Turning Charge Transfer On and Off ina Molecular Interferometer with VibronicPathwaysDequan Xiao,† Spiros S. Skourtis,*,‡ Igor V. Rubtsov,§ and David N. Beratan*,†,|

Department of Chemistry, Duke UniVersity, Durham, North Carolina 27708,Department of Physics, UniVersity of Cyprus, Nicosia 1678, Cyprus, Department ofChemistry, Tulane UniVersity, New Orleans, Louisiana 70118, and Department ofBiochemistry, Duke UniVersity, Durham, North Carolina, 27708

Received December 13, 2008; Revised Manuscript Received March 5, 2009

ABSTRACT

Inelastic electron-transfer kinetics in molecules with electron donor and acceptor units connected by a bridge is expected to be sensitive tobridge-localized vibronic interactions. Here, we show how inelastic electron transfer may be turned on and off in a double-slit style experimentthat uses the molecule as an interferometer. We describe donor-acceptor interactions in terms of interfering vibronic coupling pathways thatcan be actively selected (“labeled”) when pathway-specific vibrations are excited by infrared radiation. Thus, inelastic tunneling may beactively controlled, and we suggest strategies for building molecular scale quantum interferometers and switches based on this phenomenon.

Controlling charge flow through molecules demands ma-nipulating the dual nature of the electron. Indeed, on a largerlength scale, mesoscale devices control the quantum interfer-ence of electronic amplitude propagating along alternativepathways.1-3 Electronic coupling pathway analysis is usedwidely to elucidate bridge-mediated electron tunneling mech-anisms in molecules.4,5 More recently, significant progresshas been made in describing elastic and inelastic tunnelingthrough molecular junctions.6-15 An analytical model formolecular electron transfer (ET) mediated by two couplingpathways indicates the possibility of controlling charge flowusing inelastic tunneling in a double-slit type experiment.16,17

Here, by introducing the concept of vibronic tunnelingpathways, we show how charge transfer may be turned onand off in realistic molecules that mimic double-slit inter-ferometers. We establish a quantum mechanical vibronicframework for elastic and inelastic coupling pathways thattreats the relevant vibrational degrees of freedom that interactwith the tunneling electron. We then examine molecules inwhich activating specific local vibrational modes enables ETto be switched off and on. Finally, we outline a specificexperiment for inelastic ET control in a three-pulse visible/IR/visible transient experiment.

Charge transfer through a two-pathway structure16,17 isdepicted schematically in Figure 1a. D, A, Bi, and Bi′correspond to localized donor, acceptor, and bridge electronic

states, respectively, that couple to each other via nearest-neighbor electronic interactions td(td′), tb(tb′), and ta(ta′). Here,ti and ti′, (i ) d, b, a) denote two equivalent interactions

† Department of Chemistry, Duke University.‡ Department of Physics, University of Cyprus.§ Department of Chemistry, Tulane University.| Department of Biochemistry, Duke University.

Figure 1. (a) Vibronic model for a molecular interferometer. TheD and A electronic basis states are coupled to each other by twoparallel paths involving the bridge electronic states B1, B2 (upperpath), and B1′, B2′ (lower path). As the electron propagates alongeach path, it perturbs path-specific normal mode vibrations (thevibrational states of a mode coupled to the upper path are shownas lines in a harmonic oscillator potential). (b) An elastic vibronicpathway from |D,0⟩ to |A,0⟩. (c, d) Two different inelastic vibronicpathways from |D,1⟩ to |A,0⟩. In (c) there is exchange of energybetween the electron and the normal mode when the electronoccupies B1. In (d) the exchange of energy occurs when the electrontunnels from B1 to B2. The term ti(ti′) denotes electronic couplingbetween the localized electronic states, and τ denotes vibroniccoupling that induces transitions between the vibrational states.

NANOLETTERS

2009Vol. 9, No. 51818-1823

10.1021/nl8037695 CCC: $40.75 2009 American Chemical SocietyPublished on Web 04/02/2009

along parallel pathways. The electron at |D⟩ interacts with|A⟩ via the two parallel bridge paths (upper |B1⟩ - |B2⟩ andlower |B1′⟩ - |B2′⟩), and the amplitudes for electron propaga-tion along the paths interfere. When an electron occupiesthe upper path (|Bi⟩) states, it perturbs a local bridge vibration(e.g., a localized normal mode) whose potential energysurface and corresponding vibrational states |nu⟩ are shownin the figure. The electron-induced perturbation allowsvibrational transitions and the exchange of energy betweenthe vibration and the electron (the vibronic couplings betweenthe |nu⟩ are denoted τ in the figure). Similarly, when theelectron occupies the lower-path (|Bi′⟩) states, it perturbs adifferent bridge vibrational mode with states |nl⟩ (not shownin the figure). The system’s dynamics is described on thebasis of product (vibronic) states |I,nu,nl⟩ ) |I⟩X|nu⟩X|nl⟩ (I) D, A, Bi, Bi′). For simplicity, we will assume that thelower-path vibrational mode is not excited and remains inits ground state (nl ) 0) during the ET process, and thevibronic states are written |I,n⟩, where n ) nu.

For the molecules studied below, the electronic structureis computed at the Hartree-Fock/STO-3G level, and theanalysis is performed in a natural bond orbitals (NBO)18

basis. While limited, the STO-3G basis set describes bridge-mediated tunneling relatively well.19 Vibrations are describedin terms of normal modes, and the electron-vibrationinteraction is taken to be linear. The vibronic Hamiltonianwith a single normal mode coupled to the electronic motionis a sum of electronic, vibrational, and electron-vibrationinteractions,16,17 with matrix elements

where i and j are NBO basis function indices, n and n′ arethe normal-mode quantum numbers, Fij are the Fock matrixelements in the NBO basis for the upper mode, ∂Fij/∂y isthe linear electron-vibration coupling (y is the normalcoordinate), and ynn′ ) ⟨n|y|n′⟩. The geometry optimization,normal-mode analysis, NBO analysis, and ∂Fi,j/∂y computa-tions are performed using Gaussian 03.20 In terms of eq 1,the couplings shown in Figure 1 are td ) FD,B1

, ta ) FA,B2, tb

) FB1,B2, and τb ) (∂FB1,B1

/∂y)y1,0 (Figure 1c), or τb ) (∂FB1,B2/

∂y)y1,0 (Figure 1d).The tunneling matrix element between resonant donor and

acceptor vibronic states |D,p⟩ and |A,q⟩ is17

(p and q denote the initial and final vibrational quantumnumbers). Index i (j) denotes an NBO other than D or A,and index n (n′) denotes a vibrational quantum number. Gin,jn′

(B)

is an element of the vibronic-bridge Green’s function, G(B)

) (EtunI - HB)-1 (H(B) is the Hamiltonian submatrix in thespace of all bridge vibronic states). Etun is the tunnelingenergy (energy of resonant |D,p⟩ and |A,q⟩ states).

Vibronic tunneling pathways are derived from eq 2 via aDyson expansion of Gim,jn

(B) in terms of the off-diagonal

elements Hin,jn′ in eq 1. A tunneling pathway that visits Nintermediate electronic basis states is

where Bi is the ith NBO and ni is the vibrational state of thenormal mode when the electron occupies Bi. (HBi-1ni -1,Bini

)/(Etun

- HBini,Bini) is a vibronic pathway decay parameter with

magnitude between 0 and 1 and may correspond to thetraditional pathway decay parameter4 when ni-1 ) ni or to aninelastic decay parameter when ni-1 * ni. For example, parts cand d of Figure 1 show inelastic vibronic pathways between|D,1⟩ and |A,0⟩ involving two intermediate electronic states.Figure 1c shows a pathway of three intermediate vibronicstates, and Figure 1d a pathway of two states. TDp,Aq in eq 2is the sum over all possible vibronic pathways from |D,p⟩ to|A,q⟩.

In the context of Figure 1, we will describe how IRexcitation of the upper-path vibrational mode influencescharge transfer from D to A (assuming that the lower pathmode is always in its ground state). For elastic ET (at lowtemperature and without IR excitation), the initial systemstate is |D,0⟩. Since there is no energy exchange betweenthe tunneling electron and the bridge vibrations, ET occursif the final state |A,0⟩ is resonant with |D,0⟩. The elastic ETrate is proportional to the square of the elastic tunnelingmatrix element, TD0,A0 (eq 2 with Etun ) HD0,D0 ) HA0,A0).To lowest order in the couplings t and τ, TD0,A0 is the coherentsum of two vibronic pathways (eq 3), the upper pathwayhas intermediate states |B1,0⟩ and |B2,0⟩ (Figure 1b), whilethe lower has |B1′,0⟩ and |B2′,0⟩ (not shown in the figure).For inelastic ET, suppose that the upper vibrational state isIR-excited to |D,1⟩ prior to ET. If |D,1⟩ is resonant with |A,0⟩,an inelastic ET process |D,1⟩f |A,0⟩ may occur (where theexcess vibrational energy is absorbed by the transferringelectron). The inelastic ET rate is proportional to the squareof the tunneling matrix element TD1,A0 (eq 2 with Etun )HD1,D1 ) HA0,A0). The vibronic pathways contributing toTD1,A0 involve only the upper path electronic states Bi, i.e.,the upper-to-lower path interference is erased. This is becausethe upper vibrational mode only interacts with and exchangesenergy with an electron occupying the Bi states.16,17 There-fore, the 1 f 0 vibrational transition during inelastic ETlabels the Bi states. Two pathways that contribute to TD1,A0

are shown in Figure 1c-d.Our design principle for molecular interferometers is as

follows: (1) construct molecules with destructively interferingelastic donor-to-acceptor electron coupling paths, and (2)configure bridge localized normal modes that couple to thesepaths. Vibronic interactions can eliminate the destructiveinterference among the electronic coupling pathways and thusdramatically increase the inelastic ET rate compared to theelastic rate. It is not necessary to have a localized (path-specific) vibrational mode to destroy the destructive interfer-ence. For example, exciting an antisymmetric delocalizedvibration on parallel paths may be sufficient to destroydestructive interference. However, if the purpose is to

Hin,jn' ) [Fij + (n + 1/2)pωδij]δnn' + (∂Fij/∂y)ynn' (1)

TDp,Aq ) ∑i,n

i*D,A

∑j,n'

j*D,A

HDp,in'Gin,jn'(B) (Etun)Hjn,n',Aq (2)

HDp,B1n1HAq,BNnN

Etun - HB1n1,B1,n1

∏i)2

N HBi-1ni-1,Bini

Etun - HBini,Bini

(3)

Nano Lett., Vol. 9, No. 5, 2009 1819

perform a literal double-slit experiment, i.e., to actively selectthe electron’s tunneling path using an IR field, it is necessaryto design path-localized normal modes. This may be ac-complished using isotopically substituted IR-active groupson one of the paths to produce a localized vibrational modethat can be selectively excited. In the analysis below, weconsider both delocalized and localized vibrational normalmodes.

We examine a norbornyl bridged diene with an orthogonalspiro-cylcopropene ring (Figure 2). The π-bonds of thealkenes are treated as the electron donor and acceptor states,as in earlier studies of elastic tunneling by Jordan andPaddon-Row.21 Elastic hole transfer is symmetry forbid-den22,23 in this diene because of the donor and acceptor orbitalorthogonality. The two carbonyl 16O oxygens produce asymmetric stretch (V16O/16O

s , Figure 2a) at 2173 cm-1 and anantisymmetric stretch (V16O/16O

as , Figure 2b) at 2168 cm-1.Replacing one of the 16O’s by 18O decouples the two CdOvibrations, with the Cd16O stretch (V16O(18O), Figure 2c) at2171 cm-1, and the Cd18O stretch (V18O(16O), Figure 2d) at2130 cm-1. In the decoupled modes, 92% of the Cartesiandisplacements are localized on one CdO, 0.2% on the otherCdO, and the remainder is elsewhere on the molecule.

For the diene in Figure 2, the vibronic couplings for elastic|D,0⟩ f |A,0⟩, and inelastic |D,1⟩ f |A,0⟩ channels werecomputed for each of the four vibrational modes describedabove using eq 2 and the single-mode vibronic Hamiltonian(eq 1). The computed elastic (TD0,A0) and inelastic (TD1,A0)coupling strengths (Table 1) show little dependence on thenumber of excited normal-mode vibrational states includedin the Hamiltonian beyond n ) 1. This is because all fournormal modes are high frequency (pω = 0.25 eV), andintermediate vibronic states |Bi,n⟩ with n > 1 are strongly

off-resonant with the initial (|D,0⟩/|D,1⟩) and final (|A,0⟩)vibronic states. Therefore, all |Bi,n⟩ with n > 1 make weakpathway contributions to TDq,Aq (eq 3).

We find that the charge transfer rate arises predominatelyfrom inelastic donor-acceptor coupling because elastic ETis symmetry-forbidden. (The role of orbital symmetrylowering elastic vibronic interaction is explored below.) ForV16O/16O

as , |TD1,A0/TD0,A0| = 600, and for V16O(18O) or V18O(16O),|TD1,A0/TD0,A0| = 7. Only for V16O/16O

s is |TD1,A0/TD0,A0| = 1.Hence, exciting the modes V16O/16O

as , V16O(18O) and V18O(16O) willturn on charge transfer (the rate is proportional to |TDp,Aq|2).Excitation of V16O/16O

s will not have a significant effect on ETkinetics.

We now analyze vibronic pathways (eq 3) to probe thesource of the above observations. The diene contains 135bridge NBOs. Each NBO has two relevant vibronic stateswith n ) 0 and n ) 1 (producing 270 bridge vibronic basisstates). Elastic-tunneling pathways in this bridge (deletingHamiltonian interactions with the ketone groups) wereenumerated for purely elastic ET.21

Elastic and inelastic pathways are constructed by enumer-ating the sequences of Hin,jn′ matrix elements that propagatefrom the donor vibronic state to the acceptor vibronic state(eqs 1-3). Hin,jn′ values are shown in Tables 2 (Fi,j), and 3((∂Fij/∂y)y1,0), and visualized in Figure 3. The vibronic matrixelements (∂Fij/∂y)y1,0 depend strongly on isotope compositionand vibrational mode symmetry. In Figure 4, we showexamples of typical elastic (a) and inelastic (b-d) pathwaysfor V16O/16O

s with their Hin,jn′ interactions. The strongest inelasticpathways involve oxygen lone pair NBOs (Figure 4c).

To probe the “cross-talk” interaction between the parallelupper and lower inelastic pathways (shown in Figure 4b-dfor V16O/16O

s ), we set all cross-talk Hin,jn′ elements to zero andrecomputed TD1,A0 using eq 2. TD1,A0 remains very weak forthe symmetric mode V16O/16O

s (10-5 eV), and drops by lessthan 1% for V16O/16O

as , V16O(18O), and V18O(16O), indicating that thecross-talk couplings contribute little to the total inelastictunneling. Similarly, to quantify the interference betweenupper and lower inelastic pathways, we turn off one of thebridge routes by setting all relevant off-diagonal Hin,jn′elements to zero and then recomputing TD1,A0 with eq 2. TD1,A0

Figure 2. Diene vibrational normal modes involving the CdOgroup vibrations (with and without isotopically substituted oxygen):(a) V16O/16O

s; (b) V16O/16O

as; (c) V16O(18O); (d) V18O(16O).

Table 1. Computed Elastic (TD0,A0) and Inelastic (TD1,A0)Donor-acceptor Couplings (Equation 2) for the FourNormal Modes in Figure 2

normal mode TD0,A0 (eV) TD1,A0 (eV)

(a) v16O/16Os

-9.70 × 10-6 4.26 × 10-6

(b) v16O/16Oas

-8.67 × 10-6 -5.46 × 10-3

(c) v16O(18O) 5.19 × 10-4 -3.75 × 10-3

(d) v18O(16O) -5.55 × 10-4 -4.10 × 10-3

Table 2. Fi,j Elementsa (eV) Shown in Figure 3t1(t1′) -1.96 (1.96) t8(t8′) 1.37 (1.37) t15(t15′) 0.70 (0.70)t2(t2′) -3.10 (-3.10) t9(t9′) 3.22 (3.22) t16(t16′) 0.91 (0.91)t3(t3′) -2.79 (-2.79) t10(t10′) 3.22 (3.22) t17(t17′) 0.92 (0.92)t4(t4′) -3.03 (-3.03) t11(t11′) 0.54 (0.54) t18(t18′) 0.83 (0.83)t5(t5′) -2.90 (-2.90) t12(t12′) 0.54 (0.54) t19(t19′) 0.84 (0.84)t6(t6′) -3.60 (-3.60) t13(t13′) -2.52 (-2.52)t7(t7′) -2.88 (-2.88) t14(t14′) 2.53 (2.53)

a These elements are the same for the four normal modes.

Table 3. (∂Fij/∂y)y1,0 Elementsa (eV) Shown in Figure 3v16O/16O

sv16O/16O

asv16O(18O) v18O(16O)

τ1(τ1′) 0.38 (0.38) -0.38 (0.38) 0.02 (0.53) -0.52 (0.02)τ2(τ2′) -0.16 (-0.16) 0.15 (-0.15) -0.02 (-0.22) 0.22 (0.00)τ3(τ3′) -0.15 (-0.16) 0.15 (-0.15) -0.02 (-0.21) 0.22 (0.00)τ4(τ4′) 0.09 (0.09) -0.10 (0.10) 0.00 (0.14) -0.14 (0.01)τ5(τ5′) 0.20 (0.20) -0.20 (0.20) 0.01 (0.29) -0.27 (0.01)τ6(τ6′) -0.20 (-0.20) 0.20 (-0.20) -0.01 (-0.28) 0.27 (-0.01)

a We show here the magnitudes and signs of τ/τ′ for each normal mode y.

1820 Nano Lett., Vol. 9, No. 5, 2009

increases from 10-6 to 10-3 eV for V16O/16Os (destructive

interference between inelastic pathways is removed); TD1,A0

drops by 52% for V16O/16Oas (constructive interference is

removed); TD1,A0 drops 3% for V16O(18O) and V18O(16O) when theroute with less CdO vibrational amplitude is turned off, anddrops 92% if the route with the active CdO stretch is turnedoff. Hence, the dominant inelastic pathways for the delo-calized (symmetric and antisymmetric) vibrations passthrough both of the parallel bridge-electronic routes andinterfere destructively (symmetric mode) or constructively(antisymmetric mode). For the localized CdO vibrations,only inelastic pathways that involve one of the bridge routescontribute to the inelastic coupling. Thus, for the localizedCdO vibrations, this molecule behaves as a quantum double-

slit structure. Elastic electronic propagation (no IR) involvesthe sum of two parallel (destructively interfering) couplingpaths (TD0,A0). When one of the CdO vibrations is IR-excitedand inelastic ET occurs, only the path with the excited CdOvibration contributes (TD1,A0) and the interference among thetwo routes is eliminated.

The inelastic pathway interferences described above canbe correlated with the signs and magnitudes of the individualcoupling elements (td (td′), tb (tb′), τb (τb′) and ta (ta′)), asshown in Figure 5. In the figure, td (td′) or ta (ta′) is theelectronic coupling between the donor or acceptor NBO andthe bridge NBO, tb (tb′) represents the effective bridgeelectronic coupling (a product of all the electronic couplingsin a pathway), and τb (τb′) represents the bridge vibroniccoupling. For V16O/16O

s (Figure 5a), all t and τ elements havethe same sign, except for td and td′ (e.g., t1 ) -1.96 eV andt1′ ) 1.96 eV, Figure 4a). The two vibronic pathways are ofopposite sign, and inelastic ET is forbidden because ofdestructive interference. This interference explains why theexcitation of V16O/16O

s does not enhance the donor-acceptorcoupling (in fact, TD1,A0 is slightly smaller than TD0,A0, Table1).

For V16O/16Oas (Figure 5b), td and td′ are of opposite sign, but

τb and τb′ are also of opposite sign, (e.g., τ5 ) -0.20 eVand τ5′ ) 0.20 eV, Figure 4c). The two vibronic pathwayshave the same sign, and the total inelastic coupling is twicethe single inelastic pathway contribution. Hence, the destruc-tive interference between the two electronic paths observedfor elastic ET can be eliminated by IR excitation of thismode. The excitation creates an inelastic ET channel withconstructive interference between the parallel electronicpaths, enhancing the ET rate. In the case of V16O(18O) or V18O(16O)

(Figures 5c,d), τb or τb′ is nearly 0 (e.g., τ5 ) 0.29 eV andτ5′ ) 0.00 eV in Figure 4c). The propagation along one routeis removed by the inelastic interaction. The net TD1,A0 valueis equal to the single pathway value; electron path cancelationis thus eliminated by IR excitation and inelastic tunneling.This result agrees precisely with the qualitative predictionof the empirical two-bridge ET model.16,17

Figure 3. Electronic matrix elements Fi,j (blue t/t′) and vibronicmatrix elements (∂Fij/∂y)y1,0 (red τ/τ′) (eq 1) that make dominantcontributions to the donor-acceptor interaction (eqs 2, 3). A t/t′or τ/τ′ pair represents two equivalent elements on opposite sidesof the molecule. (a) t/t′ for nearest-neighbor σ-σ and second-nearest-neighbor σ-π interactions. (b) t/t′ associated with carbonylgroups, (c) t/t′ for second-nearest-neighbor σ-σ interactions. (d)The strongest τ/τ′ elements. The orientation of p-orbitals on thealkene, as well as the lone pairs on the two oxygens, are shown.

Figure 4. Typical purely electronic pathway (a) and vibronicpathways (b-d) for V16O/16O

s. The pathways shown are composed of

the strongest Hin,jn′ vibronic coupling elements in Figure 3. Thepathway strengths can be calculated using eq 3 and the data inTables 2 and 3. The upper and lower pathways values are -5.93× 10-5 eV and 5.93 × 10-5 eV in (a), -1.94 × 10-6 eV and 1.94× 10-6 eV in (b), -3.60 × 10-6 eV and 3.60 × 10-6 eV in (c),and 8.95 × 10-7 eV and -8.95 × 10-7 eV in (d).

Figure 5. Representation of inelastic vibronic pathway interferences.The interferences are correlated to the Fij and (∂Fij/∂y)y1,0 magni-tudes and signs for (a) V16O/16O

s, (b) V16O/16O

as, (c) V16O(18O) and (d) V18O(16O).

t (t′) represents the Fij and τ (τ′) represents the (∂Fij/∂y)y1,0 elements.For the upper or lower pathway, the pathway strength is proportionalto tdtbτbta (eq 3). |t| ) |t′| in (a-d) and |τ| ) |τ′| in (a, b).

Nano Lett., Vol. 9, No. 5, 2009 1821

The rate-switching effect derives from the couplingbetween π donor and π acceptor orbitals, and it relates tohole transfer in cation radicals.19 For photoinduced ET inneutral species, or for thermal ET of anion radicals, therelevant coupling is between the corresponding π* donorand π* acceptor orbitals.19,23 For norbornyl dienes with threeto four norbornyl units, the π*-π* coupling was shown tobe the same order of magnitude as the π-π coupling.19 Assuch, we expect similar switching effects for photoinducedET, albeit with different elastic and inelastic pathways.

The above calculations were performed for minimum energystructures. A critical question is whether thermal fluctuationsthat are static on the time scale of ET wash out rate switching.22

To address this question, we performed a 2 ps ab initiomolecular dynamics (MD) simulation of the diene at 10 K andat 300 K using the turbomole program,24 and computed MDaveraged tunneling matrix elements. At 300 K, (⟨TD0,A0

2 ⟩)1/2 ∼10-2 eV and (⟨TD1,A0

2 ⟩)1/2 ∼ 10-4 eV. At 10 K (⟨TD0,A02 ⟩)1/2 ∼

1.7 × 10-3 eV, and (⟨TD1,A02 ⟩)1/2 ∼ 3.7 × 10-3 eV. The thermal

fluctuations reduce the destructive pathway interference forelastic ET and there is no significant off-to-on ET switchinginduced by IR excitation. At 10 K the inelastic rate is predictedto be 4-fold faster than the elastic rate, and IR-induced ETswitching should be observable.

For symmetry-forbidden photoinduced electron transfer innaphthalene-norbornyl-dicyanoethylene, the experimentallyderived (⟨TD0,A0

2 ⟩)1/2 at 295 K is of the order 10-3 eV22 (avalue comparable to our computed (⟨TD0,A0

2 ⟩)1/2 at 300 K).When orbital symmetry is lowered by replacing the acceptorwith dicarboethoxyethylene, the electronic coupling increasessignificantly, by 20-30-fold, and the rate increases by 2orders of magnitude. In this case, the electronic couplingincrease is induced by lowering the symmetry of electronicorbitals. Here, we compute a much smaller 4-fold increaseof the inelastic ET rate over the elastic ET rate, induced bylowering the symmetry of vibronic states. The advantage ofmanipulating vibronic symmetry is that the charge-transferrate can be controlled by IR-excitation, without changingthe chemical structure. Further, if isotopic substitution is usedto establish localized bridge vibrations, the IR excitation canalso control the electron path.

The inelastic tunneling rate is expected to be measurablein a vis/IR/vis transient absorption experiment, by monitoringthe transient absorption signal of the excited state (D*-B-A)and the charge-separated (CS) state (D+-B-A-). Themolecule would be excited (D*-B-A) by a UV-visiblepulse. After a delay time t1, the vibrational excited state (n) 1) would be prepared on the bridge with IR laserexcitation. The charge transfer or decay rate from D*-B-Ato D+-B-A- is expected to increase by exciting theantisymmetric (V16O/16O

as ) or the single-route (V16O(18O) or V18O(16O))vibrational modes. After time t2, a UV-vis probe pulse isused to detect D+-B-A-, which arises from elastic andinelastic channels. Chopping the IR light allows determina-tion of the inelastic component.

We have used a minimal basis set (STO-3G) in theseelectronic structure computations. A larger basis set calcula-tion is likely to show an enhancement of the electronic cross-

talk between parallel electron routes.15 Further, our treatmentof the vibrational degrees of freedom does not describe thepossibility of vibrational energy redistribution among groupslocalized on different electronic coupling routes. Both longerrange electronic (vibronic) interactions and vibrational energyredistribution could destroy the double-slit character of theproposed experiment. However, for larger analogous struc-tures, where the parallel routes are more distant from eachother, both cross-talk15 and vibrational redistribution effectsare likely to be diminished. An open question is howdephasing effects would alter the behavior of the molecularinterferometer, especially for large structures with distantparallel routes. We have not addressed this effect in ourstudy. Dephasing is sensitive to temperature and solventconditions, and it could eliminate ET pathway interfer-ences.13

In summary, we have demonstrated the possibility ofturning charge-transfer on and off in a molecular interfer-ometer, by exciting specific vibrational modes. Elastic ETin the structure studied here is symmetry forbidden. Byactivating a delocalized vibrational mode, such as theantisymmetric mode (V16O/16O

as ), or a single-path-localized mode(V16O(18O) or V18O(16O)), the destructive pathway interference isremoved for inelastic tunneling. For the localized-mode case,the IR-induced elimination of pathway interferences is adouble-slit type effect, where the IR pulse selects theelectron’s tunneling path by causing the path-specific vibra-tion to exchange a quantum of vibrational energy with theelectron traversing the path. This inelastic tunneling effectis different from the elimination of interference by fluctua-tions of molecular geometry that alter the nodal structure ofthe molecular orbitals and that are static on the ET time scale.Moreover, the chopped IR experiment described above maybe able to separate the double-slit type effect from thermaleffects on ET kinetics. These mechanisms of controllingcharge-transfer should be testable in a pulsed laser experi-ment, and the effects are anticipated to be most dramatic atlow temperatures where conventional vibronic couplingeffects are minimized and pure dephasing effects are re-duced.13 This type of IR-controlled molecular interferometermay be of interest for applications in nanoelectronics,optoelectronics, or molecular sensing.

Acknowledgment. We thank NSF (CHE-0718043) andthe University of Cyprus for support of this research project,and Jeremy B. Maddox for helping with the calculation ofthe electron-phonon coupling matrix elements.

References(1) Aharonov, Y. Rohrlich, D. Quantum Paradoxes: Quantum Theory for

The Perplexed; Wiley-VCH: Cambridge, 2005.(2) Imry, Y. Mesoscopic Physics; Oxford Press: New York, 1997.(3) Datta, S. Electronic Transport in Mesoscopic Systems; Cambridge

Press: New York, 1997.(4) Skourtis, S. S.; Beratan, D. N. AdV. Chem. Phys. 1999, 106, 303.(5) Skourtis, S. S. Lin, J. Beratan, D. N. In Modern Methods for

Theoretical Physical Chemistry of Biopolymers; Starikov, E. B., Lewis,J. P., Tanaka, S., Eds.; Elsevier: Amsterdam, 2006.

(6) Galperin, M.; Ratner, M. A.; Nitzan, A. J. Phys.: Condens. Matter2007, 19, 103201.

(7) Troisi, A.; Ratner, M. A.; Nitzan, A. J. Chem. Phys. 2003, 118, 6072.(8) Cizek, M.; Thoss, M.; Domcke, W. Phys. ReV. B 2004, 70, 125406(1).

1822 Nano Lett., Vol. 9, No. 5, 2009

(9) Sergueev, N.; Roubtsov, D.; Guo, H. Phys. ReV. Lett. 2005, 95, 146803.(10) Ness, H.; Fisher, A. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 8826.(11) Maddox, J. B.; Harbola, U.; Liu, N.; Silien, C.; Ho, W.; Bazan, G. C.;

Mukamel, S. J. Phys. Chem. A 2006, 110, 6329.(12) Solomon, G. C.; Gagliardi, A.; Pecchia, A.; Frauenheim, T.; Carlo,

A. D.; Reimers, J. R.; Hush, N. S. J. Chem. Phys. 2006, 124, 094704.(13) Goldsmith, R. H.; Wasielewski, M. R.; Ratner, M. A. J. Phys. Chem.

B 2006, 110, 20258.(14) Troisi, A.; Beebe, J. M.; Picraux, L. B.; van Zee, R. D.; Stewart, D. R.;

Ratner, M. A.; Kushmerick, J. G. Proc. Natl. Acad. Sci. U.S.A. 2007,104, 14255.

(15) Ke, S-H.; Yang, W.; Baranger, H. U. Nano Lett. 2008, 8, 3257.(16) Skourtis, S. S.; Beratan, D. N. In Proceedings of the International

Conference on Computional Methods in Science and Engineering, PartB; Simos, T. E., Maroulis, G., Eds.; American Institute of Physics:College Park, MD, 2007; Vol. 2, p 809.

(17) Skourtis, S. S.; Waldeck, D. H.; Beratan, D. N. J. Phys. Chem. B2004, 108, 15511.

(18) Foster, J. P.; Weinhold, F. J. Am. Chem. Soc. 1980, 102, 7211.(19) Paddon-Row, M. N. Acc. Chem. Res. 1994, 27, 18.(20) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,

M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin,K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone,

V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa,J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene,M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.;Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin,A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.;Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.;Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas,O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.;Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.;Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen,W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, ReVisionD.02; Gaussian, Inc.: Wallingford, CT, 2004.

(21) Jordan, K. D.; Paddon-Row, M. N. Chem. ReV. 1992, 92, 395.(22) Zeng, Y.; Zimmt, M. B. J. Phys. Chem. 1992, 96, 8395.(23) Reimers, J. R.; Hush, N. S. Chem. Phys. 1990, 146, 105.(24) Ahlrichs, R.; Bar, M.; Haser, M.; Horn, H.; Kolmel, C. Chem. Phys.

Lett. 1989, 162, 165.

NL8037695

Nano Lett., Vol. 9, No. 5, 2009 1823