The Algebra of Effective Hamiltonians and Operators: Exact Operators

Crystal–field parameters from ab initio calculations

“…The theory of effective Hamiltonians has been extensively discussed by Hurtubise and Freed [5] and we have made use of some of these concepts in earlier papers [6,7].…”

Spectroscopy of High‐Energy States of Lanthanide Ions

“…However, this is not always possible in low symmetry, where, for Ce 3+ there are often more free parameters than energy levels. However, it is possible to determine the 4f N or 4f N −1 5d "effective Hamiltonian" [27], and therefore the parameters, directly, if one has the eigenvectors, as well as the energies, for the relevant states. A straight-forward way of doing this has been discussed recently [26].…”

“…[19]. Such "crystal field" calculations make use of an "effective Hamiltonian" [27,28,29] that acts solely within the 4f N and 4f N −1 5d configurations. Rather than solving for the eigenvalues and eigenstates of the full Hamiltonian, the effective Hamiltonian is diagonalized within the model space (4f N and 4f N −1 5d configurations), and the expectation values of the effective operators are evaluated between the model-space eigenvectors.…”

A Lagrange multiplier approach for excited state properties through intermediate Hamiltonian formulation of Fock space multireference coupled-cluster theory

“…Existing MRCC approaches can be divided into three basic categories: Fock space (FS) 12,13 or valance universal (VU), Hilbert space (HS) 14 or state universal (SU), and state selective (SS) [15][16][17][18][19][20] CC. The first two approaches are commonly in the class of multi-root MRCC methods, as they are built on the concept of Bloch equation based effective Hamiltonian 21,22 acting within a model space. It is important to mention here that several methods based on SRCC have been extensively developed, which are widely applicable in quasi-degenerate situations.…”