Analytical Derivatives of the Individual State Energies in Ensemble Density Functional Theory Method: II. Implementation on Graphical Processing Units (GPUs)

Conical intersections control excited state reactivity and thus elucidation and prediction of their shapes and locations is crucial for photochemistry. To locate these intersections one needs accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g. XMS-CASPT2) are computationally difficult for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn-Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units (GPUs). We demonstrate that our implementation gives the correct topography and energetics of conical intersections for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient – the observed scaling with molecular size is sub-quadratic, i.e. O(N<sup>1.77</sup>). This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.