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Temporal Raman polarizabilities of piperidine in liquid and on the Ag surface with electromagnetic enhancement
Journal of Molecular Structure 938 (2009) 336–340
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Temporal Raman polarizabilities of piperidine in liquid and on the Ag surface with electromagnetic enhancement Chao Fang, Guozhen Wu * Molecular and Nano Sciences Laboratory, Department of Physics, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 8 August 2009 Received in revised form 28 September 2009 Accepted 2 October 2009 Available online 12 October 2009 Keywords: Raman intensity Temporal bond polarizability Relaxation of virtual state Piperidine SERS
a b s t r a c t The temporal bond polarizabilities from the Raman intensities for liquid piperidine and its adsorption on the Ag electrode were obtained. The bond polarizabilities are important molecular parameters which show the bond electronic behavior during the Raman process. For the liquid piperidine, it is noted that the bond polarizability at the final stage of relaxation of the Raman virtual state is parallel to the quantum chemically calculated bond electronic density of the ground state. This opens a new way to observe the bond electronic density simply from the experimental Raman spectrum. For the piperidine adsorbed on the Ag electrode, it is inferred from the elucidated bond polarizabilities that the electromagnetic mechanism dominates the surface enhanced Raman effect, showing that the equatorial C–H bond is enhanced more than its axial companion. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It has been generally recognized that Raman process involves the excitation of the virtual state (nonresonance case) including its relaxation [1]. In the virtual state, there is vibronic coupling which shuttles the energy between the electronic and the nuclear coordinates. Thus, the information of the vibronic coupling is embedded in the scattering Raman intensity. The way to explore this information from the spectral intensity is an interesting topic since it involves the very basics of the Raman process. In our past works [2–11], an algorithm has been developed for this purpose and various systems have been tested thereby to reveal significant physical and chemical properties of the Raman virtual states. These observations demonstrate that this algorithm is effective and rewarding. Surface enhanced Raman scattering (SERS) [12] is a phenomenon for which the Raman intensity of an adsorbed molecule on the metal surface is enhanced greatly. This is due to the interaction between the adsorbed molecule and the metal surface. The mechanisms are generally believed to be due to the charge transfer between the adsorbed molecule and the metal surface and/or the electromagnetic effect due to the very strong local electric field around the adsorbed molecule on the metal surface. Piperidine is a typical molecule showing strong surface enhanced Raman effect. Some works have been devoted to its SERS, such as its charge transfer effect [13,14], applied potential dependence [15].
* Corresponding author. Tel.: +86 10 62781606 194; fax: +86 10 62781604. E-mail address: [email protected] (G. Wu). 0022-2860/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.10.006
Albeit so many works have been devoted to SERS, very few are on a systematic study on its intensity. In this sense, we address that our approach is rather unique and the importance of the elucidated bond polarizability from the Raman intensity by our algorithm in deepening our understanding of SERS will be obvious as demonstrated in this work. We have explored its SERS intensities during our early work [2] in developing this algorithm. But that work only refers to the initial moment of the Raman process. In this report, we will show the temporal development of its bond polarizabilities and conclude that its SERS effect mainly originates from the electromagnetic mechanism. This is variant from our early work. We attribute it to the different electrode surface treatments. Furthermore, this work is accompanied with that on liquid piperidine which was not tried on previously. We will see that the comparison of these results does deepen our understanding of this piperidine system by our algorithm which is based on the Raman intensity analysis. In the followings, a short summary of our algorithm will be introduced first. Then, the analysis on liquid piperidine and its adsorption on the Ag electrode surface by 514.5 nm excitation will be followed. Finally, a concluding remark will be addressed as to the significance of our study. 2. The algorithm For demonstration, we will analyze the spectral intensity in the temporal domain Ij ðtÞ (index j is for the normal mode), which is related to the wavenumber domain I0j ðmÞ, through the Fourier R 0 transform as Ij ðmÞeimt dm ¼ Ij ðtÞ. We note that for t = 0, this
C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340
R
transformation reduces to I0j ðmÞdm ¼ Ij ðt ¼ 0Þ. Hence, the integrated Raman intensity over m is just the temporal intensity at t = 0. In the Fourier transformation, the central wavenumber of I0j ðmÞ is re-set to 0. The temporal Raman intensity Ij ðtÞ of the jth normal mode with Raman shift mj is related to the electronic polarizability derivative with respect to its normal coordinate Q j through [1,2,10] (for more exposition, see Appendix A):
Ij ðtÞ
ðm0 mj Þ4
ð@ aðtÞ=@Q j Þ2
mj
where m0 is the wavenumber of the exciting laser. This is an extension of Chantry’s formula [1]:
Z
I0j ðmÞdm
ðm0 mj Þ4
mj
ð@ a=@Q j Þ2
which is just
Ij ðt ¼ 0Þ
ðm0 mj Þ4
mj
ð@ aðt ¼ 0Þ=@Q j Þ2
R if we note from the last section that I0j ðmÞdm ¼ Ij ðt ¼ 0Þ. By transforming Q j ’s to the internal coordinates Rk ’s through
Rk ¼
X
Lkj Q j
which can be obtained from the normal mode analysis [16], we have:
qffiffiffiffiffiffiffiffiffi ðm m Þ2 X 0 j Lkj ð@ aðtÞ=@Rk Þ Ij ðtÞ pffiffiffiffi
mj
@ a=@Rk will be called the bond polarizability, for convenience. In matrix notation, if only relative intensities are considered, we have
2
@ aðtÞ=@R1
6 @ aðtÞ=@R 2 6 6 6 : 6 6 : 6 6 4 : @ aðtÞ=@R3N6
2
3
6 7 6 7 6 7 7 1 6 7 ¼ ajk 6 6 7 6 7 6 7 6 5 4
pffiffiffiffiffiffiffiffiffiffi I1 ðtÞ pffiffiffiffiffiffiffiffiffiffi P2 I2 ðtÞ
P1
: : P3N6
: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I3N6 ðtÞ
3 7 7 7 7 7 7 7 7 7 5
2
ðm mj Þ where ajk ¼ 0pffiffiffi Lkj and Pj is +1 or 1. m j
We will be restricted to the bond stretching coordinates since their bond polarizabilities are large and will offer significant physical interpretations. Another reason for this choice is that the motion between the stretching and bending coordinates is generally well decoupled. Then the dimension of the above matrix equation will be reduced to the number of bonds in a molecule. From the above derivation, it is clear that @ aðtÞ=@Rk is obtainable if ½ajk 1 matrix, Ij ðtÞ’s and a fPj g set are given. ½ajk 1 can be known from the normal mode analysis. Ij ðtÞ’s can be obtained from the Fourier transform of the Raman profiles. Then, various sets of fP j g can be tried to obtain @ a=@Rk ’s which are then checked with physical considerations to rule out the inadequate fPj g sets. The bond polarizability is a measure of the charge distribution on each bond of the virtual state including its relaxation. For comparison, we need the bond electronic densities qk of the ground state. This is calculated by DFT with ub3lyp/cc-pvDZ.
337
A 50 objective was used to perform an 180° backward scattering configuration. The excitation source is 514.5 nm line of Ar ion laser. The laser power on the samples was about 10 mw. The entranceslit width was 20 lm and the integral time was 20s. For SERS spectra, a tri-electrode cell was used to perform oxidation–reduction cycle (ORC). The working silver electrode was a silver plate of 99.9% purity (polished with alumina whose particle size was about 0.3 lm and then rinsed) 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 were quoted with respect. The ORC’s were done in 0.1 M KCl solution, with applied voltage being shifted between 0.2 V (kept for 10 s) and 0.3 V (kept for 20 s) for four times. The voltage scanning speed was 50 mV s1 and the electrode potential was controlled by a CHI 600B Electrochemical Workstation. After ORC, the roughened electrode was immersed in a solution containing 103 M piperidine and 0.1 M KCl to perform the SERS measurement. Shown in Fig. 2 are the Raman spectra of liquid piperidine and its SERS spectra under various potentials. For a careful intensity measurement, the corrections due to the different responses of CCD detector and the grating mirror along different polarizations and various spectral ranges were considered. For our purpose, only the relative intensities are considered. In the case that there is spectral profile overlapping, a deconvolution software was taken to resolve the profile into Gaussian components (Lorentzian profile fit is not excellent. However, this is not crucial in the following elucidation of the bond polarizabilities). Also, the background was offset in measuring the Raman peak intensity, if necessary. We estimated that the intensities were of uncertainty less than 20%, which would lead to an uncertainty less than 10% for the calculated bond polarizabilities. The temporal Raman intensities were obtained by Fourier transformation from the experimentally recorded Raman intensities in wavenumber. 4. The normal mode analysis The molecular structure of piperidine and the definition of its bond stretching coordinates are shown in Fig. 1. The configuration of piperidine is of C s symmetry and there are 25 symmetric modes among its 45 normal modes. For calculating ½ajk 1 matrix, further normal mode analysis was tried by refining the force constants which were initially simulated by DFT with ub3lyp/cc-pvDZ till the calculated mode frequencies and the measured ones are consistent [2,17,18]. This procedure was performed for liquid piperidine and the absorbed piperidine on the silver electrode, respectively. From the normal mode analysis, it was found that the coupling between the bond stretching and bending motions was very weak for this molecule. Hence, we will focus on the 10 bond polarizabilities corresponding to the 10 bond
3. Experimental Piperidine (liquid) was purchased from Aldrich Chemical Co. Ltd. The Raman spectra were recorded with a Renishaw RM1000 micro-confocal spectrophotometer equipped with a CCD detector.
Fig. 1. The molecular structure of piperidine and its bond stretching coordinates. The proposed adsorption configuration on the Ag electrode surface and the direction of the electric field originating from the surface are also depicted.
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C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340 Table 1 The normal modes of piperidine with their observed (experimental), fitted wavenumbers, relative intensities and the main potential energy distributions. For wavenumber and intensity columns, the data on the upper are for the liquid piperidine. The intensity of the mode at 2934 cm1 is normalized to 100. The data on the lower are for the SERS case at 1.0 V. The intensity of the modes at 2842 cm1 at 1.0 V is normalized to 100. Only PED’s for liquid piperidine are shown due to those for the SERS cases are very similar. Si (i = 1, . . ., 7, 22, 23, 25) are the bond stretching coordinates. Their explicit forms are listed in Table 2. The others are the bending coordinates. Mode
m1 m2 m3 m4 m5 m6 m7 m8 m9 m10
Wavenumber/cm1
Intensity
Potential energy distribution (%)
3345 3344 2950 2943 2930 2928 2921 2917 2889 2889 2850 2850 2730 2731 1474
53 0 76 92 100 73 69 67 49 87 72 100 42 0 12
S25 ð99:1Þ
– 1450 1455 1441
1476 1453 1453 1440
0 34 1 25
–
1441
0
EXP.
Fitted
3342 – 2947 2941 2934 2924 2918 2912 2895 2886 2853 2842 2731 – 1474
S2 ð47:2Þ; S4 ð46:3Þ; S22 ð5:1Þ S22 ð50:4Þ; S23 ð47:3Þ S1 ð92:1Þ; S3 ð6:4Þ; S7 ð1:3Þ S4 ð50:0Þ; S2 ð48:9Þ S23 ð49:3Þ; S22 ð48:6Þ S3 ð93:4Þ; S1 ð3:1Þ; S7 ð2:1Þ; S7 ð41:3Þ; S5 ð30:2Þ; S18 ð14:0Þ; S12 ð10:9Þ; S24 ð2:7Þ S21 ð80:1Þ; S7 ð9:4Þ; S15 ð8:2Þ; S5 ð50:3Þ; S10 ð21:4Þ; S12 ð16:8Þ; S15 ð10:3Þ
Table 2 The symmetry coordinates Si (i = 1, . . ., 7, 22, 23, 25) in terms of the bond stretching coordinates shown in Fig. 1.
Fig. 2. The Raman spectra by 514.5 nm excitation of (a) liquid piperidine and (b) its SERS under various potentials. The 10 Raman peaks whose modes are mostly of bond stretching components are labelled by whose frequencies are listed in Table 1.
S1 ¼ r1 þ r2 ; S2 ¼ r3 þ r 4 S3 ¼ s1 þ s2 ; S4 ¼ s3 þ s4 S5 ¼ d1 þ d2 ; S6 ¼ d3 þ d4 S7 ¼ t 1 þ t2 S22 ¼ u S23 ¼ v S25 ¼ w
stretching coordinates. Therefore, only 10 Raman peaks whose modes are mostly of bond stretching components are needed. They are shown by in Fig. 2. Their observed (experimental) wavenumbers, fitted wavenumbers, (relative) intensities and potential energy distributions (PED) are tabulated in Table 1 in which for the SERS case, only the data at 1.0 V are shown. Also, only PED’s for liquid piperidine are shown due to those for the SERS cases are very similar. In conclusion, the effect of adsorption under various applied voltages on ½ajk 1 matrix is negligible so that one may use one such matrix for all the cases.
5. The calculation of temporal bond polarizabilities For the 10 Raman intensities, we have 29 possible phase combinations (note that fP i g is identical to fPi g). The criterion for the phase choice is that: all the bond polarizabilities are of the same sign as time elapses. With this criterion, we were left with only four phase solutions. However, these four solutions are very similar and one of them is chosen for demonstration. All the bond polarizabilities follow the monotonically decaying behavior as time elapses. The (relative) bond polarizabilities of u, v, w, r1, r3, s1, s3, d1, d3, t1 coordinates (their equivalents under C s symmetry
Fig. 3. The (relative) bond polarizabilities of u, v, w, r1, r3, s1, s3, d1, d3, t1 coordinates (for their definitions, see Fig. 1) for liquid piperidine at the initial (j) and final (d) stages of Raman relaxation. Also shown are the quantum mechanically calculated bond electronic densities (4) of the ground state. All data are normalized with respect to those of u bond taken as 10. It should be noted that there is no correlation of data between the bond polarizabilities and the calculated bond electronic densities.
C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340
Fig. 4. The (relative) bond polarizabilities of u, v, w, r1, r3, s1, s3, d1, d3, t1 coordinates at the initial stage of Raman process for piperidine SERS cases under various applied voltages. All data are normalized with respect to that of u bond at 1.0 V taken as 100.
Fig. 5. The relaxation characteristic times, tc , of the various bonds for the liquid and SERS piperidine cases.
are not shown for simplicity) are shown in Figs. 3 and 4 for the liquid and SERS cases, respectively. The bond electronic densities of the ground state calculated by the quantal method are also shown in Fig. 3 for comparison. The relaxation characteristic times of the bond polarizabilities are the important parameters from the viewpoint of this temporal bond polarizability study. It was found in most cases that the relaxation can be well followed by one exponential function of the form: Aet=tc þ B. The relaxation characteristic times, tc , for all the cases are shown in Fig. 5. 6. Results and discussion A. For the liquid piperidine case, we have the following observations: (1) At the initial stage of Raman excitation, the bond polarizabilities of the peripheral C–H/N–H bonds are evidently larger than those of the skeletal C–C/C–N bonds (see Fig. 3). After relaxation (as t = 8 ps), the skeletal C–C/C–N bonds do possess larger bond polarizabilities, instead. This shows that at the very initial moment of Raman excitation, the charges are excited in the virtual state and
339
are spread out toward the molecular periphery due to electronic repulsion. This phenomenon is very similar to the splashing of water (excited charges) in a pan (molecule) when a pebble (photon) is thrown into it. We have also observed this behavior in our previous works on 2,3-aminopyridine [7,8], ethylene thiourea [9,10] and methylviologen [11]. We have accessed that this is a generic property of the Raman excited virtual states and this is again confirmed in this piperidine work. We further note that at the initial stage of Raman excitation, the axial s1 and s3 bonds (and their equivalent s2 and s4. For short, we will not repeat these equivalent bonds hereafter.) possess larger polarizabilities than their equatorial companions. While after relaxation, all the axial and equatorial bonds including N–H, possess quite the same polarizabilities albeit u and v possess comparatively larger polarizabilities. All these show the fine structural information of the Raman virtual state. The significance of these observations will be more transparent if they are contrasted with those of the SERS case as shown later. (2) Notable is that the bond polarizabilities after relaxation are parallel to those bond electronic densities of the ground state by the quantal calculation: the skeletal C–C/C–N bonds of the molecular ring possess larger electronic densities/polarizabilities than those of the C–H/N–H bonds which are almost identical except that u and v bonds possess slightly larger electronic densities/polarizabilities. This is very significant if one notes that the calculated bond electronic density is but a theoretical quantity which would be very hard to observe, if not impossible. We have also observed this behavior in our previous works on 2,3-aminopyridine [7,8], ethylene thiourea [9,10] and methylviologen [11] and this is confirmed again in this piperidine case. We think our works establish one way to observe the bond electronic densities of the ground state simply from the bond polarizabilities after relaxation which can be traced to the Raman intensities. B. For the adsorption case of piperidine on the Ag electrode, we note that: At the initial stage of Raman process, we note that N–H bond, unlike in the liquid case, possesses very small polarizability (see Fig. 4). This may be just caused by adsorption. This suggests that the adsorption site is on the N–H moiety. The skeletal C–C/C–N bonds also possess bare polarizabilities during the whole SERS process, probably due to the same cause. We further note that the equatorial C–H bonds do in most cases (under various applied voltages) possess larger polarizabilities than their axial companions (note the situation is opposite in the liquid case). This observation suggests that the adsorption configuration is vertical as depicted in Fig. 1 and the SERS mechanism involved is mainly the electromagnetic one since in this way, the electric field originating from the electrode surface is parallel to the equatorial C–H bonds (also shown in Fig. 1) and these bonds are, therefore, SERS enhanced more. It is obvious in this piperidine SERS case that the main effect is barely due to the charge transfer mechanism since, otherwise, the polarizabilities of the skeletal bonds would be enhanced significantly (note that electromagnetic and charge transfer mechanisms are the two main mechanisms in SERS as generally recognized [12]). This is uncommon in the SERS molecular system [12] of which the nitrogen-containing cyclic compounds are most often via the charge transfer mechanism though the electromagnetic mechanism is not excluded. We have studied piperidine SERS back in our 1987 report [2] (but this work only refers to the Raman process at t = 0) where the polarizabilities of the skeletal C–C/C–N bonds were observed enhanced significantly and both the charge transfer and electromagnetic mechanisms were eminent therein. The variation of these two observations is, for the moment, attributed to the different surface roughening processes. The surface roughening in our 1987 work was with piperidine present (in the KCl solution), unlike in this work. These two surface treatments
340
C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340
could cause different adsorption effects and different SERS mechanisms are operative, respectively. From Fig. 4 we also note that, in general, the farther the C–H bonds are away from the adsorption site, the larger their bond polarizabilities are, except that the bond polarizability of r1 is exceptionally large, probably due to the significant electromagnetic enhancement near the surface. C. The relaxation characteristic times for the liquid and SERS cases show that the adsorption enhances the relaxation of the Raman virtual states (see Fig. 5). This is indicated by the larger characteristic times for the liquid piperidine, in general. This adsorption effect was also observed in our work on methylviologen [11]. Furthermore, w(N–H) and its neighboring s1 (axial C–H bond) bonds possess the smallest relaxation characteristic times, especially when the applied voltage is between 0.1 V and 0.3 V. This could be due to that around this voltage range, the adsorption is stronger and that these bonds are closer to the adsorption site. This is consistent with the observation that the polarizability relaxation of s1 bond is faster than that of s3 also because s1 is closer to the adsorption site. Despite of these significant interpretations, however, there is ambiguity why the polarizability relaxation of r3 is faster than that of r1 in most SERS cases. 7. Concluding remarks We have obtained the bond polarizabilities from the Raman intensities for liquid piperidine and its adsorption on the Ag electrode. The bond polarizabilities are important molecular parameters which show the bond electronic behavior during the Raman process. For piperidine adsorbed on the Ag electrode, it is inferred from the elucidated bond polarizabilities that the electromagnetic mechanism dominates the surface enhanced Raman effect, showing that the equatorial C–H bond is enhanced more than its axial companion. The study of the relaxation characteristic times for the bond polarizabilities demonstrates that adsorption enhances the relaxation of the Raman virtual states. It is noticeable that the bond polarizability at the final stage of relaxation is parallel to the quantum chemically calculated bond electronic density of the ground state in the liquid piperidine case. This is very significant if one notes that the calculated bond electronic density is but a theoretical quantity which would be very hard to observe, if not impossible. We have also observed this behavior in our previous works on 2,3-aminopyridine, ethylene thiourea and methylviologen and this is confirmed again in this piperidine case. We think our works establish one way to observe the bond electronic densities of the ground state simply from the bond polarizabilities which can be traced to the experimental Raman intensities. For this piperidine adsorption case, however, only the polarizabilities of peripheral C–H bonds are enhanced significantly by the electromagnetic mechanism. The bond polarizabilities after relaxation, therefore, are not informative enough for us to interpret the bond electronic densities under adsorption effect as we did in the ethylene thiourea and methylviologen cases where the charge transfer mechanism is evident. Acknowledgements 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 (No. 20060003050). G. Wu thanks NCTS in Taiwan for supporting his visit during which this work was finalized. Appendix A Formally, as well known, at t > 0, Ij ðtÞ is related to the product (correlation) of the polarizability derivative at time 0 and time t,
i:e:; Ij ðtÞ / ½@ aðtÞ=@Q j ½@ að0Þ=@Q j By supposing
@ aðtÞ=@Q j ¼ ½@ að0Þ=@Q j f ðtÞ where f ðtÞ is a decaying function,then
qffiffiffiffiffiffiffiffi Ij ðtÞ / ½@ að0Þ=@Q j 2 f ðtÞ ¼ ½ð@ að0Þ=@Q j Þ f ðtÞ2 We may regard
qffiffiffiffiffiffiffiffi ð@ að0Þ=@Q j Þ f ðtÞ as the formal polarizability derivative @aðtÞ=@Q j ,then
Ij ðtÞ / ½@aðtÞ=@Q j 2 Note that ð@að0Þ=@Q j Þ ¼ ð@ að0Þ=@Q j Þ since f ð0Þ ¼ 1. Hence, we can relate Ij ðtÞ to the square of the (formal) polarizability derivative at time t. For simplicity and without confusion, we may make no difference between @aðtÞ=@Q j and @ aðtÞ=@Q j as we did in the text. If f ðtÞ is an exponential function, then the decaying characteristic times of ð@aðtÞ=@Q j Þ and ð@ aðtÞ=@Q j Þ differ by a factor of 2. In the text, we refer to that of the formal polarizability derivative. From Ij ðtÞ / ½@ að0Þ=@Q j 2 f ðtÞ and Ij ð0Þ / ½@ að0Þ=@Q j 2 , we have Ij ðtÞ / Ij ð0Þf ðtÞ. Ij ðtÞ can be obtained from the Fourier transform of Ij ’ðmÞ in the wavenumber domain by re-setting its central wavenumber to 0. References [1] G.W. Chantry, Polarizability theory for the Raman effect, in: A. Anderson (Ed.), The Raman Effect, vol. 1, Marcel Dekker, New York, 1971. [2] B. Tian, G. Wu, G. Liu, J. Chem. Phys. 87 (1987) 7300. [3] Yi Huang, G. Wu, Spectrochim. Acta 45A (1989) 123. [4] Yi Huang, G. Wu, Spectrochim. Acta 46A (1990) 377. [5] G. Wu, J. Mol. Struct. 79 (1990) 238. [6] F. Zhong, G. Wu, J. Mol. Struct. 324 (1994) 233. [7] H. Wang, G. Wu, Chem. Phys. Lett. 421 (2006) 460. [8] C. Fang, G. Wu, Spectrochim. Acta 71 (2008) 1588. [9] C. Fang, G. Wu, J. Raman Spectrosc. 38 (2007) 1416. [10] C. Fang, Z. Liu, G. Wu, J. Mol. Struct. 885 (2008) 168. [11] C. Fang, G. Wu, J. Raman Spectrosc. 40 (2009) 308. [12] A. Otto, Surface-enhanced Raman scattering: ‘‘classical” and ‘‘chemical” origin, in: M. Cardona, (Ed.), Light Scattering in Solid IV, New York, 1984. [13] A. Kudelski, J. Bukowska, Surf. Sci. 368 (1996) 396. [14] C. Chenal, R.L. Birke, J.R. Lombardi, Chem. Phys. Chem. 9 (2008) 1617. [15] L.A. Sanchez, R.L. Birke, J.R. Lombardi, J. Phys. Chem. 88 (1984) 1762. [16] E.B. Wilson, J.C. Decius, P.C. Cross, Molecular Vibrations, McGraw-Hill, New York, 1955 (Chapter 9). [17] M.T. Gulluoglu, Y. Erdogdu, S. Yurdakul, J. Mol. Struct. 834–836 (2007) 540. [18] D. Vedel, O.H. Elestad, P. Klaboe, Spectrochim. Acta 32A (1976) 877 (and references therein).
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Temporal Raman polarizabilities of piperidine in liquid and on the Ag surface with electromagnetic enhancement Chao Fang, Guozhen Wu * Molecular and Nano Sciences Laboratory, Department of Physics, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 8 August 2009 Received in revised form 28 September 2009 Accepted 2 October 2009 Available online 12 October 2009 Keywords: Raman intensity Temporal bond polarizability Relaxation of virtual state Piperidine SERS
a b s t r a c t The temporal bond polarizabilities from the Raman intensities for liquid piperidine and its adsorption on the Ag electrode were obtained. The bond polarizabilities are important molecular parameters which show the bond electronic behavior during the Raman process. For the liquid piperidine, it is noted that the bond polarizability at the final stage of relaxation of the Raman virtual state is parallel to the quantum chemically calculated bond electronic density of the ground state. This opens a new way to observe the bond electronic density simply from the experimental Raman spectrum. For the piperidine adsorbed on the Ag electrode, it is inferred from the elucidated bond polarizabilities that the electromagnetic mechanism dominates the surface enhanced Raman effect, showing that the equatorial C–H bond is enhanced more than its axial companion. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction It has been generally recognized that Raman process involves the excitation of the virtual state (nonresonance case) including its relaxation [1]. In the virtual state, there is vibronic coupling which shuttles the energy between the electronic and the nuclear coordinates. Thus, the information of the vibronic coupling is embedded in the scattering Raman intensity. The way to explore this information from the spectral intensity is an interesting topic since it involves the very basics of the Raman process. In our past works [2–11], an algorithm has been developed for this purpose and various systems have been tested thereby to reveal significant physical and chemical properties of the Raman virtual states. These observations demonstrate that this algorithm is effective and rewarding. Surface enhanced Raman scattering (SERS) [12] is a phenomenon for which the Raman intensity of an adsorbed molecule on the metal surface is enhanced greatly. This is due to the interaction between the adsorbed molecule and the metal surface. The mechanisms are generally believed to be due to the charge transfer between the adsorbed molecule and the metal surface and/or the electromagnetic effect due to the very strong local electric field around the adsorbed molecule on the metal surface. Piperidine is a typical molecule showing strong surface enhanced Raman effect. Some works have been devoted to its SERS, such as its charge transfer effect [13,14], applied potential dependence [15].
* Corresponding author. Tel.: +86 10 62781606 194; fax: +86 10 62781604. E-mail address: [email protected] (G. Wu). 0022-2860/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.10.006
Albeit so many works have been devoted to SERS, very few are on a systematic study on its intensity. In this sense, we address that our approach is rather unique and the importance of the elucidated bond polarizability from the Raman intensity by our algorithm in deepening our understanding of SERS will be obvious as demonstrated in this work. We have explored its SERS intensities during our early work [2] in developing this algorithm. But that work only refers to the initial moment of the Raman process. In this report, we will show the temporal development of its bond polarizabilities and conclude that its SERS effect mainly originates from the electromagnetic mechanism. This is variant from our early work. We attribute it to the different electrode surface treatments. Furthermore, this work is accompanied with that on liquid piperidine which was not tried on previously. We will see that the comparison of these results does deepen our understanding of this piperidine system by our algorithm which is based on the Raman intensity analysis. In the followings, a short summary of our algorithm will be introduced first. Then, the analysis on liquid piperidine and its adsorption on the Ag electrode surface by 514.5 nm excitation will be followed. Finally, a concluding remark will be addressed as to the significance of our study. 2. The algorithm For demonstration, we will analyze the spectral intensity in the temporal domain Ij ðtÞ (index j is for the normal mode), which is related to the wavenumber domain I0j ðmÞ, through the Fourier R 0 transform as Ij ðmÞeimt dm ¼ Ij ðtÞ. We note that for t = 0, this
C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340
R
transformation reduces to I0j ðmÞdm ¼ Ij ðt ¼ 0Þ. Hence, the integrated Raman intensity over m is just the temporal intensity at t = 0. In the Fourier transformation, the central wavenumber of I0j ðmÞ is re-set to 0. The temporal Raman intensity Ij ðtÞ of the jth normal mode with Raman shift mj is related to the electronic polarizability derivative with respect to its normal coordinate Q j through [1,2,10] (for more exposition, see Appendix A):
Ij ðtÞ
ðm0 mj Þ4
ð@ aðtÞ=@Q j Þ2
mj
where m0 is the wavenumber of the exciting laser. This is an extension of Chantry’s formula [1]:
Z
I0j ðmÞdm
ðm0 mj Þ4
mj
ð@ a=@Q j Þ2
which is just
Ij ðt ¼ 0Þ
ðm0 mj Þ4
mj
ð@ aðt ¼ 0Þ=@Q j Þ2
R if we note from the last section that I0j ðmÞdm ¼ Ij ðt ¼ 0Þ. By transforming Q j ’s to the internal coordinates Rk ’s through
Rk ¼
X
Lkj Q j
which can be obtained from the normal mode analysis [16], we have:
qffiffiffiffiffiffiffiffiffi ðm m Þ2 X 0 j Lkj ð@ aðtÞ=@Rk Þ Ij ðtÞ pffiffiffiffi
mj
@ a=@Rk will be called the bond polarizability, for convenience. In matrix notation, if only relative intensities are considered, we have
2
@ aðtÞ=@R1
6 @ aðtÞ=@R 2 6 6 6 : 6 6 : 6 6 4 : @ aðtÞ=@R3N6
2
3
6 7 6 7 6 7 7 1 6 7 ¼ ajk 6 6 7 6 7 6 7 6 5 4
pffiffiffiffiffiffiffiffiffiffi I1 ðtÞ pffiffiffiffiffiffiffiffiffiffi P2 I2 ðtÞ
P1
: : P3N6
: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I3N6 ðtÞ
3 7 7 7 7 7 7 7 7 7 5
2
ðm mj Þ where ajk ¼ 0pffiffiffi Lkj and Pj is +1 or 1. m j
We will be restricted to the bond stretching coordinates since their bond polarizabilities are large and will offer significant physical interpretations. Another reason for this choice is that the motion between the stretching and bending coordinates is generally well decoupled. Then the dimension of the above matrix equation will be reduced to the number of bonds in a molecule. From the above derivation, it is clear that @ aðtÞ=@Rk is obtainable if ½ajk 1 matrix, Ij ðtÞ’s and a fPj g set are given. ½ajk 1 can be known from the normal mode analysis. Ij ðtÞ’s can be obtained from the Fourier transform of the Raman profiles. Then, various sets of fP j g can be tried to obtain @ a=@Rk ’s which are then checked with physical considerations to rule out the inadequate fPj g sets. The bond polarizability is a measure of the charge distribution on each bond of the virtual state including its relaxation. For comparison, we need the bond electronic densities qk of the ground state. This is calculated by DFT with ub3lyp/cc-pvDZ.
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A 50 objective was used to perform an 180° backward scattering configuration. The excitation source is 514.5 nm line of Ar ion laser. The laser power on the samples was about 10 mw. The entranceslit width was 20 lm and the integral time was 20s. For SERS spectra, a tri-electrode cell was used to perform oxidation–reduction cycle (ORC). The working silver electrode was a silver plate of 99.9% purity (polished with alumina whose particle size was about 0.3 lm and then rinsed) 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 were quoted with respect. The ORC’s were done in 0.1 M KCl solution, with applied voltage being shifted between 0.2 V (kept for 10 s) and 0.3 V (kept for 20 s) for four times. The voltage scanning speed was 50 mV s1 and the electrode potential was controlled by a CHI 600B Electrochemical Workstation. After ORC, the roughened electrode was immersed in a solution containing 103 M piperidine and 0.1 M KCl to perform the SERS measurement. Shown in Fig. 2 are the Raman spectra of liquid piperidine and its SERS spectra under various potentials. For a careful intensity measurement, the corrections due to the different responses of CCD detector and the grating mirror along different polarizations and various spectral ranges were considered. For our purpose, only the relative intensities are considered. In the case that there is spectral profile overlapping, a deconvolution software was taken to resolve the profile into Gaussian components (Lorentzian profile fit is not excellent. However, this is not crucial in the following elucidation of the bond polarizabilities). Also, the background was offset in measuring the Raman peak intensity, if necessary. We estimated that the intensities were of uncertainty less than 20%, which would lead to an uncertainty less than 10% for the calculated bond polarizabilities. The temporal Raman intensities were obtained by Fourier transformation from the experimentally recorded Raman intensities in wavenumber. 4. The normal mode analysis The molecular structure of piperidine and the definition of its bond stretching coordinates are shown in Fig. 1. The configuration of piperidine is of C s symmetry and there are 25 symmetric modes among its 45 normal modes. For calculating ½ajk 1 matrix, further normal mode analysis was tried by refining the force constants which were initially simulated by DFT with ub3lyp/cc-pvDZ till the calculated mode frequencies and the measured ones are consistent [2,17,18]. This procedure was performed for liquid piperidine and the absorbed piperidine on the silver electrode, respectively. From the normal mode analysis, it was found that the coupling between the bond stretching and bending motions was very weak for this molecule. Hence, we will focus on the 10 bond polarizabilities corresponding to the 10 bond
3. Experimental Piperidine (liquid) was purchased from Aldrich Chemical Co. Ltd. The Raman spectra were recorded with a Renishaw RM1000 micro-confocal spectrophotometer equipped with a CCD detector.
Fig. 1. The molecular structure of piperidine and its bond stretching coordinates. The proposed adsorption configuration on the Ag electrode surface and the direction of the electric field originating from the surface are also depicted.
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C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340 Table 1 The normal modes of piperidine with their observed (experimental), fitted wavenumbers, relative intensities and the main potential energy distributions. For wavenumber and intensity columns, the data on the upper are for the liquid piperidine. The intensity of the mode at 2934 cm1 is normalized to 100. The data on the lower are for the SERS case at 1.0 V. The intensity of the modes at 2842 cm1 at 1.0 V is normalized to 100. Only PED’s for liquid piperidine are shown due to those for the SERS cases are very similar. Si (i = 1, . . ., 7, 22, 23, 25) are the bond stretching coordinates. Their explicit forms are listed in Table 2. The others are the bending coordinates. Mode
m1 m2 m3 m4 m5 m6 m7 m8 m9 m10
Wavenumber/cm1
Intensity
Potential energy distribution (%)
3345 3344 2950 2943 2930 2928 2921 2917 2889 2889 2850 2850 2730 2731 1474
53 0 76 92 100 73 69 67 49 87 72 100 42 0 12
S25 ð99:1Þ
– 1450 1455 1441
1476 1453 1453 1440
0 34 1 25
–
1441
0
EXP.
Fitted
3342 – 2947 2941 2934 2924 2918 2912 2895 2886 2853 2842 2731 – 1474
S2 ð47:2Þ; S4 ð46:3Þ; S22 ð5:1Þ S22 ð50:4Þ; S23 ð47:3Þ S1 ð92:1Þ; S3 ð6:4Þ; S7 ð1:3Þ S4 ð50:0Þ; S2 ð48:9Þ S23 ð49:3Þ; S22 ð48:6Þ S3 ð93:4Þ; S1 ð3:1Þ; S7 ð2:1Þ; S7 ð41:3Þ; S5 ð30:2Þ; S18 ð14:0Þ; S12 ð10:9Þ; S24 ð2:7Þ S21 ð80:1Þ; S7 ð9:4Þ; S15 ð8:2Þ; S5 ð50:3Þ; S10 ð21:4Þ; S12 ð16:8Þ; S15 ð10:3Þ
Table 2 The symmetry coordinates Si (i = 1, . . ., 7, 22, 23, 25) in terms of the bond stretching coordinates shown in Fig. 1.
Fig. 2. The Raman spectra by 514.5 nm excitation of (a) liquid piperidine and (b) its SERS under various potentials. The 10 Raman peaks whose modes are mostly of bond stretching components are labelled by whose frequencies are listed in Table 1.
S1 ¼ r1 þ r2 ; S2 ¼ r3 þ r 4 S3 ¼ s1 þ s2 ; S4 ¼ s3 þ s4 S5 ¼ d1 þ d2 ; S6 ¼ d3 þ d4 S7 ¼ t 1 þ t2 S22 ¼ u S23 ¼ v S25 ¼ w
stretching coordinates. Therefore, only 10 Raman peaks whose modes are mostly of bond stretching components are needed. They are shown by in Fig. 2. Their observed (experimental) wavenumbers, fitted wavenumbers, (relative) intensities and potential energy distributions (PED) are tabulated in Table 1 in which for the SERS case, only the data at 1.0 V are shown. Also, only PED’s for liquid piperidine are shown due to those for the SERS cases are very similar. In conclusion, the effect of adsorption under various applied voltages on ½ajk 1 matrix is negligible so that one may use one such matrix for all the cases.
5. The calculation of temporal bond polarizabilities For the 10 Raman intensities, we have 29 possible phase combinations (note that fP i g is identical to fPi g). The criterion for the phase choice is that: all the bond polarizabilities are of the same sign as time elapses. With this criterion, we were left with only four phase solutions. However, these four solutions are very similar and one of them is chosen for demonstration. All the bond polarizabilities follow the monotonically decaying behavior as time elapses. The (relative) bond polarizabilities of u, v, w, r1, r3, s1, s3, d1, d3, t1 coordinates (their equivalents under C s symmetry
Fig. 3. The (relative) bond polarizabilities of u, v, w, r1, r3, s1, s3, d1, d3, t1 coordinates (for their definitions, see Fig. 1) for liquid piperidine at the initial (j) and final (d) stages of Raman relaxation. Also shown are the quantum mechanically calculated bond electronic densities (4) of the ground state. All data are normalized with respect to those of u bond taken as 10. It should be noted that there is no correlation of data between the bond polarizabilities and the calculated bond electronic densities.
C. Fang, G. Wu / Journal of Molecular Structure 938 (2009) 336–340
Fig. 4. The (relative) bond polarizabilities of u, v, w, r1, r3, s1, s3, d1, d3, t1 coordinates at the initial stage of Raman process for piperidine SERS cases under various applied voltages. All data are normalized with respect to that of u bond at 1.0 V taken as 100.
Fig. 5. The relaxation characteristic times, tc , of the various bonds for the liquid and SERS piperidine cases.
are not shown for simplicity) are shown in Figs. 3 and 4 for the liquid and SERS cases, respectively. The bond electronic densities of the ground state calculated by the quantal method are also shown in Fig. 3 for comparison. The relaxation characteristic times of the bond polarizabilities are the important parameters from the viewpoint of this temporal bond polarizability study. It was found in most cases that the relaxation can be well followed by one exponential function of the form: Aet=tc þ B. The relaxation characteristic times, tc , for all the cases are shown in Fig. 5. 6. Results and discussion A. For the liquid piperidine case, we have the following observations: (1) At the initial stage of Raman excitation, the bond polarizabilities of the peripheral C–H/N–H bonds are evidently larger than those of the skeletal C–C/C–N bonds (see Fig. 3). After relaxation (as t = 8 ps), the skeletal C–C/C–N bonds do possess larger bond polarizabilities, instead. This shows that at the very initial moment of Raman excitation, the charges are excited in the virtual state and
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are spread out toward the molecular periphery due to electronic repulsion. This phenomenon is very similar to the splashing of water (excited charges) in a pan (molecule) when a pebble (photon) is thrown into it. We have also observed this behavior in our previous works on 2,3-aminopyridine [7,8], ethylene thiourea [9,10] and methylviologen [11]. We have accessed that this is a generic property of the Raman excited virtual states and this is again confirmed in this piperidine work. We further note that at the initial stage of Raman excitation, the axial s1 and s3 bonds (and their equivalent s2 and s4. For short, we will not repeat these equivalent bonds hereafter.) possess larger polarizabilities than their equatorial companions. While after relaxation, all the axial and equatorial bonds including N–H, possess quite the same polarizabilities albeit u and v possess comparatively larger polarizabilities. All these show the fine structural information of the Raman virtual state. The significance of these observations will be more transparent if they are contrasted with those of the SERS case as shown later. (2) Notable is that the bond polarizabilities after relaxation are parallel to those bond electronic densities of the ground state by the quantal calculation: the skeletal C–C/C–N bonds of the molecular ring possess larger electronic densities/polarizabilities than those of the C–H/N–H bonds which are almost identical except that u and v bonds possess slightly larger electronic densities/polarizabilities. This is very significant if one notes that the calculated bond electronic density is but a theoretical quantity which would be very hard to observe, if not impossible. We have also observed this behavior in our previous works on 2,3-aminopyridine [7,8], ethylene thiourea [9,10] and methylviologen [11] and this is confirmed again in this piperidine case. We think our works establish one way to observe the bond electronic densities of the ground state simply from the bond polarizabilities after relaxation which can be traced to the Raman intensities. B. For the adsorption case of piperidine on the Ag electrode, we note that: At the initial stage of Raman process, we note that N–H bond, unlike in the liquid case, possesses very small polarizability (see Fig. 4). This may be just caused by adsorption. This suggests that the adsorption site is on the N–H moiety. The skeletal C–C/C–N bonds also possess bare polarizabilities during the whole SERS process, probably due to the same cause. We further note that the equatorial C–H bonds do in most cases (under various applied voltages) possess larger polarizabilities than their axial companions (note the situation is opposite in the liquid case). This observation suggests that the adsorption configuration is vertical as depicted in Fig. 1 and the SERS mechanism involved is mainly the electromagnetic one since in this way, the electric field originating from the electrode surface is parallel to the equatorial C–H bonds (also shown in Fig. 1) and these bonds are, therefore, SERS enhanced more. It is obvious in this piperidine SERS case that the main effect is barely due to the charge transfer mechanism since, otherwise, the polarizabilities of the skeletal bonds would be enhanced significantly (note that electromagnetic and charge transfer mechanisms are the two main mechanisms in SERS as generally recognized [12]). This is uncommon in the SERS molecular system [12] of which the nitrogen-containing cyclic compounds are most often via the charge transfer mechanism though the electromagnetic mechanism is not excluded. We have studied piperidine SERS back in our 1987 report [2] (but this work only refers to the Raman process at t = 0) where the polarizabilities of the skeletal C–C/C–N bonds were observed enhanced significantly and both the charge transfer and electromagnetic mechanisms were eminent therein. The variation of these two observations is, for the moment, attributed to the different surface roughening processes. The surface roughening in our 1987 work was with piperidine present (in the KCl solution), unlike in this work. These two surface treatments
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could cause different adsorption effects and different SERS mechanisms are operative, respectively. From Fig. 4 we also note that, in general, the farther the C–H bonds are away from the adsorption site, the larger their bond polarizabilities are, except that the bond polarizability of r1 is exceptionally large, probably due to the significant electromagnetic enhancement near the surface. C. The relaxation characteristic times for the liquid and SERS cases show that the adsorption enhances the relaxation of the Raman virtual states (see Fig. 5). This is indicated by the larger characteristic times for the liquid piperidine, in general. This adsorption effect was also observed in our work on methylviologen [11]. Furthermore, w(N–H) and its neighboring s1 (axial C–H bond) bonds possess the smallest relaxation characteristic times, especially when the applied voltage is between 0.1 V and 0.3 V. This could be due to that around this voltage range, the adsorption is stronger and that these bonds are closer to the adsorption site. This is consistent with the observation that the polarizability relaxation of s1 bond is faster than that of s3 also because s1 is closer to the adsorption site. Despite of these significant interpretations, however, there is ambiguity why the polarizability relaxation of r3 is faster than that of r1 in most SERS cases. 7. Concluding remarks We have obtained the bond polarizabilities from the Raman intensities for liquid piperidine and its adsorption on the Ag electrode. The bond polarizabilities are important molecular parameters which show the bond electronic behavior during the Raman process. For piperidine adsorbed on the Ag electrode, it is inferred from the elucidated bond polarizabilities that the electromagnetic mechanism dominates the surface enhanced Raman effect, showing that the equatorial C–H bond is enhanced more than its axial companion. The study of the relaxation characteristic times for the bond polarizabilities demonstrates that adsorption enhances the relaxation of the Raman virtual states. It is noticeable that the bond polarizability at the final stage of relaxation is parallel to the quantum chemically calculated bond electronic density of the ground state in the liquid piperidine case. This is very significant if one notes that the calculated bond electronic density is but a theoretical quantity which would be very hard to observe, if not impossible. We have also observed this behavior in our previous works on 2,3-aminopyridine, ethylene thiourea and methylviologen and this is confirmed again in this piperidine case. We think our works establish one way to observe the bond electronic densities of the ground state simply from the bond polarizabilities which can be traced to the experimental Raman intensities. For this piperidine adsorption case, however, only the polarizabilities of peripheral C–H bonds are enhanced significantly by the electromagnetic mechanism. The bond polarizabilities after relaxation, therefore, are not informative enough for us to interpret the bond electronic densities under adsorption effect as we did in the ethylene thiourea and methylviologen cases where the charge transfer mechanism is evident. Acknowledgements 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 (No. 20060003050). G. Wu thanks NCTS in Taiwan for supporting his visit during which this work was finalized. Appendix A Formally, as well known, at t > 0, Ij ðtÞ is related to the product (correlation) of the polarizability derivative at time 0 and time t,
i:e:; Ij ðtÞ / ½@ aðtÞ=@Q j ½@ að0Þ=@Q j By supposing
@ aðtÞ=@Q j ¼ ½@ að0Þ=@Q j f ðtÞ where f ðtÞ is a decaying function,then
qffiffiffiffiffiffiffiffi Ij ðtÞ / ½@ að0Þ=@Q j 2 f ðtÞ ¼ ½ð@ að0Þ=@Q j Þ f ðtÞ2 We may regard
qffiffiffiffiffiffiffiffi ð@ að0Þ=@Q j Þ f ðtÞ as the formal polarizability derivative @aðtÞ=@Q j ,then
Ij ðtÞ / ½@aðtÞ=@Q j 2 Note that ð@að0Þ=@Q j Þ ¼ ð@ að0Þ=@Q j Þ since f ð0Þ ¼ 1. Hence, we can relate Ij ðtÞ to the square of the (formal) polarizability derivative at time t. For simplicity and without confusion, we may make no difference between @aðtÞ=@Q j and @ aðtÞ=@Q j as we did in the text. If f ðtÞ is an exponential function, then the decaying characteristic times of ð@aðtÞ=@Q j Þ and ð@ aðtÞ=@Q j Þ differ by a factor of 2. In the text, we refer to that of the formal polarizability derivative. From Ij ðtÞ / ½@ að0Þ=@Q j 2 f ðtÞ and Ij ð0Þ / ½@ að0Þ=@Q j 2 , we have Ij ðtÞ / Ij ð0Þf ðtÞ. Ij ðtÞ can be obtained from the Fourier transform of Ij ’ðmÞ in the wavenumber domain by re-setting its central wavenumber to 0. References [1] G.W. Chantry, Polarizability theory for the Raman effect, in: A. Anderson (Ed.), The Raman Effect, vol. 1, Marcel Dekker, New York, 1971. [2] B. Tian, G. Wu, G. Liu, J. Chem. Phys. 87 (1987) 7300. [3] Yi Huang, G. Wu, Spectrochim. Acta 45A (1989) 123. [4] Yi Huang, G. Wu, Spectrochim. Acta 46A (1990) 377. [5] G. Wu, J. Mol. Struct. 79 (1990) 238. [6] F. Zhong, G. Wu, J. Mol. Struct. 324 (1994) 233. [7] H. Wang, G. Wu, Chem. Phys. Lett. 421 (2006) 460. [8] C. Fang, G. Wu, Spectrochim. Acta 71 (2008) 1588. [9] C. Fang, G. Wu, J. Raman Spectrosc. 38 (2007) 1416. [10] C. Fang, Z. Liu, G. Wu, J. Mol. Struct. 885 (2008) 168. [11] C. Fang, G. Wu, J. Raman Spectrosc. 40 (2009) 308. [12] A. Otto, Surface-enhanced Raman scattering: ‘‘classical” and ‘‘chemical” origin, in: M. Cardona, (Ed.), Light Scattering in Solid IV, New York, 1984. [13] A. Kudelski, J. Bukowska, Surf. Sci. 368 (1996) 396. [14] C. Chenal, R.L. Birke, J.R. Lombardi, Chem. Phys. Chem. 9 (2008) 1617. [15] L.A. Sanchez, R.L. Birke, J.R. Lombardi, J. Phys. Chem. 88 (1984) 1762. [16] E.B. Wilson, J.C. Decius, P.C. Cross, Molecular Vibrations, McGraw-Hill, New York, 1955 (Chapter 9). [17] M.T. Gulluoglu, Y. Erdogdu, S. Yurdakul, J. Mol. Struct. 834–836 (2007) 540. [18] D. Vedel, O.H. Elestad, P. Klaboe, Spectrochim. Acta 32A (1976) 877 (and references therein).