The discovery of very large enhancements of the Raman signal induced by proximity to a metal surface has led to numerous interesting and valuable developments in nanoscience. The consequence of all this interest is that the numerous manifestations of the effect are difficult to explain using a simple theory. It was first realized that the nature of the conduction band of the metal and the need for nanoscale surface features implies that a surface plasmon resonance (SPR) must be important for the effect to be observed. However, examination of the potential dependence of the effect in electrochemical experiments led several investigators to propose that a charge-transfer resonance between the molecule and the metal was also of importance , . More recently, even larger enhancements have been discovered, by examining systems on the single molecule level. These were observed with single molecules adsorbed on one or between two or more Ag nanoparticles. Most of these single molecule experiments were carried out choosing molecules, which in addition to the surface plasmon and charge-transfer resonances, also have a molecular resonance in the range of excitation. These considerations lead to the conclusion that it is important to consider the molecule and metal as a single system. The states involved in various resonances should be regarded as part of this molecule-metal system, and all properties are affected by this interaction. The plasmon resonance is mostly a property of the metal, while the molecular resonances are properties mostly of the molecule. The charge-transfer states are properties of the combined system. Thus, in order to fully explain the observations, three types of resonance may need to be invoked. However, at any single excitation frequency, it is often difficult to distinguish the degree to which each of the type of resonance contributes to the overall enhancement. In order to obtain a complete picture of the relative contribution of each resonance, experiments must be carried out at a wide variety of excitation wavelengths, by electrochemically varying the applied potential or possibly by varying the location of the surface plasmon resonance by carefully controlling particle size or interparticle distance. We have shown that we if we are in the region of a charge-transfer or molecular resonance, the enhancement of the non-totally symmetric bands relative to the totally symmetric bands will vary. In the absence of charge-transfer contributions, the relative enhancement of both types of bands should be the same. We present a single expression for the enhancement, which includes all three types of resonance in the denominator, while all three effects are linked by a product of four matrix elements in the numerator. This means that surface-enhanced Raman spectroscopy (SERS) need not be explained as a coincidence of several disparate effects, but must be considered a single effect drawing on up to three resonances which are intimately tied to each other and cannot easily be considered separately , . Depending on the parameters assoiated with each resonance at each excitation wavelength as well as the selection rules, the various resonances contribute differing amounts to the enhancement, and we are able to clarify the ways in which each contribution may be extracted. We examine the resonances separately, starting with the surface plasmon resonance. We show that even far from charge-transfer or molecular resonance, these transitions can influence the observed spectrum. We examine the differences between SERS and normal Raman spectroscopy, to identify the special contributions made to the Raman spectrum by proximity to the metal surface. Especially important is the preferential polarization of light normal to the surface, and this leads to an examination of the sources of the surface selection rules. We then examine the additional contributions due to an overlap of the surface plasmon resonance with either a charge-transfer or molecular resonance (or both). This imposes further symmetry requirements on the spectrum and leads us to examine the resulting Herzberg-Teller-surface selection rules. As a stringent test of these selection rules, we apply them to the observed SERS spectra of a series of rather symmetric molecules, including the azines, benzene, and the less symmetric berberine. Some of these comparisons are necessarily qualitative, due to lack of sufficient data, so that we then examine more quantitatively the spectrum of a molecule (p-aminothiophenol) for which considerable data has been obtained. We define an experimental parameter (the degree of charge transfer), which enables us to examine the various contributions to the SERS intensity for a wide variety of excitation wavelengths and substrates.
Return to research interests
Art, Architecture, Archeology, Forensic Science all have in common that
positive identification of components are needed, but sometimes only trace
Theoretical Studies-Momentum Representation.
An exploration of the other half of Quantum Mechanics.
Most Quantum mechanical wave functions are obtained as functions of the positions of particles.
An equivalent, but less widely utilized representation is in terms of the momentum
of the particles. The usual description states that the momentum representation
is the Fourier Transform of the position representation. However, this holds
only for Cartesian coordinate systems. For curvilinear coordinates we must use the
"DeWitt" transform. This allows an operator formalism in which the important 1/r
operator has a simple integral form in momentum space.
First we derive the wave functions for the hydrogen atom  by transforming the
Schrodinger equation into an appropriate integral equation in momentum space.
The results are extended to He , and a two electron function is derived in which 90%
of the correlation energy is obtained with only one parameter . A relativistic formulation
for the Hydrogen atom is obtained , and the effect of the Yukawa potential is explored .
Finally, we examine ways to find molecular functions with a study of the hydrogen
molecule ion .
1. "The Hydrogen Atom in the Momentum Representation", Phys. Rev. A, 22, 797 (1980).
2. "The Helium Atom in the Momentum Representation", J. Phys. Chem., 86, 3513 (1982).
3. "A Correlated One-Parameter Momentum Space Wave Function for Helium," J. Chem.
Phys., 78, 2476 (1983).
4. "Relativistic Hydrogen Atom in the Momentum Representation," Phys. Rev. A, 27, 1275
5. "The Yukawa Potential in the Momentum Representation," J. Chem. Phys. 85, 949
6. "The Hydrogen Molecule-ion in the Momentum Representation", C.Abrams, Ph.D.
Thesis submitted to the City University of New York, 1992.
Return to research interests
Transition metal clusters are produced in an ultra high vacuum chamber by sputtering a metal target with high energy agron ions. The ionized clusters are mass selected by passing through a Wien filter. The selected cluster is then neutralized and deposited on a substrate at 14K in a rare gas matrix. We then may study absorption, fluorescence and resonance Raman spectra. Systematic study of Raman spectra of transition metal dimers has resulted in filling in the periodic table with measured force constants. We have also examined the Raman spectra of several trimers and two tetramers (Ta4 and Sc4).
References to these works can be obtained in a recently published a review article in Chemical Reviews, 102,
2431 (2002). See also a discussion of the relationship between force constant and internuclear distance in transition metal dimers, as well as a suggested experimental bond order.
Return to research interests
For a complete list of publications, click here