Multireference Computational Methods for Organic Electronics

A.Ya. Freidzon, A.A. BagaturyantsPhotochemistry Center, Russian Academy of Sciences

Industrial R&D Simulation Know-how

Small model objects

Accurate methods

Large-scale calculations of

large molecules

Fast methods

Basic research Theory Understanding the nature

Using accurate Using accurate methods in applied methods in applied

researchresearch

Organic Electronic DevicesOrganic Electronic Devices

• Photovoltaics– Light sensors (e.g., in photo cameras)– Solar cells

• Light-emitting devices

• Field-effect transistors

• Chemical sensors

Problem of efficiency and chemical stabilityProblem of efficiency and chemical stability

Processes in Organic ElectronicsProcesses in Organic Electronics• Light absorption

• Light emission

• Exciton recombination

• Charge separation

• Exciton transport

• Charge transport

• Chemical reactions– Intermolecular complexes in chemical sensors– Chemical degradation in excited or charged states

These processes are usually simulated using density functional theorydensity functional theory

Density Functional vs. Multireference MethodsDensity Functional vs. Multireference Methods

• Cheap and relatively fast

• Allows for large-scale calculations

• Allows for calculations of large molecules

• Easily automated and good for screening

• Relatively slow and expensive

• Requires focusing on only few molecules

• Moderate-size molecules can be calculated

• Unique custom calculations

So why multireference methods should So why multireference methods should be used in organic electronics?be used in organic electronics?

Density Functional vs. Multireference MethodsDensity Functional vs. Multireference Methods

N

N

Where is the hole?

Here?

Here?

Here?Somewhere

in the molecule…

Directly show states with

different hole localization

Why it is important?

Charge localization in the molecule influences charge mobility and chemical stability of the material

Density Functional Density Functional vsvs. Multireference Methods. Multireference Methods

• Overestimate the extent of charge or exciton delocalization

• Known issue with excited charge-transfer singlet states

• Underestimate triplet state energies wrt. excited singlets

• Correctly predict charge and exciton localization

• Correctly predict relative positions of excited states

• Accurate excited state energies

Why it is important?For predicting energy transfer pathways, emission efficiency,

and chemical stability of the material

What is Multireference Method?What is Multireference Method?Single-reference molecular wavefunctionSingle-reference molecular wavefunction is single

Slater determinant 0 (+ possible minor corrections)

= C00 + iCii

Multireference molecular wavefunctionMultireference molecular wavefunction is linear combination of Slater determinants i with comparable weights

(+ possible minor corrections)

= iCii + jCjj

Minor correction

Minor correction

HF, MP2, DFT, CC

MCSCF, MRMP, MRCC

Dominant contribution

Dominant contribution

Advantages of Multireference MethodsAdvantages of Multireference Methods

• Account for static correlation effects in (quasi)degenerate states

• Treats equally important states on equal grounds

• Not limited to single excitations

ButBut

• Not a black-box method

• Requires experience and professional skills

When Multireference Methods When Multireference Methods Should Be Used?Should Be Used?

• In the case of strict or quasi-degeneration of states– Partially filled f shell of lanthanides or d shell of transition

metals– Charge hopping

• In studying potential energy surfaces where (quasi)degeneration is expected– Many chemical and photochemical reactions fall within

this case

• When DFT gives definitely wrong results, and Coupled-Cluster methods are too expensive

Examples of Application of Examples of Application of Multireference MethodsMultireference Methods

Energy transfer pathways in lanthanide complexes

Accurate calculation of ligand-localized triplet states helps one to find the best antenna ligands

Examples of Application of Examples of Application of Multireference MethodsMultireference Methods

Phosphorescence rate constant in iridium complexes

Ir(Ppy)3

-1535.650

-1535.625

-1535.600

-1535.575

-1535.550

-1535.525

-1535.500

-1535.475

-1535.450

-1535.425

-1535.400

S0 3-MLCT 3-LC

S0

S1

T1

Calculated:kr = 1.71·106 s–1; r = 0.59 s

Examples of Application of Examples of Application of Multireference MethodsMultireference Methods

Charge hopping profiles in Bebq2 dimersHole hopping

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1 .0

h o le o n L 2 m id p o in t 1 -2 h o le o n L 1 m id p o in t 1 -3 h o le o n L 3 m id p o in t 3 -4 h o le o n L 4

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

0 .7

0 .8

0 .9

1 .0

h o le o n L 2 m id p o in t 1 -2 h o le o n L 1 m id p o in t 1 -3 h o le o n L 3 m id p o in t 3 -4 h o le o n L 4

Electron hopping

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

1 .4

e le c tro n o n L 2 m id p o in t 1 -2 e le c tro n o n L 1 m id p o in t 1 -3 e le c tro n o n L 3 m id p o in t 3 -4 e le c tro n o n L 4

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

1 .4

e le c tro n o n L 2 m id p o in t 1 -2 e le c tro n o n L 1 m id p o in t 1 -3 e le c tro n o n L 3 m id p o in t 3 -4 e le c tro n o n L 4

Understanding charge transfer mechanism in Bebq2 helps one to understand the same mechanisms in similar complexes, such as AlQ3

Examples of Application of Examples of Application of Multireference MethodsMultireference Methods

Chemical stability in a series of OLED hostsExcited state dissociation

energies

TerphCarb

0.4

1.6

DPTZCarb

1.9

0.7

Carbazolyl detachment is more probable

TerphTriphen

1.9

0.9

DPTZTriphen

2.1

1.3

Phenyl detachment is more probable

More stable

In all these cases single-reference methods (DFT or HF+MP2) fail

Conclusions• Multireference methods are not suitable for

screening

• However, they provide better values of important physical parameters

• And deeper insight into mechanisms of charge and energy transfer and chemical processes in organic electronics

Thank you for your attention!Thank you for your attention!

Personal acknowledgements

K.G. Komarova (PC RAS)A.A. Safonov (PC RAS)

S.V. Emelyanova (PC RAS)A.V. Odinokov (PC RAS)A.V. Scherbinin (MSU)

K.A. Romanova (KNRTU, Kazan)D.N. Krasikov (Kintech Lab)