Concept Of Effective Hamiltonian Research Articles

Coupled cluster downfolding methods: The effect of double commutator terms on the accuracy of ground-state energies.

Downfolding coupled cluster techniques have recently been introduced into quantum chemistry as a tool for the dimensionality reduction of the many-body quantum problem. As opposed to earlier formulations in physics and chemistry based on the concept of effective Hamiltonians, the appearance of the downfolded Hamiltonians is a natural consequence of the single-reference exponential parameterization of the wave function. In this paper, we discuss the impact of higher-order terms originating in double commutators. In analogy to previous studies, we consider the case when only one- and two-body interactions are included in the downfolded Hamiltonians. We demonstrate the efficiency of the many-body expansions involving single and double commutators for the unitary extension of the downfolded Hamiltonians on the example of the beryllium atom, and bond-breaking processes in the Li2 and H2O molecules. For the H2O system, we also analyze energies obtained with downfolding procedures as functions of the active space size.

Direct calculation of energy differences, such as ionization potentials

Indirect methods for the calculation of energy differences imply that two separate calculations of the involved states are performed first and then the difference is taken. In a ‘direct’ method the transition energy is calculated without an attempt to calculate either of the states between which transition takes place. The theory of direct calculations of energy differences is reviewed with emphasis on ionization potentials and special attention to the method of a common unitary transformation of two model states. Results for the ionization potentials of a few small molecules are presented. The elements of a more general theory are outlined in which the Liouvillean superoperator (and its resolvent) as well as the Fock space formulation of quantum chemistry (especially the concept of effective Hamiltonians in Fock space) play a key role.