Download PREFACE The Thesis entitled "Spectroscopic properties of diatomic

PREFACE
The Thesis entitled "Spectroscopic properties of diatomic molecules ' deals
with the results of the electronic spectra of the diatomic molecules H2. NdO,
CaO, SiO, SiO+, FeH, N2+, VO, CaF and BaF. The thesis is divided into five
chapters and a brief summary of each chapter is as follows:
Chapter 1 describes the spectroscopic properties of diatomic molecules
which are useful in the fields of astrophysics, gas kinetics, chemical physics etc.
Some of the applications are as follows: The abundance (concentration) of
molecular species can be estimated from the intensities of interstellar lines. The
temperature of interstellar atmosphere can be determined by band-spectroscopic
methods. And, the study of interstellar band spectra specifically gives information
about abundance ratio of isotopes. The spectroscopic data allows to predict
reliable values of heat capacities even for chemically unstable diatomic gases for
which direct thermal measurements are impossible. In addition to heat content
and heat capacity, the entropy and free energy of a gas can be calculated once the
partition function has been obtained from the spectroscopic data.
Also, the
equilibria of chemical reactions in gases can be predicted on the basis of
spectroscopic data.
The nuclear properties such as nuclear magnetic moment,
nuclear quadruple moment etc., can be determined from the investigations of
molecular spectra. The heats of the elementary chemical reactions, which are not
accessible to direct measurement, can be calculated accurately from the
dissociation energies of the molecules involved.
Molecular spectra provide the most useful data for determining molecular
structures and bond energies, and are a key means of verifying the presence of
various elements or molecules and monitoring the concentrations of chemical
species in laboratory, industrial, atmospheric and interstellar environments.
Frank-Condon factors are important parameters for every molecular band
system, since they enter into the calculation of the relative band intensity, which is
a significant source of information in quantitative spectroscopy, high-temperature
chemistry, astrochemistry and cometary spectra. They are also important for the
determination of the molecular structure, population of the vibrational levels in
the upper electronic state involved in a transition, radiative lifetime, vibrational
temperature and kinetics of energy transfer in stellar and other astrophysical
atmospheres containing molecular species. On the other hand, knowledge of rCentroids has been found to be very useful in the discussion of the variation of the
electronic transition moment with internuclear separation and in other molecular
properties. Variation of r-Centroids with band wavelengths (or wavenumbers)
provides a useful bridge between experimental measurements, which are often
expressed as a function of wavelength and theoretical studies, which are often
made in terms of internuclear separation.
The electronic and vibrational energy levels of a diatomic molecule in a
given electronic state are often described by a potential energy (Y-axis) internuclear distance (X-axis) diagram. Each electronic state of a molecule is a
characteristic of its own potential energy curve. Consequently, the collection of a
number of such potential energy curves, presents an equivalent representation of
the corresponding electronic states of the molecules.
The potential energy curve for any electronic state of a diatomic molecule
can be represented by an empirical potential function. Morse function is one of the
most successful empirical potential functions among a number of simple and
approximately good empirical analytical functions. However in many cases, the
assembly of energy levels cannot be an exact representative model of the molecule
over a wide experimental range of energies. In order to overcome this problem and
to obtain appropriate potential energy curves from the band spectroscopic data
Vanderslice et al, developed a modified method known as Rydberg-Klein-ReesVanderslice (RKRV) method.
n
Chapter 2 describes the details of the RKRV method for the construction of
potential energy curves of certain diatomic molecules.
The construction of experimental potential energy curves for the selective
26 electronic states of 10 specified diatomic molecules dealt in this chapter and,
listed below:
S.No.
Molecule
Electronic states
1
h2
X 'l+g, B 'X+u and C 'flu
2
NdO
X( 1)4, (1)3 and [10.935]4
3
CaO
X , A 'l+ and a 3flo-
4
SiO
X r and E T
5
SiO+
X 2I, A
6
FeH
X4A and F 4A
7
NT
X 2X~. A 2n{1 and B2X~
8
VO
X4X k and 2[]i
9
CaF
X 2IT A 2n and B 2X+
10
BaF
X 2I^ and A 2n
2n
and B 2X+
2
In accordance with the report of Wilkinson the information of dissociation
energies and ionization potentials of diatomic molecules is helpful to decipher
many astrophysical, as well as physical and chemical problems. Chapter 3
emphasis the details of several methods exist in the literature for the determination
of the bond energies.
Nevertheless, the determination of dissociation energy is also carried out
by the spectroscopic method based on pre-dissociation limit. In the case of
diatomic molecules, the pre- dissociation limit yields only the upper limit of the
dissociation energy. As per Henri, this phenomenon in which the bands
corresponding to transitions to low vibrational levels of the upper electronic state
exhibit a normal type of rotational structure consists of various sharp lines. But.
iii
the transition to higher vibrational levels gives bands in which the lines of the
rotational fine structure are relatively diffused. The reason of this diffuseness as
attributed to some instability in the molecules is also discussed.
As any of the experimental potential energy curves are insufficient by
themselves for the estimation of dissociation energy of a molecule, a relevant
analytical expression developed is felt very much needed owing of their greater
influence.
In the present work, Hulburt-Hirschfelder function, is chosen to estimate
dissociation energies of H2, NdO, CaO, SiO, SiO+, FeH, N2+, VO, CaF and BaF.
Chapter 4 gives the importance of the internuclear distance in describing
the structure and properties of diatomic molecules. When a molecule absorbs
visible or ultraviolet light, a new excited state with modified electronic structure
replaces the original electronic structure. This occurs on such a short time scale
that there is no significant change in the internuclear distance (i.e., in the position
of the nuclei) of the molecule. Such a change i.e., the transition between the two
states is described as vertical.
An overview of the vibrational wave functions pertaining to the ground and
excited states are revealing that the overlap of these wave functions will determine
the intensity of the transition. After an electronic transition, the excited state
immediately restores back to its equilibrium bond length. The concept of a vertical
transition i.e.. at constant internuclear distance stands as the central point for the
discussion of the Franck-Condon principle.
The concept of r-Centroids was introduced by Fraser, Nicholls and Jarmain
during their study of the variation of molecular parameters with internuclear
separation. It is defined as the r-coordinate of the Centroids of the area represented
by the overlap integral and takes a unique value for each band of a transition
system.
IV
In the present work, the r-Centroids are determined using quadratic
equation method of Nicholls and Jarmain for the following 7 transitions in the case
of 7 diatomic molecules. They are:
Transitions
S.No.
Molecule
1
h2
2
CaO
a3no. - X
3
VO
1U2- x4 rk
4
n2+
A2riu,
5
SiO+
A2n-* x2r
6
SiO
E 'S+-^ Xf+
7
BaF
A 2if -+ X2I+
B'ru-
-
vlv+
A i-* a
x4eu"
The trends of r-Centroids for the characteristics transitions are discussed in
detail, in the wake of the qualitative importance of atoms that constitute the
molecule under study.
The dependence of relative intensity (of vibrational bands in spectra) on the
square of the vibrational overlap integrals (of the electronic states) which are
involved in the transitions is discussed in this Chapter.
These transitions are
usually known as the vibrational transition probabilities (Franck-Condon factors).
Chapter 5 highlights the importance of Franck-Condon factors and their wide
applicability in many branches of physics and chemistry.
In the spirit of Franck's mathematical idea and as later developed (on
wave mechanical basis) by Condon, a possible explanation for the intensity
distribution in the energy level band system of a diatomic molecule, is also
explained.
As such, the resulting Franck-Condon factor arrays happen to be the basic
molecular data needed in the interpretation of intensities of molecular spectra.
The important role of Franck-Condon factors for the calculation of vibrational
transition probabilities of diatomic molecules is presented.
A vivid literature
survey with details of different methods employed to evaluate the Franck-Condon
factors, is also presented.
In the present work, the Franck-Condon factors are evaluated by the
specific approximate analytical method of Fraser and Jarmain.
The Franck-Condon factors are determined for the following 15 systems
belonging to 10 different diatomic molecules during the specified transitions.
S.No,
Molecule
1
h2
2
NdO
3
CaO
4
FeH
5
VO
6
NT
7
SiO+
X ’x+„
(1)3 - X(l)4,
AX+X,
F4A- x4a
1 2Um ■ X
A2nul
X 4XU+
A2n- x 2r,
8
SiO
E 'Xf-
9
CaF
A2n- x 2r,
10
BaF
A2nr-
A
comparative
Transitions
B 'X+u
and
cnu-- X 'x+
[10.935]4 -■* X 'x+
a Jn» -->x
b 2r-> x 2r
xr
b 2r-^ x 2r
X2X+
systematic
study
of Franck-Condon
factors
corresponding to different transitions is described as a function of characteristic
properties of the constituent atoms of the molecule.
VI
Major portion of the work presented in the thesis has been published by the
author in the following scientific journals.
1. Spectroscopic Studies of Astrophysical important molecules.
Astrophysics and Space Science (Submitted for publication) .
22.Dissociation Energies of VO, FeH, BaF and NdO Molecules.
Indian Journal of pure and Applied Physics. (In Press).
3. Estimation of Potential Energy curves, Dissociation Energies,
Condon Factors and r-Centroids of Fl2. CaF and SiO+ Molecules.
(Submitted to JQSRT).
Vll
Franck-