Hybrid Time-Dependent Density Functional Theory in CASTEP Part 2
This Distributed Computational Science and Engineering (dCSE) project was the second part of the project for implementing Time-dependent density functional theory (TDDFT) in the density functional theory code CASTEP. This report focusses on an implementation for computing atomic forces in electronic excited states that are determined through linear response TDDFT in the Tamm-Dancoff approximation. This completes the work to implement excited-state force calculations for geometry optimisations and molecular dynamics in CASTEP.
TDDFT has become a well-established technique for modelling excited state properties in molecular systems. The availability of TDDFT in CASTEP will now give the UK electronic structure community an opportunity to address cutting-edge scientific problems in areas such as inorganic and organic photovoltaic materials, catalytic reactions at surfaces, light-emitting polymer materials for optical displays, and femtosecond laser chemistry. CASTEP in particular has an excellent record of use in high performance computing and is one of the most used codes on HECToR. TDDFT in CASTEP provides a platform for complementing a wide range of other property calculations at the same level of theory, within the same code. The implementation of hybrid functionals promises to address some of the limitations that have previously hindered the application of TDDFT to extended systems.
The individual achievements of the project were :
- Implement the calculation of forces on excited states using the formalism of Hutter. A finite-difference approximation was developed for the third functional derivative of the exchange-correlation energy with respect to the density response. For the matrix of Lagrange multipliers associated with the stationarity of the Kohn-Sham orbitals i.e. the Z vector, forces are estimated using the Handy-Schaefer Z vector formula, in its periodic extension.
- Implement Born-Oppenheimer ab initio molecular dynamics on excited state surfaces. This now in place within CASTEP and can be achieved by performing a full TDDFT calculation for each step of dynamics, followed by a force calculation and a propagation step. This has yet to be tested as it was beyond the scope of this project.
- Demonstrate the reliability and robustness of excited-state force calculations for optimisations and molecular dynamics. The computed forces for geometry optimised structures of formaldehyde (CH2O) were tested for correctness, by validation with the results of Hutter.