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When is a Hydrogen Bond not a Hydrogen Bond? What is a Hydrogen Bond? The Need for a Quantum-mechanically Consistent Definition University of Kentucky, Lexington KY 20-21 October 2003 Roger A. Klein Institute for Physiological Chemistry

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When is a Hydrogen Bond not a Hydrogen Bond? The Need for a Quantum-mechanically Consistent Definition

University of Kentucky, Lexington KY 20-21 October 2003 Roger A. Klein

Institute for Physiological Chemistry Medical Faculty University of Bonn, Germany

R.A. Klein - Lexington KY, October 2003

What is a Hydrogen Bond?

R.A. Klein - Lexington KY, October 2003

What is a Hydrogen Bond?

■ the interaction between an electron-deficient

hydrogen atom with a centre of relative electron excess, e.g., electronegative atoms such as F, N, or O, or with a π-electron cloud

■ Morokuma decomposition: electrostatic (65%),

polarisation (24%) and charge-transfer (11%) for water dimer - Mó et al. [2000]

■ electrostatic / covalent resonance hydrid (Pauling) -

Isaacs et al. [1999]

R.A. Klein - Lexington KY, October 2003

Importance of Hydrogen Bonding

■ liquid water and ice - protic solvents ■ solution structure and hydration shell - ionic

and non-ionic solutes

■ protein folding ■ purine/pyrimidine (GC/AT(U)) base-pairing

in nucleic acids

■ chemical and enzymatic reactions

R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003

Monomeric water

Properties of the Group VI Hydrides

  • 100
  • 50

50 100 150 H2O H2S H2Se H2Te MW FPt. BPt.

R.A. Klein - Lexington KY, October 2003

°C

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2

R.A. Klein - Lexington KY, October 2003

Ice I

Isaacs; Shukla; Platzmann; Hamann; Barbiellini; Tulk; Phys. Rev. Lett. 1999, 82, 600 R.A. Klein - Lexington KY, October 2003 Isaacs; Shukla; Platzmann; Hamann; Barbiellini; Tulk; Phys. Rev. Lett. 1999, 82, 600

Weak Hydrogen Bonds

(VDW complexes)

R.A. Klein - Lexington KY, October 2003

CF3H.....H2O ...... CH4.....H2O

==>> Strong Hydrogen Bonds

(cis-enols)

R.A. Klein - Lexington KY, October 2003

Nitromalonamide

enol TS

R.A. Klein - Lexington KY, October 2003

from Desiraju, G.R.; Steiner, T. (1999)

Hydrogen-Bonding

■ Acceptor-Donor -H...A-

– typically -H...O- or -H...N-

■ Geometry dependent

– (a) -H...A-X angle – (b) -H...A- distance

■ dielectric constant ■ partially electrostatic, partially covalent ■ long-range (1/r)

R.A. Klein - Lexington KY, October 2003

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SLIDE 3

3 Topological criteria (AIM Theory)

■ BCP with δρ

δρ δρ δρ(r)=0 and (3,-1) topology;

■ 0.002

0.002 0.002 0.002<ρ ρ ρ ρ(r)<0.040

■ Laplacian of ρ

ρ ρ ρ(r), L L L L2ρ ρ ρ ρ(r), > 0 and in range 0.015- 0.150 a.u.

■ mutual penetration ■ HD net positive charge

increased

■ energetically destabilised ■ decreased dipolar

polarisation

■ reduction in atomic

volume

R.A. Klein - Lexington KY, October 2003

Electron Density Topology (AIM)

R.A. Klein - Lexington KY, October 2003

Electron Density Topology (AIM)

R.A. Klein - Lexington KY, October 2003

Why Glycol-Water Systems?

■ Modelling hydration of carbohydrates ■ Cryoprotectants

■ natural ■ synthetic

■ Hydrogen-bonding in aqueous solution ■ Structuring of water in the presence of

solutes

R.A. Klein - Lexington KY, October 2003

4C1-Galactopyranose

Ethane-diol Synthon

R.A. Klein - Lexington KY, October 2003

Diols

■ (n,n+1)

– 12ED, 23BD

■ (n,n+2)

– 13BD, 25PD

■ (n,n+3)

– 14BD, 25HD

■ (n,n+4)

– 15PD

■ (n,n+5)

– 16HD R.A. Klein - Lexington KY, October 2003

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Electron Density (12EG)

R.A. Klein - Lexington KY, October 2003

Ethane-1,2-diol

MPW1PW91/6-311+G(2d,p) 6D 10F

Electron Density (13PG)

R.A. Klein - Lexington KY, October 2003

Propane-1,3-diol

MPW1PW91/6-311+G(2d,p) 6D 10F

Electron Density (14BD)

R.A. Klein - Lexington KY, October 2003

Butane-1,4-diol

MPW1PW91/6-311+G(2d,p) 6D 10F R.A. Klein - Lexington KY, October 2003

BCP Electron Density and Laplacian

Diol rho L L L L2rho f(h) ellipt. BCP 12EG

  • no

13PG

0.02163 +0.0845 0.3713 0.02293 yes

14BD 0.03186

+0.1128 0.3479 0.04764 yes

15PD

0.02576 +0.0987 0.3532 0.06160 yes

16HD 0.02282

+0.0802 0.3513 0.02240 yes

R.A. Klein - Lexington KY, October 2003

Atomic Charge

R.A. Klein - Lexington KY, October 2003

Dipolar Polarisation

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5

R.A. Klein - Lexington KY, October 2003

Atomic Volume Distance versus Laplacian

R.A. Klein - Lexington KY, October 2003

Ethane-1,2-diol / Water Complexes

R.A. Klein - Lexington KY, October 2003

Effect of medium dielectric constant

R.A. Klein - Lexington KY, October 2003

Electron Density

R.A. Klein - Lexington KY, October 2003

12EG/H2O confB

MPW1PW91/6-311+G(2d,p) 6D 10F

Electron Density

R.A. Klein - Lexington KY, October 2003

12EG/H2O confC

MPW1PW91/6-311+G(2d,p) 6D 10F

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R.A. Klein - Lexington KY, October 2003

Diols for -O-HD.....OA

  • OA...HD-O- Interaction Energy

R.A. Klein - Lexington KY, October 2003

1 2 3 4 5 6 7 8 9 Energy kcal/mol 1,2-diol 1,3-diol 1,4-diol 1,5-diol 1,6-diol 1:1 (HOH) 1:1 (-OH) 1:1 (bifurc)

red: D(OH) green: V(CP) blue: CBS-QB3

R.A. Klein - Lexington KY, October 2003

IR red-shift for -O-HD

1.8 2 2.2 2.4 100 200 300 1.8 2 2.2 100 200 300

red-shift (cm-1) H...O interaction distance (Å) R.A. Klein - Lexington KY, October 2003

NMR downfield shift for -O-HD

1.8 2 2.2 2.4 1 2 3 4 5 1.8 2 2.2 2.4 1 2 3 4 5

HD...OA interaction distance ∆HPPM n = 17 n = 8 n = 3 n = 12 R.A. Klein - Lexington KY, October 2003

Dipolar polarisation for -O-HD

840 880 920 960 1000 0.12 0.14 0.16 0.18 0.12 0.14 0.16 0.18 840 880 920 960 1000

Hydrogen µ(Ω) - dipolar polarisation Force constant (N/m)

α,ω-Diols - NBO Analysis

R.A. Klein - Lexington KY, October 2003

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SLIDE 7

7

R.A. Klein - Lexington KY, October 2003

2-Haloethanols

F Cl Br

Glucopyranose 4C1 g+ / trans

R.A. Klein - Lexington KY, October 2003

Glucopyranose 1C4 g+

R.A. Klein - Lexington KY, October 2003

Van der Waals Radii and Interpenetrability

R.A. Klein - Lexington KY, October 2003

Van der Waals Radii

■ Interpenetration limits for hydrogen

bonding based on VDW radii

■ Pauling

– O:...H = 1.4 + 1.2 = 2.6 Å – N:...H = 1.5 + 1.2 = 2.7 Å

■ Bondi

– O:...H = 1.52 + 1.2 = 2.72 Å – N:...H = 1.55 + 1.2 = 2.75 Å

■ Bader / Popelier ρ = 0.001 au (0.002 au)

– O:...H = 1.68 + 1.52 = 3.20 Å (2.89 Å) – N:...H = 1.77 + 1.52 = 3.29 Å (2.96 Å) R.A. Klein - Lexington KY, October 2003

All too high!!

VDW Radii

R.A. Klein - Lexington KY, October 2003

MPW1PW91/6-311+G(2d,p)

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VDW Radii - hydrogen bonding O...HO

R.A. Klein - Lexington KY, October 2003

■ calculate ρ(r) at

donor-acceptor distances based

■ which radius? ■ 0.001 or 0.01 au?

Hydrogen Bonding O...HN and O...HC

R.A. Klein - Lexington KY, October 2003

Modified “VDW” Radii

R.A. Klein - Lexington KY, October 2003

■ with ρ = 0.010 at BCP

– -O:...H- = 2.31 Å – -N:...H- = 2.44 Å

■ with ρ = 0.020 at BCP

– -O:...H- = 2.02 Å – -N:...H- = 2.13 Å

Modified “VDW” Radii

Atom Bondi Pauling Rowland IP Clementi Roetti Klein (B) (P) r R 0.001 0.002 0.001 0.005 0.010

H 1.20 1.2 1.10 1.09 1.06 1.52 1.34 1.34 0.98 0.82 N 1.55 1.5 1.64 1.61 1.36 1.77 1.62 1.81 1.46 1.31 O 1.52 1.40 1.58 1.56 1.27 1.68 1.55 1.68 1.33 1.20

R.A. Klein - Lexington KY, October 2003

Cooperativity

  • r

Non-additive Effects

R.A. Klein - Lexington KY, October 2003

Hydrogen Bond Cooperativity

R.A. Klein - Lexington KY, October 2003

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Hydrogen Bond Cooperativity

■ Energy per H-bond in

kcal/mol for H2O

■ 1,2-diols = -6.85±0.44 – -4.01 (bifurc. sym.) ■ Glucose / 5 x H2O

= -9.69±1.12

■ BCP electron density and

Laplacian of rho +30%

R.A. Klein - Lexington KY, October 2003

GaussView

Hydrogen Bond Cooperativity

R.A. Klein - Lexington KY, October 2003

What is a Hydrogen Bond?

■ the interaction between an electron-deficient

hydrogen atom with a centre of relative electron excess, e.g., electronegative atoms such as F, N, or O, or with a π-electron cloud

■ Morokuma decomposition: electrostatic (65%),

polarisation (24%) and charge-transfer (11%) for water dimer - Mó et al. [2000]

■ electrostatic / covalent resonance hydrid (Pauling) -

Isaacs et al. [1999]

R.A. Klein - Lexington KY, October 2003

What is a Hydrogen Bond?

■ In addition

■ a bond critical point (BCP) of (3,-1) topology with (ρ) and

Laplacian of (ρ) in the correct range - also a ring critical point (RCP) of (3,+1) topology for intramolecular hydrogen bonds

■ charge transfer from the acceptor lone pair (LP) electrons

to the σ* anti-bonding orbital of the donor HD-O

■ Cooperativity

■ enhanced (ρ) and Laplacian of (ρ) at BCP as a result of nH

σ* destabilsation of the HD-O: lone pair

■ IR phase-locking or synchronisation of O-H stretch

frequencies

R.A. Klein - Lexington KY, October 2003

Does Glucose show Cooperativity?

R.A. Klein - Lexington KY, October 2003

O-H σ* Occupancies for Donor-Acceptor Geometries

R.A. Klein - Lexington KY, October 2003

Unit O-HD O-HW OA-HW OA-H 12eg_confB_TIP3 0.02655 0.00083 0.02109 0.00528 12eg_confD_TIP3 0.02782 0.00086 0.02194 0.00705 Glucose_4C1_TIP3 H2O (1) 0.03290 0.00158 H2O (2) 0.03446 0.00143 H2O (3) 0.03594 0.00143 H2O (4) 0.03010 0.00144 H2O (5) 0.04330 0.00104 H2O (6) 0.04501 0.00129 O1-H1 0.06033 0.06033 O2-H2 0.04644 0.04644 O3-H3 0.04596 0.04596 O4-H4 0.04589 0.04589 O6-H6 0.02880 0.02880 Diol OA-H (acceptor) O-HD (donor) 12eg_conB 0.00511 0.00921 12eg_confD 0.00724 0.01118 13pg_confA 0.00581 0.01534 14bd_confA 0.00542 0.02926 15pd_confA 0.00594 0.02187 16hd_confA 0.00521 0.02045 Glucose 4C1 O1-H1 0.00736 Glucose 4C1 O2-H2 0.00652 Glucose 4C1 O3-H3 0.00712 Glucose 4C1 O4-H4 0.00767 Glucose 4C1 O6-H6 0.00908

Monomers Cooperative

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O-HD Bond Lengths and Cooperativity

(Ångstroms: MPW1PW91/6-311+G(2d,p))

R.A. Klein - Lexington KY, October 2003

■ ‘Diol’ synthon (isolated) – 12EG(confB)

0.958058 0.962074

– 12EG(confD)

0.960096 0.962983

– Glucose-4C1

0.961501 ± 0.000569

■ Cooperative water complexes – 12EG(confB)

0.959031 0.970413

– H2O

0.958747 0.972152

– 12EG(confD)

0.960697 0.971199

– H2O

0.959034 0.972475

– Glucose-4C1

0.980017 ± 0.000543

– H2O

0.958664 0.979031

Semantics?

■ Is it a matter of just semantics what the

definition of a hydrogen bond is?

■ without a (3,-1) BCP no donor-acceptor cooperativity ■ σ* occupancies and bond lengths in glucose not

cooperatively increased compared to ethane-1,2-diol

■ IR red-shifts and synchrony ■ hydrogen tunnelling

– de Broglie wavelength (uncertainty) λ = h/√ (2mE)

λH = 0.58 Å; λD = 0.41 Å; λT = 0.34 Å

■ the answer is probably “no”

R.A. Klein - Lexington KY, October 2003

References

R.A. Klein - Lexington KY, October 2003

1

  • S. O. Jonsdottir, R. A. Klein, and K. Rasmussen (1996)

“UNIQUAC interaction parameters for alkane / amine systems determined by Molecular Mechanics” Fluid Phase Equilibrium 115:59-72. 2

  • S. O. Jonsdottir and R. A. Klein (1997)

“UNIQUAC interaction parameters for molecules with -OH groups on adjacent carbon atoms in aqueous solution determined by molecular mechanics - glycols, glycerol and glucose” Fluid Phase Equilibrium 132:117-137. 3

  • S. O. Jonsdottir, W. J. Welsh, K. Rasmussen, and R. A. Klein (1999) “The critical role
  • f force-fields in property prediction” New Journal of Chemistry 1999:153-163.

4

  • R. A. Klein and V. Pacheco (2001) “Binary Diol - Water Systems Studied by

17O

Nuclear Magnetic Resonance Spectroscopy. Interpretation of the Effect of Diol Structure on the

17O - Water Chemical Shift. Formation of Networks of Water

Molecules Stabilised by Weak C-H...O Interactions” Journal of Physical Chemistry A 105(40):9298-9304; ibid. (2002) Journal of Physical Chemistry A 106(16):4290. 5

  • R. A. Klein. (2002) “Ab Initio Conformational Studies on Diols and Binary Diol-

Water Systems Using DFT Methods. Intramolecular Hydrogen Bonding and 1:1 Complex Formation with Water” Journal of Computational Chemistry 23(6):585-599. 6

  • R. A. Klein. (2002) “Electron Density Topological Analysis of Hydrogen Bonding in

Glucopyranose and Hydrated Glucopyranose” Journal of the American Chemical Society 124(46), 13931-13937. 7

  • R. A. Klein. (2003) “Hydrogen Bonding in Diols and Binary Diol-Water Systems

Investigated Using DFT Methods. II. Calculated Infrared OH-Stretch Frequencies, Force Constants, and NMR Chemical Shifts Correlate with Hydrogen Bond Geometry and Electron Density Topology. A Reevaluation of Geometrical Criteria for Hydrogen Bonding” Journal of Computational Chemistry 24(9):1120-1131.

On-going Work

■ highly cooperative hydrogen bonding in large

water clusters (n ≤ 24)

■ applicability of continuum methods in highly

cooperative systems

■ non-classical hydrogen bonding in clathrates

R.A. Klein - Lexington KY, October 2003

Acknowledgements

■ Aberdeen

  • Mark Zottola

■ Bonn

  • Ernst Bause
  • Victor Pacheco
  • Rudi Hartmann

■ Pisa

  • Jacopo Tomasi
  • Benedetta Mennucci

■ Copenhagen

  • Svava Jónsdóttir
  • Kjeld Rasmussen

R.A. Klein - Lexington KY, October 2003