Introduction to Computational Quantum Chemistry
Lesson 12: Calculations of UV/VIS
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 1 / 8
UV-VIS spectroscopy
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∗ ...
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 2 / 8
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
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 3 / 8
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
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 4 / 8
Gaussian TDDFT output
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 5 / 8
Colors of dihalogens
Calculate the vertical excitation energies of F2, Cl2 and, Br2
Calculate the emission energy from the “allowed” state
Use PBE1PBE/6-311+G(2d) method
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 6 / 8
Thermodynamic cycle
GS - Ground state WF
EXC - Excited state WF
eq - equliribrium geometry
noneq - nonequilibrium geometry
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 7 / 8
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)
Martin Novák (NCBR) Response properties: UV/VIS 9. prosince 2014 8 / 8