Electrodes as Polarizing Functional Groups: Correlation Between

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

Electrodes as Polarizing Functional Groups: Correlation Between Hammett Parameters and Electrochemical Polarization Sohini Sarkar, Joel G Patrow, Matthew J. Voegtle, Anuj K Pennathur, and Jahan M Dawlaty J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b12058 • Publication Date (Web): 04 Feb 2019 Downloaded from http://pubs.acs.org on February 4, 2019

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The Journal of Physical Chemistry

Electrodes as Polarizing Functional Groups: Correlation Between Hammett Parameters and Electrochemical Polarization Sohini Sarkar, Joel G. Patrow, Matthew J. Voegtle, Anuj K. Pennathur, and Jahan M. Dawlaty∗ Department of Chemistry, University of Southern California E-mail: [email protected]

∗ To

whom correspondence should be addressed

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ACS Paragon Plus Environment

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Abstract Bridging the concepts of homogeneous and heterogeneous reactions is an important challenge in modern chemistry.Towards that end, here we connect the homogeneous chemistry concept of Hammett parameter, used by organic and organometallic chemists to quantify the electron-withdrawing capability of a functional group, to the electrochemical concept of polarization induced by a biased electrode. Since these two effects share similar origins, a theoretically motivated and experimentally verifiable link between them can be established. A convenient experiment that links the two is measuring the shift of a vibrational frequency that is induced by these factors. To achieve this, first we have measured the vibrational frequency of the nitrile stretch of 4-R-benzonitrile for a series of functional groups R spanning a Hammett parameter range −0.83 ≤ σ p ≤ +1.11 . Since the nitrile stretch is sensitive to molecular polarization, its frequency depends on the Hammett parameter of the polarizing functional groups. Second, we have measured the nitrile vibrational frequency of 4-mercaptobenzonitrile tethered on a gold electrode and polarized in an electrochemical cell as a function of potential from -1.4 V to +0.6 V vs Ag/AgCl. Comparison of the nitrile stretch frequency between the two experiments allows us to correlate the polarization caused by a functional group to that induced by the electrode. The data suggests an equivalence between the Hammett parameter σ p and the local electric field at the electrode interface, therefore allowing a polarizing electrode to be treated as a functional group. Computational work supports the experimental results and allows for a quantitative relation between the interfacial electric field and σ p . We anticipate the benefits of this correlation, in particular in linking concepts between homogeneous and heterogeneous reactions.

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Introduction We create a fundamental link between seemingly two distinct concepts in two different fields of chemistry − the concept of electron withdrawing by a functional group as measured by the Hammett parameter and the concept of polarizing electric fields at electrochemical interfaces. The former is used in synthetic organic and organometallic chemistry and homogeneous catalysis, while the latter is used in electrochemistry and heterogeneous catalysis. The induced polarization is intimately related to reactivity via influencing the stability of reactive intermediates, and the energetics of transition states. Molecular polarization is controlled by either functional groups or by an external electrochemical potential. While it seems natural and intuitive that a fundamental link must exist between the polarization induced by a functional group and that created by an external field, surprisingly, no work has been done to establish this connection. We present experimental and computational evidence to create such a link that we anticipate will benefit several areas of chemistry. The link will serve as part of a common language between heterogeneous and homogeneous chemistry to facilitate transfer of ideas between the two fields, and connect seemingly disparate phenomena in these realms. For example, if one understands how an organometallic catalyst responds to the Hammett parameter of a functional group within its ligands, one can extrapolate its behavior when it is attached to an electrochemical interface. The link can also shed light on the persistent and difficult electrochemical problem of estimating pKa of molecules near a biased interface. Similarly, the influence of a substituent on a homogeneous reactive center can be interpreted as an effective electrochemical potential, and therefore its redox properties can be estimated. This paper is organized as follows. First, we introduce the concepts of Hammett parameter, interfacial fields, and their interconnection with particular reference to their measurement using vibrational spectroscopy. Second, we present our experimental results, supported by computations, showing vibrational frequency shifts of benzonitrile as a function of Hammett parameter and applied electrochemical potential. Third, we will discuss how Hammett parameter and electric field are fundamentally connected to each other. Finally we will discuss the consequences and 3



limitations of this correlation for understanding chemical phenomena both at interfaces and in the bulk.

The Hammett Parameters, Interfacial Fields, and their Vibrational Signature In this section we set the scene by introducing the concepts and tools that are used in this work. In this work, we use the term polarization to mean a shift in electronic charge density in a molecule. The Hammett parameter (σ ) is a metric commonly used by organic and organometallic chemists to express the polarizing influence that a functional group exerts on a chemical system. It is traditionally defined by the influence that a functional group R exerts on an acid dissociation reaction. 1,2 The acid dissociation constant K0 of unsubstituted benzoic acid is often taken as a reference (pKa = 4.2). Then the acid dissociation constants K of a series of R-substituted benzoic acids are measured. Electron-withdrawing (EW) groups help stabilize the anionic benzoate and therefore favor the reaction towards more dissociated or larger equilibrium constants K. Electron-donating (ED) functional groups exert the opposite influence. The Hammett parameter sigma is defined as σ = (1/ρ) log K/K0 , where ρ is a constant (that is set to 1 for benzoic acid). Positive σ values indicate EW substituents, while negative σ value indicate ED substituents. Several variants of the Hammett parameter exist, with some that attempt to distinguish between the resonance and inductive effects of a substituent. 3 In this work we consider the commonly used Hammett parameter σ p based on para-substituted benzoic acids. Both experimental and computational works show correlation between a substituent’s σ p value and an extraordinarily diverse range of chemical properties, including catalytic activity, 4 photoacidity, 5 photobasicity, 6 π-conjugation strength in aromatic systems, 7 even mechanical properties, 8 along with many others. 9–18 This general applicability justifies fundamental work to further understand its relation to other fields, in particular to electrochemistry. Similar to the polarizing effect of a functional group, a biased electrochemical interface has a polarizing influence on the nearby molecules. The applied potential on an electrode in contact with a high ionic strength electrolyte decays rapidly due to screening by ions, often over length scales 4


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on the order of ∼ 10 nm. Therefore, modest electrochemical potentials (∼ 1 V) correspond to very large potential gradients or electric fields near the electrode (∼ 1 MV/cm). 19,20 Such large fields polarize the molecules near the surface, and when large enough, they drive redox reactions. Interestingly, similar to the electrochemical fields, it is proposed that enzymes maintain large electric fields within their reactive sites that help catalyze reactions. 21 While the importance of electrostatic fields in chemical reactions is known for several decades, 22,23 the topic has gained special attention recently, 24–27 with particular emphasis towards creating oriented electric fields for driving catalytic reactions. 28 Thus, viewing chemical reactivity from the electric field perspective has wider utility and is not limited to interfacial electrochemistry alone. Measuring electric fields and correlating them to existing chemical concepts, as is done in this work, is a necessary endeavor. To measure local electric fields in a chemical environment often Vibrational Stark shift spectroscopy is used. Probe molecules, bearing vibrational tags, are placed at desired locations. 29–33 Their measured frequency shifts with respect to reference environments is related to the local electric fields within the linear Stark shift approximation as hν = −∆~µ · ~F, where ~F is the electric field and ∆~µ, also known as the Stark tuning rate, is the change in dipole moment between the ν0 and ν1 vibrational levels. The field ~F in the Stark equation is an external field, either applied by an electrode, in a Stark cell, by the solvents or any other environments surrounding the molecule. This field does not arise from the internal charge distribution in the molecule. Often the nitrile group, which has a relatively isolated and narrow vibrational signature, is used as a probe. 34 Benzonitriles, with a Stark tuning rate of ∆~µ = 0.022 D ∼ 0.36 cm−1 /(MV /cm) have been used by us and others for measuring local fields. 33,35–39 The influence of charge redistribution on vibrations of a molecule is known for more than half a century. Prime examples are partial electronic charge transfer between ligand and metal centres in metal-carbonyls, 40–42 metal cyanides, 43–46 and metal isocyanides 47 that changes the corresponding vibrational frequencies of the ligands. This influence is routinely used by inorganic chemists to assess the degree of charge redistribution in organometallic complexes. The effect that we are investigating here is very similar. A nitrile group is attached to a polarizable benzene ring (fig-

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ure 1). An electron-donating group situated in the para position with respect to the nitrile can release electronic charge density toward the ring which will overlap with the antibonding orbitals of the nitrile resulting into its red shift. An electron-withdrawing group will create the opposite effect. This frequency shift is very similar to electronic charge redistribution in metal-cyanides that is heavily studied in the inorganic chemistry community. Furthermore, this description of frequency shift in benzonitriles is not original to us and has been explained previously. 48,49 Similarly, when the unsubstituted benzonitrile is placed in an electric field that is aligned with the long axis of the molecule and pointing away from the nitrogen of the nitrile, the electronic charge density moves against this field and introduces more charge on the nitrile. Analogous to the parasubstituent effect, this charge overlaps with orbitals that have nitrile antibonding character which red shifts the nitrile vibrational frequency. This is indeed the property that endows benzonitrile its slightly larger sensitivity to electric field (∼ 0.36 cm−1 /(MV /cm) ) compared to nitriles attached to aliphatic systems and makes it a useful Stark shift probe. 35,50,51 Of course, a nitrile group that is not attached to a highly polarizable conjugated system (for example attached to an aliphatic chain) also changes frequency in response to the field, albeit with a somewhat smaller sensitivity (∼ 0.3 cm−1 /(MV /cm) ). In the second case, the field influences the electronic structure of the nitrile mostly locally, while in the former case, the field influences the entire benzonitrile molecule. In both cases, the vibration is a useful field reporter with different spatial resolutions. It is important to comment on the locality of the fields that are associated with frequency shift of the nitrile group. The polarizability of the entire molecule, and not just the nitrile group, gives rise to the sensitivity of nitrile to the electric field. One may theoretically compute fields at an arbitrary location within the body of a molecule or in its vicinity. However, using polarizable molecules of finite size, there is no experimental method to measure fields at a pin-point location with submolecular resolution. This does not take away from the utility of benzonitrile as a field reporter. However, one has to understand that the reported fields are an average representation over the entire molecule and will not have spatial resolution smaller than a molecule. In some instances, one may use nitriles attached to aliphatic chains to get a slightly better spatial resolution. For our purpose,

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i.e. comparison of field and substituents on polarization of conjugated systems, benzonitrile is a better choice. Given the common underlying mechanism for frequency change in benzonitriles in the presence of a field or under the influence of a substituent (i.e. polarization of the molecule), it is desirable to find out what amount of field would be necessary to cause a frequency shift equivalent to one unit of electron-withdrawing power (Hammett parameter) of the substituent. That is the goal that we are pursuing in this work.

𝐹Ԧ

𝐹Ԧ 𝑒ҧ Figure 1: Cartoon illustrating the influence of field-only and field and electron density migration on nitrile vibration. In both cases shown above, the nitrile vibration is a relatively local mode, indicated by the dotted circle. When the nitrile is attached to an aliphatic chain (top), for the most part, only field lines penetrate into the dotted circle. In the bottom, the nitrile group is conjugated with the highly polarizable benzene ring, and electron density can shift from benzene to the nitrile group under the influence of a field or a substituent. Therefore, the frequency of nitrile is indicative of the polarization of the entire benzene molecule. To make the connection between the two central concepts in this work, vibrational spectroscopy is a natural choice. We choose benzonitriles as our probe molecule as shown in figure 2. It is well-known that the frequency of the nitrile stretch in benzonitrile is sensitive to changes in Hammett parameter. 21,30,31,33,52 This is likely because the substituent polarizes the benzene π electrons which have some overlap with the antibonding orbital of the nitrile moiety. Therefore any agent, be it an electron donating substituent or an external field, that pushes charge density from the ring 7



towards the nitrile group will red-shift the stretch frequency. 53,54 Similarly any effect that polarizes the charge density in the ring away from the nitrile group will blue-shift its stretch frequency. Thus, the nitrile stretch is a natural, and convenient choice for assessing polarizing forces both arising from functional groups and from external fields. Both of the above properties of benzonitrile are established from extensive earlier work. The effect of substitution on the nitrile stretch of 4-R-benzonitrile demonstrated a clear frequency shift with respect to σ p . 52 Additionally, 4mercaptobenzonitrile has been used previously to probe fields at electrified metal interfaces, and Stark behavior of the CN moiety at the surface is well documented by us and others. 19,20,33,55 Our purpose here is to unite these two views, which has not been performed so far.

Hammett Electron Withdrawing Parameter

Electric Field

Field

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Figure 2: Picture depicting the effect of polarizing electric field at electrochemical interface and an electron withdrawing functional group on the nitrile stretch. To understand the influence of the Hammett parameter of a substituent on the nitrile frequency, we measure the vibrational frequencies of a series of benzonitrile molecules that are substituted at the para-position with functional groups spanning a wide range of Hammett parameters. To understand the influence of electrochemical potential on the nitrile frequency, we tether 4-mercaptobenzonitriles on a gold surface and polarize it in an electrochemical cell. Using vibrational Sum Frequency Generation (vSFG) spectroscopy, we measure the nitrile frequency shift as a function of applied potential. Nitrile vibrational frequencies are sensitive to solvation 8


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environments both in the bulk and near a surface as noted by us and others. 19,56,57 Therefore, it is critically important to keep the solvent the same between the electrochemical and Hammett measurements. This restriction precludes aqueous electrolytes since many of the substituted molecules in the Hammett series are not soluble in water. Furthermore, the relatively narrow electrochemical window of water limits the range of potential that can be applied. We chose an ionic liquid as a solvent and electrolyte, since ionic liquids exhibit wider electrochemical windows and can easily dissolve a wide range of organic molecules, including all of our Hammett series molecules.

Experimental and Computational Methods FTIR spectra of benzonitrile and para-substituted benzonitriles were recorded using a Bruker Vertex 80 FTIR spectrometer. A series of compounds spanning the Hammett parameter σ p from -0.83 to +1.11 were used. The names of the molecules and their Hammett parameters are listed in the SI and also appear in figure 4. The Hammett parameters values are based on previous literature. 2,3 For each of the compounds, the concentration was maintained to be ∼ 2 mmol. All compounds were dissolved in 1-Ethyl-3-methylimidazolium tetrafluoroborate abbreviated as [EMIM]+ [BF4]− . The ionic liquid (IL), [EMIM]+ [BF4]− , was purchased from Sigma Aldrich and nitrogen was bubbled through the liquid at 600 C to remove oxygen and water. 58 The solutions in IL were injected between two calcium fluoride plates separated by a 100 µm spacer and held together using a demountable liquid FTIR cell (International Crystal Laboratories). A table with the names of substituents, their Hammett parameters, and the -CN stretch frequencies are given in the SI. Silicon wafers with a 10 nm Ti adhesion layer and 100 nm of Au purchased from LGA Thin Films, Inc were used to prepare self-assembled monolayers (SAMs) of 4-mercaptobenzonitrile (4MBN). The wafers were sonicated in acetone and then in ethanol twice for 8 min each time to ensure cleaning. The cleaned wafers were immersed in a 0.03 M solution of 4-MBN in ethanol for at least 24 h, which ensures full surface coverage for good signal quality. After soaking in the 4-MBN solution, the wafers were removed and again sonicated twice in fresh ethanol for 8 min

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each. For recording the electrochemical sum frequency generation spectra, the SAM-modified Au samples were mounted in the liquid FTIR cells (International Crystal Laboratories) adapted for this purpose. The front window comprised a 4 mm thick CaF2 window with two holes using for filling. The back window of the cell was replaced with the SAM-containing wafer. The two windows were separated by a 25 µm Teflon spacer. The entire assembly was held firmly together using stainless steel plates and screws (Figure 3 b.). The cell was then placed under a N2 atmosphere where the IL was then injected via a large syringe into the cell. After injection, the syringe was disconnected from the cell and its plunger was removed. Then, syringe (now without a plunger) was reconnected to one of the cell’s filling ports and used as a reservoir to hold the counter and reference electrodes. The working electrode consisted of the SAM-modified Au samples with attached wires to connect to the potentiostat; The reference electrode was Ag/AgCl (purchased from Gamry); A Pt wire was used as the counter electrode. A Gamry Reference 3000 potentiostat was used for applying potentials. The optical light source was a Ti-sapphire amplified laser (Coherent) that generates ultrafast near-IR pulses at 1 KHz repetition rate. 1 W of the average power was directed to an optical delay stage followed by a 4f filter that significantly narrowed the spectrum. The 4f filter built using two transmissive volume phase gratings (BaySpec, Inc.), two cylindrical lenses, and a variable width slit could filter near-IR pulse to a spectral width of 8.0 cm−1 , centered at 783.35 nm. Another portion (2 W) of the Ti-sapphire average power was fed into an optical parametric amplifier (OPA;Coherent OPerA Solo) that generated mid IR pulses via difference frequency generation in a AgGaS2 crystal. Pulse energies at sample position for near IR and mid IR pulses were ∼ 8 µJ and ∼ 6.5 µJ respectively. vSFG spectra were acquired by spatially and temporally overlapping these two pulses after they were focused using a common parabolic mirror. The resulting vSFG signal was collected with a second parabolic mirror and passed through a 750 nm short-pass filter to reject the majority of the scattered near-IR photons prior to being sent to a spectrometer (Horiba iHR320)with a CCD camera (Syncerity) for spectral analysis. All spectra were acquired under a

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CO2 and H2 O free atmosphere. Each spectrum was obtained by integrating for 120 seconds. The spectral resolution of this setup is discussed in our previous work. 19

Filling Syringe

A V

25μm Teflon spacer

5 mm thick CaF₂ window

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-

-

-

Counter electrode

+

Reference electrode

+

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Metal scaffold Contact to working electrode

(a)

100nm gold layer on Si Wafer

(b)

(c)

Figure 3: (a) Diagram showing a cross section of the cell used in experiments. (b) Cartoon diagram of SAM-modified Au sample in [EMIM]+ [BF4]− . (c) Representative spectrum (blue) and its fit (red) at V = 0.0 V. The dip around 2230 cm−1 is due to the nitrile stretch. The electrochemical vSFG studies were carried out as a function of the applied potential. The electrolyte used was [EMIM]+ [BF4]− which is a room temperature ionic liquid. Ideal room temperature ionic liquids are organic salts with mobile anions and cations and no solvent. The ionic liquids have decent ionic and electrical conductivity, electrochemical stability, low vapour pressure and ability to dissolve a wide range of substances. Correspondingly they have found applications in batteries, fuel cells, solar cells, and electrochemistry. 59–61 We chose [EMIM]+ [BF4]− as an electrolyte for performing electrochemical vSFG owing to its wider electrochemical window (∼ 4V) compared to that of water. 62,63 The SAM has a narrow potential window from -1.4 V to +0.6 V where the adsorbed thiol on gold is electrochemically stable. A cyclic potential scan was performed where the applied potential was scanned from 0.0 to +0.6 V then to -1.4 V and then back to 0.0 V with a step size of 0.2 V. After application of each potential step, a transient capacitive current was observed. Six minutes was allowed to let the transient current decay before acquisition of the vSFG spectra. This ensures that the steady state of the electrode is measured for each potential value. At each potential, three vSFG spectra were obtained each with 120 s integration times. As known from prior literature, the nitrile stretch appears as a negative narrow Lorentzian line interfering with a broader Gaussian background arising from the non-resonant response of the gold 11



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electrode. 19,33,64 Following previous work, we used the following equation to fit our experimental data and obtain the centre frequencies of the nitrile stretch: ISFG (ω) = ANR eiφ +

2 2 (ω − ω ) g exp − ω − ωCN + iΓCN σg2 B

(1)

The above model utilized by Benderskii et al. 65 is for the total vSFG signal arising from the interference of a nonresonant background signal from gold, and a resonant signal from the benzonitrile adhering to the gold surface. An amplitude ANR with relative phase φ is used to model the constant non-resonant background. The resonant signal adopts a Lorentzian line shape with amplitude B, center frequency ωCN , and width ΓCN . Both the signals are multiplied by an Gaussian IR pulse, with center frequency ωg and σg . A background spectrum was obtained by walking off the temporal overlap of the IR-near-IR pulses under otherwise identical conditions. This background was subtracted from the raw vSFG spectra. All of the fitting parameters for the vSFG spectra are listed in Supporting Information (SI). Each vSFG spectrum at each potential was independently fit to the above equation using Matlab’s nonlinear least-squares fitting algorithm and same initial guess. A representative spectrum with its fit is shown in figure 3. We emphasize that fitting the intensity (homodyne) data as an interference between a nonresonant background and a complex Lorentzian as described above is necessary. Otherwise, a phase shift between the two may be misinterpreted as frequency shift. Here, the reported frequencies are not the apparent intensity dips in the data, but rather are retrieved from fits that account for such phase shifts. As the applied potential is scanned from 0.0 V to +0.6 V, the electrode is positively polarized which in turn polarizes the probe molecule that stiffens the CN vibration resulting in blue shift. For potentials much larger than +0.6 V the nitrile stretch begins to disappear due to the instability of the SAM to oxidative chemistry. Thus +0.6 V is the upper limit of our electrochemical window. In the positive potential regime negligible current traverses the interface. For negative potentials, some electrochemical current along with some hysteresis both in the current and in the nitrile frequencies is observed. A plot showing current vs applied potential is given in SI. Figure 5.b. 12


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shows the frequency of the nitrile stretch as a function of applied potential. Variations due to hysteresis, along with variations within several replication of the experiment (see SI for further detail), are all accounted for in the error bars. Computational work was carried out using the quantum chemistry package Q-Chem. 66 Density functional methods were used for geometry and frequency calculation using B3LYP functional and the 6-311G(d,p) basis set for the substituent and field studies. The field calculations were performed by generating arrays of point charges to produce a uniform electric field across a benzonitrile molecule. The method is described in more detail in our previous work. 64 Briefly, the arrays were generated to mimic the two oppositely charged plates of a capacitor. Fields of different strengths were simulated by uniformly altering the magnitude associated with the charges within the array. Geometry and frequency calculations were completed as described above in fields rangMV MV to 100 . Charge densities on the nitrile nitrogen were obtained ing in strength from -100 cm cm through CHELPG and Mulliken charge analysis as printed in the Q-Chem output file. The plots for charge densities on nitrile nitrogen obtained from Mulliken charge analysis are provided in the SI. Molecular dipole changes as a function of field and Hammett parameter were also calculated and included in the SI.

Results FTIR spectra of p-substituted benzonitriles are shown in Figure 4. The substituents have been varied spanning a wide range of Hammett parameters (σ p ) from -0.83 to +1.11, with increasing Hammett parameter corresponding to more electron withdrawing by the substituent. As mentioned earlier, σ p = 0 corresponds to unsubstituted (i.e. hydrogen-substituted) benzonitrile and the positive (negative) values correspond to more (less) electron-withdrawing groups with respect to hydrogen. Consistent with previous work, 30,31,52 we observe that as the Hammett parameter increases, the nitrile frequency blue shifts (4.b.). This is likely because the charge density on the benzene ring has some overlap with the CN antibonding orbital and that any external influence that

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polarizes this charge density away (towards) the nitrile group will result into blue (red) shift of its vibrational frequency. 48 This trend is clearly seen in figure (4.b.). where nearly 25 cm−1 of shift is observed within the studied range of σ p . A certain level of scatter is observed in the data. It is natural to suspect whether interaction with the solvent results into deviation from an otherwise stronger correlation. To understand whether the scatter arises from variation of solvatochromic shift within the series, we computed the nitrile frequencies for the molecules within this series in the gas phase. The computed frequencies (figure 4.c) confirm the overall trend of increasing frequency with increasing Hammett parameter. In addition, they also show a qualitatively similar range of scatter as in the experimental data. The scatter shows that the frequency shift cannot be exactly determined by the Hammett parameter with full accuracy, even though an obvious trend exists. Indeed, the other molecular details of the various substituents are important and influence the frequency shift separately. Given that the data is a correlation between very different observablesfrequency in benzonitrile obtained from spectroscopy and Hammett parameter in benzoic acids obtained from titration experiments- the observed level of correlation is quite reasonable. Since the purpose of the computation here was to understand the trend and not the absolute frequencies, exact matching of each data point between experiment and computation is unnecessary and unexpected at this level of theory. As expected and known for DFT-level computations, frequencies are always overestimated. 67 This is reflected in the data shown in the figure4.c. Small shoulders were observed in three of the spectra (cyano, iodo, and unsubstituted benzonitrile). The origin of these shoulders could be Fermi resonances, arising from mixing with the lower frequency ring modes. The influence of such Fermi resonances on nitrile-containing conjugated rings has been studied before. 68 Fermi resonances shift the vibrational frequencies through an effect separate from electronic polarization, and their influence should be appreciated. In fact, one of the many possible reasons for the scatter in the experimental data in figure 4.b. could be contribution from Fermi resonances. For the nitriles tethered on the electrochemically biased interface, vSFG spectra were obtained as discussed in the experimental section. The nitrile stretch frequencies νCN were retrieved from the

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(a)

(b)

(c)

Figure 4: (a) Representative FTIR absorption spectra of the compounds in the nitrile stretch region. (b) Experimentally determined central frequencies of the nitrile stretch in a series of parasubstituted benzonitriles versus the Hammett parameters of the substituents. (c) Computed central frequencies of the nitrile stretch for the Hammett series. fitting procedure as discussed earlier. Spectra of the nitrile stretch segregated from the nonresonant background are plotted at different applied potentials (Figure 5 ). The nitrile frequency at 0.0 V with respect to the Ag/AgCl reference electrode is 2229.4 cm−1 . Positive potentials polarize the electron density in the benzonitriles towards the electrode and away from the nitrile group. Therefore, similar to the influence of the EW groups, electron density on the antibonding orbital of the CN decreases and blue shifts the CN stretch. At negative potentials the molecule is polarized such that electron density is pushed on to the CN antibonding orbital, resulting into softening of the CN bond. This behavior is manifested in the data in figure 5a-b. The error bars in the figure include variations over several iterations of the experiment and account for the slight hysteresis in electrochemical cycles. Further details on the error bars is given in the SI. We note that equivalent surface spectroscopy can also be performed using FTIR-ATR or reflection FTIR. 69,70 However, they demand different cell geometries and electrode types. In some cases the size, granularity, and penetration depth of the IR light, bring some challenges that are addressable, but need to be considered. Within the potential window of 2 V we observe a 9.1 cm−1 shift or nearly 4.5 cm−1 /V. Such frequency change with respect to potential is comparable to that observed in our previous study 33 when the electrolyte was ∼ 100 mM KCl solution.

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(a)

(b)

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(c)

Figure 5: (a) The nitrile stretch spectra isolated from vSFG spectra. The data shows variation of the spectra as a function of applied potential. (b) Experimentally obtained nitrile stretch frequency as a function of applied potential. (c) Computed nitrile stretch frequency with varying applied field. It is important to note that the interfacial electric field, and not the electrochemical potential, is the fundamentally important quantity in considering the polarization experienced by the tethered molecules. The applied electrochemical potential decays away from the electrode into the electrolyte in a way that is dependent on the electrolyte type and concentration. The electric field, or the gradient of this potential, is not only a function of the externally applied potential, but also a function of the electrolyte type and concentration. Conventionally, while the potential can be easily controlled and measured electrochemically, interfacial fields can only be inferred from a model of how the applied potential decays. Fortunately, placing a Stark shift reporter with known properties at the interface makes it possible to measure the field spectroscopically, without heavily relying on a model. A body of literature on the Stark properties of benzonitrile, including our work for the case of electrode-electrolyte interfaces and interfacial solvation, 33,53 exists. Therefore, it is possible to convert our spectroscopic frequency shifts to electric field values as will be done in the next section. To further verify the validity of using linear Stark shift within this range, we computed frequencies for benzonitrile in the gas phase in electric fields as explained in the computational methods. Just as with the computations for the Hammett series, it is neither expected nor necessary to match the experimental and computed frequencies exactly. The result verifies that linear Stark shift is a reasonable model within this range and that computationally retrieved Stark 16


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tuning rate ∆µ = 0.35cm−1 is very close to the previously reported experimental values. 64 As will be shown in the next section, to match the entire range of the Hammett series to electric fields it will become necessary to go beyond the linear Stark approximation. Finally, as shown in Figure 5.a, the line width of the nitrile stretch is a function of the applied potential, with the line width narrowing for more positive potentials. Interestingly, a similar effect can be seen in the line widths of the Hammett series (figure 4.a.), where larger Hammett parameters also correspond to narrower lines. This intriguing observation further suggests the common origin for not only the central frequency of the nitrile between the two sets of experiments, but also its line width. Spectral broadening associated with substituents has been observed in previous work investigating the carbonyl stretches of substituted acetophenones. 71 The observed broadening was associated with the thermal population of rotational states and interconversion between cis and trans isomers. However, due to the symmetry and structure of the benzonitrile molecule in the bulk ionic liquid and within the Au monolayer, we can rule out the above as sources of our observed broadening. Detailed study of the line widths in these experiments is the subject of future studies since they relate to solvation and spectral dynamics which are outside the realm of this paper.

Discussion Based on the experimental and computational data presented so far, we will arrive at a relation between the Hammett parameter σ p and the electric field F using the nitrile stretch frequency as a tool. We will perform this task at three levels. First we will use the range of frequencies for which we have overlapping experimental data for both electrochemistry and the Hammett series. Second, due to the limited range of the electrochemical data, we will use the entire range of frequencies spanned by the Hammett series against computed Stark shifts, including nonlinear behavior of frequency at large field values. Finally, we discuss a direct relation between the two concepts that does not rely on the nitrile frequency and is based on computed charge densities.

17



Page 18 of 35

First, we use the known Stark tuning parameter ∆µ = 0.36cm−1 /(MV /cm) 33,35 to convert the experimentally measured frequencies as a function of potential to electric field values F. The use of linear Stark shift in the relatively narrow range of experimentally observed frequency changes is justified as was explained in the previous section. If we measure the electric field relative to the field when the applied potential is zero, we can write the following relation:

νCN (F) = (0.36

cm−1 ) F + 2229.4 cm−1 MV /cm

(2)

where ν0 = 2229.4 cm−1 is the frequency at zero applied potential relative to the reference electrode. The above relation is applied to the experimental data and plotted in figure 6.a. The data spans a range of frequencies from 2224 cm−1 to 2232 cm−1 . Although it is desired to experimentally apply a wider range of electric fields, but unfortunately this range is limited by the tolerance of the SAM to redox chemistry and the electrochemical window of the electrolyte.

(a)

(b)

Figure 6: (a) Experimentally determined frequency shifts correlated with field using the mercaptobenzonitrile Stark tuning rate. (b) Experimentally obtained frequencies as a function of Hammett parameter σ p ranging from -0.37 to +0.45. Second, within the same range of frequencies that were spanned by the electrochemical measurements, we collect the frequencies of all of the molecules in the Hammett series and plot them versus their Hammett parameter (Figure 6.b), yielding essentially a zoomed in version of figure 4.b. As commented in the earlier section, the scatter in this data is not a consequence of experimental noise or solvatochromic differences between different molecules, but rather inherent to the 18


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molecules and is reproduced in computations. Fitting this data to a linear relation yields:

νCN = (10.15 ± 4 cm−1 )σ p + (2228 ± 0.86 cm−1 )

(3)

As argued before, the CN frequency responds to the polarization of the molecule, whether that polarization is induced by an external field or by a functional group. Therefore, it justifies comparing equation 2 and equation 3 to yield a relation between electric fields F and σ p as:

F = 27.5 (MV /cm)σ p − 2.71 (MV /cm)

(4)

This relation is our first main result that can be used to inter-convert between the Hammett parameter σ p and the electric field F. Two main limitations should be considered when using this relation. First, the range of experimentally applied fields is relatively narrow, spanning a Hammett range of −0.37 ≤ σ p ≤ 0.45 as seen in figure 6.b. Second, the assumption of linear fit of frequencies to Hammett parameter clearly does not hold for larger values as seen in figure 4.b. To understand this problem, we extend the range of electric fields in our computation to span a wider range of Stark shifts (figure 7.a). Interestingly, the computed results in figure 7.a show that while a linear dependence of frequency versus field is valid over a narrow range, the computed frequencies deviate from linear dependence in a way that is very similar to the dependence of frequency on the Hammett parameter. At large positive fields and Hammett parameters the nitrile frequency change tapers off and does not change as rapidly as for large negative fields and Hammett parameters. This observation is yet another piece of evidence in favor of the fundamental relation between these two concepts over a wide range. To create a νCN (F) relation that would be valid over a larger range, we fit the computational results presented in figure 7.a to a second order polynomial:

νCN (F) = A F 2 + B F +C −1

−1

(5)

cm cm −1 B = 0.37 (MV with the fit yielding A = −0.003 (MV /cm) and C = −0.19 cm . This fit, /cm)2

along with the computed frequencies, is shown in figure 7.a. 19



(a)

(b)

Page 20 of 35

(c)

Figure 7: Computed nitrile frequencies as a function of (a) applied field (b) Hammett parameters σ p . Red circles are the data points and black lines are the fits. (c) Relation between electric field and σ p . Next, to create the νCN (σ p ) relation, we return to the computed frequencies for the Hammett series presented in figure 7.b. Use of computed frequencies is reasonable since they will be correlated with computed Stark shifted frequencies. Fitting the frequencies versus the Hammett parameters to a second order polynomial yields:

νCN (σ p ) = A σ p2 + B σ p +C

(6)

where A = −3.94 ± 2.75 cm−1 , B = 9.90 ± 1.82 cm−1 and C = 2349.5 ± 1 cm−1 . Figure 7.b shows this fit superposed on the computed data. Equipped with equations 5 and 6, we arrive at a relation between electric field and Hammett parameter that is based on a broader range of parameters and accounts for the nonlinear behavior of frequency versus either of the two parameters. This relation is presented in figure 7.c. When fitted to a second order polynomial, it yields:

F = A σ p2 + B σ p +C

(7)

where A = −4.84 ± 0.12, B = 24.56 ± 0.08 and C = −3.25 ± 0.05. This is our second and refined result for connecting the Hammett parameter to electric field. A plot of this relation is shown in figure 7. 20


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Finally, unlike in the experiments, computation allows for directly estimating the charge density ρ on any atom in the molecule either as a function of substituent or external field. Just like the frequency, charge density is also sensitive to the external field and Hammett parameter. 18,27 Therefore, as an alternate means of connecting the Hammett parameter to electric field, we choose to use the charge density on the nitrogen atom of the CN moiety as a reference. Towards this goal, we plot the charge density on nitrogen ρN as a function of external field and as a function of Hammett parameter. The plots show that ρN has a reasonably strong linear correlation with respect to both field and the Hammett parameter. This is in accordance with the intended wide usage of the Hammett parameter in chemistry and is consistent with previous studies. 4,9,14 However, here we take an additional step by studying ρN with respect to an external field to allow linking external fields with the Hammett parameter. Following a similar approach as for the frequency data, ρN can be fitted as a function of F and σ p , and the two resulting equations correlated with each other and fitted to the following linear relation:

F = 16 ± 3(MV /cm) σ p

(8)

Therefore, based on this method, one unit of Hammett parameter corresponds to about 16 MV/cm of polarizing external field. There is no offset in this relation because the reference molecule for both the Hammett-ρN and field-ρN relations is unsubstituted benzonitrile in zero field. The error in the above comes mainly from the fit of charge density on nitrogen with respect to Hammett parameter (figure 8.b). The error in charge density with respect to field is quite small as evidenced by a good linear fit (figure 8.a). Figure 9 summarizes the results of the three methods used in our study to correlate Hammett parameter σ p and electric field. To reiterate, these methods are based on experimental frequency changes, computational frequency changes, and charge density changes on nitrogen in response to both σ p and electric field. It is important to note that the relation retrieved based on experimental results matches very closely with the relation retrieved from computational results for frequencies. The experimental 21



(a)

(b)

Page 22 of 35

(c)

Figure 8: Computed ρN as a function of (a) applied field (b) Hammett parameters σ p . Red circles are the data points and black lines are the fits. (c) Relation between electric field and σ p .

From expt. From calc. From

CN CN

N

Figure 9: Relation between σ p and electric field based on experimental frequency changes (blue), computational frequency changes (green), and charge density changes on nitrogen ρN (red)

22


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relation (blue line) is retrieved from two very different experiments - electrochemical vSFG Stark shift spectroscopy of molecules tethered on a surface and bulk FTIR spectroscopy of the Hammett series molecules. The computational relation (green line) is based on frequency calculations at DFT level within an electric field and for the Hammett series. The fact that they corroborate each other is a testament to the reasonability of our approach. To identify the extent of nuclear displacement under the influence of electric field, we have also extracted CN bond lengths as a function of electric field and Hammett parameter. The results are shown in the SI. In summary, we find that the bond lengths do not change appreciably in response to both field and Hammett substituents. Therefore, confirming that the origin of the induced polarization is electronic in nature. The change in nuclear displacement computed here is in reasonable conformity to the values reported earlier in the literature. 72 We also note that the relation based on charge density ρN (red line) deviates from that retrieved based on frequency measurements and calculations (blue and green lines), especially in the negative Hammett parameter region. This deviation suggests that the results should be used with some restriction. To understand this better, we clarify with an example. If one places a conjugated system perpendicular to an electrode and apply a field of about 8 MV/cm along its body oriented toward the electrode, the influence of this field on the charge density on the terminus away from the electrode would be roughly analogous to attaching a CF3 group (σ p ∼ 0.5) to the para position of the molecule. However, a much larger field (about -18 MV/cm) would be necessary to produce a frequency shift that is equivalent to a functional group of σ p = −0.5 (green line in the figure). Therefore, in assessing the equivalence of the electric fields to the Hammett parameters, one should consider the molecular property that is expected to be influenced. It is reasonable to question the extent to which the thiol bond to the gold electrode allows leakage and conjugation of electrons from gold to the benzene ring (and eventually to the antibonding orbital of the CN group). The extent of this hybridization with the gold electrode would manifest itself as a frequency shift on nitrile, with more electron donation from gold leading to more red-shift in frequency. Therefore, it is important to compare the frequency of gold-bound mercap-

23



tobenzonitrile in contact with air with that of benzonitrile in a low dielectric constant solvent (to avoid large solvatochromic shifts). The frequency of the former is 2229 ± 1 cm−1 , 19,33,64 while that of the latter is 2232 cm−1 (benzonitrile in cyclohexane). The proximity of these numbers indicates that while some electron donation from gold to the nitrile may be possible, it is certainly not so large that it would deviate from the extent of donation by a low-Hammett parameter substituent. Although it is common in molecular electronics field to treat the thiol junction as electronically conductive, 73,74 it should be born in mind that very large fields are applied in those instances. The next question that arises is whether during the application of potential, we transfer a significant amount of charge from gold to the molecules. We are quite sure that mercaptobenzonitrile does not get reduced in the range of potential studied (i.e. full unit charge or one electron per molecule is not transferred from the gold to the nitrile layer). It is well known that a reduced benzonitrile will undergo a very large (∼ 150cm−1 ) red shift, 75 which is definitely not what we observe. Of course, with increasing reducing potentials the above will be possible and can lead to reductive desorption of the molecules, sometimes irreversibly. However, we have remained clear of those limits. As to whether partial charge transfer between gold and benzonitrile is possible or not during our experiments, we cannot comment, since our experiment (vibrational frequency shift) is unable to uniquely decipher that. Experiments with less-conducting linkers are desirable, but it should be born in mind that in those cases the benzene ring will also be placed farther away from the surface, therefore it would be difficult to isolate the field-only versus partial electronic charge transfer effects from each other. For this work, the proximity of the values of frequency of mercaptobenzonitrile tethered on gold and benzonitrile in low-dielectric environment (quoted above), gives us some reason to believe that the electron leakage from gold into the benzene ring is within the limits that is normally expected for a low-Hammett parameter substituent, and therefore remains within the realm of treatment in this work. Finally, we highlight the utility of the relations between field and Hammett parameter that we have discussed so far. These relations can be used to connect seemingly different homogeneous and heterogeneous chemistry phenomena. For example, charge density on an atom, such as a hete-

24


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rocyclic nitrogen in a conjugated system, is clearly related to the Hammett parameter of functional groups in that system and this charge density influences its pKa . If such a system is placed at an electrochemical interface, the interfacial field can also change the pKa of that nitrogen. Using the relations in this work, it will be possible to estimate the pKa as a function of interfacial field, and consequently as a function of electrochemical potential. Similarly, the substituents in the periphery of a homogeneous organometallic system affect the energetics of the frontier orbitals of the metal center. If that system is placed near an electrode, similar changes can be achieved using a polarizing field. The relations discussed in this work are useful in estimating the fields necessary to achieve these changes. Caution should be exercised when using these relations in cases where inhomogeneous fields are applied, or when the molecules have a more complicated substitution pattern. The polarizing effect of a substituent at ortho or meta position may not be conveniently described by a homogeneous field, or not by a field at all. It may be possible to study such effects in molecular junctions, where large fields can be applied directly at the single molecule level with somewhat controllable orientation. Further work is needed to understand such intricacies. As we pointed out in an earlier section, Hammett parameters are retrieved from comparison of pKa values of substituted benzoic acids. It is desirable to arrive at a generalized parameter that would serve the purpose of quantifying the polarizing effect of various substituents without relying on a reference molecule. We hope in the future our data can inspire work in that direction.

25



Acknowledgement The authors gratefully acknowledge support from several sources. SS and JD were supported by the Air Force Office of Scientific Research AFOSR award FA9550-18-1-0021. JP and JD were supported by the NSF CAREER Award (1454467).

Supporting Information Available The supplementary information has experimental plots, further computational details and fit parameters with confidence interval. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Graphical TOC Entry Hammett Electron Withdrawing Parameter

Electric Field

𝐹 = 𝐴 𝜎2 + 𝐵 𝜎 + 𝐶

Field

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Hammett Parameter 𝝈𝒑

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Electrodes as Polarizing Functional Groups: Correlation Between

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