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welcome back to the lectures in chemistry
and the introduction to molecular spectroscopy
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series that i been giving ok so in this lecture
we will get to the practical aspects of the
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elementary aspects of rotational raman spectra
and in the last two ah lectures i talked about
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polarizability and the fact that it is a tenser
and ah it is connected to the or it is measured
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by which the induced dipole moment depends
on the external electric field so now we will
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get to the actual spectroscopic details so
we will start from the fact that mu induced
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is alpha times e we will write it this way
for the time being that is as a scalar and
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then we do the actual spectral specta intensity
computation we will use the factor alpha e
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is a tenser ok mu is proportional to alpha
e now please remember for a an external static
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electric field alpha is a constant because
the induced dipole moment depends on the the
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electric field e ok but alpha is not a static
quantity because the molecule is not stationary
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the molecule is actually vibrating it is vibrating
say with the frequency angular frequency omega
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ok lets call it as a vibration frequency so
if the molecule is vibrating then alpha is
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actually also vibrating is also changing in
time by the simple relation alpha naught plus
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alpha one sin ah omega vibration times t ok
this is the polarizability as a function of
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time ok this is due to the vibrations in the
molecule in the case of rotation of course
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in a rigid rotation we dont worry about it
we only worry about alpha zero we dont need
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to know what alpha one is but in general molecule
undergoes both rotation vibration and so far
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we have been ah i mean our considerations
have been simple enough to treat this has
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to different phenomena two independent phenomena
so if you do that then for the vibrational
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sake you will have both alpha naught and alpha
one sin omega vibrational times t but alpha
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naught will not be relevant for the vibrational
spectroscopy for vibrational spectroscopy
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alpha one will be relevant because thats a
changing polarizability exactly the same way
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the mu has to change during the vibration
the mu induced also has to change during the
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vibration therefore the mu induced now will
become as a function of molecular vibration
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it will become alpha naught plus alpha one
sin omega vibration times t
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but please remember in the case of the ah
electromagnetic radiation the electric field
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of the electromagnetic radiation is not a
constant is not a constant time it is actually
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itself a sinusoidal function therefore the
electric field itself will be e naught in
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some direction say let us call it as a z direction
if you wish ok and it will be sin omega t
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ok plus five if you want to put in as a phase
factor but we will consider very simple thing
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namely that the induced dipole moment changes
during the vibration as a function of time
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due to two things there are two oscillating
components an oscillating component due to
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the vibration and an oscillating component
due to rotation now this is the physical picture
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now what is the raman effect ok we will start
with this raman effect so let us keep this
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in the background when we need it we will
come back to this what is a raman effect
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light of some frequency nu naught radiates
a sample and this is some sample the scattered
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light which comes out this a transparent sample
therefore what happens is a small portion
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of the light gets scattered bulk of the light
is transparent and it goes straight through
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and the very small portion of the light that
is scattered seem to have not only the nu
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zero which is the frequency of the incident
light incident electromagnetic radiation but
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the scattered lights seems to have nu naught
plus delta nu one nu naught plus delta nu
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two thats all series of ah frequencies of
radiation which are emitted as well as nu
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naught minus delta nu one nu naught minus
delta nu two i mean its not the same delta
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some value now so if you want to write it
as d nu one if you want to make it different
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its d nu two so on ok so that is also another
group of frequencies which are seen in the
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light that gets scattered that is the scattered
light has been modulated over the incident
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light frequencies by these additional frequencies
or this depleted frequencies its somewhat
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easy to understand this from the quantum mechanical
stand point why light that falls on the system
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comes back with the a different frequency
you have already seen that because if you
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think about this as a photon and the photon
frequency matches with some transition between
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rotational energy levels or transition between
vibrational energy levels it is possible that
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the photon gets absorbed and the scattered
light may have some amount of energy reduced
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from it to give radiation of this kind or
an excited molecule which actually comes down
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to a lower energy level introduces an additional
a different photon with the frequency which
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is different from nu naught buy slightly more
than that ok
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now there is also of course nu naught a fairly
large amount of light that is scattered does
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not have any intensity does not have any change
in the frequency this nu naught to nu naught
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this is called rayleigh scattering ok these
two together is called raman scattering this
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is the raman scattering effect of course the
lines have very specific names light which
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has a frequency less than that of the incident
frequency this is this phenomenon of reduced
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frequency is called stokes phenomena ok or
stokes radiation and radiation which has a
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frequency which is higher than the incident
frequency due to the interaction of the radiation
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the sample whose energy levels are quantized
and therefore there is a lot of energy exchange
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in them leading to changes in the frequency
this is called anti stokes phenomena so we
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will write that here anti stokes radiation
so you get both you get the rayleigh scattering
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you get the stokes scattering and you get
the anti stoke scattering now how do we understand
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this we understand this from the last line
that we wrote before we introduced to the
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raman effect namely the induced dipole moment
we wrote down is alpha naught plus alpha one
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sin omega vibrational t times e naught sin
omega t this is the radiation frequency this
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this omega is what we call let us call this
as omega naught because we are using the symbol
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nu naught and the relation between omega naught
and nu naught is it is two pi nu naught this
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is angular frequency and this is the regular
frequency in the form of hertz this is in
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terms of the angle ok
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now please remember sin a sin b is one half
cos a minus b plus cos a plus b ok therefore
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if you remember this relation ok what you
see here from this one is alpha naught e naught
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sin omega naught t thats the first term and
then you have alpha one e naught by two times
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cos omega vibration minus omega naught t minus
cos omega vibration plus omega naught t therefore
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you see that the induced dipole moment now
has components ok components that correspond
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to dipole oscillating with the same frequency
as the incident radiation the dipole moment
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oscillating as the omega vibration minus omega
naught meaning that omega naught is no longer
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omega naught but it is changed by it is after
all cosine so if you want to write this you
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can say omega naught minus omega vibration
and this is also omega naught plus omega vibration
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therefore the dipole moment thus has its own
oscillation and this results in the energy
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exchange and therefore the radiation that
comes out also has frequencies corresponding
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to the original ah the radiation of the original
frequency nu naught and radiation with frequency
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differences corresponding to some vibrational
motion internal vibration of the molecule
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internal vibrational motion of the molecule
this is very elementary simplified picture
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to tell you why there is a modulation of the
radiation that comes out ok see that frequencies
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are different and there can be many because
we consider only one vibrational motion but
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molecules have more than one degree of freedom
and also the molecules when they rotate the
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induced dipole moment undergoes rotation and
the rotation indu induces its own frequencies
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and rotation is connected to the alpha naught
e naught because for a pure rigid rotor we
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dont have alpha one that is no vibration for
the polarizabilities is the static polarizability
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but the static polarizability is a second
rank tensor it has x x component xy the yy
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component and zz component in the principle
directions and therefore there are three polarizability
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static polarizability components which are
part of the induced dipole moment so even
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if the molecule does not have a dipole moment
the presence of the electromagnetic radiation
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induces a dipole moment due to the fact that
the molecule can actually polarize itself
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to the positive part of the electric and the
negative part of the electric field and continue
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to do that either through rotation or through
vibration so since there is a an induced dipole
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moment even in the absence of vibration now
there is a microwaves spectrum that one can
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see and that spectrum can be seen in the raman
lines ah in ah the next step ok ok
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so the rotational spectrum ah when the molecule
does not have a permanent dipole moment it
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still has an induced dipole moment due to
the the electric field and the induced dipole
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moment also is proportional to the alpha so
if you recall mu induced now we will use the
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tonsorial form that we had used suppose we
had mu induced in the z direction which is
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probably that direction of the symmetry axis
of the molecule then the mu induced is given
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by alpha z x e x plus alpha zy ey plus alpha
zz ez therefore this is the one which causes
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the molecular rotational energies to be accessible
by raman spectroscopy because now they have
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polarizability which is also rotating because
of the molecule is rotating the polarizability
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tensor the the quantity is also rotate the
mu induced is ah directly given by two directions
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alpha zx or alpha zy or alpha zz barrrier
when we studied microwave spectroscopy the
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hamiltonian that we were worried about had
basically the interaction with the external
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electric field is mu dot e its a scalar the
mu is the doipole moment vector and e is the
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electromagnetic radiation and therefore what
you have is this mu is due to the mu induced
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and so the hamiltonian due to this mu induced
is this and this hamiltonian is responsible
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for that transition this is the one which
leads to the transition between rotational
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levels
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so this mu induced is now a function of two
coordinates or two directions so it is like
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mu induced is like the molecular property
of a coordinate z and a coordinate x earlier
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the mu in microwave spectroscopy was simply
mu x of x plus mu y of y plus mu z of z ok
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and these were the dopile moment components
in some chosen direction and xyz are the coordinate
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system that we ah start with and therefore
these are the mu x mu y mu z are the components
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of the arbitrary dipole moment in the direction
of the coordinate system here the mu induced
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now depends on two coordinates and therefore
what this leads to is the selection rule of
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a delta j not plus or minus one but delta
j two also there is a invariant component
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alpha zero and alpha zero is usually defined
as one third of alpha xx plus alpha yy plus
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alpha zz and i told you that this quantity
does not change between different coordinate
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systems therefore this is called the scalar
of the polarizability and this alpha naught
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which is a constant ok does not have any direction
dependence everything has been summed here
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this constant therefore ah also gives raise
to what is called delta j is equal to zero
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ah transition in microwave spectroscopy you
dont have a delta j is equal to zero because
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there is no micro waves spectroscopy there
delta j is plus minus one for a rigid molecule
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in the case of rotational raman this the static
polarizability which does not have what is
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called scalar component which does not have
any direction leads to delta j is equal to
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zero and the actual mu induced dipole which
involves two directions leads to delta j is
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equal to plus minus two therefore the selection
rule for rotational raman is zero plus minus
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two and that is also for molecules which do
not have a permanent dipole moment therefore
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now you have a beautiful handle of being able
to detect the microwave spectrum of hydrogen
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molecule the most elementary molecule that
you have microwave spectra could not detect
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that raman lines rotational raman spectroscopy
tells you how if the hydrogen the electrons
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between the two hydrogen atoms if they are
polarized due to the presence of the electromagnetic
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field then there is a polarizability that
comes into the picture and this poilarizability
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has one scalar component and several vectorial
tensorial components two in this case the
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stab parallel and perpendicular polarizability
and this polarizability allows us to actually
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look at the rotational energy levels of hydrogen
so raman spectroscopy is a beautifully complimentary
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spectroscopy to study systems which are otherwise
in accessible to the spectroscopic techniques
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so molecules which dont have permanent dipole
moment are not seen in microwave all those
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molecules which have any measurable polarizability
i mean unless the bonds are extremely rigid
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and therefore the polarizability is extremely
small see if you are a very very rigid the
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feel does not basically affect the electron
density but if the molecule is already undergoing
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some vibration and the you know zero ponit
vibration and the molecular bonds are slightly
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flexible then you the polarizability leads
to an immediate measurement of the microwave
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spectrum of molecules
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now what is the microwave spectrum of molecule
they have the following features so if the
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selection rules are delta j is equal to zero
plus minus two remember we have what is called
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a ah nu naught this is the rayleigh line the
frequency that we have so thats the center
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frequency ok no modulation of the incident
light that passes right through scattering
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ah equipment detects that right away so there
is no change in that ok now on either side
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we have delta j is equal to zero or plus minus
two ok so which side is which lets write down
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the energy levels for a simple diatomic molecule
we have the energy levels e zero which is
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zero because j is zero the next one e one
is b j into j plus one it is two b j is equal
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to one it is two b therefore the the gap is
two b but then j is equal to two it is e two
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is six b same energy level spacing that we
are familiar with micro wave but now between
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zero and six b you have a transition because
delta j has to be two there is no transition
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between zero and one there is no transition
between one and two what about e j e three
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is equal to twelve b and this is j is equal
to three there is a transition between one
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and three ok whats the difference between
the two this is delta e is twelve b minus
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two b ok twelve b minus two b and that is
ten b ok what is the lowest frequency that
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we would measure this delta e is the difference
between zero and six b therefore this is six
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b ok
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whats the next one let us draw say j is equal
to two here and thats a six b and the next
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let us draw j is equal to four j is equal
to four four is four into five so it is ah
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twenty b ok the gap between j is equal to
two and four is now fourteen b ok you calculate
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this you will see every difference that you
can measure in raman spectroscopy for rotational
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lines barring the first one which is six b
will always be four b away from this ten b
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fourteen b eighteen b twenty two b and so
on therefore what you will see n the rotational
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raman line is ah on either side this is absorption
of radiation ok therefore what happens if
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this radiation is absorbed i mean supposing
this is the frequency reduction n the scattered
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radiation then that is seen on this side of
the frequency because this is rayleigh and
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this is the increasing direction on the frequency
therefore this is stokes side and this is
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the antistokes side therefore the first line
that you will see is six b the next line that
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you will see is ten b from here zero zero
to no transition at this point j is zero therefore
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j is equal to zero j is equal to two then
this is j is equal to one to three and then
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the next line is fourteen b eighteen b and
so on what about another side is exactly the
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same the other one is ah the emission of radiation
because the transition happens from higher
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energy state to lower energy state but remember
usually fewer molecules are there in the higher
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energy state and more molecules are there
in the lower energy state therefore getting
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transitions down from very high energy state
to very low energy because so few molecules
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are there the intensity of that such radiation
that is the antistokes radiation usually weaker
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than the intensity of the stokes radiation
where nothing but absorption is happening
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therefore the radiation that comes out does
not have those frequencies ah these are the
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nu naught minus six b nu naught minus ten
b nu naught minus fourteen b and so on therefore
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i would say i would put something like six
b eight b ah this is six b this is ten b this
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is fourteen b due to this process due to this
process due to this process ok
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so you see a very symmetric eighteen b spectrum
on either side of it for a rigid rotor the
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gap between the zero and the first rotational
line is six b and every other line is four
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b and what is b you know from microwave spectroscopy
that for a rigid diatomic molecule that we
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00:26:28,200 --> 00:26:40,190
are looking at he value of b is ah h by eight
pi square ic and therefore if you have delta
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00:26:40,190 --> 00:26:51,030
nu is equal to six b the first gap the first
appearance of a rotational roman line hydrogen
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is a beautiful example ok and benzene many
other molecules all molecules which are homo
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00:26:56,450 --> 00:27:03,620
nuclear no microwave spectrum every one shows
off in the raman in the gas phase and what
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00:27:03,620 --> 00:27:13,380
you see is he first line six b is for j is
equal to zero to j is equal to two ok and
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00:27:13,380 --> 00:27:27,020
yeah and the next line is every gap is four
b therefore delta nu by four is the gap between
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00:27:27,020 --> 00:27:46,860
successive lines gap between successive raman
lines is four b ok and that delta nu and therefore
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00:27:46,860 --> 00:27:59,580
delta nu by four is h by eight pi square c
mu r square you know the ah reduced mass therefore
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00:27:59,580 --> 00:28:06,640
you can calculate the bond length very very
accurately for the molecule if you can measure
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00:28:06,640 --> 00:28:13,630
rotational roman lines ok this is as simple
as what one can expect they were much more
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00:28:13,630 --> 00:28:19,570
things in rotational raman spectroscopy particularly
if the molecule is slightly non rigid then
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00:28:19,570 --> 00:28:24,020
there are centrifugal effects we never studied
centrifugal effects in this course even in
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00:28:24,020 --> 00:28:30,140
the pure microwave spectrum of molecules having
permanent dipole moment therefore i dont want
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00:28:30,140 --> 00:28:36,559
to introduce that here but remember this is
the starting point of understanding the selection
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00:28:36,559 --> 00:28:43,750
rules the selection rule being delta j is
equal to plus minus to and the delta j is
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00:28:43,750 --> 00:28:52,470
equal to zero is right here ok no change ok
and so what you see is that this is how to
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00:28:52,470 --> 00:28:58,550
interpret elementary raman spectra a looking
at the spacing and then calculating the bond
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00:28:58,550 --> 00:29:04,670
length or the ah the vice versa if you know
the bond length exactly where the raman line
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00:29:04,670 --> 00:29:06,140
will be and so on
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00:29:06,140 --> 00:29:13,570
now in the next small bit i would talk about
the vibrational raman spectrum and then we
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00:29:13,570 --> 00:29:18,400
will come to an end with respect to this particular
course on the molecular spectroscopy there
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will be one introductory lecture in another
three or for days ah you will also see ah
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00:29:24,320 --> 00:29:31,100
on electronic spectroscopy the last segment
of this introductory lectures on raman spectroscopy
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00:29:31,100 --> 00:29:41,300
so we will look at vibrational raman spectra
also only for the very elementary case of
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00:29:41,300 --> 00:29:48,690
a simple harmonic model or ah similar to that
in the normal mode model for a poly atomic
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00:29:48,690 --> 00:29:59,260
molecule now remember vibrational spectroscopy
the intensity of the infrared transition is
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00:29:59,260 --> 00:30:10,360
due to the rate of change of the dipole moment
with respect to the displacement coordinate
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00:30:10,360 --> 00:30:22,680
so suppose x is the displacement coordinate
and during that displacement the dipole moment
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00:30:22,680 --> 00:30:28,740
changes it is the rate of change of the dipole
moment with respect to displacement thats
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00:30:28,740 --> 00:30:36,140
responsible and this is ah how do we write
that we will write in a formal way we will
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write mu at a position x is mu naught which
is basically mu at x is equal to zero no displacement
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00:30:47,650 --> 00:30:58,650
so or at equilibrium displacement and then
you have this is ah yeah plus d mu by dx evaluated
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00:30:58,650 --> 00:31:04,680
at the displacement being zero times x plus
and so on ok
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00:31:04,680 --> 00:31:13,410
it is this rate of change of dipole moment
evaluated with respect to the equilibrium
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00:31:13,410 --> 00:31:28,059
geometry that is responsible for the intensity
of infrared spectra there are other terms
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00:31:28,059 --> 00:31:32,210
like this rate of rate of change that second
degree then then is a third degree and so
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00:31:32,210 --> 00:31:37,540
on that basically determines the extent to
which the molecular motion is no longer harmonic
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00:31:37,540 --> 00:31:42,900
and its highly non linear and therefore higher
order terms come in but if we restrict ourself
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00:31:42,900 --> 00:31:49,070
to this term this leads to the selection rule
delta v is equal to plus minus one this static
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00:31:49,070 --> 00:31:55,620
dipole moment is irrelevant as far as the
infrared spectrum intensities concerned because
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00:31:55,620 --> 00:32:02,309
thats a fixed component there is no association
with the position because it is a constant
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00:32:02,309 --> 00:32:08,510
but if the dipole moment keeps changing during
the vibration you immediately see that that
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00:32:08,510 --> 00:32:13,190
vibration mode is detected by the infrared
spectrum thats this coordinate the rate of
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00:32:13,190 --> 00:32:19,150
change the the rate of change as well as this
coordinate it is this which is the molecular
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00:32:19,150 --> 00:32:26,940
level operator i should say ok the position
coordinate it is that which connects the vibrational
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00:32:26,940 --> 00:32:33,910
eigen function which contains one hermite
polynomial to another vibrational eigen function
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00:32:33,910 --> 00:32:50,130
which contains another en prime en ah double
prime and en prime if these two have to be
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00:32:50,130 --> 00:33:00,350
connected it is this mu and technically it
is the the x operator which connects the psi
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00:33:00,350 --> 00:33:08,450
n prime the psi n double prime to give you
an intensity that of the transition between
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00:33:08,450 --> 00:33:16,210
n double prime to n prime as being proportional
to the absolute square of the integral psi
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00:33:16,210 --> 00:33:26,940
n prime x x psi n double prime of x dx square
ok
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00:33:26,940 --> 00:33:32,860
therefore you see that because it is linear
it is x not x square not x to the one half
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00:33:32,860 --> 00:33:39,450
or anything else because it is linear in the
limit of what is call the harmonic approximation
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00:33:39,450 --> 00:33:43,660
where the rate of change of dipole moment
alone is sufficient for us to consider the
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00:33:43,660 --> 00:33:49,590
motion thats because the displacements are
very small harmonic motion therefore the selection
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00:33:49,590 --> 00:34:01,809
rule wholes ah because this integral is non
zero only for n double prime is equal to n
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00:34:01,809 --> 00:34:10,300
prime plus or minus one so this is the essence
of the vibrational intensity i might have
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00:34:10,300 --> 00:34:15,599
talked about this in the lectures earlier
if i didnt this is how we actually calculate
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00:34:15,599 --> 00:34:21,041
the vibrational intensity the intensity is
proportional to this square of what is call
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00:34:21,041 --> 00:34:29,079
the matrix element between the state psi n
double prime one of the energy states and
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00:34:29,079 --> 00:34:36,700
its next state psi n prime and therefore this
is also possible this is absorption this is
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00:34:36,700 --> 00:34:49,609
emission therefore delta v can be plus or
minus one this picture doesnt change in the
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00:34:49,609 --> 00:34:54,629
case of rotational in the case of vibrational
raman spectrum why because of the following
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00:34:54,629 --> 00:35:12,349
for vibrational raman spectroscopy we are
looking at mu induced now this mu induced
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00:35:12,349 --> 00:35:19,690
is going to change also as a function of x
please remember the polarizability is now
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00:35:19,690 --> 00:35:27,789
absorbed in the mu induced x itself and the
mu induced x is going to involve alpha times
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00:35:27,789 --> 00:35:46,190
r e and this is the alpha is the ah e hence
that and so what you have is d mu induced
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00:35:46,190 --> 00:35:57,650
sorry lets write the other way around therefore
if we write mu induced x in terms of no ah
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00:35:57,650 --> 00:36:08,539
there is when ah no when there is no vi vibrational
amplitude it will be mu induced zero plus
269
00:36:08,539 --> 00:36:16,829
d mu by d x induced times x ok
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00:36:16,829 --> 00:36:23,460
so the molecular property that is responsible
for vibrational motion is again this rate
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00:36:23,460 --> 00:36:31,730
of change of the d mu index evaluated at x
is equal to zero which contains essentially
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00:36:31,730 --> 00:36:38,430
the rate of change of alpha with respect to
x ok because if you substitute that you are
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00:36:38,430 --> 00:36:46,309
going to get d alpha x x or whatever some
quantity either the x quantity or the y quantity
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00:36:46,309 --> 00:36:56,089
but lets take the scalar quantity is d alpha
by d x again with respect to x is equal to
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00:36:56,089 --> 00:37:02,450
zero multiplied by the x but please remember
this d alpha by d x is equal to zero doesnt
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00:37:02,450 --> 00:37:12,259
have anything to do with vibrational motion
it is a static ah dipole ah the ah polarizability
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00:37:12,259 --> 00:37:18,859
due to the external electric magnetic field
therefore it is this component which is still
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00:37:18,859 --> 00:37:33,319
responsible for raman but vibrational exactly
the same way that the dipole movement must
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00:37:33,319 --> 00:37:44,029
change during the vibration it is important
that the polarizability changes during vibration
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00:37:44,029 --> 00:37:51,849
and in that case this leads to the same matrix
element type that you have psi n prime of
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00:37:51,849 --> 00:37:59,529
x x psi n double prime of x dx prime dx because
this evaluated with no displacement is actually
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00:37:59,529 --> 00:38:05,039
independent of this x but it is needed without
which you will not see this term at all if
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00:38:05,039 --> 00:38:14,670
this is zero this term will not be there therefore
vibrational raman spectroscopy requires essentially
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00:38:14,670 --> 00:38:22,559
the polarizability to change during the vibration
but the matrix element that connects the vibrational
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00:38:22,559 --> 00:38:28,660
states have made this elements are identical
in terms of the eigen functions of the vibrational
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00:38:28,660 --> 00:38:37,609
state to the single coordinate x therefore
the selection role for vibrational raman is
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00:38:37,609 --> 00:38:46,430
also plus minus one no changes ok but if you
consider higher order terms and if you consider
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00:38:46,430 --> 00:38:52,769
un harmonic terms and if you consider polarizabilies
are very large if the molecule has a very
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00:38:52,769 --> 00:38:58,839
large polarizability during due to the ah
weakness of the forces between the different
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00:38:58,839 --> 00:39:03,380
atoms and so one so that the external electric
field can actually pull these molecules apart
291
00:39:03,380 --> 00:39:07,999
from each other then its possible that other
terms the higher order of polarizability may
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00:39:07,999 --> 00:39:15,769
get involved and so on but the lowest level
the vibration selection rule for raman spectroscopy
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00:39:15,769 --> 00:39:20,309
does not change by much i mean doesnt change
anything still delta v is equal to plus minus
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00:39:20,309 --> 00:39:26,390
one but there is a significant ah change in
the rotational raman spectroscopy where the
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00:39:26,390 --> 00:39:35,539
selection rule is delta j is plus minus two
and zero ok so these are usually a mentioned
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00:39:35,539 --> 00:39:39,999
in any of the elementary text box but i will
leave this lecture with one last note
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00:39:39,999 --> 00:39:46,660
i will make this as a statement and a very
nice and simple explanation of this statement
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00:39:46,660 --> 00:39:53,319
is of course is already there in the one of
the beautifully written elementary text box
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00:39:53,319 --> 00:39:58,349
on molecular spectroscopy i have also refered
to that book as a additional reference for
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00:39:58,349 --> 00:40:08,770
you the book by banwell and mc cash alian
mc cash the statement that i would say make
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00:40:08,770 --> 00:40:14,950
or the raman spectroscopy is the following
molecules which have a center of symmetry
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00:40:14,950 --> 00:40:40,299
with centre of symmetry ok those have ir spectra
or raman vibrational spectra but not both
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00:40:40,299 --> 00:40:53,460
meaning that if there are many modes for example
carbon dioxide itself elementary molecules
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00:40:53,460 --> 00:40:59,289
even hydrogen for that matter hydrogen have
a polarizability that changes during the vibration
305
00:40:59,289 --> 00:41:04,609
hydrogen vibration doesnt lead to any change
in the permanent dipole movement which is
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00:41:04,609 --> 00:41:10,190
always zero but the induced dipole movement
will be there for a molecule such as hydrogen
307
00:41:10,190 --> 00:41:15,490
therefore hydrogen vibration motion cannot
be seen by infrared spectrum but there is
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00:41:15,490 --> 00:41:26,119
a very nice and beautiful explanation in bangwell
and mc cash on how polazibality changes during
309
00:41:26,119 --> 00:41:32,779
the vibration from positive to zero to negative
and therefore that leads to raman vibration
310
00:41:32,779 --> 00:41:38,130
spectrum for that molecule this is the same
thing with all molecules which have centre
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00:41:38,130 --> 00:41:43,670
of symmetry such as carbon dioxide carbon
dioxide has a centre of symmetry at carbon
312
00:41:43,670 --> 00:41:50,460
and its symmetric stretch does not have any
dipole movement change but during the symmetric
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00:41:50,460 --> 00:41:56,650
stretch the polarizability changes therefore
the symmetric stretch is not detectable by
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00:41:56,650 --> 00:42:03,700
ir but it can be seen in raman spectroscopy
therefore they are mutually exclusive molecules
315
00:42:03,700 --> 00:42:20,049
with centre of symmetry have mutually exclusive
ir spectra and raman spectra those vibrational
316
00:42:20,049 --> 00:42:26,049
degrees of freedom for which the dipole movement
change during the vibration they will be seen
317
00:42:26,049 --> 00:42:32,220
by the ir spectrum but they will not be seen
by raman spectra raman spectroscopy those
318
00:42:32,220 --> 00:42:37,480
degrees of freedom for which there is no dipole
movement change such as a symmetric stretch
319
00:42:37,480 --> 00:42:42,049
in carbon dioxide and many other symmetric
stretches in every molecule which has a centre
320
00:42:42,049 --> 00:42:49,070
of symmetry you will see them either some
modes are ir detective and those modes which
321
00:42:49,070 --> 00:42:56,210
are ir detective ir active some modes are
ir active and those modes which are ir active
322
00:42:56,210 --> 00:43:01,940
or not raman active and vice versa but this
is applicable only in the case of molecules
323
00:43:01,940 --> 00:43:03,589
with centre of symmetry
324
00:43:03,589 --> 00:43:14,160
water for example has both rotational vibrational
microwave and raman rotational spectrum because
325
00:43:14,160 --> 00:43:18,859
it doesnt follow any of these things i mean
the dipole movement changes there is an induced
326
00:43:18,859 --> 00:43:24,239
dipole movement and therefore there is a polarizability
change in every one of these vibrations therefore
327
00:43:24,239 --> 00:43:29,559
all three modes of water molecules are both
raman active and all three modes are also
328
00:43:29,559 --> 00:43:37,650
infrared active the molecule also has some
microwave spectrum it has a rotational raman
329
00:43:37,650 --> 00:43:43,049
spectrum so many more things can be said and
this is a great contribution by an indian
330
00:43:43,049 --> 00:43:48,369
scientist in the early twenties and thirties
to the evolving field of quantum mechanics
331
00:43:48,369 --> 00:43:55,499
and spectroscopy and therefore ah in later
lectures we will study more of this ah ah
332
00:43:55,499 --> 00:44:00,569
in another course with some details so the
actual calculations of some of these matrix
333
00:44:00,569 --> 00:44:07,200
elements and the polarizability matrix and
so on this sort of formally completes the
334
00:44:07,200 --> 00:44:15,420
lecture on infrared and microwave ah spectroscopy
that i intended to give for this course i
335
00:44:15,420 --> 00:44:21,150
wish you all the best in the test and the
tutorials as well as the examination and hope
336
00:44:21,150 --> 00:44:25,349
that you will come back to the next course
that would be offered again in this area of
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00:44:25,349 --> 00:44:27,130
sometime later by me
thank you