Introduction to Computational Quantum Chemistry
Lesson 10: Electronic Transitions (UV/Vis)
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 1
Quick Review: Spectroscopy
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Lesson 10 - Electronic Transitions (UV/Vis) 2
atoms and molecules interact with
electromagnetic radiation (EMR)
stimulates different types of motion
in atoms and molecules
the patterns of absorption and/or
emission ‘spectra’.
interpretation of spectra in terms of
atomic and molecular structure
(and environment).
Quick Review
absorption spectroscopy from 160 nm to 780 nm
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 3
Quick Review: Beer’s Law
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Lesson 10 - Electronic Transitions (UV/Vis) 4
BEER Law, for a light absorbing
medium, the light intensity falls
exponentially with increasing
sample conc.
Quick Review: Beer’s Law
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 5
the negative logarithm of T is called
the absorbance (A) and this is
directly proportional to sample
depth (called pathlength, l) and
sample concentration (c).
Quick Review: Beer’s Law
electronic transitions:
π, σ, and nonbonding electrons
d and f electrons
charge transfer
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 6
electronic transitions occur when
the molecule absorbs energy.
UV Spectroscopy
electronic transitions occur when the molecule absorbs
energy.
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 7
Wavefunction Based: Excited States
the SE is written as HΨ = EΨ, however, that obscures the reality that
there are infinitely many solutions to the SE, so it is better to
writeHΨn = EnΨn
Hartree-Fock theory provides us a prescription to construct an
approximate ground-state wave function as a Single Slater determinant.
construct an excited state wavefunction? by expanding it!
Ψ = a0ΨHF +
occ.
i
vir.
r
ar
i Ψr
i +
occ.
i<j
vir.
r<s
ar
ijsΨr
ijs + · · ·
the bigger the CI matrix, the more electron correlation can be captured.
the CI matrix can be made bigger either by increasing basis-set size
(each block is then bigger) or by adding more highly excited
configurations (more blocks). The ranked eigenvalues correspond to the
electronic state energies.
the higher eigenvalues are treated as the energies of the excited states.
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 8
Density Based: Excited States
REVIEW on the Density Functional Theory (DFT)
E = Te + Vee −
Zee
|r − R|
the DFT properties of a many-electron system were uniquely
determined by an electron density
ρ(r) =
n
i=1
ni|φi(r)|2
the energy is decomposed into kinetic and potential contributions
EDF T (ρ) = T(ρ)+V (ρ) = -1/2 2
+ Vtot(r) φi(r) = iφi(r)
the potential part is broken down to classical Vcl and non-classical Vxc
part: Vtot(r) = Vcl(r) + Vxc(r)
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 9
Density Based: Excited States
Time Dependent - Density Functional Theory (TD-DFT), the most used
method to extract excitation energy, frequency-dependent response
properites, photo-absorption spectra... particularly for its robustness
and versatility.
E = Te + Vee −
Zee
|r − R|
+ r cosωt
the density now has time element, a physical time-dependent
observable of a many-electrons system is a unique functional of
time-dependent electron density ρ(r, t) and of the initial state
φ0
i (r, t = 0)
ρ(r, t) =
n
i=1
ni|φi(r, t)|2
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 10
Density Based: Excited States
the unknown exchange-correlation is now a ’time-dependent’ potential.
Vxc is also functional of the ’initial’ and the ’dynamic’ state as a function
of time.
−1/2 2
+ Vtot(r, t) φi(r, t) = iφi(r, t)
time dependence all the way to classical Vcl and non-classical Vxc
part: Vtot(r, t) = Vcl(r) + Vxc(r, t)
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 11
Time Dependent-Density Functional Theory (TD-DFT)
TD-DFT tends to be more accurate than CIS
(Configuration Interaction Singles) but is sensitive to
choice of functional and certain special situations.
eigenvectors analogous to those predicted by CIS are
provided.
charge-transfer transitions (electron-donor-acceptor
complex is an association of two or more molecules) are
particularly problematic.
NOTE: there’s a Semi-Empirical Method, INDO/S, that
produces good excitation energy numbers relative to the
experiment at least for small not complicated system.
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 12
ACTIVITY 1
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Lesson 10 - Electronic Transitions (UV/Vis) 13
Molecule: 2-Propenal
draw the molecule using
Avogadro, create a Gaussian
input file using Extension Menu
optimized and calculate the
frequency calculation using
Gaussian using PBE0-31G(d)
verify that the optimization
reached a minimum, all
calculated frequencies must be
positive
UV Spectra (NIST) of 2-Propenal
shown here:
ACTIVITY 1
Visualizing the orbitals: 2-Propenal
calculate the molecular orbitals (MOs) at the optimized geometries
use this the route section: #n pbe1pbe/6-31G(d) pop=full formcheck
after the successful job, open the *FChk file in Avogadro
click on Extensions > Create Surface > select Molecular Orbital as
surface type.
resolution: High ; Iso Value: 0.02 ; Color Type: MO
examine the first three highest frontier (virtual and occupied) orbitals.
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 14
ACTIVITY 1
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Lesson 10 - Electronic Transitions (UV/Vis) 15
Visualizing the orbitals: 2-Propenal
cont.
successful run look will produce orbitals
like this (right Figure):
in the Gaussian output file, look for the
keyword Orbital energies and kinetic
energies , it will report which orbitals are
occupied (marked O) and virtual (marked
V) as well as their corresponding energies.
identify the characters of the frontier
orbitals. Using Avogadro rotate and
examine each orbitals and make a
conclusion which orbitals are σ, π, n,
bonding, anti-bonding??
ACTIVITY 1
Calculation of UV Spectra: 2-Propenal
calculate the UV (vertical excitation) at the respective optimized
geometry using Time-Dependent Density Functional Theory (TDDFT).
use this the route section: #n pbe1pbe/6-31G(d) TD
If you have done a successful calculation, look for the keyword
Excitation energies and oscillator strengths in the output file
It will report orbital excitations (e.g. MO14 > MO16, etc)
It will report the wavelength where the oscillator strength is strongest;
the f is directly related to intensity of the absorption.
It will report the energy of the excitations as well as its coefficients;
these coefficients refers to the contribution of the respected transition to
the wavefunction.
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 16
ACTIVITY 1
calculation of UV Spectra: 2-Propenal, cont.
characterize the excitations (e.g. π π∗
, ...) for the first few excited
states.
identify which orbitals were involved in the excitations?
what’s the nature of the excitation is it singlet or triplet?
compare the values with exp. excitations E1 3.71 ev E2 6.41 ev
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 17
ACTIVITY 1
Visualization of the UV Spectra Calculation: 2-Propenal
you can use various visualization software such as GaussView,
Gabedit, Avogadro, etc for UV
one of the simplest is to use Gabedit
in the Gabedit, Menu Bar : Tools > UV Spectrum > Read energies
and intensities from Gaussian output file
it will report the integrated intensity of the absorbance with respect
to the wavelength.
take note once have the figure, you can readjust the range and
units to suit your preference.
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 18
ACTIVITY 1
Extension
try to calculate 2-Propenal with CIS and INDO/S methods on the
excitations
has the order of orbitals change?
are there transitions that were reported that aren’t present on the
PBE1 method? on the first and second, 3rd transitions, etc?
which method has closer fit to experimental excitations?
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 19
ACTIVITY 2 (OPTIONAL)
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Lesson 10 - Electronic Transitions (UV/Vis) 20
try to evaluate the peaks of these
three ringed systems and see if
they can be reproduced by TDDFT.
use the same method as stated in
this lecture:
identify which orbital transitions
were responsible for these peaks?
what significant orbital transitions
that’s showed in the experiment
BUT were suggested missing in
the calculation? (if there are any)
END
(Prepared by Radek Marek Research Group)
Lesson 10 - Electronic Transitions (UV/Vis) 21