Advanced Spectroscopy

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Advanced Spectroscopy
Prerequisite basic knowledge in Quantum
Mechanics.1.Brief Review of Basics of quantum
mechanics,- Harmonic oscillator, particle in the
box, transition dipole moments, symmetry.2.
Vibrational spectroscopy - IR spectroscopy,
including FTIR, Raman scattering 3. Electronic
spectroscopy, Lasers 4. Vibronic spectroscopy,
including resonance Raman. 5. Surface
spectroscopy 6. Nonlinear optics and
spectroscopy
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7. Time resolved spectroscopy 8. Single
molecule spectroscopy 9. Photoelectron
spectroscopyBooks 1. Physical Chemistry,
Mcquarrie and Simon, University Science books2.
Modern Spectroscopy, J. M. Hollas, John Wiley
Sons3. Molecular Vibrations, Wilson, Decius and
Cross, Dover PublicationsCourse requirements
Final Examination2 hours lecture 1 hour
excercise
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Quantum mechanics- an ultrafast refresher In
1924 Louis de Broglie proposed that with any
moving body there is associated a wave and that
the momentum of the particle and the wavelength
are related by ph/?. It can be shown that as a
result of this relation one obtains also the
Heisenberg uncertainty principle ?p ? x h.
Hence in order that an electron will reside in a
radius around a nucleus a standing wave must
exist in which
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The Schrödinger Equation

• Postulates of quantum mechanics
• The state of the system is completely specified
  by a wave function.
• For every observable there is an operator.
• The observed values are the eigenvalues of the
  operator.
• The wave function evolves according to the
  Schrödinger equation.

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If the Hamiltionian does not depend explicitly on
time we can separate variables.
Substituting in the Schroedinger equation and
dividing we find
Since there are no shared variables between the
two sides, they must both be equal To a constant
which we denote by E. Then we get the
time-independent Schroedinger equation
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The Hamiltonian
Consists of the kinetic energy part and the
potential energy part
For example, in the hydrogen atom, which has a
single nucleus and one electron
And in a polyelectronic atom (with a nuclear
charge Z)
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The Molecular Hamiltonian
Contains term for all nuclei (n) as well as
electrons (e)
In the Born-Oppenheimer approximation one assumes
that the nuclei are much heavier than the
electrons so that they can be treated as if they
dont move, while the electrons now evolve
according to
with
Ee can be treated as part of the potential the
nuclei feel so for the nuclei
with
and the total wave function
with q, Q the positions of electrons and nuclei
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The Harmonic Oscillator The potential energy
of a harmonic oscillator behaves according
to where k is the spring constant.
Transforming to a coordinate we write The
harmonic oscillator potential is an approximation
for each potential near the equilibrium point. To
show this, we expend a general potential function
in a Tailor series about equilibrium and note
that vanishes exactly. Far
from the equilibrium point, this approximation
must fail!
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In a quantum harmonic oscillator the energy is
quantized
with
where m is the mass of the oscillator. An
important consequence is the zero-point energy.
The wave functions of the harmonic oscillator are
Hermite polynomials multiplied by a Gaussian
function
where
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The first few Hermite polynomials are
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Electromagnetic radiation and its interaction
with atoms and molecules
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n
En
E
Em
m
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