Electrochemical proton relay at the single-molecule level

Electrochemistry Communications 11 (2009) 1170–1173

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Electrochemical proton relay at the single-molecule level A.M. Kuznetsov a, I.G. Medvedev a, J. Ulstrup b,* a b

A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russ. Acad. Sci., Leninskii prospect 31, 119991 Moscow, Russia DTU Chemistry and NanoDTU, Technical University of Denmark, DK-2800 Kgs., Lyngby, Denmark

a r t i c l e

i n f o

Article history: Received 13 March 2009 Received in revised form 25 March 2009 Accepted 26 March 2009 Available online 2 April 2009 Keywords: Proton transfer Hydrogen atom transfer Single-molecule processes Concerted electron/proton transfer Scanning tunneling microscopy

a b s t r a c t A scheme for the experimental study of single-proton transfer events, based on proton-coupled two-electron transfer between a proton donor and a proton acceptor molecule confined in the tunneling gap between two metal leads in electrolyte solution is suggested. Expressions for the electric current are derived and compared with formalism for electron tunneling through redox molecules. The scheme allows studying the kinetics of proton and hydrogen atom transfer as well as kinetic isotope effects at the single-molecule level under electrochemical potential control. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Recent experimental and theoretical efforts have opened new approaches to interfacial molecular electron transfer (ET) at levels even of the single-molecule [1,2]. Local environments have been both electrochemical [1,2,4] and non-electrochemical [3,4] pure and modified metallic surfaces, particularly Au(111)- and Pt(111)-surfaces. Three-electrode systems have disclosed tunneling spectroscopic features, and new tunneling spectroscopic concepts and formalism have been explored in considerable detail with notable experimental support [1,2]. Field-induced proton transfer (PT) reactions were suggested early as a basis for single-molecule information storage elements [5], with focus on asymmetric double-PT molecular systems. Double-PT processes have been in later experimental [6] and theoretical focus [7] but not in the context of electrochemical singlemolecule functional elements. PT and H-atom transfer in solution are elementary processes in a wealth of chemical and biological processes and have been experimental and theoretical targets for decades [8–10]. The first quantum mechanical theory of PT processes to include strong interaction with polar solvent dynamics was introduced in the late 1960s [11,12] and further developed in many reports [13–24]. Experimental studies have broadly supported the theoretical expectations [25]. Proton-coupled ET processes have also come to attract attention over the last decade [26–32]. A detailed analysis was offered in [33,34]. Two main types of transitions can be distinguished, i.e., concerted and step-wise * Corresponding author. Tel.: +45 45252359; fax: +45 45883136. E-mail address: [email protected] (J. Ulstrup). 1388-2481/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.elecom.2009.03.040

ET/PT [33,34] of which we presently address only the former. Concerted ET/PT rests on ‘‘synchronous” transition of the electron and proton in a single elementary act, i.e., essentially H-atom transfer (see, however, below). In this sense it does not differ formally from PT reactions and may be addressed using theory for the latter [11,12,14–16]. Unlike ET processes, for which studies of singlemolecule ET events are available, PT kinetics has so far been restricted to ensemble averages over a large number of reaction events. As for ET, this conceals, however, details of the microscopic mechanism. We propose here a simple theoretical formalism and an experimental scheme for a first step towards addressing single-molecule PT processes to the same level as current investigations of singlemolecule ET processes based on a concerted ET/PT mechanism. ET and PT processes display close analogies, particularly the quantum mechanical (tunneling) nature of the transferring particle and the strong electron- or proton-environmental coupling. Differences are low-lying (but still quantum mechanical) excited vibrational states of the proton/H-atom and the much greater importance of gating in PT/H-atom transfer. The latter is caused by the much shorter range of PT/H-atom transfer than of ET. The formalism below offers a first step towards incorporation of these PT/H-atom transfer features into a scheme for accessing PT/H-atom transfer processes at the single-molecule level. 2. A scheme for operation by concerted ET/PT The scheme representing e.g., in situ STM is shown in Fig. 1. A molecule A (proton or H-atom acceptor) is attached to a metal electrode ML (STM substrate). The STM tip serves as the second

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tively. The superscripts denote the direction of PT (from D to A, DA, or from A to D, AD). The steady-state electric current for the kinetic scheme is

V

DA AD

e

H+

jconct: ¼ e e

A

D H

MR

DA

metal electrode MR with a different molecule D (proton or H-atom donor) attached. The proton may be bound to either of the molecules, forming the molecular states AH and DH. The tunnel contact is immersed in electrolyte solution. The bias voltage eV is defined as the difference between the electrochemical potentials of the left and right electrodes. Two kinetic processes can take place in the complex ML-A-H-DMR in the concerted ET/PT mechanism (subscripts denote left and right electrodes)

ML ðeÞ-A þ H-D-MR $ ML -A-H þ D-MR ðeÞ

ð1Þ

ML -A-H þ D-MR $ ML -A þ H-D-MR

ð2Þ

Reaction (1) is the electrochemical process that involves synchronous transfer of the proton between the molecules A and D and two-electrons between the left electrode and molecule A and the right electrode and molecule D. The overall process is thus viewed as concerted proton-coupled two-ET. The second process is purely chemical hydrogen atom transfer between the molecules. It is also assumed that, due to the large electrostatic potential created by proton, the highest occupied electron valence level of H–D and its lowest unoccupied level lie well below and well above the Fermi level of the right electrode so that two-step electron tunnelAD ing [1,2] is suppressed. The rate of reaction (2), kH is practically independent of the electrochemical potentials and should be exoDA AD thermic (i.e., kH  kH ) for the system to operate at positive V. DA The rate of the forward reaction (1) kp , however, increases with increasing bias voltage whereas the rate of the reverse reaction AD kp decreases. The transfer of hydrogen from D to A is thus by PT while H-atom transfer dominates the reverse transition. The system operational mode at positive bias voltage is that the first step is PT (H+) from D to A with simultaneous transfer of twoelectrons (from D to the right electrode and from the left electrode to A). The second step that closes the cycle is H-atom transfer from A to D. One electron thus passes through the electrochemical contact in each cycle and electric current flows under steady-state conditions. Ideally the system allows studying the potential dependence of the interfacial rate constants and the distance dependence of the PT reaction (by varying the distance between tip and substrate) as well as kinetic isotope effects of the processes. 3. Electric current and rate constants for concerted ET/PT

AD

kp

AD

ð4Þ

DA

  F DH  F AH kB T   F AH þ eFR  F DH  eFL DA ¼ kp exp kB T AD

where e is the absolute value of the electronic charge, and PDH and PAH the probabilities to find the proton in molecule D and A, respec-

ð6Þ

jconct:

h  i DA AD kp kH 1  exp  keV BT  i ¼ e DA h AD þ kH ½1 þ K DA  kp 1 þ K1DA exp  keV BT

ð7Þ

where the equilibrium constant KDA (<<1) is defined as DA

K DA ¼

kH

ð8Þ

AD

kH

DA

Eqs. (7) and (8) show that if, at small V the rate constant kp is small AD compared to kH the dependence of the current on the potential is determined by the former. DA

jconct:  ekp

At large V when ter, i.e.

ð9Þ DA kp



AD kH

the current is determined by the lat-

AD

jconct:  ekH

ð10Þ

In principle this scheme allows studying the rates of both proton and H-atom transfer. The detailed expressions for the rate constants depend on the microscopic mechanism of the PT or H-atom transfer [14–16]. Presently we restrict ourselves to the totally nonadiabatic limit [11,12] and strong interaction of the proton with the surrounding medium. In this limit the H-atom transfer rate constant, Eq. (2) can be represented in the form [11,12] i

AD

kH ¼

i

  xeff 1 X H EmkBET 0 Z j e exp F amn =kB T 2p H m;n mn

ð11Þ

where xeff is the effective frequency of a (set of) vibrational mode(s) to which the hydrogen atom is coupled. jHmn and F amn are the transmission coefficient and activation Gibbs free energy for H-atom transfer between the initial and final H-atom vibrational states m and n, Z H the vibrational partition function of these states in the initial electronic state and Eim the energy of the mth vibrational state. The rate constant of concerted ET/PT is more complicated

kp ¼ ð3Þ

ð5Þ

where kB is Boltzmann’s constant and T the temperature, FAH and FDH the Gibbs free energies of the reaction complex when the proton is located on molecule A and D respectively, and eFL and eFR the Fermi levels of the left and right electrode. Since eV = eFLeFR, we obtain for the current

DA

A general equation for the steady-state electric current is

jconct:

AD

kH ¼ kH exp

Fig. 1. A scheme of concerted single-proton relay. The first step is proton-coupled two-electron transfer. The second step is H-atom transfer in the opposite direction (dashed line).

  DA AD ¼ e PDH kp  PAH kp

DA

kp þ kH þ kp þ kH

where kH with appropriate superscripts are the rate constants for Hatom transfer between the molecules A and D. The rate constants for the forward and reverse transitions are related by

H+

ML

AD DA

kp kH  kp kH

Z

deL deR fL ðeL Þ½1  fL ðeR ÞqL ðeL ÞqR ðeR ÞW Hþ ðeL ; eR Þ

ð12Þ

where fM and qM (M = L,R) are the Fermi functions and densities of electron states in the electrodes at the electronic energy level eM. W Hþ is the transition probability per unit time between a given pair

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of electronic energy levels (eL, eR) and has a form similar to Eq. (11) [11,12]

  þ xeff 1 X Hþ EmkBET 0 Z Hþ jmn e exp F Hmn ðeL ; eR Þ=kB T 2p m;n i

W Hþ ðeL ; eR Þ ¼

i

ð13Þ

All the quantities have the same meaning as in Eq. (11) but now refer to electron-coupled PT. The transmission coefficients for both steps are formally similar [11,12,14–16]

jmn ðRÞ ¼

 2 2p ðEr kB TÞ1=2 hui jV int juf i2 vim jvfn hx

ð14Þ

and involve the environmental reorganization Gibbs free energy Er, the squared electronic coupling factor and the overlap integral of the proton wave functions (the last two factors, respectively). The activation Gibbs free energy depends on the electric potential [35] þ

F Hmn ¼ ½Er  DF 0 þ eL  eFL  eR þ eFR þ Efn  Ef0  Eim þ Ei0 2 =4Er ð15Þ In the spinless model [35]

DF 0 ¼ F DH  F AH þ eV

ð16Þ

It is noted that unlike redox-mediated electron tunneling [36] the current is independent of the overpotential, Eqs. (15) and (16). This is because the driving force in Eq. (1) is essentially the electric field in the tunneling gap and the character of Eq. (1) as H-atom transfer between the neutral molecules DH and AH. The proton overlap integral is averaged over the intramolecular vibrations [14,15] but still depends strongly on the distance between the donor and acceptor molecules. Eqs. (7), (11)–(16) describe the charge transfer kinetics in the contact represented by Fig. 1. We note that when the proton vibrations are quantum mechanically frozen only the ground initial and final proton vibrational states (m = n = 0) contribute. The pre-exponential factors in both steps are, further likely to differ mainly by the electronic factor since electron exchange between the molecules and the electrodes is only involved in the PT step. The current is proportional to the squared overlap integral of the ground state

proton wave functions. In this case for example the kinetic isotope effect in the current would then be practically independent of the bias voltage. Fig. 2 shows representative current–bias voltage relationships. The current reaches constant values at large V determined by the rate constant of the H-atom transfer step. 4. Discussion and concluding remarks We have proposed an approach to studies of proton and H-atom transfer reactions in aqueous electrolyte towards the single-molecule level. The approach follows concepts from theoretical and experimental studies of condensed matter single-ET processes [1,2]. With the level of understanding and technology of the latter, implementation of the proton/H-atom transfer scheme suggested appears realistic. The approach both opens routes to new aspects of PT and H-atom transfer processes and adds new substance to molecular electronics aspects of PT systems. The scheme being realized would allow investigating single acts of PT and H-atom transfer in well-defined spatial geometry and with controlled electrochemical potential. Variation of the proton/H-atom transfer distance, a long-standing issue, could also be illuminated. The electrochemical potential and distance dependence of the tunneling current and kinetic isotope effect may further discriminate between various mechanisms of the elementary PT. A suitable change of the configuration in Fig. 1 could finally address electrochemical proton reduction to an adsorbed H-atom at different substrate and tip metal surfaces. We do not presently address the sequential mechanism in which ET and PT represent different reaction steps. The sequential scheme is quite different from concerted ET/PT. and resembles electron tunneling through a double quantum dot [37]. The interfacial rate constants also depend on both bias voltage and overpotential [35] because separate molecular electrochemical ET steps are involved. This raises, however, issues of strong competition from two-step electron tunneling that may conceal the PT step. An analysis of this mechanism will be given elsewhere. Acknowledgement J.U. acknowledges support from the Danish Research Council for Technology and Production Sciences.

80

3

70 60 50

jnorm. 40 30 20

2

10

1

0

0

10

20

30

40

eV/kBT Fig. 2. The dependence of the normalized current on the bias voltage for concerted ET/PT in the totally non-adiabatic limit. PT between the vibrational ground states. The H-atom transfer reaction is considered to be activationless, i.e., FAHFDH = Er with Er taken to be 5kBT. The current is normalized to the pre-exponential factor of the PT rate constant. The curves correspond to different values of the ratio of the pre-exponential factors of PT and H-atom transfer, c. 1: c = 0.1; 2: 0.05; 3: 0.01.

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