In the following section a short description of the research areas we are interested in will be presented. Our research interests cover research problems that expand to the domains of traditional areas such as physical chemistry and chemical physics, and to the domains of the rapidly developing fields of chemistry such as: materials chemistry, environmental chemistry, and biochemistry and biophysics.
1- Development of Theoretical Methods to Calculate Ro-vibrational Energy Levels of Van
der Waals Clusters
Traditional methods to study the spectra and dynamics of polyatomic molecules deal with normal coordinates to describe molecular vibrations and the Eckart axes to describe the orientation of the system. The application of these methods is quite successful when the systems exhibit small amplitude vibrations,1 for which perturbation theory converges fast in the calculation of ro-vibrational energy levels.
Fig.1. Tunneling bending mode for (HX)2 (X = F, Cl, Br, I) van der Waals dimers is illustrated. This is a typical example of large amplitude anharmonic vibrational motion, where the traditional method of vibrational dynamics fails. The molecule here can vibrate between two equivalent equilibrium minimum structures causing the splitting of the ground ro-vibrational state.
For van der Waals clusters, where large amplitude motions are present such as the tunneling bending (depicted in Fig.1) and torsional motions of the (H2O)n and (HF)n clusters, traditional normal mode treatments and Eckart frame formulations are no longer appropriated. The theoretical approaches to solve these problems start with the selection of curvilinear coordinates. These allow one to describe the large amplitude anharmonic motion taking advantage of the symmetry of the system, and obtaining a compact matrix representation of the ro-vibrational Hamiltonian. We are interested in developing a pseudo-spectral approach technique, which allows us to express the matrix elements of the kinetic energy operator in diagonal or in analytical form in the spectral representation, and the matrix elements of potential in the grid representation, where it is diagonal. To diagonalize the large sparse matrices resulting from the spectral matrix representation of the ro-vibrational Hamiltonian, we use optimized basis from classical orthonormal polynomials, which allow to tridiagonalize the matrix representation of the Hamiltonian. Using this approach we can take advantage of the Lanczos’s algorithm,2 in the diagonalization procedure.
One of our main objectives is the development of computational methods to treat large amplitude anharmonic motions in larger clusters (3-10 molecules) and weak solvation complexes. Of particular importance to us, is the coupling between intra and intermolecular modes. The understanding of the mechanism of the intra-intermolecular coupling is of fundamental and practical importance to study energy transfer processes in condense phases. Due to the interaction between fast harmonic and slow anharmonic motions (or interaction between short and large scale anharmonic motions in the terminology of molecular dynamics), the study of this coupling mechanism can also be used to understand the energy transfer processes in proteins.
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2J. Castillo-Chará, R. R. Lucchese and J. W. Bevan, Comp. Phys. Comm.
145, 48-63 (2002).
In this area our main interest is the application of the supermolecule approach to the calculation of interaction energies of medium size clusters. We are interested in the development and implementation of a basis sets that allow the efficient evaluation of interaction energies. Of particular importance to us is the exploration of mid bond bases, which have been demonstrated to be quite accurate in the calculation of the interaction energies in small systems.1
Fig. 2. Cyclophane is a very well known system studied experimentally to test cation –π interaction in biological systems.2
We are also interested in the interaction of cations with large aromatic systems such as cyclophane derivatives shown in Fig.2. Our main interest is the calculation of interaction energies and development of ab initio potentials that will allow us to reveal the nature of forces operating in these systems that control the cation selectivity of these complexes. These studies are of relevance in guest-host interactions and ion transfer processes commonly found in biological systems.
1G. Chalasinski, and M. Szczesniak, Chem. Rev. 100, 4227 (2000).
2D. A. Dougherty, Science 271, 163 (1997).
Calculation of high quality ab initio potential energy surfaces (PES) to predict the far infrared, Raman collision induced absorption spectra of weakly bound dimers that exhibit few bound states (1-10 vibrational states). This unique characteristic feature makes these systems very useful to carry out theoretical studies of spectroscopic features, from which insights about the elementary dynamics processes occurring in these systems can be obtained. Dynamic studies such as calculation of life times and the width of the orbiting resonances of these small clusters can be used to understand energy transfer processes by rotational translation channel.
These studies also can be used to interpret scattering experiments using the new developed interaction potentials. The knowledge of the interaction potential near to the dissociation limit is of fundamental and practical importance to understand processes such as recombination and radiative association of molecules in the earth and many other interstellar atmospheres.1
The study of the far infrared spectra of these complexes can be used to detect characteristic signatures of the Van der Waals dimers relevant in the chemistry of the earth atmosphere. Some examples of these clusters are the N2H2, N2O2 heterodimers, for which very few theoretical and experimental studies have been carried out.1 In particular, the N 2O2 dimer has been proposed to be a contributor in the atmospheric reaction channels that participate in the formation of NO, which is believed to be one of the species involved in the stability of the O3 layer in the earth atmosphere.2
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2E. C. Zipf and S. S. Prasad, Science 279, 211(1998).
In particular, we are targeting trimers and medium size clusters with high symmetry, where it is possible to calculate accurate ab initio interaction potentials at reasonable computational cost. Trimers play a central role in the evaluation of three-body effects in molecular interactions, since these clusters are the smallest species, where these effects can be calculated and tested.1 Theoretical and experimental evidence suggests that this term is the most important non-additive many-body contribution to the interaction potential in larger clusters.1 The evaluation of this contribution allows the construction of an interaction potential, from which ro-vibrational dynamics calculations of large amplitude anharmonic motions can be used to interpret high-resolution spectroscopic data and virial expansion coefficients. At the same time, testing the potential with spectroscopic data allows to improve the potential where the ab initio theory is deficient using scaling techniques.2 The final potential can be used to carry out molecular dynamics simulations, solvation dynamics, and photo dissociation dynamics of caged reactive species.
Fig.3. The first solvation sphere of the ammoniated ammonia ion NH4+(NH3)n (n = 4) is illustrated by a circle.
We are interested in clusters that can be used to describe the first solvation sphere of a given solvation system. The (OCS)n, (CO2)n, (HCN)n, (H)9+ and NH4+(NH3)n clusters are among those unique systems, where simple models of solvation spheres can be visualized. In Fig.3, the first solvation sphere of NH4+(NH3)n (n = 4) is shown. Because of its high symmetry (tetrahedral) theoretical calculations in this system can be reduced significantly. These studies can be used to understand proton transfer mechanisms (proton tunneling) relevant in proteins and conductivity in solids.
1P. E. S. Wormer, and A. van der Avoird, Chem. Rev. 100, 4109 (2000).
2J. Castillo-Chará, R. R. Lucchese, and J. W. Bevan, J. Chem. Phys. 115, 899 (2001).
Metal nanoparticles of approximately few nanometers have been of interest for more than a century. The interest comes from the unique optical properties such as the strong characteristic absorption peak observed for these particles and absent in bulk material. As an example of this is the gold colloidal suspensions, whose absorption peak exhibits a beautiful ruby-red color. These properties are originated from the confinement of electrons, holes and phonons in small volumes, which is also known as the quantum size effect. Recently, nanoparticles have received a great deal of attention since the possibility of using these materials as optical devices.1,2 Because of the applications mentioned above, optical properties have been studied considerable; however, the confinement of vibrational modes (phonons) and electron-phonon coupling has been less studied.1 The latter are believe to be a key factor in determining very important dynamical processes such as: transport and inelastic electron scattering in nanoparticles and bulk materials.
a) Radial mode b) Spheroidal (quadrupolar mode) c) Toroidal (torsional mode)
Fig.4. Low frequency modes of the elastic sphere problem are illustrated in two-dimensional space: a) radial expansion and contraction of the sphere volume, b) the volume of the sphere deforms between oblate and prolate shapes, and c) the arrows indicate the twist between two hemispheres, which oscillate with respect to the nodal plane between them.
Low frequency modes (acoustic modes) in nanoparticles depicted in Fig.4 are very important because they are confined vibrations directly related to the cluster size. These modes are discrete and absent in a single cell or in a molecule. Therefore, acoustical modes are unique entities of a nanoparticle and their careful study may provide clues about the properties of these interesting materials.
Raman spectroscopy is a powerful tool to study nanoparticles. Using this technique is possible to detect the Mie’s band, which is known as a dipolar surface plasmon excitation (collective electronic excitation). Low frequency vibrational modes can couple with the plasmon mode. This allows observing in the inelastic Raman spectra, the Raman shift of the acoustic modes.
The ab initio treatment of acoustical modes in a metallic nanoparticle is practically impossible considering the number of atoms and electrons (20,000) involved.3
Acoustical modes are delocalized over many unit cells, which may be mimicked effectively by the bulk elastic constants. This suggest that the elastic sphere problem solved more than 100 years ago by Lamb4 might be a good approach to deal with the nanoparticle low frequency modes. Recently, this theoretical treatment has been extended to oblate and prolate symmetries5,6 making this method more relevant to the low frequency vibrations of nanoparticles. In Fig. 5, the most commonly observed nanoparticle shapes are illustrated.
Fig.5. Different shapes of silver nanoparticles are illustrated: spherical, prolate, oblate and spherocylindrical. These nanoparticles have been used in single-molecule experiments of hemoglobine absorbed on Ag nanoparticles.7
Classically, a nanoparticle can be imagined as a homogenous elastic sphere, where the low frequency modes are the vibrational eigenmodes of the elastic sphere problem. Therefore, the methods cited above seem to be very attractive to deal with the complex problem of the low frequency vibrations of spheroidal bodies.
We propose to treat the low frequency vibrations of a cluster nanoparticle by a classical treatment similar to that of Lamb.4 Extending this treatment to include more realistic symmetries besides the spherical such as prolate, oblate and spherocylindrical symmetries, we strongly believe that we can be able to carry out a more complete interpretation of the inelastic Raman spectra of metal nanoparticles (silver and gold).
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New developments in optical spectroscopy and microscopy have provided a new perspective in chemistry and molecular physics to deal with nanoscale phenomena. Single- molecule spectroscopy is a rapidly developing field, where spectroscopic techniques such as fluorescence, photoluminescence along side with scanning tunneling microscopy (STM) and inelastic electron tunneling spectroscopy (IETS) are being applied successfully to study single-molecules.1 The amazing capabilities of STM to provide imaging and spatial resolution of molecular size samples are unprecedented. This technique based on the electron tunneling phenomena, where the electron tunnel from the tip to the sample has allowed to observe a series of very interesting new phenomena occurring in molecules adsorbed on metallic surfaces. Selective excitation of molecular rotations and vibrations, conformational changes and even chemical reactions are just few examples. In these phenomena, inelastic scattering of electrons in the sample is believed to be the excitation source.2 Due to the fact that electron tunneling is a wide spread phenomenon in chemistry and central to quantum mechanics, the theoretical investigation of the most simple single-molecule phenomena could provide insights about the mechanisms involved. The other reason to study this phenomenon is based on the prediction that in the next generation electronic devices will be based on single-molecules capable of performing as nano-devices to transport electrons. Therefore, experimental and theoretical studies that foster the understanding of mechanisms of electron transport by single-molecules are not only of basic research interest, but also of practical relevance.
Fig. 6. A novel single-molecule experiment of pyrrolidine adsorbed on a metallic surface shows the excitation of the large amplitude motion by inelastic electron scattering.3
In recent work, Ho and coworkers1, 3 have found negative differential resistant effect in STM experiments of pyrrolidine adsorbed on metallic surfaces. This striking effect has been attributed to the novel discovery: the conductivity in single-molecules can be modified by inelastic electron-vibrational coupling and by conformational changes. In Fig.6, pyrrolidine conformational changes induced by inelastic electron scattering are depicted. In these experiments the vibrational spectra of single-molecules adsorbed in metallic surfaces are measured by using STM and IETS. The vibrational modes are selectively excited by mechanisms quite different from those of the traditional vibrational spectroscopic methods (infrared, Raman).
Recently, density functional (DFT) calculations have been shown to be very useful in calculations of medium size metal clusters (15-20 atoms).4 Clusters of these sizes have been used effectively to model metal surfaces.5,6 These new developments in ab initio computational methods have made possible to deal with new challenges such as those posted by single-molecules adsorbed on metallic surfaces.
We are interested in developing methodology to carry out theoretical calculations of floppy systems such as pyrrolidine adsorbed on metallic surfaces to treat especially the large amplitude motions. These motions are responsible for conformational changes and cannot be treated accurately by the traditional methods used to study localized vibrations.
Theoretical calculations of single-molecule vibrational spectra can be used to gain understanding of how solvent effects and other external effects perturb the molecule under study. The analysis of the calculations can be done by comparison of the theoretical single-molecule vibrational spectrum with the experimental bulk and single-molecule vibrational spectra.
To interpret vibrational single-molecule spectra, we propose DFT calculations of infrared and Raman spectra to determine by comparison with the experimental spectra the origin of the frequencies not active in infrared and Raman spectra. From these results is possible to find out the frequencies excited by electron scattering. In these calculations one of the big challenges is to describe the metal cluster where the molecule is to be adsorbed; however, medium size clusters can be used to model metallic surfaces at very reasonable accuracy by DFT and 6-31G** basis sets.4 To study the conformational changes in pyrrolidine and the frequencies associated with them, we proposed to calculate the potential energy surface along the coordinate that promote this interconversion. This calculation will be useful to understand how the interconversion process occurs and the relative stability of the two conformers.
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