Analytical energy gradients for internally contracted second-order multireference perturbation theory

The theory for computing analytical energy gradients for second-order multireference perturbation theory (MRPT2) with arbitrary multiconfiguration self-consistent field (MCSCF) reference functions is derived and implemented. MRPT2 with complete active space reference functions (CASPT2) is a special case. In our method the configurations with two electrons in the external orbital space are internally contracted. This ansatz strongly reduces the length of the configuration expansion as compared to uncontracted wave functions, but avoids bottlenecks occurring when fully contracted first-order wave functions are used. The method, which also allows the use of state-averaged MCSCF reference functions, is applied to optimize the structures of low-lying valence and Rydberg states of Pyrrole. Nonplanar equilibrium structures and large geometry relaxation effects on the excitation energies are found for the valence states. From the results it can be concluded that CASPT2 underestimates the excitation energies of the valence states, but leads to accurate results for the Rydberg states. (C) 2003 American Institute of Physics.