what is a hydrogen bond? importance of hydrogen …hydrogen bonds charge transfer from the acceptor...

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When is a Hydrogen Bond not a HydrogenBond?

The Need for a Quantum-mechanicallyConsistent Definition

University of Kentucky, Lexington KY 20-21 October 2003

Roger A. KleinInstitute for Physiological Chemistry

Medical FacultyUniversity of Bonn, Germany

R.A. Klein - Lexington KY, October 2003

What is a Hydrogen Bond?



the interaction between an electron-deficienthydrogen atom with a centre of relative electronexcess, e.g., electronegative atoms such as F, N, orO, or with a π-electron cloud

Morokuma decomposition: electrostatic (65%),polarisation (24%) and charge-transfer (11%) forwater dimer - Mó et al. [2000]

electrostatic / covalent resonance hydrid (Pauling) -Isaacs et al. [1999]


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



Monomeric water Properties of the Group VI Hydrides

-100

-50

0

50

100

150

H2O H2S H2Se H2Te

MWFPt.BPt.


°C

2


Ice I

Isaacs; Shukla; Platzmann; Hamann; Barbiellini; Tulk; Phys. Rev. Lett. 1999, 82, 600


Isaacs; Shukla; Platzmann; Hamann; Barbiellini; Tulk; Phys. Rev. Lett. 1999, 82, 600

Weak Hydrogen Bonds(VDW complexes)


CF3H.....H2O

......

CH4.....H2O

==>> Strong Hydrogen Bonds(cis-enols)


Nitromalonamideenol

TS


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)


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Topological criteria (AIM Theory)

BCP with δρδρδρδρ(r)=0 and(3,-1) topology;

0.0020.0020.0020.002<ρρρρ(r)<0.040 Laplacian of ρρρρ(r), LLLL2ρρρρ(r),

> 0 and in range 0.015-0.150 a.u.

mutual penetration

HD net positive chargeincreased

energetically destabilised decreased dipolar

polarisation reduction in atomic

volume


Electron Density Topology (AIM)


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


4C1-Galactopyranose

Ethane-diol Synthon


Diols

(n,n+1)– 12ED, 23BD

(n,n+2)– 13BD, 25PD

(n,n+3)– 14BD, 25HD

(n,n+4)– 15PD

(n,n+5)– 16HD


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Electron Density (12EG)


Ethane-1,2-diol

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

Electron Density (13PG)


Propane-1,3-diol

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

Electron Density (14BD)


Butane-1,4-diol

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


BCP Electron Density and Laplacian

Diol rho LLLL2rho 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


Atomic Charge


Dipolar Polarisation

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Atomic Volume Distance versus Laplacian


Ethane-1,2-diol / Water Complexes


Effect of medium dielectric constant


Electron Density


12EG/H2OconfB

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

Electron Density


12EG/H2OconfC

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

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Diols for -O-HD.....OA -OA...HD-O- Interaction Energy


0123456789

Energykcal/mol

1,2-

diol

1,3-

diol

1,4-

diol

1,5-

diol

1,6-

diol

1:1

(HO

H)

1:1

(-O

H)

1:1

(bifu

rc)red: D(OH)

green: V(CP)blue: CBS-QB3


IR red-shift for -O-HD

1.8 2 2.2 2.4

0

100

200

300

1.8 2 2.2

0

100

200

300

red-

shift

(cm

-1)

H...O interaction distance (Å)


NMR downfield shift for -O-HD

1.8 2 2.2 2.4

0

1

2

3

4

5

1.8 2 2.2 2.4

0

1

2

3

4

5

HD...OA interaction distance

∆HPP

M

n = 17

n = 8

n = 3

n = 12


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

Hyd

roge

n µ(

Ω) -

dip

olar

pol

aris

atio

n

Force constant (N/m)

α,ω-Diols - NBO Analysis


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2-Haloethanols

F Cl Br

Glucopyranose 4C1 g+ / trans


Glucopyranose 1C4 g+


Van der Waals Radiiand

Interpenetrability


Van der Waals Radii

Interpenetration limits for hydrogenbonding 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)


All too high!!

VDW Radii


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

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VDW Radii - hydrogen bonding O...HO


calculate ρ(r) atdonor-acceptordistances based

which radius? 0.001 or 0.01 au?

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


Modified “VDW” Radii


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” RadiiAtom Bondi

PaulingRowland IP Clementi

RoettiKlein

(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


Cooperativityor

Non-additive Effects


Hydrogen Bond Cooperativity


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Energy per H-bond inkcal/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 andLaplacian of rho +30%


GaussView




the interaction between an electron-deficienthydrogen atom with a centre of relative electronexcess, e.g., electronegative atoms such as F, N, orO, or with a π-electron cloud

Morokuma decomposition: electrostatic (65%),polarisation (24%) and charge-transfer (11%) forwater dimer - Mó et al. [2000]

electrostatic / covalent resonance hydrid (Pauling) -Isaacs et al. [1999]


What is a Hydrogen Bond? In addition

a bond critical point (BCP) of (3,-1) topology with (ρ) andLaplacian of (ρ) in the correct range - also a ring criticalpoint (RCP) of (3,+1) topology for intramolecularhydrogen bonds

charge transfer from the acceptor lone pair (LP) electronsto 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 stretchfrequencies


Does Glucose show Cooperativity?


O-H σ* Occupanciesfor Donor-Acceptor Geometries


Unit O-HD O-HW OA-HW OA-H12eg_confB_TIP3 0.02655 0.00083 0.02109 0.0052812eg_confD_TIP3 0.02782 0.00086 0.02194 0.00705

Glucose_4C1_TIP3H2O (1) 0.03290 0.00158H2O (2) 0.03446 0.00143H2O (3) 0.03594 0.00143H2O (4) 0.03010 0.00144H2O (5) 0.04330 0.00104H2O (6) 0.04501 0.00129

O1-H1 0.06033 0.06033O2-H2 0.04644 0.04644O3-H3 0.04596 0.04596O4-H4 0.04589 0.04589O6-H6 0.02880 0.02880

Diol OA-H (acceptor) O-HD (donor)12eg_conB 0.00511 0.0092112eg_confD 0.00724 0.0111813pg_confA 0.00581 0.0153414bd_confA 0.00542 0.0292615pd_confA 0.00594 0.0218716hd_confA 0.00521 0.02045

Glucose 4C1 O1-H1 0.00736Glucose 4C1 O2-H2 0.00652Glucose 4C1 O3-H3 0.00712Glucose 4C1 O4-H4 0.00767Glucose 4C1 O6-H6 0.00908

Monomers Cooperative

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O-HD Bond Lengths and Cooperativity(Ångstroms: MPW1PW91/6-311+G(2d,p))


‘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 thedefinition 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


1 S. O. Jonsdottir, R. A. Klein, and K. Rasmussen (1996) “UNIQUAC interactionparameters for alkane / amine systems determined by Molecular Mechanics” FluidPhase Equilibrium 115:59-72.

2 S. O. Jonsdottir and R. A. Klein (1997) “UNIQUAC interaction parameters formolecules with -OH groups on adjacent carbon atoms in aqueous solution determinedby molecular mechanics - glycols, glycerol and glucose” Fluid Phase Equilibrium132:117-137.

3 S. O. Jonsdottir, W. J. Welsh, K. Rasmussen, and R. A. Klein (1999) “The critical roleof 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 17ONuclear Magnetic Resonance Spectroscopy. Interpretation of the Effect of DiolStructure on the 17O - Water Chemical Shift. Formation of Networks of WaterMolecules Stabilised by Weak C-H...O Interactions” Journal of Physical Chemistry A105(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 1:1Complex Formation with Water” Journal of Computational Chemistry 23(6):585-599.

6 R. A. Klein. (2002) “Electron Density Topological Analysis of Hydrogen Bonding inGlucopyranose and Hydrated Glucopyranose” Journal of the American ChemicalSociety 124(46), 13931-13937.

7 R. A. Klein. (2003) “Hydrogen Bonding in Diols and Binary Diol-Water SystemsInvestigated Using DFT Methods. II. Calculated Infrared OH-Stretch Frequencies, ForceConstants, and NMR Chemical Shifts Correlate with Hydrogen Bond Geometry andElectron Density Topology. A Reevaluation of Geometrical Criteria for HydrogenBonding” Journal of Computational Chemistry 24(9):1120-1131.

On-going Work

highly cooperative hydrogen bonding in largewater clusters (n ≤ 24)

applicability of continuum methods in highlycooperative systems

non-classical hydrogen bonding in clathrates


Acknowledgements Aberdeen

• Mark Zottola

Bonn• Ernst Bause• Victor Pacheco• Rudi Hartmann

Pisa• Jacopo Tomasi• Benedetta Mennucci

Copenhagen• Svava Jónsdóttir• Kjeld Rasmussen


what is a hydrogen bond? importance of hydrogen …hydrogen bonds charge transfer from the acceptor...

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