A simple approach to the state-specific MR-CC using the intermediate Hamiltonian formalism.

This paper presents a rigorous state-specific multi-reference coupled cluster formulation of the method first proposed by Meller et al. [J. Chem. Phys. 104, 4068 (1996)]. Guess values of the amplitudes of the single and double excitations (the T operator) on the top of the references are extracted from the knowledge of the coefficients of the Multi-Reference Singles and Doubles Configuration Interaction (MR-CISD) matrix. The multiple parentage problem is solved by scaling these amplitudes from the interaction between the references and the singles and doubles. Then one proceeds to a dressing of the MR-CISD matrix under the effect of the triples and quadruples, the coefficients of which are estimated from the action of exp(T). This dressing follows the logic of the intermediate effective Hamiltonian formalism. The dressed MR-CISD matrix is diagonalized and the process is iterated to convergence. As a simplification, the coefficients of the triples and quadruples may in practice be calculated from the action of T(2) only, introducing 5th-order differences in the energies. The so-simplified method is tested on a series of benchmark systems from Complete Active Spaces (CASs) involving 2-6 active electrons up to bond breakings. The comparison with full configuration interaction results shows that the errors are of the order of a few millihartree, five times smaller than those of the CAS-CISD, and the deviation to strict separability is lower than 10 µ hartree. The method is totally uncontracted, parallelizable, and extremely flexible since it may be applied to selected MR and/or selected CISD. Some potential generalizations are briefly discussed.

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.

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.

A local contracted treatment of single and double excitations.

Starting from localized bond or lone-pair Hartree-Fock molecular orbitals, one may define contracted doubly excited functions for each pair of bond molecular orbitals. These functions are obtained from local single- and double-configuration interaction (CISD) of moderate size. Then one may build a contracted CISD matrix for the whole molecule, spanned by the Hartree-Fock determinant and these contracted doubly excited functions, the number of which is indeed moderate, as scaling at most as the square of the number of bonds. The calculation of the off-diagonal elements of this matrix is straightforward. Its diagonalization provides an upper bound to the lowest CISD eigenvalue. The well-known size-consistency error may be overcome through self-consistent dressings such as coupled-electron pair approximations, and cutoff criteria will lead to linear scaling. Numerical tests on a series of covalent and ionic systems show that the results are very close to that of coupled-cluster calculations. Possible improvements of this already efficient algorithm are suggested.

Metal-metal bond length variability in Co(3)(dipyridylamide)(4)Cl(2): bond-stretch isomerism, crystal field effects, or spin transition process? A DFT study.

The unprecedented structural behavior of Co(3)(dipyridylamide)(4)Cl(2), characterized in two crystalline forms in which the tricobalt framework is either symmetric or highly nonsymmetric at room temperature is investigated by means of gradient-corrected DFT calculations. The isolated molecule is assigned a single energy minimum associated with a low-spin (doublet) electronic configuration. The optimal geometry closely reproduces the X-ray structure observed for the isomer displaying equivalent metal-metal distances. However, the ground-state potential energy surface is extremely shallow with respect to a distortion of the Co(3) framework. A "weak" distortion, similar to that observed for the unsymmetrical complex at low temperature (Deltad(Co-Co) = 0.08 A at 110 K) induces a destabilization of 1.1 kcal.mol(-1) only. The distortion observed at room temperature (Deltad(Co-Co) = 0.17 A) destabilizes the isolated complex by 4.2 kcal.mol(-1). These results are rationalized in terms of the "three-electron three-center" concept applied to the sigma-bonding electrons of the cobalt framework. A phenomenological model based upon the Heisenberg Hamiltonian successfully reproduces the calculated potential energy curve and assigns the relative stability of the symmetric structure to local forces (Pauli repulsion, ligand bite, etc.) distinct from delocalized sigma bonding. In view of these results, the two structures characterized from X-rays cannot be termed "bond-stretch isomers" according to the strict definition given by Parkin. To investigate the origin of the distorted form, an electric field was applied to the isolated molecule, but it did not shift the equilibrium position toward asymmetry, despite a strong polarization of the electron density. Finally, the quartet state of lowest energy ((4)A state) has an optimal structure that is distorted and that reproduces most of the distinctive features observed in the nonsymmetric structure. Despite the high relative energy calculated for this quartet state, we assign the occurrence of the nonsymmetric form and its extreme variability with temperature to a progressive population of this excited state as temperature increases.