Investigating Optical Properties

with Materials Studio 5.5

Part of the “What’s New in Materials Part of the “What’s New in Materials

Studio 5.5” Webinar Series

George Fitzgerald, Ph.D.

17 November 2010

• Key themes:

– Increasing computational

performance

– Predicting more properties for a

broader range of materials

MS 5.5: Release Themes

– Bridging the modeler and

experimentalist

• Significant enhancements to

CASTEP, DMol3, Forcite, QMERA

• Predict UV spectra and non-

linear optical properties

• Applicable to analytical

chemistry, pigments, opto-

electronic materials, etc.

• Applications include

Feature Highlight: DMol3 TDDFT

• Applications include

– Excited state energies

– UV/visible spectra

– Non-linear optical materials

– LEDs

– Chemistry of radicals

• DMol3 uses density functional theory (DFT) to

predict properties of materials

– Molecular or 3D periodic calculations

– Energies, geometries, reaction energetics, etc.

• Increasing emphasis on computing properties

DMol3

• Increasing emphasis on computing properties

that can be related to experiment, e.g., Spectra

• New in MS 5.5: UV/visible spectra for molecules

• Time-independent Schrödinger equation

–

– Yields energy for a given arrangement of atoms

– Use this to find total energy, minimum energy structures, etc.

• Time-dependent Schrödinger equation

TD-DFT Theoretical Background

Ψ=Ψ+Ψ+Ψ∇ EVV xcc

2

• Time-dependent Schrödinger equation

–

– Use this to describe what happens in the presence of a time-dependent field like a photon of frequency ω

– When included as part of a DFT calculation TD-DFT

t

ihVV xcc

∂

Ψ∂=Ψ+Ψ+Ψ∇

π2

2

• TDDFT must determine the change in the wavefunction induced by a photon– Determine the lowest roots of QF = ΩF

– How big is Q? • Of order (#occupied * # unoccupied)

• Example: benzene in DND basis = 1 575

• Example: procion blue = 80 676

TD-DFT is Time-Consuming

• Example: procion blue = 80 676

• How long does this take?– Typically, each excited state costs the same as the

ground-state SCF

• Details:– Delley, J. Phys.: Condens. Matter 22 (2010) 384208

• Comparison of transition energies (eV) for

TDDFT and Kohn-Sham calculations

– Kohn-Sham (KS) is difference in orbital eigenvalues

Results for simple cases

Case Level Expt TDDFT KS TDDFT err KS err

Be 2s-2p 5.28 5.55 3.78 0.27 -1.50Be 2s-2p 5.28 5.55 3.78 0.27 -1.50

Be 2s-3s 6.77 6.66 6.53 -0.11 -0.24

Mg 3s-3p 4.34 4.57 3.44 0.23 -0.90

Zn 4s-4p 5.79 6.42 5.06 0.63 -0.73

N2 Πg 9.31 9.18 8.27 -0.13 -1.04

N2 Σg 9.92 9.64 9.64 -0.28 -0.28

C2H4 B1u 8.00 8.04 7.30 0.04 -0.70

|avg| 0.24 0.77

• Uses of modeling spectra:

– Assist in identification of unknowns by computing

fingerprints

– Structure determination

• E.g., Several candidate structures may be consistent with

Comparisons of spectroscopic results

•

a given spectrum

– Design optical materials by predicting spectra for

new compounds

• Color changes with pH

– In strong acid (pH<4.4) the molecular form

dominates

– In weak acid (pH > 4.4) proton can dissociate from

the –COOH

Example: Methyl Red

• Molecular Form

Methyl Red

– High energy region ~210-310nm reproduced well

– Long wavelength region shifted ~520 to ~470nm

Experimental spectrum from the USCA database

http://www.usca.edu/chemistry/spectra/

• Ionic Form

Methyl Red

– As in molecular case, good agreement in short

wavelength region, but long wavelength peaks are

shiftedExperimental spectrum from the USCA database

http://www.usca.edu/chemistry/spectra/

• How does substituent affect absorption peak?

• Use TDDFT, including solvation effect via COSMO

Effect of Substituents

SubstituentsSubstituentsSubstituentsSubstituents DMol3/PBEDMol3/PBEDMol3/PBEDMol3/PBE ExpExpExpExp ErrorErrorErrorError

- 300 307-309 -8

5-Me 309 315 -6

Coumarin

6-Cl 295 321 -26

7,8-diOH 329 335 -6

6,7-diOH 369 354 15

6-NH2 303 370 -67

6,7-OH-4-Me 365 348 17

6,7,8-MeO 358 330 28

4-Br 304 277 27

6-OH 297 280 17

7-MeO,8-OH 333 325 8

• Zeolite TS-1 used as catalyst

for various green oxidation

processes

– Well-characterized structure:

isolated tetrahedral Ti+4

– UV band ~213 nm

Structural Elucidation of Ti Zeolites

– UV band ~213 nm

• New Ti-substituted structures

can be even more active

– Structure unknown

– UV band near ~222 nm

• Can we figure out the

structure?Coauthors: Liang (Accelrys) & Halasz (PQ Corp)

Work to be presented at NAM22

(www.22nam.org)

• TDDFT limited to molecules

• QM/MM optimization of geometry followed by DMol3

TDDFT of QM region

– ~100 atoms in QM region

• Screen a number of structures for new zeolite

including Ti(OH)

Computational Details

including Ti(OH)4

Results

180 200 220 240 260 280 300 320 340

Intensity [arbitrary units]

Wavelength [nm]

211 221

315

265

Isolated

Tetrahedral Ti4+ Octahedral Ti4+

180 200 220 240 260 280 300 320 340

211 224

Wavelength [nm]

Inte

nsi

ty [a

rbit

rary

un

its]

267

• Experimental (left) and computed

UV spectra show excellent

agreement

• Ti(OH)4 units are consistent with

experimental observation

Wavelength [nm]

Coauthors: Liang (Accelrys) & Halasz (PQ Corp)

Work to be presented at NAM22 (www.22nam.org)

• Calculations can use any

functional

• Calculations limited to

closed-shell ground states

• Must use basis version 4.4

Practical Considerations using MS 5.5

• Must use basis version 4.4

– Contains diffuse functions

important for excited states

• Limited to energies – no

excited state geometry

optimization

• Limited to molecules

• Calculations can be

combined with COSMO to

include solvation effects

• Options for the

Practical Considerations

• Options for the

calculation

– Number of excited states:

more states required more

time

– Type of TDDFT

approximation

TDDFT Approximations

klijlkjijiklijklij KQ ,

2

, ))((2)( εεεεεεδδ −−+−=

In the simplest approximation, Q is

simply the difference in orbital

eigenvalues (KS)

Various approximations can be

used for K

Including all terms gives the adiabatic local

density approximation (ALDA)

TDDFT Approximations: ALDAx

klijlkjijiklijklij KQ ,

2

, ))((2)( εεεεεεδδ −−+−=

Including just 2 terms gives the adiabatic local

density exchange approximation (ALDAx)

TDDFT Approximations: RPA

klijlkjijiklijklij KQ ,

2

, ))((2)( εεεεεεδδ −−+−=

Including just 1 term gives the random

phase approximation (RPA)

• TDDFT equations are solved iteratively

– Approximations may reduce time per iteration but may converge more slowly

• Average absolute error (nm) of approximations compared to ALDA results for lowest 20 states

Comparison of Approximations

Structure KS error ALDAx error RPA error

H2O 2.30 0.13 1.63

• ALDAx and RPA are good approximations, but on average did not save compute time

H2O 2.30 0.13 1.63

Ethane 2.70 0.17 1.57

Benzene 8.47 0.27 2.23

Procion Blue 21.17 0.30 2.87

Procion Orange 16.37 0.20 2.53

Procion Red 15.60 0.53 1.93

Cu phthalocyanine 31.1 0.20 4.93

• Output file contains details of the excitations

energies and molecular orbitals involved

Output and Analysis

• Output file contains details of the excitations

energies and molecular orbitals involved

Output and Analysis

Primary MO’suse ‘Print Eigenvectors’

to see coefficients

TDDFT and Kohn-

Sham excitation

energy in nm

Intensity

Overlap

between

MO’s can

gauge

reliability of to see coefficients

TDDFT and Kohn-

Sham excitation

energy in eV

energy in nm

TDDFT excitation

energy in Ha

reliability of

TDDFT

Examples of MO Overlap

MO #20 MO #22 (LUMO)

Overlap 0.8

When overlap < ~0.3

then TDDFT results MO #20 MO #22 (LUMO)

MO #18 MO #23

Overlap 0.2

then TDDFT results

are not as reliable

• Uses DMol3 analysis

dialog to display spectra

– Select ‘Optics’

• Simulated spectrum or

table of results

Analysis

• Choice of units

– nm, cm-1, eV

• Simulated spectrum

indicates all transitions

• DMol3 TDDFT provides a fast and reliable way to

predict excitations energies and optical spectra

• Agreement with experiment is generally good

– Trends are quite good, e.g., procion red

• Developments such as this make it easier for

Summary

• Developments such as this make it easier for

modelers to establish connections with

experimental results

– Part of a trend in MS to simulate spectroscopic

results like IR, NMR, EELS, Raman

• Questions? Comments? Suggestions?