Download Research Plan

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.