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Adrian Kaminski Ph.D. Research Plan Date: March 27, 2011 Desired starting date of the Project: anytime Duration of the Project: the period of time will vary from 1 to 2 years. It is dependent on how many molecules will be examined. Title(s) I. II. The collision – induced influence on wings intensity of Raman scattering for the case of top gas molecules. The conjunction of all point group representations on the base of symmetry and geometry. Abstract I. Molecular dynamics simulations on Raman bands of gas linear top molecules (NO, C2H2, CS2 ), symmetric top (CH4, CCl4) as well as asymmetric top (C6H5F, C5H5N, C2H4) are intended to be reported. Induced effects are account for the dipole – induced – dipole (DID) mechanism. In order to determine the DID mechanism influence for the wings intensity, the tensoralgebra techniques will be used. The correlation function will be modified in such a way to take a form in which is more applicable to calculate integral intensity of Raman scattering. II. Apart from the above problem, the irreducible representations and their characters didactic way of analysis is meant to be portrayed. The threedimensional molecules are going to be given a substantial consideration. Introduction I. The most molecular physics phenomena are triggered of as well as isolated molecules and their collision-induced (CI) interactions. This – in turn – influences on the molecule polarizability and manifests in the spectrum. In the case of isotropic system, the Raman scattering spectrum is very narrow forming the Q line. Its wings originate from purely interaction mechanism and are intended to be investigate with reference to the selected linear, symmetric and asymmetric molecules. The Nonlinear Optics Division, Adam Mickiewicz University team earlier made research pertaining to the interaction-induced polarizability of Raman scattering [1,2]. Some other significant results in this domain of scientific research have been achieved [3 – 11]. The pursuing research are meant to be expanded on the different-formed molecules, for which the integral intensity of collision-induced Raman scattering will be analytically and numerically discussed. II. The second problem which will be analyzed is the potential possibility to apply a figure or a group of figures to depict the irreducible representations of different point groups. The author earlier conducted research [12,13,14] indicated on such a possibility with reference to D3h, D4h, D6h, D∞h, C2v, C3v, Td, Oh point groups, and the rest of known groups are going to be the subject of explorations. The figure’s transformation results lead to the characters of representation, and account for the simulations and computer programs data. Owing to the figure’s transformation and computer program interconnection, the method is expected to applicable by physics and/or chemistry undergraduate and graduate students. Problem statement I. The correlation function can be used in order to describe integral intensity of the Raman light scattering, as well as in the isotropic and anisotropic case. The angular-radial-tensor form correlations, which appear in the function are of high significance for the light intensity. One can calculate the angular-radial contribution impact on the integral intensity by expanding the correlation function in the set of spherical harmonics. The outcome bring us to interrelation between the laboratory frame molecular parameter and the computer simulation one. That allows to count respective, one by one, contributions for the intensity of the scattered light. The Adam Mickiewicz University, Nonlinear Division team conducted investigation on N2, CO2, CH4, CF4, SF6 in dense media [1,3,4]. Some significant results for CO2 and N2 in fluid phase are gathered in the table 1. Molecule S – model Two bodies angular-radial contribution Three bodies angular-radial contribution Total angular-radial contribution Outcome CO2 4.31·10–3 – 3.89·10–3 1.56·10–3 – 2.33·10–3 1.98·10–3 N2 8.64·10–4 – 6.80·10–4 2.90·10–4 – 3.89·10–4 4.75·10–4 Tab.1. The correlation function contributions. All quantities in Ǻ7. The numerical results obtained indicate on significant two- and three bodies contribution for the spectrum wings. It occurs S-model large reduction. Analogical effects might be expected for molecules in gas phase. But this time – instead of correlation function experimentally tabled – we are going to use the function as molecules interaction potential and energy of thermal movement dependent. Then, the correlation function may be on the power series expanded. This, together with the tensor technique application are very likely to bring appropriate effects of the top gas molecules spectra intensities. The method, simultaneously, will allow to assess the CI mechanism influence on the Raman scattering spectra. II. In order to determine the figure-based representation, the projector application has been substantial. The projectors of the form (1) have been used to find figure’s shape and sign-structure. They act on the atomic function, which belongs to a given molecule. The operation results in potential geometrical figure construction. t l (1) P t S t S h S Pt – the ts irreducible representation projector lt – the ts irreducible representation dimension h – the group’s rank χ – the irreducible representation character S – the symmetry operator The figure(s) account for a point group representation, earlier unknown in the literature. The Dnh, Cnv, Td, Oh, have been previously elaborated by the author. It would be desirable to spread the method out on the rest of point groups and their representations in order to obtain the overall geometry and visualization based model. What is more, the symmetrybased representations are assumed to be mathematically conjugated to get the representation definition fulfilled. For this purpose, the numerical results of the figure transformations are going to be widely analyzed and their interrelations will be given. The vibration simulations of various molecules, computer programs counting the number and kind of vibrations as well as dipole moment and its change are intended to be prepared, too. Objectives The author, within the confines of the research, will pursue to answer the following questions: 1. Is it any predictable, collision – induced influence on the spectrum intensity of the linear (NO, C2H2, CS2 ), symmetric (CH4, CCl4) and asymmetric (C6H5F, C5H5N, C2H4) molecules? 2. If there is answer on first question positive, then, what would be the intensity increase/decrease with reference to the so called Smodel? 3. There is a coherent, symmetry based method, earlier elaborated, to portray geometrically the representation of the Dnh, Cnv, Td, Oh groups. If so, is it possible to extend the model on all the points groups? One can answer it positively with big credibility. 4. If the question included in the third point is positive, then, how could the representations be arrange in order to satisfy the Great Orthogonality Theorem? Methodology I. 1. The correlation function for each molecule investigated will be derived, according to: g(R)=Exp[-V/kB*T], (2) where V – molecules interaction potential kB – Boltzmann constant T – temperature 2. The expansion of the correlation function in the power series will be performed. 3. Tensor-algebra techniques, which leads to the molecular parameters general form, will be used. 4. The computer simulations will be applied in order to calculate the respective contributions on the overall Raman scattering intensity. II. 1. The projectors of the form (1) for obtaining molecular orbitals appropriately symmetrized will be applied. 2. The symmetry based representation figures will be constructed. 3. The transformation, description numbers will be attributed to each figure. The number attribution way originates from the modified matrixes of transformation. 4. The numbers arrangement according to the Great Orthogonality Theorem principles will be given. Evaluation and Significance I. The collision – induced effect has been measured for a number as well as linear and non-linear molecules. Therefore, the investigation extension on earlier mentioned molecules and CI mechanism corroboration, is of high importance. The research has a theoretical background and, on account of that, its effective evaluation is due to experimental stage. The cooperation with some experimental track institutions will be sustained. These are: Non-linear Division, Adam Mickiewicz University; Laboratoire des Proprietes Optiques des Materiaux et Applications, Universite d’Angers; Dipartamento di Chimica-Fisica, Universita DorsoDuro. The theoretical and experimental results comparison are going to be carried out. II. This is the first visual model geometrically which is designed for didactic way of molecular problem analysis. One of the model intensions is to facilitate the understanding and thus learning process. Its application for the physics and chemistry student classes is meant to be implemented. The model effectiveness, understood as the will to learn, as the ability to rapid application by students, is the best way to evaluate it. The results achieved by students are going to be estimated and marked. List of References [1] Bancewicz T., Kaminski A., “The intensity of collision – induced wings of isotropic Raman scattering”, J.Mol.Liquids, 124, 21–24, (2009). [2] Bancewicz, T., Mol. Phys., 50 (1983) 173. [3] Bancewicz, T., Le Duff, Y., i Godet, J. L., “Multipolar polarizabilities from interaction – induced Raman scattering” Modern Nonlinear Optics, Part 1, Second Edition volume 119 of Advances in Chemical Physics, pp. 267 – 307 J. Wiley New York M. Evans edition 2001. [4] Bancewicz, T., Elliasmine, A., Godet, J.-L., i Le Duff, Y., Collision – induced depolarized light scattering by CF4 in a Raman vibrational band, J. Chem. Phys., 108 (1998) 8084. [5] Bancewicz, T., i Kielich, S., J. Chem. Phys., 75 (1981) 107. [6] Ben-Reuven, A., i Gershon, D., J. Chem. Phys., 51 (1969) 893. [7] DeSantis, A., i Sampowi, M., Chem. Phys. Lett., 102 (1983) 425 – 428. [8] De Santis A., Sampoli M., Chem. Phys. Lett. 102 (1983) 425 [9] De Santis A., Sampoli M., Mol. Phys. 51 (1984) 97. [10] De Santis A., Sampoli M., R. Vallauri, Mol. Phys. 53 (1985) 695. [11] De Santis A., Frattini R., Sampoli M., Vallauri R., Europhys. Lett. 2 (1986) 17. [12] Kaminski A., „Normal mode of molecules vibrations – spectral activity and directions of atomic cores deflections”, My Phys., 16 (2007). [13] Bancewicz T., Kaminski A., „The geometrical model for obtaining the D3h group’s characters of irreducible representation and symmetry types” Chem.Ed.J, 12 (1), 2009. [14] Bancewicz T., Kaminski A.,“The visual derivation of characters for irreducible representations of D6h group”, Chem.Ed.J , Vol. 13, No 2, (2010) Selected Bibliography (1) R. L. Carter, Molecular Symmetry and Group Theory, (J. Wiley and Sons, N.York, 1997) (2) J. F. Cornwell, Group Theory in Physics, (Academic Press, London, 1984) (3) J.M. Hollas, Basic Atomic and Molecular Spectroscopy, (Royal Society of Chemistry, 2002). (4) Berne, B. J., i Pecora, R., Dynamic Light Scattering ( New York: John Wiley and sons, 1976). (5) C.G. Gray, K.E. Gubbins, Theory of molecular fluids, Fundamentals, vol.1, Clarendon Press, Oxford, 1984.