T)/ G(2d,2p)
Eint,cp = kJ mol-1
Eint,cp = kJ mol-1
J.Lundell, J.Phys.Chem. 99, 1995,14290 J.Lundell, Z.Latajka, J.Phys.Chem. A 101, 1997, 5004

30. H2O...CO : Experiments
In situ photolysis of formic acid in a solid argon matrix
+13
2130
+10
2148
1656 +2
1596
-22
3826 -9
3628
-17
3864
3724 Dw
calc. Dn
exp.
JPC 99, 1995, 14290: MP2/ G(2d,2p) JPC 99, 1995, 14301: Ng-matrices
HOH...CO

31. H2O...CO : Experiments Annealing the matrix after photolysis argon
krypton
xenon

32. H2O...CO : Experiments Both HOH...CO and HOH...OC can be made -2 2118
+10
2130
calc. -5
2128 +8
2142 Xe -6 +9
2145 Kr
+11
2149 Ar
2154
Gas phase
HOH...CO
HOH...OC
MP2/ G(2d,2p)
CO stretch

33. Can we do more?

34. Anharmonic calculations: cc-VSCF
Vibrational Schrödinger equation in mass-weighted normal mode coordinates
single-mode wavefunctions, energies and effective potentials
2nd order perturbation theory for correlation effects between different vibrational modes
pairwise interactions between normal modes

35. Anharmonic calculations: cc-VSCF
Grid-approach of PES:
- 8  8 or 16  16 grids
- points chosen equidistantly over an interval defined by the harmonic frequency of a vibrational mode: Qmax ~ inverse square root of the frequency G.M.Chaban, J.O.Jung, R.B.Gerber, J.Phys.Chem. A 104, 2000, 2772
Implemented in GAMESS-US

36. MP2/aug-cc-pVTZ + cc-VSCF
* CO2...H2

37. MP2/aug-cc-pVTZ + cc-VSCF

39. The formic acid monomer: Two conformers
MP2/ G(2d,2p)
4544 cm-1
1488 cm-1
trans
cis
Exp: 4842 cm-1
Exp: 1362 cm-1

40. IR-pumping at 6934 cm-1 (2 nOH) cis IR trans
M.Pettersson, J.Lundell, L.Khriachtchev, M.Räsänen, JACS 119, 1997, 11715

41. HCOOH anharmonic calculations
trans-HCOOH
anharmonic
harmonic
cis-HCOOH
E.M.S.Macoas, J.Lundell, M. Pettersson, L.Khriachtchev, R.Fausto, M.Räsänen, J.Mol.Spectrosc. 219, 2003, 70.

42. Isomerisation of formic acid: The monomer
vibr exc
tunneling
trans
cis
K. Marushkevich, L.Khriachtchev, M.Räsänen, J.Phys.Chem. A 111, 2007, 2040
Tunneling can be stopped by complexation X

43. The trans-trans formic acid dimers
FAD-tt3
2.408
2.509
Ecp,int (MP2)=
FAD-tt5
1.896
2.406
Ecp,int (MP2)=
FAD-tt1
1.684
Ecp,int (MP2)= kJ mol-1
FAD-tt4
1.927
1.968
Ecp,int (MP2)=
FAD-tt2
1.774
2.337
Ecp,int (MP2)=
FAD-tt6
2.417
Ecp,int (MP2)=
MP2/ G(2d,2p)

44. The trans-trans –dimer (FAD-tt1)
MP2/ G(2d,2p) cc-VSCF without mode coupling
FAD-tt1 in solid argon
From M.Gantenberg, M.Halupka, W.Sander, Chem.Eur.J. 6, 2000, 1865

45. Solid argon FAD-tt1 FAD-tt2
A.Olbert-Majkut, J.Ahokas, J.Lundell, M.Pettersson, Chem.Phys.Lett. 468, 2009, 176.

46. The trans-trans formic acid dimers
Computed relative energies
FAD-tt2
FAD-tt3
FAD-tt4
FAD-tt5
FAD-tc2
FAD-tt6
FAD-cc3
FAD-tt1
FAD-tc3
FAD-tc4
FAD-tc5
FAD-tc1
FAD-cc4
FAD-cc2
FAD-cc1
FAD-cc5
cis-FA
trans-FA
Experimentally observed
excitation at cm-1 (C-H str)
FAD-tt3 FAD-tt6

47. Pumping O-H str in trans-trans dimer ?
FAD-tt1 (CD) * *
FAD-tt2 ( * )
Excitation at 3540 cm-1 * * *
K.Marushkevich, L.Khriachtchev, J.Lundell, M.Räsänen, JACS 128, 2006, 12060

48. The cis-trans formic acid dimers
FAD-tc3
1.814
Ecp,int (MP2)=
FAD-tc1
1.761
2.287
Ecp,int (MP2)= kJ mol-1
FAD-tc5
1.857
Ecp,int (MP2)=
FAD-tc4
2.502
2.387
Ecp,int (MP2)=
FAD-tc2
1.950
1.852
Ecp,int (MP2)=
MP2/ G(2d,2p)

49. The cis-trans formic acid dimers
FAD-tc1
FAD-tt2
1.774
2.337
1.761
2.287
hn (IR)
cc-VSCF//MP2 computed wavenumbers [cm-1]
x 5
FAD-tc1
FAD-tt2
trans-FA
x 1

50. The cis-trans formic acid dimers
cm-1
cm-1
cm-1
cm-1
MP2/ G(2d,2p)

51. Photoisomerisation of formic acid dimers:
Computed relative energies
FAD-cc4
FAD-cc2
FAD-tc4
FAD-cc1
FAD-cc5
FAD-tc5
FAD-tt3
FAD-tc3
FAD-tt6
FAD-tc2
FAD-tt5
FAD-tc1
FAD-tt4
FAD-tt2
cis-FA
Experimentally observed
trans-FA
FAD-tt1

52. The cis-cis formic acid dimers
FAD-cc1
Ecp,int (MP2)= kJ mol-1
1.878
2.765
FAD-cc2
1.853
Ecp,int (MP2)=
FAD-cc3
2.370
Ecp,int (MP2)=
FAD-cc4
2.006
Ecp,int (MP2)=
2.684
FAD-cc5
1.816
Ecp,int (MP2)=
MP2/ G(2d,2p)

53. The cis-cis formic acid dimers
Computed relative energies
FAD-tt2
FAD-tt3
FAD-tt4
FAD-tt5
FAD-tc2
FAD-tt6
FAD-cc3
FAD-tt1
FAD-tc3
FAD-tc4
FAD-tc5
FAD-tc1
FAD-cc4
FAD-cc2
FAD-cc1
FAD-cc5
cis-FA
trans-FA
Experimentally observed ? ?

54. Current topics (Horizons in Hydrogen Bond Research, Paris, Sept 2009)
Blue-shifting hydrogen bonds vs red-shifting hydrogen bonds
Dihydrogen bonds (for example, H-O-H…HXeH )
Biomolecular systems
- Water as biolubricant
“Fast spectroscopy” (also dynamic simulations )