Raman intensity interpretation of pyridine liquid and its adsorption on the Ag electrode via bond polarizabilities

Spectrochimica Acta Part A 77 (2010) 948–953

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Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy journal homepage: www.elsevier.com/locate/saa

Raman intensity interpretation of pyridine liquid and its adsorption on the Ag electrode via bond polarizabilities Chao Fang a,b , Guozhen Wu a,∗ a b

Molecular and Nano Sciences Laboratory, Department of Physics, Tsinghua University, Beijing 100084, China Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China

a r t i c l e

i n f o

Article history: Received 14 April 2010 Received in revised form 14 July 2010 Accepted 4 August 2010 Keywords: Raman intensity Bond polarizability Pyridine SERS

a b s t r a c t The temporal bond polarizabilities of pyridine adsorbed on the Ag electrode under various applied voltages are obtained from their surface enhanced Raman intensities. In so doing, the delicate bond behaviors of pyridine molecule in the surface enhanced Raman process are well demonstrated, including the effects by the charge transfer and electromagnetic mechanisms. Furthermore, the adsorption effect is well reflected by the bond polarizabilities after relaxation as contrasted with the calculated bond electronic densities in the ground state. The work of pyridine liquid is also shown because its comparison with that under adsorption deepens our understanding of the Raman process. Though the method is semiclassical and simple as contrasted with those based on the quantum chemistry, it indeed offers us a very clear physical picture. This work demonstrates that this approach is quite universal for the Raman active systems even under adsorption as far as their Raman profiles are well measured. © 2010 Elsevier B.V. All rights reserved.

1. Introduction We have paid attention to analyzing the Raman intensity from the viewpoint of bond polarizability [1–8]. We note that polarizability is a measure how strong the charges are bound to the nuclei and how many they are in a molecule. The stronger the binding force is to the nuclei, the smaller the polarizability is. The more the charges are, the larger the polarizability is. The philosophy is that embedded in the intensity, there is a lot of information about the molecular electronic structure during the Raman process. The main theme of this approach is to obtain the polarizability for each bond from the Raman intensity. In so doing, very detail molecular properties as far as the Raman process is concerned can be obtained. In fact, the bond polarizabilities show the properties of the Raman excited virtual state including its decaying (relaxation) in the non-resonance case. More specifically, the bond polarizabilities reflect the molecular electronic distribution as evidenced by the vibronic coupling in the virtual state. This approach offers us a very clear physical picture for the electronic structure of the virtual state which would be very hard to figure out by the traditional quantum-chemical algorithm. This is because that the virtual state is not an eigenstate with which the quantum-chemical algorithm mainly deals. It needs emphasis that our approach is based on the experimental Raman intensity and its analysis and therefore is not a purely theoretical one. In fact,

∗ Corresponding author. Fax: +86 10 62781604. E-mail address: [email protected] (G. Wu). 1386-1425/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.saa.2010.08.026

our approach is very similar to the X-ray structural determination as far as the algorithm is concerned though it is in the visible (UV) light region and it is the bond polarizability that is to be determined, instead. We start from the Chantry’s formula [9]: Ij ∼I0

(v0 − vj )4



vj

∂˛ ∂Qj

2

Here Ij is the Raman intensity of the jth normal mode with

wavenumber vj . ∂˛/∂ Qj is the electronic polarizability derivative with respect to the normal coordinate Qj . v0 is the wavenumber of the exciting laser. In fact, we can have the temporal Raman intensity Ij (t) from the experimental Raman signal in the wavenumber domain (Ij ()) by Fourier transformation (by setting the central peak position to 0), that is,



Ij (v)ei2vt dv = Ij (t) As t = 0, this turns out to be



IJ (v) dv = Ij (0) Hence, we note that the integrated Raman signal over the wavenumber domain just corresponds to the intensity in the time domain at t = 0 (This is defined as the initial moment of the virtual state). Thus, the Chantry’s formula was originally proposed for t = 0 and it is for this reason that it is extended to nonzero t [6]. For a

C. Fang, G. Wu / Spectrochimica Acta Part A 77 (2010) 948–953

just reasoning of this extension of Chantry’s formula from the correlation viewpoint, an appendix has been shown in Ref. [8] and is reproduced in Appendix A here for convenience. We thus have

 (v0 − vj )2   ∂˛(t)  ± Ij (t)∼ I0  Lkj 

∂Sk

vj

by transforming Qj to the bond coordinates Sk ’s through Sk =



Lkj Qj

which can be obtained from the normal mode analysis [10]. By defining ajk =

(v 0 − v j ) 2



vj

Lkj

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The relative bond polarizabilities can be figured out if the above equation set is inverted and if the phases preceding the intensities can be determined. For the phase determination, various sets of {Pj } can be assumed to obtain ∂˛/∂Sk ’s which are then checked with physical considerations to rule out the inadequate {Pj } sets. In our previous study [1–8], it was found that quite often, a unique or a limited number of {Pj } sets can be figured out with physically significant ∂˛/∂Sk ’s. This concludes the main theme of our algorithm. In this work, we will report our work on the surface enhanced Raman scattering (SERS) of pyridine on the Ag electrode. For contrast, the work of pyridine liquid will also be demonstrated. Pyridine was the first SERS case reported [11–15]. We will see indeed that unique results can be obtained and, to our best knowledge, they have not been reported previously. In the discussion, the commonly recognized mechanisms for SERS will be adopted [14,15]. They are the electromagnetic and the charge transfer mechanisms.

we have the following matrix equation set:

⎛

P1

 I1 (t)

⎞

⎛

⎞

∂˛(t)/∂S1 ⎜ P2 I2 (t) ⎟ ⎜ ∂˛(t)/∂S2 ⎟ ⎜ ⎟ ⎜ ⎟ . ⎜ ⎟ . ⎟ ⎜ ⎟ = [ajk ] · ⎜ ⎜ ⎟ . . ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ . .  ∂˛(t)/∂S3N−6 P3N−6 I3N−6 (t) Here, the phase Pj is + or − which cannot be obtained from the experiment or calculation and needs determination. In this formalism, only the relative magnitudes of the Raman intensities will be of concern. So are the relative bond polarizabilities.

2. The experimental The pyridine liquid (analytical reagent) was purchased from Aldrich Chemical Co. Ltd. without further purification. Its Raman spectrum was recorded with Renishaw RM1000 micro-confocal spectrophotometer. A 50× objective was used to perform an 180◦ backward scattering configuration. The excitation source is the 514.5 nm line of Ar ion laser and the laser power on the sample was about 10 mW. The slit width for scattering light entrance was 20 ␮m and the integral time was 20 s.

Fig. 1. The Raman spectra of (a) pyridine liquid and (b) pyridine SERS under different potentials. The * symbol for (a and b) are those peaks that are employed for the elucidation of the bond polarizabilities. (c) The deconvolution for the spectral profile (SERS at −0.7 V) due to the C–H vibration. The dash lines are the deconvoluted components. See text for details.

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C. Fang, G. Wu / Spectrochimica Acta Part A 77 (2010) 948–953 Table 1 The A1 symmetry coordinates of pyridine in terms of the bond stretching and angular coordinates. ˛i,j,k shows the angular deformation defined by the atoms i, j and k. See Fig. 1 for the atomic numberings. Symmetry coordinates

Representation

S1

√1 (N1C2 + N1C6) 2 √1 (C2C3 + C5C6) 2 1 √ (C3C4 + C4C5) 2 √1 (C2H7 + C6H11) 2 1 √ (C3H8 + C5H10) 2

S2 S3 S4 S5

C4H9 √1 (˛6,1,2 − ˛1,2,3 + ˛2,3,4 − ˛3,4,5 + ˛6,5,4 − ˛1,6,5 )

S6 S7

6 1 √ (2˛6,1,2 − ˛1,2,3 − ˛2,3,4 + 2˛3,4,5 2 3 1 (˛1,2,7 − ˛3,2,7 + ˛1,6,11 − ˛5,6,11 ) 2 1 (˛2,3,8 − ˛4,3,8 + ˛6,5,11 − ˛4,5,10 ) 2

S8 S9 S10

Fig. 2. The atomic numberings of the pyridine molecule. Also shown is its presumed adsorption configuration on the Ag electrode. The arrow shows the direction of the electric field operating in the electromagnetic mechanism for SERS. See text for details.

In order to obtain the SERS spectrum of pyridine, a tri-electrode cell was used to perform oxidation–reduction cycle (ORC). The working electrode was a silver plate of 99.9% purity (polished with alumina of size 0.3 ␮m) and a platinum wire was used as the counter electrode. A saturated calomel electrode (SCE) was employed as the reference to which all the potentials are referred. Ten ORC’s in 0.1 M KCl solution were done with applied voltage shifted between −0.2 V (kept for 5 s) and 0.6 V (kept for 10 s) to roughen the electrode. The scanning speed of the applied voltage was 40 mV s−1 and the electrode potential was controlled using a CHI 600B electrochemical workstation. After ORC, the roughened electrode was immersed in a solution containing 10−3 M pyridine for the SERS measurement. The SERS measurement condition was the same as that for the pyridine liquid except that the power focused on the electrode was about 5 mW and the entrance-slit width was 30 ␮m. Shown in Fig. 1(a) and (b) are the Raman spectra of pyridine liquid and its SERS under different potentials, respectively. In order to obtain accurate Raman intensity, the corrections due to the variant responses of the grating mirror and CCD detector in the various spectral ranges and polarizations were considered. The spectra were taken in a duration as short as possible to minimize the factors that might affect the environment the sample stays. In this work, only the relative intensities are considered. A deconvolution software was taken to resolve the intensity profile into Gaussian components if there is overlapping. Shown in Fig. 1(c) is the deconvolution of the spectral region due to the C–H vibration of SERS case at −0.7 V, for demonstration. The other situations including the liquid case are quite the same. The uncertainty of Raman intensities is less than 20%. The temporal Raman intensities were obtained by Fourier transformation from the experimental Raman intensities in the wavenumber domain.

− ˛6,5,4 − ˛1,6,5 )

The procedure of the normal mode analysis was to refine the force constants which were initiated by DFT with ub3lyp/cc-pvDZ till the calculated mode frequencies and the measured ones were consistent. This procedure was performed for pyridine liquid and its SERS cases, respectively, with reference to Refs. [16–18]. However, for pyridine liquid and its SERS cases, the corresponding [Lkj ] matrices are very similar (even for the SERS cases under various applied voltages with minor wavenumber shifts) and so are their potential energy distributions (PED). The corresponding observed wavenumbers, fitted wavenumbers, relative intensities (integrated over wavenumber) and PED are tabulated in Table 2. Once [Lkj ] matrix is obtained, [ajk ]−1 matrix can be calculated. 4. The elucidation of the bond polarizabilities For the elucidation of the bond polarizabilities, for each set of {Ij (t)}, we just tried various phase combinations {Pj } to obtain ∂˛(t)/∂Sk ’s which are then checked if they are appropriate. The criterion for the phase choice is that: all the bond stretching polarTable 2 The experimental Raman wavenumbers, the fitted wavenumbers, their relative intensities and the potential energy distributions (only those larger than 10 are shown) for pyridine liquid (the upper ones) and its SERS on the Ag electrode, at −0.7 V (the lower ones). Since their fitted wavenumbers are the same, they share the same PED and L matrix. See text for details. Raman shift (cm−1 )

Intensity

Potential energy distribution (%)

No.

Exp.

Fitted

514.5 nm

1

3068 3070

3069

30 22

S5 67 ; S6 32

2

3055 3055

3056

100 88

S6 63 ; S5 30

3

3030 3033

3030

34 34

S4 80 ; S5 13

16 100 4 9

S2 46 ; S3 17 ; S10 13 ; S9 11

4 5

1583 1583 1482 1482

1582 1480

S9 45 ; S10 28 ; S1 15 ; S3 12

3. The normal mode analysis

6

1219 1213

1220

20 79

S9 44 ; S1 23 ; S10 19 ; S2 13

The atomic numberings of the pyridine molecule are shown in Fig. 2. Its configuration is realized by the density functional optimization (DFT algorithm with ub3lyp/cc-pvDZ) and is considered to be of C2v symmetry with 10 modes of A1 symmetry. This symmetry is preserved if the pyridine molecule is adsorbed vertically on the electrode surface through its nitrogen atom as shown therein. The 10 mode peaks are labeled by * in Fig. 1(a) and (b). The 10 symmetry coordinates adopted [16] are also shown in Table 1.

7

1071 1067

1073

3 15

S10 40 ; S3 20 ; S1 19 ; S7 15

8

1029 1029

1027

20 56

S7 42 ; S3 38 ; S2 17

9

991 1002

997

22 94

S1 38 ; S7 30 ; S2 19 ; S3 10

10

603 622

611

10 26

S8 97

C. Fang, G. Wu / Spectrochimica Acta Part A 77 (2010) 948–953

Fig. 3. The relative bond polarizabilities for (a) pyridine liquid (both the values at the initial moment () of Raman excitation and the final stage (䊉) of relaxation). Shown therein are also the relative calculated bond electronic densities () of the ground state of pyridine molecule. Those of C3–C4 are normalized to 10, for convenience. Note that there is no correlation between the values of the bond polarizabilities and the bond electronic densities. (b) Pyridine SERS case (initial moment of Raman excitation). The bond polarizability of C2–C3 at −0.7 V is normalized to 100. Note those of the equivalent bonds are not shown for short. See text for details.

izabilities be positive as time elapses [19]. (The polarizabilities for the angular coordinates are usually very small as compared with those of the stretching coordinates. Hence, we will only pay attention to the bond stretching polarizabilities. For short, they are called the bond polarizabilities, hereafter.) With this criterion, we found that there are two phase solutions for pyridine liquid and the SERS cases. However, we are very fortunate that among these two solutions, the corresponding bond polarizabilities are very similar, both for the cases of liquid and SERS. They are shown in Fig. 3(a) and (b) (note that the equivalent bonds are not shown for short). Finally, we will need the relative bond electronic densities of the ground state of pyridine molecule to help the interpretation of the bond polarizabilities after relaxation (roughly about 8 ps after the initial excitation). These bond electronic densities of the ground state were calculated by DFT with ub3lyp/cc-pvDZ. 5. Results and discussion For the pyridine liquid (Fig. 3(a)), we note that at the very initial moment of excitation, the polarizability of the C4–H9 bond is the largest and those of the rest C–H bonds are also larger than those of the skeletal C–N and C–C bonds. This indicates that the excited charges tend to the molecular peripheral C–H bonds at the initial moment of the Raman process. We will see that this behavior will

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change in the adsorption case. After relaxation (roughly about 8 ps after the initial excitation), the bond polarizabilities and the (relative) calculated bond electronic densities are very parallel. Both the bond polarizabilities and the calculated bond electronic densities of the C–C and C–N bonds are slightly larger than those of the C–H bonds. This indicates that we may approach the (relative) bond electronic densities from the experimental Raman intensities via their resolvation into bond polarizabilities. This will be very promising for us to obtain the (relative) bond electronic densities in other complicated systems of which these quantities are very hard to calculate. We will see this usage in the adsorption case. For pyridine adsorbed on the Ag surface (Fig. 3(b)), the enhancement of the polarizabilities of the C4–H9 bond (as compared with the C2–H7 and C3–H8 bonds) and the skeletal bonds, especially the C2–C3 bond (and their equivalent bonds. For short, we will not repeat the equivalent bonds, hereafter.) during the whole voltage range is obvious. In the voltage range from −0.1 to −0.7 V (w.r.t. SCE), the bond polarizability of the C4–H9 bond stays rather constant, though it enhances slightly. Then, it drops instantly as the voltage reaches −0.8 V. We may regard that SERS effect of the C4–H9 bond originates mainly from the electromagnetic mechanism. The argument is that the C4–H9 bond is vertical to the adsorption surface, and hence parallel to the electric field from the metal surface if the vertical adsorption configuration is adopted. By this orientation, the polarizability of the C4–H9 bond will be more enhanced by the electric field than the rest two C–H bonds just as observed since the latter two C–H bonds are not so parallel to the electric field. Furthermore, one notes that the charge transfer in SERS, if it does occur, will hardly involve the C4–H9 bond (and the rest two C–H bonds) due to its deficiency of the benzenoid  charge which would play the main role for the charge transfer mechanism. As this behavior of the C4–H9 bond is compared with those of the skeletal bonds which enhance significantly as the voltage sweeps from −0.4 to −0.7 V, we assert that, in this voltage range, the polarizabilities of the skeletal bonds are enhanced more through the charge transfer mechanism through the benzenoid  charge. (Of course, their enhancement through the electromagnetic mechanism is not completely ruled out.) We note that the polarizability enhancements of the N1–C2 and C3–C4 bonds are of the same order and less than that of the C2–C3 bond. This hints the conjugation effect if the charge transfer to/from the electrode surface is drawn. The polarizability enhancements of the C2–H7 and C3–H8 bonds are barely eminent during the whole voltage range. As noted previously that this is not unexpected if their deficiency of the  charge and that they are not so parallel to the electric field from the metal surface are noted. After relaxation (about 8 ps), as shown in Fig. 4, the polarizability of the N1–C2 bond is eminently the largest. As this observation is compared to the (relative) calculated bond electronic densities of the ground state of pyridine molecule (also shown in Fig. 4) in which the polarizability of the N1–C2 bond is not so distinct and unique, we infer that the adsorption site is indeed on the N atom. We note that for the liquid case, the bond polarizabilities after relaxation (shown in Fig. 3(a)) are very congruent to the bond electronic densities. Therefore, these bond polarizabilities retrieved from the Raman intensities under adsorption, in fact, reflect the adsorption effect. All the relaxations of the temporal bond polarizabilities follow an exponentially decaying function. Their relaxation characteristic times, tc , are shown in Fig. 5 by the fit to the function of A exp( − t/tc ) + B. It is found that the characteristic times of the skeletal bonds are larger than those of the peripheral C–H bonds (under a designated applied voltage). This trend is opposite to the liquid case (also shown in Fig. 5). This can be interpreted as due to that the skeletal C–C and C–N bonds are more involved

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C. Fang, G. Wu / Spectrochimica Acta Part A 77 (2010) 948–953

is also shown for its comparison with that under adsorption. This comparison deepens our understanding of the Raman processes both in the liquid and adsorption cases. The essential of our approach is the temporal extension of Chantry’s formula for the Raman process and its exposition for the retrieval of the bond polarizabilities from the experimental intensities. Though the method is semi-classical and simple as contrasted with those based on the quantum chemistry, it indeed offers us a very clear physical picture for the molecular behaviors in the Raman process via the vibronic coupling. This work demonstrates that our approach is quite universal for the Raman active systems even under adsorption as far as their Raman profiles are well measured. Acknowledgements

Fig. 4. The relative bond polarizabilities after relaxation (8 ps after initial excitation) for pyridine SERS. Also shown are the relative calculated bond electronic densities of the ground state. The values of C2–H7 under various applied voltages and its bond electronic density are normalized to 10 for convenience. Note that there is no correlation between the values of the bond polarizabilities and the bond electronic densities.

This is supported by the National Natural Science Foundation of China (grant no. 20773073), the Key grant Project of Chinese Ministry of Education (No. 306020) and the Specialized Research Fund for the Doctoral Program of Higher Education. Appendix A. Formally, as well known, at t > 0, Ij (t) is related to the product (correlation) of the polarizability derivative at time 0 and time t, i.e.,

Ij (t) ∝

∂˛(t) ∂Qj



By supposing ∂˛(t) = ∂Qj

∂˛(0) ∂Qj





∂˛(0) f (t) ∂Qj

where f(t) is a decaying function, then

Ij (t) ∝

∂˛(0) ∂Qj

2

f (t) =

∂˛(0)  f (t) ∂Qj

2

We may regard Fig. 5. The relaxation characteristic times, tc , for the bond polarizabilities of pyridine adsorbed on the Ag electrode under various applied voltages and the liquid case.

in the charge transfer mechanism than the peripheral C–H bonds. This is based on the conjecture that the bond polarizability relaxation for the charge transfer mechanism will be longer than that for the electromagnetic mechanism since the former involves the transfer of charges and therefore needs longer time for its relaxation. We note also that as the applied voltage is shifted from −0.1 toward −0.7 V, the characteristic times become larger for all the bonds, in general, and notably for the skeletal bonds. This shows that the charge transfer mechanism becomes more eminent as the applied voltage is shifted toward −0.7 V and that this mechanism is more involved with the skeletal bonds as discussed previously. 6. Concluding remarks In this work, the temporal bond polarizabilities of pyridine adsorbed on the Ag electrode under various applied voltages are obtained from their SERS intensities. In this way, the delicate bond behaviors of the adsorbed pyridine molecule in the Raman process are well demonstrated, including the effects by the charge transfer and electromagnetic mechanisms from the electrode surface. Furthermore, the adsorption effect is well reflected by the bond polarizabilities after relaxation as contrasted to the calculated bond electronic densities of the ground state. The work of pyridine liquid



∂˛(0) ∂Qj



f (t)

as the formal polarizability derivative ∂a(t)/∂ Qj , then

Ij (t) ∝

∂a(t) ∂Qj

2

Note that ( ∂ a(0)/∂ Qj ) =(∂ ˛(0)/∂ Qj ) since f(0) = 1. Hence, we can relate Ij (t) to the square of the (formal) polarizability derivative at time t. For simplicity and without confusion, we may make no difference between ∂a(t)/∂ Qj and ∂˛(t)/∂ Qj as we did in the text. If f(t) is an exponential function, then the decaying characteristic times of ( ∂ a(t)/∂ Qj ) and ( ∂ ˛(t)/∂ Qj ) differ by a factor of 2. In the text, we refer to that of the formal polarizability derivative. From Ij (t) ∝[∂ ˛(0)/∂ Qj ]2 f(t) and Ij (0) ∝[∂ ˛(0)/∂ Qj ]2 , we have Ij (t) ∝ Ij (0)f(t). Ij (t) can be obtained from the Fourier transform of Ij  () in the wavenumber domain by re-setting its central wavenumber to 0. References [1] [2] [3] [4] [5]

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