A detailed comparison of ΔSCF methods with the constraint-based orbital-optimized excited state method

Orbital-optimized methods to variationally determine electronically excited states are becoming increasingly popular for overcoming some of the well-known shortcomings of linear-response theories. In this work we compare established ΔSCF methods with the recently proposed constraint-based orbital-optimized excited states method (COOX). In order to be able to accurately analyze the differences between both approaches, we apply the COOX method to specific orbital rotations, as defined in ΔSCF, to propose a ΔCOOX method. The main differences between these methods, as well as their performance regarding accuracy and stability, are discussed in detail. We present results for a variety of molecular systems including valence-, core-, Rydberg-, double-, and charge-transfer excitations obtained with both methods. The analysis provided in this work clearly shows that the COOX approach is superior to established ΔSCF methods in many instances, in particular regarding the overall stability for variational excited state calculations, while providing results of comparable quality.