Advances in CHEMICAL PHYSICS · 2013-07-23 · ADVANCES IN CHEMICAL PHYSICS VOLUME 111 . EDITORIAL BOARD BRUCE J. BERNE, Department of Chemistry, ... Institute for Theoretical Atomic

Advances in CHEMICAL PHYSICS

Edited b j

I. PRIGOGINE

Center for Studies in Statistical Mechanics and Complex Systems The University of Texas

Austin. Texas and

International Solvay Institutes Universitt Libre de Bruxelles

Brussels, Belgium

and

STUART A. RICE

Department of Chemistry and

The James Franck Institute The University of Chicago

Chicago, Illinois

VOLUME 111

AN INTERSCIENCE ' PUBLICATION JOHN WILEY & SONS, INC.

NEW YORK CHICHESTER WEINHEIM BRISBANE SINGAPORE TORONTO

ADVANCES IN CHEMICAL PHYSICS

VOLUME 111

EDITORIAL BOARD

BRUCE J. BERNE, Department of Chemistry, Columbia University, New York, New York, U.S.A.

KURT BINDER, Institut fur Physik, Johannes Gutenberg-Universitat Mainz, Mainz, Germany

A. WELFORD CASTLEMAN, JR., Department of Chemistry, The Pennsylvania State University, University Park, Pennsylvania, U.S.A.

DAVID CHANDLER, Department of Chemistry, University of California, Berkeley, California, U.S.A.

M. S. CHILD, Department of Theoretical Chemistry, University of Oxford, Oxford, U.K.

WILLIAM T. COFFEY, Department of Microelectronics and Electrical Engineering, Trinity College, University of Dublin, Dublin, Ireland

F. FLEMING CRIM, Department of Chemistry, University of Wisconsin, Madison, Wisconsin, U.S.A.

ERNEST R. DAVIDSON. Department of Chemistry, Indiana University , Bloomington, Indiana, U.S.A.

GRAHAM R. FLEMING, Department of Chemistry, The University of Chicago, Chicago, Illinois, U.S.A.

KARL F. FREED, The James Franck Institute, The University of Chicago, Chicago, Illinois, U.S.A.

PIERRE GASPARD, Center for Nonlinear Phenomena and Complex Systems, Brussels, Belgium

ERIC J. HELLER, Institute for Theoretical Atomic and Molecular Physics, Harvard- Smithsonian Center for Astrophysics, Cambridge, Massachusetts, U.S.A.

ROBIN M. HOCHSTRASSER, Department of Chemistry, The University of Pennsylva- nia, Philadelphia, Pennsylvania, U.S.A.

R. KOSLOFF, The Fritz Haber Research Center for Molecular Dynamics and Depart- ment of Physical Chemistry, The Hebrew University of Jerusalem, Jerusalem, Israel

RUDOLPH A. MARCUS, Department of Chemistry, California Institute of Techno- logy, Pasadena, California, U.S.A.

G. NICOLIS, Center for Nonlinear Phenomena and Complex Systems, UniversitC Libre de Bruxelles, Brussels, Belgium

THOMAS P. RUSSELL, Department of Polymer Science, University of Massachusetts, Amherst, Massachusetts, U.S.A.

DONALD D. TRUHLAQ Department of Chemistry, University of Minnesota, Minnea- polis, Minnesota, U.S.A.

JOHN D. WEEKS, Institute for Physical Science and Technology and Department of Chemistry, University of Maryland, College Park, Maryland, U.S.A.

PETER G. WOLYNES, Department of Chemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois, U.S.A.

Advances in CHEMICAL PHYSICS

Edited b j

I. PRIGOGINE

Center for Studies in Statistical Mechanics and Complex Systems The University of Texas

Austin. Texas and

International Solvay Institutes Universitt Libre de Bruxelles

Brussels, Belgium

and

STUART A. RICE

Department of Chemistry and

The James Franck Institute The University of Chicago

Chicago, Illinois

VOLUME 111

AN INTERSCIENCE ' PUBLICATION JOHN WILEY & SONS, INC.

NEW YORK CHICHESTER WEINHEIM BRISBANE SINGAPORE TORONTO

This book is printed on acid-free paper.@

An Interscience" Publication

Copyright k 2000 by John Wiley & Sons. Inc All right5 reterbed

Published simultaneously in Canada.

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Library of Congress Catalog Number: 58-9935

ISBN 0-471-34990-9

1 0 9 8 7 6 5 4 3 2 1

CONTRIBUTORS TO VOLUME 111

AKIRA HAMADA, Department of Physics, Yamaguchi University, Yamaguchi, Japan

YUKIKAZU ITIKAWA, Institute of Space and Astronautical Science, Saga- mihara, Japan

MINEO KIMURA, Graduate School of Science and Engineering, Yamaguchi University, Ube, Japan and Institute for Molecular Science, Okazaki. Japan

DANIELA KOHEN, Department of Chemistry. University of California. Irvine. Irvine, CA 92697

ROBERT A. LIONBERGER, Department of Chemical Engineering. University of Michigan, Ann Arbor, MI 48109

J. ODDERSHEDE, Department of Chemistry, Odense University, DK-5230 Odense M, Denmark

J. F. OGILVIE, Center for Experimental and Constructive Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6 Canada

W. B. RUSSEL, Department of Chemical Engineering, Princeton University, Princeton, NJ 08544

STEPHAN P. A. SAUER 111, Department of Chemistry, University of Copen- hagen, DK-2100 Copenhagen 0, Denmark

OSAMU SUEOKA, Graduate School of Science and Engineering, Yamaguchi University, Ube, Japan

DAVID J. TANNOR Department of Chemical Physics, Weizmann Institute of Science, Rehovot, 76100 Israel

GEORG ZUNDEL, Institute of Physical Chemistry, University of Munich, D- 80333 Munich, Germany: Bruno-Walter-Strasse 2, A-5020 Salzburg, Austria

INTRODUCTION

Few of us can any longer keep up with the flood of scientific literature, even in specialized subfields. Any attempt to do more and be broadly educated with respect to a large domain of science has the appearance of tilting at windmills. Yet the synthesis of ideas drawn from different subjects into new, powerful, general concepts is as valuable as ever, and the desire to remain educated persists in all scientists. This series. Advances in Chemical Physics, is devoted to helping the reader obtain general information about a wide variety of topics in chemical physics, a field that we interpret very broadly. Our intent is to have experts present comprehensive analyses of subjects of interest and to encourage the expression of individual points of view. We hope that this approach to the presentation of an overview of a subject will both stimulate new research and serve as a personalized learning text for beginners in a field.

1. PRICOGINE STUART A. RICE

vii

CONTENTS

HYDROGEN BONDS WITH LARGE PROTON POLARIZABILITY AND

PROTON TRANSFER PROCESSES IN ELECTROCHEMISTRY AND BIOLOGY 1

By Georg Zundel

PHASE SPACE APPROACH TO DISSIPATIVE MOLECULAR DYNAMICS

By Daniela Kohen and David J. Tannor

MICROSCOPIC THEORIES OF THE RHEOLOGY OF STABLE COLLOIDAL DISPERSIONS

By Robert A. Lionberger and W B. Riissel

THE ROTATIONAL g FACTOR OF DIATOMIC MOLECULES IN

STATE ‘c+ OR O +

By J. E Ogilvie, J. Oddershede, and Stephan P. A. Sauer III

A COMPARATIVE STUDY OF ELECTRON- AND

POSITRON-POLYATOMIC MOLECULE SCATTERING

By Mineo Kimura, Osatnu Sueoka, Akira Hamada, and Yukikazu Itikawa

AUTHOR INDEX

SUBJECT INDEX

219

399

475

537

623

639

1x

HYDROGEN BONDS WITH LARGE PROTON POLARIZABILITY AND PROTON

TRANSFER PROCESSES IN ELECTROCHEMISTRY AND BIOLOGY

GEORG ZUNDEL

Institute of Physical Chemistn, Universih of Munich, 0-80333 Miinich, Germany

CONTENTS

I. The Proton Polarizability of Homoconjugated Hydrogen Bonds A.

B. C. D. E. Intramolecular Polarizable Hydrogen Bonds F. G. Heteroconjugated Hydrogen Bonds With Large Proton Polarizabilities A. B. C. D.

E. F. G. The Energy Surfaces H. Intramolecular Hydrogen Bonds Interaction Effects of Easily Polarizable Hydrogen Bonds With Their Environments- Their Behavior in Crystals A. B.

A Continuous Absorption in the Infrared Spectra and the Discovery of the Proton Polarizability Various Homoconjugated Hydrogen Bonds Showing a Large Proton Polarizability Deuteron Bonds and Deuteron Polarizabilities Negatively Charged Hydrogen Bonds With a Large Proton Polarizability

The pK, Dependence of the Proton Polarizability Rayleigh Wings-A Second Proof for the Large Proton Polarizability

The Carboxylic Acid-N-base Family of Systems ApK;" Values With Various Families of Systems Determination of the Molar Polarizability Nonspecific and Specific Interactions of Polarizable Hydrogen Bonds With Their Environments The Specific Interaction With Water Molecules In K ~ T and the Thermodynamic Quantities AHo and ASo

11.

Ill.

The Interaction of the Polarizable Hydrogen Bonds With Polaritons The Interaction of the Polarizable Hydrogen Bonds With the Phonons of Their Environment

Advances in Chemical Phjsics, Vo[urne 11 1, Edited by I. Prigogine and Stuart A. Rice ISBN 0-471-34990-9. 2000 John Wiley & Sons, Inc.

1

2 GEORG ZUNDEL

C. The Proton Dispersion Forces D. E. Hydrogen-Bonded Chains With a Large Proton Polarizability due to Collective Proton Motion-Pathways for Protons in Biological Membranes A. Poly-a-Aminoacid-Dihydrogenphosphate Systems B. Intramolecular Hydrogen-Bonded Chains C. I).

E. F. L ic , N a + , K', and Be2+ Bonds-IR Continua and Cation Polarizabilities of These Bonds A. Homoconjugated B ' M , , , B + B , . , M + B Bonds B. H e t e r o c o n j u g a t e d . 4 - M f . . ~ B = A - . . . M - B Bonds C. Wavenumber Regions with H', D'. Lii , and Na' Bonds D. Cation Polarizabilities due to Collective Cation Motion

1. Crown Ethers Electrochemistry: Hydrogen Bonds With a Large Proton Polarizability and the Molecular Understanding of Processes in Acid and Base Solutions A. The Degree of Dissociation B. Nature of the Hydrate Structures C. Anomalous Proton Conductivity D. Acids With pK, Values > 0 E. Phosphorous-Containing Acids and Arsenic Acids F. H30F With Strong Bases Large Proton Polarizability With Families of Systems in Various pK, Regions-MIR, FIR, and NMR Results A. B. C. I).

E. Easily Polarizable Hydrogen Bonds in Proteins-Studies of Model Systems A. Homoconjugated Hydrogen Bonds B. Heteroconjugated Hydrogen Bonds C. Influence by Hydration D. E. F, Phosphates in Biological Systems Significance of Hydrogen Bonds With a Large Proton Polarizability in the Catalytic Mechanisms of Enzymes A. Proteinases

Hydrogen Bonds With Large Proton Polarizability in Crystals Reason for the Presence of IR Continua in Crystals

IV.

Insertion of Water Molecules in Intramolecular Hydrogen-Bonded Chains Proton Pathways in Biological Systems The L550 Intermediate of Bacteriorhodopsin The Fo Subunit of ATP Synthases

V.

VI.

VII.

The Carboxylic Acid + Trimethylamine N-Oxide (TMAO) Systems The R-Phenol + Trimethylamine N-Oxide (TMAO) Family The Dimethanephosphinic Acid (DMP) + N-Base Systems The Methanesulfonic Acid + Sulfoxide, Phosphinoxide, Arsinoxide Family The Methanesulfonic Acid + Pyridine N-Oxide Family

VIII.

Proton Transfer Equilibria and Conformation Poly-a-Amino Acid + Dihydrogenphosphate Systems

IX.

1. Serine Proteinases 2. Aspartate Proteinases

B. Alcohol Dehydrogenases C. Maltodextrinphosphorylase

References

HYDROGEN BONDS WITH LARGE PROTON POLARIZABILITY 3

I. THE PROTON POLARIZABILITY OF HOMOCONJUGATED HYDROGEN BONDS

A. A Continuous Absorption in the Infrared Spectra and the Discovery of the Proton Polarizability

About 40 years ago the author studied membranes of the strongly acidic polyelectrolyte polystyrenesulfonic acid by means of infrared spectroscopy [1,2]. The fixed ions of this polymeric acid are -S020H groups. After dissociation occurs, -SOT ions are present.

Figure 1 shows the IR spectrum of this acid that was observed. An intense continuous absorption is found to occur if this polymeric acid is hydrated, and hence, the -S020H groups dissociated [2-41.

dissociation -SO?OH + 2 H 2 0 - -SO, + HsO:

where

V,,(SOZ) at 1350cm-'

v(S-0) at 907cm-'

va5(S0,) doublet at about 1200cmp'

r s ( S O j ) at 1040cm-'

U , ( S O Z ) at 1170cm-' (1)

In the case of the sodium salt of this acid, no continuum is observed. Figure 2 shows that with the removal of the proton from the sulfonic acid

group, bands at 1350 cm - ', 1 170 cm - ', and at 907 cm - vanish. The bands at 1350 and 1170cm- ' are the asymmetrical and symmetrical

stretching vibration bands of (SO,) of the S020H groups. The r (S-0) stretching vibration of the S-0 single bond at 907 cm - is the most suitable criterion for determining the degree of dissociation.

-- 3800 3400 3000 2600 2200 1800 1400 1000 650

Wave number cm-'

FIGURE 1. IR spectra for a polystyrenesulfonic acid membrane, thickness 5 pm (solid line) and, for comparison, Na- salt of this membrane (doshed line). From Ref. [3].

4 GEORG ZUNDEL

Wave number cm-i

FIGURE 2. Polystyrenesulfonic acid, H 2 0 hydrated, measured after three days at 1.98%, 4.3370, 6.1170, 7.5%, and 8.3% relative atmospheric humidity. Curves 6-1 1, incompletely dried; 12, thoroughly dried membrane. From Ref. [Z].

The -SO, ions cause an asymmetrical stretching vibration at 1200 cm- '. This band is observed as a doublet, since the degeneracy of v,,(SO;) is removed by asymmetrical environments. The symmetrical stretching vibration v,(SO;) is found at 1040cm- '. These bands arise if the protons are removed from the anions. Thus, the degree of dissociation can be determined from these bands.

Figure 3 shows the intensity of this continuum as a function of the degree of dissociation for various polystyrenesulfonic acid membranes. The intensity increases in proportion to the degree of dissociation.

Figure 4 shows the number of water molecules Z present per dissociated S020H group. The extrapolation of these curves demonstrates that the dissociation may occur if two water molecules per dissociated proton are present. The intensity of the continuum increases in proportion to the degree of dissociation.

Both results, taken together, demonstrate that the excess proton with two water molecules, i.e., H501, is responsible for this IR continuum [2,4]. In this group, a so-called homoconjugated hydrogen bond is present. The homoconjugated bonds are bonds formed among the same types of groups, in this case water molecules. These hydrogen bonds are structurally symmetrical. Thus, when they are considered in isolation from their environments, symmetrical proton potentials are present in the case of these bonds.

Figure 5 shows the IR continuum observed in aqueous HCI solutions, as a function of the acid concentration. We observed such IR continua for all


5 3 c c .- - 8 a, 0 S m e a a a

FIGURE 3.

0.2 0.4 0.6 0.8 1 .o

u degree of dissociation

Absorbance of the continuum shown in FIGURE 1 as a function of (1. the degree of dissociation. From Ref. [2]

12

10

8

6

4

2

1 1 1 1 1 1 1 1 1

0.2 0.4 0.6 0.8 1 .o

a degree of dissociation

FIGURE 4. Number, A, of water molecules available to the excess proton as a function of a, the degree of dissociation. From Ref. [ 2 ] .

6 GEORG ZUNDEL

5: a

4000 3(

I J

I , : ’,

2000 1500 1000 500 200

Wave number (cm-1)

FIGURE 5. IR spectra for aqueous solutions of HC1 at 28 “C. Layer thickness, 13.6 pm. In the order of sequence of increasing absorbance of the background, solutions shown are 0.0, 1.21, 2.43, 4.85, 7.28. 8.49, and 10.95moleHC1dm~3.

aqueous solutions of strong acids. The intensity of these continua increases in proportion to the acid concentration. This is true for concentrations that are not too high.

Figure 6 shows the H20 scissor vibration of a highly concentrated aqueous solution of a strong acid. If two or fewer than two water molecules

0.2

a, 0 S (II e 5: 0.4

< a

0.7

1 .o

2: l q

J- \,

i i

\

\ \

I

/*‘

/ /

f

I I

1900 1800 1700 1600 1500

-Wave number cm-I

FIGURE 6. The H 2 0 scissor vibration of aqueous solutions of a strong acid. Ratio of moles of water per mole acid: 2: 1 (solid line); 3: 1 (dotted line); 5 : 1, (dashed line). Pure water (dashed-dotted line), for comparison. From Ref. [ 5 ] .


0.0

8 0.2 c a a In 5 0.4

9 0.7 1 .o 12

4000 3500 3000 2500 2000 1500 1000 650

Wave number cm-’

FIGURE 7. IR spectra of poly5tyrenesulfonic acid. hydrated at 3 3 9 relative air humidity, at 292 K (dotted line), and 85 K (solid line). From Ref. [6].

per proton are present, only one H 2 0 scissor vibration is observed [ 5 ] . Hence, the excess proton influences both water molecules of H50; to the same extent. Thus, the excess proton fluctuates in H50; with a frequency of about l o 1 Hz.

Figure 7 shows the IR spectrum of a hydrated polystyrenesulfonic acid membrane. The spectrum drawn with the dotted line is the one of the membrane at 292 K, and that drawn with the solid line is that of the sample at 85 K. Thus, the continuum of these homoconjugated hydrogen bonds is almost independent of temperature [6].

It seemed highly probable that this IR continuum has something to do with this very fast proton fluctuation. Therefore, we solved the Schrodinger equation for the proton motion within a double minimum potential (Fig. 8). Furthermore, we added to this Schrodinger equation a term - p F , the dipole moment of the hydrogen bond times electrical field strength. This term takes into account the local electrical fields present in solutions [7].

The wave function of the proton ground state in such a potential is symmetrical, while that of the first excited state antisymmetrical, as illustrated in Figure 8. We then built a basis set by adding or subtracting both wave functions (Fig. 9).

If c & are the coefficients of the wave functions GO+ and yo-, the coefficients of v,. and 211 are

8 GEORG ZUNDEL

X

X I FIGURE 8. Double minimum proton potential and wave functions Q0+ and Q o - of the

two lowest states (see text). From Ref. [7].

FIGURE 9. The wave functions Q r and Q,. From Ref. [7].

The weights of the proton limiting structures, G, and G I are

G, = af

G I = a , 2 (4)

G I gives the weight of the structure O + H . . 0, i.e., when the proton is on the left, and G, gives the weight when the proton is on the right-hand side, i.e., the weight of the structure 0 . . H'O. In the Schrodinger equation, we introduced the term - p F . Hence, these weights were derived as a function of the electrical field strength in hydrogen bond direction.

In this way we obtained the important result [7] that hydrogen bonds having a double minimum proton potential show polarizabilities as a result of shifts of the proton within these bonds. The unexpected fact that these so- called proton polarizabilities are about two orders of magnitude higher than the usual polarizabilities arising by distortion of electron systems was considered highly unusual and noteworthy.


The fact of high proton polarizabilities does, however, become understandable in the light of the following consideration (see Fig. 8). For a double minimum proton potential, the ground state is symmetrical, while the first excited state is antisymmetrical. These two states are very close. Thus, even a small electrical field can admix the first excited state to the ground state and in this way induce an asymmetrical charge distribution, i.e., result in polarization. The shift of the energy levels Eo+ by the field F is

Here, uo is the tunneling frequency and p is the maximum induced dipole of the hydrogen bond. The lowest level is lowered and the first excited level is raised, as illustrated in Figure 10.

To clarify whether this is really the case, we performed ab initio (SCF) studies of H 5 0 1 [8,9]. The calculations give the 0-0 distance in the gas phase. This distance is much increased because of the environment, as is

I I

P 5 10

F [ in 10 2 1 -

FIGURE 10. The dependence of the shift of the energy levels in a hydrogen bond with a tunneling proton on the electrical field F (tunneling approximation, only the two lowest levels are considered). From Ref. [ 7 ] .

10 GEORG ZUNDEL

known from various experimental results [ 10- 121. Therefore we artificially increased this distance to 2.55-2.65 A, with these calculations. We obtained the energy surface and the dipole moment surface p. Using these surfaces, we solved the Schrodinger equation for the proton motion, again adding the term - p F (dipole moment surface p times electrical field strength) to take into account the influence of the local electrical fields F in the solutions.

From these calculations, proton polarizabilities about two orders of magnitude higher than the usual polarizabilities due to the distortion of electron systems were obtained [8,9].

Figure 11 shows these proton polarizabilities as a function of the electrical field strength and of the temperature. These polarizabilities decrease significantly, however, if the hydrogen bonds are polarized. The upper scale is the difference between the two minima, i.e., a measure of the asymmetry induced by the external electrical field.

Figure 12 shows the hyperpolarizabilities (,3). These quantities are also very high [8]. From the same calculations, we obtained the line spectra as a function of the electrical field strength [9]. They are shown for an 0-0 distance of 2.6A in Figure 13. All transitions are significantly shifted as a function of the electrical field strength: some transitions vanish, while some

AV[crn-’]

367 713 1789 3569 - 0

N 0-0 = 2.6A I

70

8 60

50

40

30

20

10

Y

1 2 3 4 5

FIGURE 11. The proton polarizability Q of the hydrogen bond in the H50: group at various temperatures in degrees Kelvin, plotted against the field strength F and against AV, the energy difference between the two minima: also shown is the tunneling approximation in the case of 300 K (dotred l ine). From Ref. [9].


4 6]/42000 a

6

4

2

1 2 3 4 5

FIGURE 12. The proton hyperpolarizability 3 of the H-bond in the H50; grouping at various temperatures in Kelvin degrees, plotted against the field strength F and against AV. the energy difference between the two minima of the potential. From Ref. [8].

others newly arise. The interaction effect that we consider is an induced dipole interaction. It is due to this induced dipole interaction that the transitions largely shift.

Using these calculated transition moments, and assuming a reasonable electrical field distribution and a hydrogen bond length distribution, we calculated the IR continua. In Figure 14(A) the IR continuum calculated in this way is compared with the experimental IR continuum [Fig. 14(B)]. The extent of the agreement is highly satisfactory [13].

We then performed the following experiment [ 141. We added neutral salts to an HC1 solution in which the HC1 concentration was kept constant. Figure 15 shows the intensity of the continuum as a function of the neutral salt concentration. Figure 16 shows again that the intensity of the IR continuum decreases if LiCl is added. Thus, when Li + ions are present in the solution, the local electrical fields at the hydrogen bonds with a large proton polarizability are stronger than those found in the pure acid solutions. The opposite is true when alkylammonium ions are present.

These results demonstrate yet again that one important reason for the appearance of the IR continua is the induced dipole interaction between the hydrogen bonds having a large proton polarizability and the local electrical fields in the solutions. There are also other strong effects of the interaction of hydrogen bonds having a large proton polarizability with their environment. These are discussed in Section 111.

12

?

GEORG ZUNDEL

100- l i j

50 -

I 0-0 = 2.6A

0 0.0 V/cm "

>L

0

li j

50 51.4 lo6 V/cm !

25.7 lo6 V/cm

(00-03,OO-10) 00-20 O 00-01

10.3 lo6 V/cm

51.4 lo6 V/cm


A - -

1

- J)

Wave number cm-l

FIGURE 14. Infrared continuous absorption of HsO;. Shown are (A) calculated continuum, a mean field strength F = 5 x lo6 V/cm. with molarity x layer thickness (in pm) = 100, and also (B) that of a 13 M aqueous HCI solution at 21 'C, having a layer thickness of 8 p m (solid line), along with HzO shown for comparison (dashed line). From Ref. [ 131.

I I I

It is a fact of great importance that the presence of hydrogen bonds having a large proton polarizability is always indicated by IR continua.

B. Various Homoconjugated Hydrogen Bonds Showing a Large Proton Polarizability

Our analytical treatment of the B + H . . . B + B . . Ht B bonds was not limited to H50;. Thus, all homoconjugated bonds of this type should show a large proton polarizability.

In Figure 17, the spectra of solutions of acid in alcohol are given [15]. With increasing acid concentration, an intense IR continuum also arises. It is

FIGURE 13. Relative absorption intensities of the transitions of H50; (0-0 distance 2.6A) as a function of the electrical field strength F in the hydrogen bond direction. Temperatures: 0, 0; I, 100; A, 200; -. 300; x . 400K. The length of the lines is equal to the relative absorption intensities, for negative electrical fields l h , ( - F ) = I , , (tF). From Ref. (91.

14 GEORG ZUNDEL

Wave number cm-I

0.00 B

- - - - -

- co I I I 4000 3000 2000 1000 0

Wave number cm-I

FIGURE 15. Dependence of the continuum on local electrical fields. (A) IR spectra of 5 M aqueous HC1 solutions containing 0 (solid line), 2 (dashed-dotted line), 6 (dotted line). and 10MLiCl (dashed line), having a thickness of 13.6 pm, at a temperature of 25 'C, with the spectrum of pure H 2 0 shown for comparison. (B) calculated continua for 2: = 3.5 x lo6 V/cm (solid line), 5 x 106V/cm, and 8.0 x 106V/cm (dashed line), with molarity x layer thickness (in pm) = 100. From Ref. [14].

caused by the 0 H . . ' 0 + 0 . . . H - 0 bonds formed by protonated alcohol with alcohol molecules and proves that these bonds are easily polarizable as well.

Figure 18 shows the intensity of the IR continuum of an aqueous imidazole solution as a function of the degree of protonation [16]. In the range of 0-50% protonation, hydrogen bonds having a large proton polarizability are formed between imidazolium and imidazole. At protonation degrees above 50% the continuum again decreases and almost completely vanishes at 100% protonation. The reason for the latter change is that at 100% protonation all imidazole molecules are protonated, and no free imidazole molecules are available as acceptors. Therefore, no N + H . . . N + N . . . H + N bonds can be formed. After 100% degree of protonation has been achieved, the intensity of the continuum again strongly increases, since the excess protons now form H502 with water molecules.


I N HCI

2 4 6 8 1 0

Mo l i l

FIGURE 16. Absorbance of the continuum caused by H50; as function of the concentration of added neutral salt. From Ref. [14].

When a strong acid is added to dimethylsulfoxide [15], an intense IR continuum is found, too, as shown in Figure 19. Here, the S O ' H . . . 0s + SO. .HfOS bonds are strong. easily polarizable hydrogen bonds.

If N-methylimidazole [ 161 is protonated as shown in Figure 20, an intense IR continuum arises, indicating that the N'H . . . N + N ' . H N bonds

Wave number, cm-i

FIGURE 17. The IR spectra of nonaqueous systems (completely water-free) of p - toluene sulfonic acid solutions in CH30H at 30°C having a layer thicknes5 of IOpm. Spectrum 1. a concentration of 1.96 mole dm-3; spectra 1 to 8 decreasing concentration. while spectrum 9 is pure alcohol. From Ref. [ l j ] .

16 GEORG ZUNDEL

0.3 I

0 20 40 60 8010012(

Protonation [“h]

FIGURE 18. Absorbance of the IR continuum of an aqueous imidazole solution as a function of the protonation. From Ref. [16].

formed between the respective N-methylimidazole molecules also show a very large proton polarizability.

The results obtained for the N-methylimidazole and dimethylsulfoxide systems are particularly interesting. They show that for the appearance of the continua to occur, the groups having the polarizable hydrogen bonds must not be cross-linked with their environment via further hydrogen bonds.

Wave number, cm-’

FIGURE 19. The IR spectra of nonaqueous systems (completely water-free) of p - toluenesulfonic acid solutions in dimethylsulfoxide (DMSO) at 30 ‘C, having a layer thickness of 10 pm. Spectrum I shows a saturated solution (3.29 mole dm ’), spectra 1 to 8 decreasing concentration, and spectrum 9 pure DMSO. From Ref. [15].


8 s 0.2

FIGURE 20. Water-free N-methylimidazole as a function of the degree of the Q protonation with HCI. From Ref. [16].

..a \-/-->, ..'".. ' /*'*,-,-'-' ';., :' ',. , -..,

. - -. \, . , ; : I

;.: - .' I

.,,! ,;....... -... ., ' ._ ._. . . - '. '. '.

' 5 , , .' I .' I

C. Deuteron Bonds and Deuteron Polarizabilities

In turning our attention now to deuteron bonds [17], we compare the IR continuum caused by H50T with the IR continuum caused by D50T. The spectrum drawn with the solid line in Figure 21 is the spectrum of an HC1 solution in H20, while the one drawn with the dashed line is that of a DCI solution in DzO. The continuum caused by H50; begins at the t.(OH) vibration, and the D50; IR continuum at the zl(0D) vibration. Furthermore, the intensity of the D50T IR continuum is only about half of that caused by H50Z. Thus, the deuteron polarizability of deuteron bonds is about half the proton polarizability of hydrogen bonds.

This result is in very good agreement with the theoretically obtained IR continua, as shown in Figure 22. In the case of D50;, the IR continuum

Wave number 0 cm-' FIGURE 21. The IR spectra of various solutions having a layer thickness 12.5pm. at a temperature of 293 K. 3.4mole dm- ' HCI in H 2 0 ( d i d l ine). 3.6moledm-' DCI in DzO (dashed l ine) , pure HzO (dotted lir7e). and pure DzO (dushed-doffed line). From Ref. [17].

GEORG ZUNDEL 18

0

a, 0

2 0.25 e 5: 0.5 2 0.75

1 .o 1.5

53

Wavenumber v cm-l

FIGURE 22. Calculated IR continua for H50: (solid line) and D50; (dashed line). From Ref. [17].

begins at smaller wavenumbers and is less intense than for H502f. The latter difference is immediately understandable, since the amplitude of D is much less than that of H' .

Figure 23 shows acetonitrile solutions of semiprotonated and semideut- erated quinuclidine [18]. In the semiprotonated system, an intense IR continuum is observed, beginning at about 3000cm-' and extending to smaller wavenumbers. This result shows that the N t H . . . N + N. . . H + N bonds are easily polarizable. For the deuteron bonds, the IR continua begin at smaller wavenumbers and are less intense. Thus, the N+D . . . N + N. . . D'N bonds show a much lesser amount of deuteron polarizability.

In sum we can state that all positively charged homoconjugated hydrogen and deuteron bonds show a large proton or deuteron polarizability, respec- tively. The deuteron polarizability makes up about half of the proton

0.0

0,

C a a

0 0.2

$ 0.4

a 0.7 1 .o 1.5

Q

53

4000 3500 3000 2500 2000 1800 1600 1400 1200 1000 800 600

Wave number cm-l

FIGURE 23. IR spectra of acetonitrile solutions of quinuclidine: pure base, (dusked line), (NH ' ' N) complex (solid line), and (ND . ' N) complex (dotted line). From Ref. [181.

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Advances in CHEMICAL PHYSICS · 2013-07-23 · ADVANCES IN CHEMICAL PHYSICS VOLUME 111 . EDITORIAL BOARD BRUCE J. BERNE, Department of Chemistry, ... Institute for Theoretical Atomic