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 Medical Faculty University of Bonn, Germany R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 What is a Hydrogen Bond? Importance of Hydrogen Bonding ■ liquid water and ice - protic solvents ■ the interaction between an electron-deficient hydrogen atom with a centre of relative electron ■ solution structure and hydration shell - ionic excess, e.g., electronegative atoms such as F, N, or and non-ionic solutes O, or with a π -electron cloud ■ protein folding ■ Morokuma decomposition: electrostatic (65%), ■ purine/pyrimidine (GC/AT(U)) base-pairing polarisation (24%) and charge-transfer (11%) for water dimer - Mó et al. [2000] in nucleic acids ■ electrostatic / covalent resonance hydrid (Pauling) - ■ chemical and enzymatic reactions Isaacs et al. [1999] R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Monomeric water Properties of the Group VI Hydrides 150 100 °C 50 MW FPt. 0 BPt. -50 -100 H2O H2S H2Se H2Te R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 1
Isaacs; Shukla; Platzmann; Hamann; Barbiellini; Tulk; Phys. Rev. Lett. 1999 , 82, 600 Isaacs; Shukla; Platzmann; Hamann; Barbiellini; Tulk; Phys. Rev. Lett. 1999 , 82, 600 Ice I R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Weak Hydrogen Bonds ==>> Strong Hydrogen Bonds (VDW complexes) ( cis -enols) Nitromalonamide enol ...... CF 3 H.....H 2 O TS CH 4 .....H 2 O R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 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) from Desiraju, G.R.; Steiner, T. (1999) R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 2
Topological criteria (AIM Theory) Electron Density Topology (AIM) ■ BCP with δρ δρ (r) =0 and δρ δρ ■ H D net positive charge (3,-1) topology; increased ■ 0.002 0.002 0.002<ρ 0.002 ρ ρ ρ (r) <0.040 ■ energetically destabilised ■ Laplacian of ρ ρ ρ (r) , L ρ L 2 ρ ρ ρ ρ (r) , ■ decreased dipolar L L > 0 and in range 0.015- polarisation 0.150 a.u. ■ reduction in atomic ■ mutual penetration volume R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Electron Density Topology (AIM) 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 R.A. Klein - Lexington KY, October 2003 4 C 1 -Galactopyranose Diols ■ (n,n+1) Ethane-diol Synthon – 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 R.A. Klein - Lexington KY, October 2003 3
Electron Density (12EG) Electron Density (13PG) Ethane-1,2-diol Propane-1,3-diol MPW1PW91/6-311+G(2d,p) 6D 10F MPW1PW91/6-311+G(2d,p) 6D 10F R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Electron Density (14BD) BCP Electron Density and Laplacian Diol L 2 rho rho L L L f(h) ellipt. BCP 12EG -- -- -- -- no Butane-1,4-diol 0.02163 +0.0845 0.3713 0.02293 yes 13PG 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 MPW1PW91/6-311+G(2d,p) 6D 10F R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Atomic Charge Dipolar Polarisation R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 4
Atomic Volume Distance versus Laplacian R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Ethane-1,2-diol / Water Complexes Effect of medium dielectric constant R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Electron Density Electron Density 12EG/H 2 O 12EG/H 2 O confB confC MPW1PW91/6-311+G(2d,p) 6D 10F MPW1PW91/6-311+G(2d,p) 6D 10F R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 5
Diols for -O-H D .....O A -O A ...H D -O- Interaction Energy 9 8 7 6 Energy 5 kcal/mol 4 3 2 1 0 red: D (OH) 1,2-diol 1,3-diol 1,4-diol 1,5-diol 1,6-diol 1:1 (HOH) 1:1 (-OH) 1:1 (bifurc) green: V (CP) blue: CBS-QB3 R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 NMR downfield shift for -O-H D IR red-shift for -O-H D 1.8 2 2.2 1.8 2 2.2 2.4 300 300 5 5 4 4 n = 12 200 200 red-shift (cm-1) 3 3 n = 3 ∆ H PPM n = 8 2 2 100 100 1 1 n = 17 0 0 0 0 1.8 2 2.2 2.4 1.8 2 2.2 2.4 H...O interaction distance (Å) H D ...O A interaction distance R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 α,ω -Diols - NBO Analysis Dipolar polarisation for -O-H D Force constant (N/m) 840 880 920 960 1000 0.18 0.18 Hydrogen µ ( Ω ) - dipolar polarisation 0.16 0.16 0.14 0.14 0.12 0.12 840 880 920 960 1000 R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 6
2-Haloethanols Glucopyranose 4 C 1 g+ / trans F Cl Br R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Glucopyranose 1 C 4 g+ Van der Waals Radii and Interpenetrability R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Van der Waals Radii VDW Radii ■ Interpenetration limits for hydrogen MPW1PW91/6-311+G(2d,p) bonding based on VDW radii ■ Pauling – O:...H = 1.4 + 1.2 = 2.6 Å – N:...H = 1.5 + 1.2 = 2.7 Å All too high!! ■ 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 R.A. Klein - Lexington KY, October 2003 7
VDW Radii - hydrogen bonding O...HO Hydrogen Bonding O...HN and O...HC ■ calculate ρ (r) at donor-acceptor distances based ■ which radius? ■ 0.001 or 0.01 au? R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 Modified “VDW” Radii Modified “VDW” Radii ■ with ρ = 0.010 at BCP Atom Bondi Rowland IP Clementi Klein Pauling Roetti – -O:...H- = 2.31 Å (B) (P) r R 0.001 0.002 0.001 0.005 0.010 – -N:...H- = 2.44 Å H 1.20 1.2 1.10 1.09 1.06 1.52 1.34 1.34 0.98 0.82 ■ with ρ = 0.020 at BCP N 1.55 1.5 1.64 1.61 1.36 1.77 1.62 1.81 1.46 1.31 – -O:...H- = 2.02 Å – -N:...H- = 2.13 Å 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 R.A. Klein - Lexington KY, October 2003 Hydrogen Bond Cooperativity Cooperativity or Non-additive Effects R.A. Klein - Lexington KY, October 2003 R.A. Klein - Lexington KY, October 2003 8
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