Jean-Paul Malrieu

New approach to the state-specific multireference coupled-cluster formalism

A new development is presented in the framework of the state-specific multireference (MR) coupled-cluster (CC) theory (MRCC). The method is based on the CASSCF (complete active space self-consistent field) wave function and it is designed specifically for calculating excited electronic states. In the proposed approach, the cluster structure of the CC wave operator and the method to determine this operator are the key features. Since the general formulation of the CASCC method is uncontracted, i.e., allows the interaction between the nondynamic and dynamic correlation effects to affect both the CAS reference function and the CC correlation wave operator, the method is expected to perform better than contracted perturbative approaches such as the CASPT2 (second-order perturbation theory based on the CAS wave function) method. Also, the CASCC method is not a perturbative approach and is not based on selection of an unperturbed Hamiltonian, which in the case of the CASPT2 method often leads to the “intruder s...

Is it possible to determine rigorous magnetic Hamiltonians in spin s=1 systems from density functional theory calculations?

The variational energies of broken-symmetry single determinants are frequently used (especially in the Kohn-Sham density functional theory) to determine the magnetic coupling between open-shell metal ions in molecular complexes or periodic lattices. Most applications extract the information from the solutions of m(s)(max) and m(s)(min) eigenvalues of S(z) magnetic spin momentum, assuming that a mapping of these energies on the energies of an Ising Hamiltonian is grounded. This approach is unable to predict the possible importance of deviations from the simplest form of the Heisenberg Hamiltonians. For systems involving s=1 magnetic centers, it cannot provide an estimate of neither the biquadratic exchange integral nor the three-body operator interaction that has recently been proven to be of the same order of magnitude [Phys. Rev. B 70, 132412 (2007)]. The present work shows that one may use other broken-symmetry solutions of intermediate values of m(s) to evaluate the amplitude of these additional terms. The here-derived equations rely on the assumption that an extended Hubbard-type Hamiltonian rules the interactions between the magnetic electrons. Numerical illustrations on a model problem of two O(2) molecules and a fragment of the La(2)NiO(4) lattice are reported. The results obtained using a variable percentage of Fock exchange in the BLYP functional are compared to those provided by elaborate wave function calculations. The relevant percentage of Fock exchange is system dependent but a mean value of 30% leads to acceptable amplitudes of the effective exchange interaction.

Physical analysis of the through-ligand long-distance magnetic coupling: spin-polarization versus Anderson mechanism

The physical factors governing the magnetic coupling between two magnetic sites are analyzed and quantified as functions of the length of the bridging conjugated ligand. Using wave-function-theory based ab initio calculations, it has been possible to separate and calculate the various contributions to the magnetic coupling, i.e. the direct exchange, the spin polarization and the kinetic exchange. It is shown in model systems that while the Anderson mechanism brings the leading contribution for short-length ligands, the spin polarization dominates the through-long-ligand couplings. Since the spin polarization decreases more slowly than the kinetic exchange, highly spin polarizable bridging ligands would generate a good magneto-communication between interacting magnetic units.

Multireference self‐consistent size‐extensive state‐selective configuration interaction

In this work, we propose a state‐specific self‐consistent ‘‘dressing’’ of the multireference configuration interaction (MRCI) space to include all single‐ and double‐substituted determinants for the most important reference configurations. The aim of the method is to provide a size‐extensive description of the dynamic electron correlation effects for states which mandate a multideterminantal reference wave function. Such states can represent electronic excited states or ground states of the molecular systems which are significantly deformed from their equilibrium structures. The proposed approach follows the concept introduced in our recently proposed quasilinear ansatz for the state‐selective multireference coupled‐cluster method. The purpose of the dressing procedure is to eliminate the contributions which introduce size‐extensivity violating terms in the MRCI approach.

Can the second order multireference perturbation theory be considered a reliable tool to study mixed-valence compounds?

In this paper, the problem of the calculation of the electronic structure of mixed-valence compounds is addressed in the frame of multireference perturbation theory (MRPT). Using a simple mixed-valence compound (the 5,5() (4H,4H())-spirobi[ciclopenta[c]pyrrole] 2,2(),6,6() tetrahydro cation), and the n-electron valence state perturbation theory (NEVPT2) and CASPT2 approaches, it is shown that the ground state (GS) energy curve presents an unphysical well for nuclear coordinates close to the symmetric case, where a maximum is expected. For NEVPT, the correct shape of the energy curve is retrieved by applying the MPRT at the (computationally expensive) third order. This behavior is rationalized using a simple model (the ionized GS of two weakly interacting identical systems, each neutral system being described by two electrons in two orbitals), showing that the unphysical well is due to the canonical orbital energies which at the symmetric (delocalized) conformation lead to a sudden modification of the denominators in the perturbation expansion. In this model, the bias introduced in the second order correction to the energy is almost entirely removed going to the third order. With the results of the model in mind, one can predict that all MRPT methods in which the zero order Hamiltonian is based on canonical orbital energies are prone to present unreasonable energy profiles close to the symmetric situation. However, the model allows a strategy to be devised which can give a correct behavior even at the second order, by simply averaging the orbital energies of the two charge-localized electronic states. Such a strategy is adopted in a NEVPT2 scheme obtaining a good agreement with the third order results based on the canonical orbital energies. The answer to the question reported in the title (is this theoretical approach a reliable tool for a correct description of these systems?) is therefore positive, but care must be exercised, either in defining the orbital energies or by resorting to the third order using for them the standard definition.

Determination of spin Hamiltonians from projected single reference configuration interaction calculations. I. Spin 1/2 systems

The most reliable wave-function based treatments of magnetic systems usually start from a complete active space self-consistent field calculation of the magnetic electrons in the magnetic orbitals, followed by extensive and expensive configuration interaction (CI) calculations. This second step, which introduces crucial spin polarization and dynamic correlation effects, is necessary to reach reliable values of the magnetic coupling constants. The computational cost of these approaches increases exponentially with the number of unpaired electrons. The single-determinantal unrestricted density functional Kohn-Sham calculations are computationally much simpler, and may provide reasonable estimates of these quantities, but their results are strongly dependent on the chosen exchange-correlation potential. The present work, which may be seen as an ab initio transcription of the unrestricted density functional theory technique, returns to the perturbative definition of the Heisenberg Hamiltonian as an effective Hamiltonian, and proposes a direct estimate of its diagonal energies through single reference CI calculations. The differences between these diagonal terms actually determine the entire Heisenberg Hamiltonian. The reference determinants must be vectors of the model space and the components on the other vectors of the model space are cancelled along the iterative process. The method is successfully tested on a series of bicentric and multicentric spin 12 systems. The projected single reference difference dedicated CI treatment is both accurate and of moderate cost. It opens the way to parameter-free calculations of large spin assemblies.