Frequency dependence 4- pyridine

Here and Ss are the frequency-dependent dielectric constants of the metal and the solution, respectively. Using known pyridine polarizability and silver dielectric data, large enhancements could be obtained (up to 10 ). In terms of the molecular picture, a several-eV decrease of level spacing was involved. This shift, however, strongly depends on the frequency, through the dielectric constant of the metal. This is a dynamic shift and the resonance is really a joint metal-molecule-photon excitation. This is different from a shift of levels under static fields. This point has often been misunderstood. 

Recently, we have proposed a methodology [71] similar to the last approach, but using semiempirical molecular orbital methods instead of TDHE methods, to calculate the frequency-dependent polarizability properties of the molecule-surface complex. Although this is a lower level description of the electronic structure, the use of semiempirical methods allows us to describe more complex molecules than has been considered in earlier studies. In the following, we present some recent results for the pyridine-copper tetramer system, and we examine the influence of molecule-metal distance on the Raman intensities for this model. There are two components to the calculation of the Raman intensity (1) calculation of the ground state structure and normal coordinates and (2) calculation of the derivative of the frequency-dependent... 

Fig. 4.12 presents the static SER spectra of pyridine, a CU4 cluster, and the CU4-pyridine complex. The structure of the Cu4-pyridine complex is also presented, while Fig. 4.13 gives the experimental and the calculated frequency-dependent SER spectra of pyridine only. Note that we have used a Y-shaped CU4 cluster structure, rather than the global minimum rhombus shape, as this leads to better behaved DFT calculations. As we can see from Fig. 4.12, the static INDO/S and DFT spectra are in reasonable agreement for all except the mode at 1253 cm for pyridine, and 1253 and 1500 cm for the CU4-pyridine complex. The intensities of these modes are suppressed in the INDO/S results relative to DFT, but as shown in Fig. 4.13, the frequency-dependent INDO/S-SOS results match experiment reasonably well, with the four major SERS-active vibrational modes at around 630, 993, 1050, and 1600 cm having about the right relative intensities. Moreover, both the DFT and INDO/S results in Fig. 4.12 suggest that for the CU4-pyridine complex orientation considered here, the spectrum of Cu4-pyridine complex is approximately a combination of the spectmm of pyridine and that of CU4. 

Fig. 4.13. (a) Frequency-dependent SER spectrum of pyridine, INDO/S-SOS, with applied field being 2.81 eV. (b) Experimental SER spectrum of pyridine absorbed on a rough silver electrode in water at - 0.25 V vs a saturated Ag/AgCl/KCl reference electrode. 

To estimate the and constants for unsubstituted pyridyl groups, Pasternak and Tomasik attempted to use the dependence of the frequencies of symmetric (vj and asymmetric (VaJ NO2 stretching vibrations in substituted nitrobenzenes (2) on the Hammett substituent constants (75BAP923). The pyridyl group constants obtained from the data of the IR spectra of the nitrophenyl pyridines in CHClj and CHBrj have considerable scatter in their values depending on the solvent. Most of the and values estimated from Vs-NOa Jiff widely from the respective values obtained from v noj even for the same solvent. Four of the seven Hammett-type relationships used by the above authors to calculate the a values have a low correlation coefficient (r = 0.949-0.965). The method in question, just as polarography, is suitable only for a rough estimation of constants. 

The earliest studies on the IR spectra of crown ethers and their complexes were carried out by Pederson (B-78MI52101). Since then IR spectroscopy has been applied a number of times to solve structural problems in crown ether chemistry including ion pair interactions and conformational analysis (B-79MI52103). A low frequency vibration of the cation within the macrocycle has been identified which is dependent on the cation but not on the solvent (214 cm for Na -dibenzo[18]crown-6 in both DMSO and pyridine). This is in contrast to the frequency of cation vibration within a solvent cage, which for Na is 202 cm in... 

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