Introduction to Computational Quantum Chemistry
Calculations of electronic excited states
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Electronic excited states
Uses electromagnetic radiation in UV
and visible region
UV light: ~190 to 400 nm
VIS light: 400 to 700 nm
Excitations in valence electronic
structure
n → π∗, π → π∗ ...
X-RAYS: High-energy irradiations excitation
of core electrons
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Selection rules
“Allowed” and “forbidden” transitions
Nonzero transition dipole moment:
µi = Ψfinal ˆµiΨinitialdτ = 0 (1)
Intensities according to size of TD
Blue - vertical excitation
Green - emission
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Linear Response Time-dependent DFT
Vertical excitation energies vs adiabatic excitation energies
Energy quantum absorbed by molecule
The time-dependent Schrödinger equation:
i
∂
∂t
Ψ(r, t) = ˆH(r, t)Ψ(r, t) (2)
ˆH = ˆT(r) + ˆW(r) + ˆVext(r, t) (3)
Check for low-lying excited states using TDDFT
Use DFT with caution for molecules with ES lower than ~1.5 eV
General problem - Functionals are fitted to GS not ES
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ReSpect
http://rel-qchem.sav.sk/
Relativistic Spectroscopy
Developed at Slovakian Academy of Science and University of
Tromsø
Up to four-component (fully relativistic) approach
Calculation of NMR, EPR and electronic excitations
Under heavy development - Cutting edge methods
No proper manual. :(
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Real Time TDDFT
Alternative approach to investigate excited states
Free evolution of excited wavefunction irradiated by pulse
Fourier transformation of induced dipole moments
(Compare with FT-NMR, FT-IR, FT-Raman)
All excitations in a single simulation (valence to core)
Computationally EXTREMELY demanding method
−0.01
−0.005
0
0.005
0.01
0 200 400 600 800 1000
Induceddipole(a.u.)
Simulation Time (a.u.)
TCB−Br
−
Induced dipole moment, pulse from X−axis
X Y Z
0
4
8
12
0 100 200 300 400 500 600 700 800
Intensity
Energy (eV)
Absorption spectrum for TCB−Br−
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Simulation setup
In most general case 3 independent simulations needed
Irradiation from x-, y-, z- directions
For symmetric systems can be reduced to
2 - C∞v, D∞d
1 - spherical
Setup of calculation:
EOM_SOLVER: propagation scheme (always use MAGNUS)
ITERATIONS: SCF convergence threshold followed by maximum
allowed microiterations per step
TIME: Time step size (in a.u.) and number of steps
FIELD: DELTA (i.e. Dirac delta pulse) and field size
FIELD_DIRECTION: x- y- and z- component of the field vector
CHECKPOINT: save information to WF every N steps
ANALYSIS ORBITALS: virutal and occupied range of orbitals
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Important remarks
Maximum microiterations between steps: 6 (3-4 is fine)
1000 a.u. of time from each independent direction
Typically time steps around 0.1 a.u.
Higher energy excitations require lower timestep - higher
frequency oscillations
Fiddle a bit with values to obtain stable simulation
Induced dipole should have at least 4 significant digits with
respect to SCF during propagation
Orbital analysis must be set in advance (cannot be recovered after
simulation)
Energy must be conserved
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ReSpect: K-edge spectrum of Ne
Start with the template distributed in IS
This is a minimal input for ReSpect SCF
TDSCF section is almost ready, just commented out (# initiates a
comment line)
Go to the manual page and fill in the calculation details
Use NR/B3LYP/aug-ucc-pvtz method
Run SCF first, then select the orbitals you wish to include for the
analysis
K-edge means excitations from 1st period orbital
Four numbers define the orbital contributions in output:
V IR1 V IRN OCC1 OCCN
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Running ReSpect & Analysing Results
Respect is within modules
Usage:
$ respect --help # perform ReSpect calculation
$ spectrum.py --help # Fourier Transformation of data
$ ./analysis_matrix_block.py --help # Orbital analysis
Results:
input.out # general output of calculation
input_spectrum.out # Spectrum itself (plot 2:6 for energy in eV)
input_peaks.out # Lists only peaks
inputENERGY_TMatrix.out # Matrix of orbital excitations
Martin Novák (NCBR) Response properties: UV/VIS November 22, 2016 10 / 15
Gaussian: K-edge spectrum of Ne
Keyword “TD”
Calculate 200 singlet excited states
Use same basis set as in ReSpect
Basis set directory:
/software/ncbr/softrepo/ncbr/respect/4.0.0-
beta.4+Sep15/x86_64/para/BAS/mdks_gaussian_format/
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Experimental spectrum of the K-edge of Neon
Figure : K-edge spectrum of Neon.1
1
http://www.bessy.de/rglab/beamline3.html#Neon
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Colors of dihalogens
Calculate the vertical excitation energies of Cl2
Calculate the emission energy from the “allowed” state
Use PBE1PBE/6-311+G(2d) method
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Thermodynamic cycle
GS - Ground state WF
EXC - Excited state WF
eq - equliribrium geometry
noneq - nonequilibrium geometry
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Hints
TDDFT manual page:
http://www.gaussian.com/g_tech/g_ur/k_td.htm
Calculate first three excited triplet and singlet states
td=(nstates=3,50-50)
Select the allowed states and optimize the first excited one:
opt=readfc td=(nstates=3,{singlets/triplets},root=1,read)
Excitations/emissions including solvent effects are described at
Gaussian SCRF manual page
∆E =
hc
λ
(4)
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