Rosa Caballol

Specific CI calculation of energy differences: Transition energies and bond energies

Abstract A general strategy for the calculation of energy differences is proposed. It proceeds through the definition of a minimal model space and the low-order perturbative development of the corresponding Hamiltonian is used to establish a set of determinants contributing to the searched energy difference. The so-selected CI is treated variationally. This general strategy is applied here to the calculation of observables basically involving two electrons in two orbitals. The first one concerns the transition energies from the ground state to the lowest singlet and triplet states of atoms (Ar 1 S → 3,1 P, Ca 1 S → 3,1 P) or molecules (CH 2 1 A 1 → 3 B 1 , 2 1 A 1 ). The second problem concerns the CH bond energy in ethylene. In all cases the agreement of the results of that simple procedure with either experiment or full-CI is quite satisfactory.

Variational calculation of small energy differences. The singlet-triplet gap in [Cu2Cl6]2−

Abstract Based on the theory of effective Hamiltonians, a variational procedure to calculate singlet—triplet energy differences in diradical systems is described, which includes all the differential second-order contributions. When applied to [Cu2Cl6]2−, for which the singlet—triplet gap ranges between −40 and 80 cm−1, depending on the structural parameters, a good agreement is reached. For large systems, a truncation procedure of the MO set based on singlet—triplet gap-dedicated MOs is described, which allows the dimension of the molecular integrals file to be reduced significantly without loss of efficiency.

Analysis of the magnetic coupling in binuclear complexes. I. Physics of the coupling

Accurate estimates of the magnetic coupling in binuclear complexes can be obtained from ab initio configuration interaction (CI) calculations using the difference dedicated CI technique. The present paper shows that the same technique also provides a way to analyze the various physical contributions to the coupling and performs numerical analysis of their respective roles on four binuclear complexes of Cu (d9) ions. The bare valence-only description (including direct and kinetic exchange) does not result in meaningful values. The spin-polarization phenomenon cannot be neglected, its sign and amplitude depend on the system. The two leading dynamical correlation effects have an antiferromagnetic character. The first one goes through the dynamical polarization of the environment in the ionic valence bond forms (i.e., the M+⋯M− structures). The second one is due to the double excitations involving simultaneously single excitations between the bridging ligand and the magnetic orbitals and single excitations of...

Magnetic interactions in molecules and highly correlated materials: physical content, analytical derivation, and rigorous extraction of magnetic Hamiltonians.

Physical Content, Analytical Derivation, and Rigorous Extraction of Magnetic Hamiltonians Jean Paul Malrieu,† Rosa Caballol,‡ Carmen J. Calzado, Coen de Graaf,‡,∥ and Nathalie Guiheŕy*,† †Laboratoire de Chimie et Physique Quantiques, Universite ́ de Toulouse 3, 118 route de Narbonne, 31062 Toulouse, France ‡Departament de Química Física i Inorgaǹica, Universitat Rovira i Virgili, Marcel·lí Domingo s/n, 43007 Tarragona, Spain Departamento de Química Física, Universidad de Sevilla, Profesor Garcia Gonzalez s/n, 41012 Sevilla, Spain Institucio ́ Catalana de Recerca i Estudis Avanca̧ts (ICREA), Passeig Lluis Companys 23, 08010 Barcelona, Spain

Analysis of the magnetic coupling in binuclear complexes. II. Derivation of valence effective Hamiltonians from ab initio CI and DFT calculations

Most interpretations of the magnetic coupling J between two unpaired electrons rest upon simple valence models that involve essentially the ferromagnetic direct exchange contribution, Kab, and the antiferromagnetic effect of the delocalization resulting from the interaction between neutral and ionic determinants, tab, whose energy difference is U. Ab initio valence-only calculations give very poor estimates of J, whatever the definition of the magnetic orbitals, and large CI expansions are required to evaluate it properly. It is, however, possible to define valence effective Hamiltonians from the knowledge of the eigenenergies and the eigenvectors of these accurate CI calculations. When applied to four different complexes, this strategy shows that spin polarization may change the sign of the direct exchange interaction, Kab, and that dynamical correlation results in a dramatic reduction of the effective repulsion U. The present article also shows how Kab, tab, and U effective parameters can be extracted f...

Analysis of the magnetic coupling in binuclear systems. III. The role of the ligand to metal charge transfer excitations revisited

In magnetic coordination compounds and solids the magnetic orbitals are essentially located on metallic centers but present some delocalization tails on adjacent ligands. Mean field variational calculations optimize this mixing and validate a single band modelization of the intersite magnetic exchange. In this approach, due to the Brillouins theorem, the ligand to metal charge transfer (LMCT) excitations play a minor role. On the other hand the extensive configuration interaction calculations show that the determinants obtained by a single excitation on the top of the LMCT configurations bring an important antiferromagnetic contribution to the magnetic coupling. Perturbative and truncated variational calculations show that contrary to the interpretation given in a previous article [C. J. Calzado et al., J. Chem. Phys. 116, 2728 (2002)] the contribution of these determinants to the magnetic coupling constant is not a second-order one. An analytic development enables one to establish that they contribute at higher order as a correlation induced increase in the LMCT components of the wave function, i.e., of the mixing between the ligand and the magnetic orbitals. This larger delocalization of the magnetic orbitals results in an increase in both the ferro- and antiferromagnetic contributions to the coupling constant.

AN ITERATIVE DIFFERENCE-DEDICATED CONFIGURATION INTERACTION. PROPOSAL AND TEST STUDIES

Abstract An earlier work proposed a difference-dedicated configuration interaction method based on effective Hamiltonian arguments and was essentially devoted to the calculation of transition energies and binding energies. Using the resulting density matrices, the procedure may be made independent of the choice of starting molecular orbitals. This iterative redefinition of the MOs improves the quality of the results, as shown by comparing to full-CI results on CH 2 , CH 2 + and SiH 2 vertical and adiabatic transition energies. The efficiency of the method for the treatment of weakly avoided crossings and for the determination of binding energies is illustrated on the LiF molecule. The mean deviation of the iterative difference-dedicated CI results to FCI energy differences is lower than 0.1 eV.

On the applicability of multireference second-order perturbation theory to study weak magnetic coupling in molecular complexes.

The performance of multiconfigurational second‐order perturbation techniques is established for the calculation of small magnetic couplings in heterobinuclear complexes. Whereas CASPT2 gives satisfactory results for relatively strong magnetic couplings, the method shows important deviations from the expected Heisenberg spectrum for couplings smaller than 15–20 cm−1. The standard choice of the zeroth‐order CASPT2 Hamiltonian is compared to alternative definitions published in the literature and the stability of the results is tested against increasing level shifts. Furthermore, we compare CASPT2 with an alternative implementation of multiconfigurational perturbation theory, namely NEVPT2 and with variational calculations based on the difference dedicated CI technique.

Multireference self‐consistent size‐consistent singles and doubles configuration interaction for ground and excited states

One proposes a state‐specific self‐consistent dressing of the configuration interaction (CI) matrix built on a multireference space and all the singly and doubly substituted determinants. The dressing insures size consistency [and separability when localized molecular orbitals (MOs) are used]. In the here‐proposed solution, which generalizes a previous single reference method [(SC)2CI, J. Chem. Phys. 99, 1240 (1993)] valid only for the research of the ground state, all the reference determinants play an equal role and the method is applicable to excited states. The implementation will be simpler if the reference space is a complete active space, but this restriction is not compulsory.

SINGLET-TRIPLET ENERGY GAP IN HALOGEN-SUBSTITUTED CARBENES AND SILYLENES :A DIFFERENCE-DEDICATED CONFIGURATION INTERACTION CALCULATION

Ab initio calculations including correlation energy are reported on a series of halogen-substituted carbenes and silylenes: CH2, CHF, CF2, CHCl, CCl2, CHBr, CBr2, SiH2, SiHF, SiF2, using the difference-dedicated configuration interaction method. All these compounds with the exception of CH2 have singlet ground states. The singlet-triplet energy differences are in very good agreement with experiment when available, as well as with other high level calculations. The singlet-triplet separation is also determined in trifluoromethyl carbenes, CHCF3, CFCF3, CClCF3 and CBrCF3. The CF3 substituent has little influence on the energy gap since CHCF3 like CH2 has a triplet ground state, with a gap of 11·1 kcal mol-1, and CFCF3, CClCF3 and CBrCF3 have singlet ground states, like CHF, CHCl and CHBr, with gaps of -17·6, -5·4, and -3·5 kcal mol-1.