Calculation of UV-VIS
Spectra
Prepared by: Ben Joseph R. Cuyacot
2
➢ Atoms and molecules interact with electromagnetic radiation
(EMR) in a wide variety of ways and may absorb and/or emit
EMR.
➢ Absorption of EMR stimulates different types of motion in
atoms and/or molecules
➢ The patterns of absorption (wavelengths absorbed to some
what extent) and/or emission (wavelengths emitted and their
respective intensities) are called ‘spectra’.
➢ The field of spectroscopy is concerned with the
interpretation of spectra in terms of atomic and molecular
structure (and environment).
Spectroscopy
3
➢ Ultraviolet radiation stimulates
molecular vibrations and electronic
transitions.
➢ Absorption spectroscopy from 160
nm to 780 nm
➢ Identification of inorganic and organic
species
➢ the BEER-LAMBERT LAW, for a
light absorbing medium, the light
intensity falls exponentially
with increasing sample conc.
➢ 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).
UV Spectroscopy
4
➢ Electronic transitions occur
when the molecule absorbs energy.
➢ Electronic transitions:
• π, σ, and nonbonding electrons
• d and f electrons
• charge transfer
UV Spectroscopy
5
UV Spectroscopy
➢ Electronic transitions occur
when the molecule absorbs energy.
6
➢ basically the Schrödinger equation is written as 𝐻Ψ = 𝐸Ψ, However, that obscures the reality that there are
infinitely many solutions to the Schrödinger equation, so it is better to write 𝐻Ψ 𝑛 = E 𝑛Ψ 𝑛
• Hartree-Fock theory provides us a prescription construct an approximate ground-state wave function (as a
single Slater determinant.
• How do we build from there to construct an excited state wave function?
• 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.
Excited States in Computational Chemistry
7
➢ Review on Density Functional Theory
ρ(r) – electron density : the properties (such as energy) of a many-electron system are uniquely determined by
an electron density that is a function of spatial coordinates (r)
𝝆(𝒓) = ෍
𝒊=𝟏
𝒏
𝒏𝒊|𝝋𝒊 (𝒓)| 𝟐
DFT Energy[ρ] = T[ρ] + V [ρ] : the energy is decomposed into kinetic and potential contributions to the total
interactions; this is the “DNA” of density functional theory as well as WF based
methods.
−
𝟏
𝟐
𝛁𝒊
𝟐
+ 𝑽 𝒕𝒐𝒕(𝒓) 𝝋𝒊 𝒓 = ε𝒊 𝝋𝒊 𝒓 : the potential part is broken down to classical (Vcl) and nonclassical (Vxc) part,
the “flavor” or type of DFT (e.g. B3LYP, PBE0, etc) represents how the method
𝑽 𝒕𝒐𝒕 𝒓 = 𝑽 𝒄𝒍 𝒓 + 𝑽 𝒙𝒄 𝒓 solves exchange-correlation potential (Vxc).
We will use the Time-Dependent DFT overview
𝑯 = 𝑻 𝒆 + 𝑽 𝒆𝒆 − ෍ ෍
𝒁 𝒆 𝟐
|𝒓 − 𝑹|
8
➢ TDDFT : on the other hand is a DFT with time dependent elements, its the most used method to extract
features like excitation energies, frequency-dependent response properties, and photo-absorption
spectra, particularly for its robustness and versatility.
𝝆(𝒓, 𝒕) = σ𝒊=𝟏
𝒏
𝒏𝒊|𝝋𝒊 (𝒓, 𝒕)| 𝟐
: the density now has time element, means expectation value of any 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 𝝋𝒊
𝟎
(𝒓,𝒕=0)
−
𝟏
𝟐
𝛁𝒊
𝟐
+ 𝑽 𝒕𝒐𝒕(𝒓, 𝒕) 𝝋𝒊 𝒓, 𝒕 = ε𝒊 𝝋𝒊 𝒓, 𝒕 : Unknown exchange-correlation time-dependent potential. Vxc
functional of the density at all times and of the initial state. This is
becoming more complicated and weirder.
𝑽 𝒕𝒐𝒕 𝒓, 𝒕 = 𝑽 𝒄𝒍 𝒓, 𝒕 + 𝑽 𝒙𝒄 𝒓, 𝒕
Time-Dependent DFT overview
𝑯 = 𝑻𝒆 + 𝑽𝒆𝒆 − ෍ ෍
𝒁 𝒆 𝟐
|𝒓 − 𝑹 |
+ ෍ 𝒓 €𝒄𝒐𝒔ω𝒕
9
➢ TD DFT tends to be more accurate than CIS but this is sensitive to choice of functional and certain special
situations.
➢ Charge-transfer transitions are particularly problematic.
➢ No wave function is created, but eigenvectors analogous to those predicted by CIS are provided.
➢ 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.
Time-Dependent DFT overview
10
Exercise
➢ Calculate the UV Spectra 2-propenal
GEOMETRY UV SPECTRA from NIST
11
Exercise
#1 Construct the molecule
➢ Draw the molecule using Avogadro
➢ Create a Gaussian input file using “Extension
Menu”
➢ Optimized and Calculate the Frequency
calculation using Gaussian
#n pbe1pbe/6-31G(d) opt freq
• After the successful job, verify that the optimization
reached a minimum on the potential energy surface.
All calculated frequencies must be positive (a single
negative (imaginary) frequency defines a transition
state; more than one negative frequency represent
higher-‐order saddle points usually without physical
meaning.
#2 Visualizing the orbitals
➢ Calculate the molecular orbitals (MOs) at the
optimized geometries
#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 2 highest occupied and
lowest unoccupied MO’s.
12
Exercise
MO#
MO#
MO#
MO#
MO#
MO#
MO#
MO#
MO#
MO#
#2 Visualizing the orbitals (continuation)
➢ Successful run look would produce orbitals
like this (left figures). In the 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.
➢ Which MO is the HOMO and which is the
LUMO?
➢ Rotate and examine each orbitals and
make a conclusion which orbitals are σ,
π, n, bonding, antibonding, ??
???
13
#3 Calculation of UV Spectra
➢ Calculate the UV (vertical excitation) at the respective optimized geometry using Time-Dependent Density Functional Theory (TDDFT).
#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 > MO 16, 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.
➢ Characterize the excitations (e.g. π → π*, …) for the first few excited states.
* Identify which orbitals were involved in the excitations? * compare the values with exp. excitaitons
* What’s the nature of the excitation is it singlet or triplet?
Exercise
E1 3.71 ev
E2 6.41 ev
14
#3 Graphic Visualizations of the Output File
➢ You can use various visualization software such as GaussView, Gabedit, Avogadro, etc for UV
➢ One of the simplest is to use Gabedit
Module Add 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.
Exercise
Prepared by: Ben Joseph R. Cuyacot
Try to calculate Acrolein 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?
Home Work
GAUSSIAN MANUAL
https://gaussian.com/man/
Prepared by: Ben Joseph R. Cuyacot
Try to evaluate the peaks of these three ringed
systems and judge 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 orbital transitions were missing in the
experiment if there are?
Home Work
Happy End
Prepared by: Ben Joseph R. Cuyacot