Simultaneous calculation of Rydberg and valence excited states of formaldehyde

The presence of low-lying Rydberg states interspersed among valence states constitutes a substantial challenge for the accurate quantum chemical calculation of electronically excited states because of the need to treat a relatively large number of states simultaneously. We present a general and efficient scheme that allows the treatment of a large number of Rydberg and valence states at the MR-CISD, MR-CISD + Q and MR-AQCC levels while using only a fraction of the size of the configuration space as compared to a full complete-active-space reference wave function. This scheme is applied to the calculation of vertical excitations and various avoided crossings between ten Rydberg and five valence singlet states of formaldehyde including transition dipole moments and oscillator strengths. Basis set effects, choice of configuration space and size-extensivity corrections have been considered. It is found that size-extensivity effects as computed by MR-CISD + Q and MR-AQCC play an important role especially for the description of the pi-pi* state and for avoided crossings in which this state is involved.