Introduction to Solving the Time- Dependent Schrödinger Equation. Tom Penfold

Transcription

1 Introduction to Solving the Time- Dependent Schrödinger Equation Tom Penfold

2 Outline 1 Introduction to Solving the Time-Dependent Schrödinger Equation What problems are we trying to solve? How can we use theory? What are the different levels of theory 2 Solving the Time-Dependent Schrödinger Equation II How to use quantum dynamics The MCTDH Method Developing a model potential energy surface. 3 Beyond Born-Oppenheimer Design of Thermally Activated Delayed Fluorescence Emitters The role of molecular vibrations in TADF The effect of nonadiabatic coupling Perspectives

3 Because it s the first lecture.. TADF is not a new phenomenon. First discovered in 1924! Studied by CA Parker et al. in 1961 and named E-type Delayed Fluorescence after Eosin. The equilibrium picture make design straightforward....or does it!! What else contributes and how do we understand it?

4 How do we provide more insight? o Calculate a Jablonski Diagram Advantages i. Quick! ii. Can give a pretty good insight into potential performance. Disadvantages i. Generally focused on one geometry. ii. iii. Purely electronic picture. Does not include the Role of vibrational energy levels (Franck-Condon Overlaps).

5 The Next Level S 1 k nr k isc k risc k isc exp(-δe S1-T1 /k b T) ΔE S1-T1 k risc T 1 k nr k f k ph S 0 o Calculate rates using Perturbation Theory Advantages i. Quick(ish) ii. Good description into the excited state mechanisms. Disadvantages i. No insight into actual dynamics ii. In principle limited to weak coupling. iii. Limited (generally) to two coupled states.

6 The Full Picture, Maybe! Energy S 1 IC# ISC# T 1 GS o Perform Excited State Dynamics Advantages i. Rigorously correct within limit of approximations made (discussed later). ii. Direct inclusion of the electronic and nuclear degrees of freedom and their coupling Disadvantages i. Not exactly ii. straightforward! Time Consuming. {Q}

7 What can Theory Provide Complete Understanding! Perturbation Theory Coupled Nuclear- Electronic Dynamics Quantum Chemistry: Electronic Structure

8 What can Theory Provide Complete Understanding! Perturbation Theory Coupled Nuclear- Electronic Dynamics Quantum Chemistry: Electronic Structure

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10 Designing a Computational Project Unfortunately approximations have to be made- and it is important to understand them!

11 An Important Consideration: Experimental and Theoretical Synergy Tavernelli, I. Accounts of Chemical Research 48 (2015):

12 Potential Consideration for High Performing TADF OLEDs Electron-hole transfer dynamics Molecular Vibrations Aligning Energy Levels High Performing TADF OLEDs Effect of Embedding Environment Molecular Structure

13 Designing the Project Choose the right tools to approach the problem 1 What electronic structure method is required? a) Density functional Theory b) Post Hartree-Fock c) Semi-Empirical 2 Which is the most appropriate basis set? 3 Are relativistic effects important? 4 Are dynamics important? a) Coarse grained MD. b) Classical dynamics MD. c) Ab initio MD. d) Quantum Dynamics. 5 Are environment effects important? a) Atomistic description b) Continuum model. Important

14 High-throughput: Scan the landscape Nature Materials 15, (2016) This is static! Not designed to be super accurate, just quick!

15 Let s Discuss Dynamics. Classical Molecular Dynamics Ab initio Molecular Dynamics Ab initio Excited State Dynamics Quantum Dynamics

16 Classical Molecular Dynamics to probe TADF dynamics Classical MD sampled with TDDFT

17 Time-Dependent Schrödinger Equation Born-Huang Ansatz

18 Main Approaches to Solving Dynamics

19 Breakdown of Born-Oppenheimer If this is true, then a molecular excited state lives forever!!

20 The Complication of Breakdown of Born-Oppenheimer

21 Conclusions 1 Many different ways to develop a computational chemistry project. Care must be taken in choosing the appropriate approach, which may not necessarily be the best! 1 Range of approaches for solving the time-dependent Schrödinger equation, more on that next lecture. 1 The breakdown of Born-Oppenheimer approximation is crucial to the accuracy of excited state dynamics.