**2.2.4 Configuration Interaction Singles (CIS)**

CIS is a useful tool to model low-lying excited states caused by transitions among near HOMO-LUMO levels in a semi-quantitative fashion (Foresman *et al.*, 1992). A tendency of CIS to overestimate excitation energies is compensated for by CIS(D) in which the orbital relaxation energy for an excited state of interest as well as the differential correlation energy from the ground state correlated at the MP2 level (Head-Gordon *et al.*, 1994). Both CIS and CIS(D) have been introduced to multilayer FMO (MFMO; Fedorov *et al.*, 2005) in ABINIT-MP (Mochizuki *et al.*, 2005a, 2007a). Very recently, Mochizuki implemented the parallelized FMO3-CIS gradient calculation, based on the efficient formulations with Fock-like contractions (Foresman *et al*., 1992). The dynamics of excited states is now traceable as long as the CIS approximation is qualitatively correct enough. The influence of hydration on the excited state induced proton-transfer (ESIPT) has been attracting considerable interest, and we have started related simulations for several pet systems such as toropolone.

### **2.2.5 Unrestricted Hartree-Fock (UHF)**

UHF is the simplest method for handling open-shell molecular systems, as long as care for the associated spin contamination is taken. The UHF gradient was implemented by preparing - and β-density matrices. Simulation of hydrated Cu(II) has been underway at the FMO3-UHF level, and the Jahn-Teller distortion of hexa-hydration has been reasonably reproduced (Kato *et al.*, in preparation). The extension to a UMP2 gradient is planned as a future subject, where the computational cost may triple the MP2 gradient because of the three types of transformed integrals, (,), (,), and (,) (Aikens *et al.*, 2003).
