Electronic structure and optical spectra of transition metal complexes by the effective Hamiltonian method

Electronic Structure and d-d Spectrum of Metal-Organic Frameworks with Transition-Metal Ions

The electronic structure of metal-organic frameworks (MOFs) containing transition metal (TM) ions represents a significant and largely unresolved computational challenge due to limited solutions to the quantitative description of low-energy excitations in open d-shells. These excitations underpin the magnetic and sensing properties of TM MOFs, including the observed remarkable spin-crossover phenomenon. We introduce the effective Hamiltonian of crystal field approach to study the d-d spectrum of MOFs containing TM ions; this is a hybrid QM/QM method based on the separation of crystal structure into d- and s,p-subsystems treated at different levels of theory. We test the method on model frameworks, carbodiimides, and hydrocyanamides and a series of M-MOF-74 (M = Fe, Co, Ni) and compare the computational predictions to experimental data on magnetic properties and Mössbauer spectra.

Theoretical and computational methodologies for understanding coordination self-assembly complexes

This perspective highlights three theoretical and computational methods to capture the coordination self-assembly processes at the molecular level: quantum chemical modeling, molecular dynamics, and reaction network analysis. These methods cover the different scales from the metal-ligand bond to a more global aspect, and approaches that are best suited to understand the coordination self-assembly from different perspectives are introduced. Theoretical and numerical researches based on these methods are not merely ways of interpreting the experimental studies but complementary to them.

A model electronic Hamiltonian for the self-assembly of an octahedron-shaped coordination capsule

A model electronic Hamiltonian to describe ligand exchange reactions of palladium(ii) complexes with pyridine (Py) and tridentate (L) ligands was developed. It was shown that the model Hamiltonian can adequately reproduce the structures and potential energies of the reactant/product, intermediate, and transition state of the ligand exchange reaction of [PdPy₄]²⁺ with free Py. The model Hamiltonian was extended to describe reactions of multi-metal complexes and was adequately applied to describe various clusters, [Pd_aL_bPy_c]^2a+, in the self-assembly of an octahedron-shaped coordination capsule, [Pd₆L₈]¹²⁺. The heterogeneity in the energetics of intermediate species [Pd_aL_bPy_c]^2a+ was strongly suggested by the calculations, and the underlying microscopic interactions were clarified with the geometrical motif. The present framework provides a way to examine the reaction mechanisms of complex metal ligand self-assembly, which can be complementary microscopic information to the recently investigated novel experimental results for the real time evolutions.

Magnetism and lattice dynamics of FeNCN compared to FeO

The Mössbauer spectra of FeNCN at 6 and 296 K reveal that, in contrast to the usual behaviour, the hyperfine magnetic field is reduced upon cooling.

d-d Spectra of transition-metal carbodiimides and hydrocyanamides as derived from many-particle effective Hamiltonian calculations

We apply the local many-particle method of the Effective Hamiltonian of Crystal Field (EHCF) to analyze the magnetic ground state and the low-energy excitation spectra of the transition-metal carbodiimides MNCN with M = Fe-Ni. Experimentally, these materials represent a uniform group of (high-spin) antiferromagnetic, optically transparent, colored insulators with absorption lines in the visible spectrum. These findings are fully supported by the EHCF numerical modeling. In all three cases, we arrive at high-spin ground states in agreement with the results of previous magnetic measurements as well as the presence of the d-d intrashell transitions for the visible absorption spectra. Remarkably enough, the EHCF approach resolves the controversial case of FeNCN which was earlier predicted to be metallic by density-functional theory even when including explicit electronic correlation (GGA+U). We also address the ground state and the low-energy excitation spectra of the transition-metal hydrocyanamides of the general formula M(NCNH)(2) with M = Fe-Ni, another uniform group of optically transparent colored insulators. EHCF also arrives at high-spin ground states and visible d-d intrashell transitions.

Modeling molecular crystals formed by spin-active metal complexes by atom-atom potentials

We apply the atom-atom potentials to molecular crystals of iron(II) complexes with bulky organic ligands. The crystals under study are formed by low-spin or high-spin molecules of Fe(phen)(2)(NCS)(2) (phen = 1,10-phenanthroline), Fe(btz)(2)(NCS)(2) (btz = 5,5',6,6'-tetrahydro-4H,4'H-2,2'-bi-1,3-thiazine), and Fe(bpz)(2)(bipy) (bpz = dihydrobis(1-pyrazolil)borate, and bipy = 2,2'-bipyridine). All molecular geometries are taken from the X-ray experimental data and assumed to be frozen. The unit cell dimensions and angles, positions of the centers of masses of molecules, and the orientations of molecules corresponding to the minimum energy at 1 atm and 1 GPa are calculated. The optimized crystal structures are in a good agreement with the experimental data. Sources of the residual discrepancies between the calculated and experimental structures are discussed. The intermolecular contributions to the enthalpy of the spin transitions are found to be comparable with its total experimental values. It demonstrates that the method of atom-atom potentials is very useful for modeling molecular crystals undergoing the spin transitions.

Efficient Multipole Model and Linear Scaling of NDDO-Based Methods

Fast growth of computational costs with that of the system's size is a bottleneck for the applications of traditional methods of quantum chemistry to polyatomic molecular systems. This problem is addressed by the development of linear (or almost linear) scaling methods. In the semiempirical domain, it is typically achieved by a series of approximations to the self-consistent field (SCF) solution. By contrast, we propose a route to linear scalability by modifying the trial wave function itself. Our approach is based on variationally determined strictly local one-electron states and a geminal representation of chemical bonds and lone pairs. A serious obstacle previously faced on this route were the numerous transformations of the two-center repulsion integrals characteristic for the neglect of diatomic differential overlap (NDDO) methods. We pass it by replacing the fictitious charge configurations usual for the NDDO scheme by atomic multipoles interacting through semiempirical potentials. It ensures invariance of these integrals and improves the computational efficiency of the whole method. We discuss possible schemes for evaluating the integrals as well as their numerical values. The method proposed is implemented for the most popular modified neglect of diatomic overlap (MNDO), Austin model 1 (AM1), and PM3 parametrization schemes of the NDDO family. Our calculations involving well-justified cutoff procedures for molecular interactions unequivocally show that the proposed scheme provides almost linear scaling of computational costs with the system's size. The numerical results on molecular properties certify that our method is superior with respect to its SCF-based ancestors.

Low- and high-spin iron (II) complexes studied by effective crystal field method combined with molecular mechanics

A computational method targeted to Werner-type complexes is developed on the basis of quantum mechanical effective Hamiltonian crystal field (EHCF) methodology (previously proposed for describing electronic structure of transition metal complexes) combined with the Gillespie-Kepert version of molecular mechanics (MM). It is a special version of the hybrid quantum/MM approach. The MM part is responsible for representing the whole molecule, including ligand atoms and metal ion coordination sphere, but leaving out the effects of the d-shell. The quantum mechanical EHCF part is limited to the metal ion d-shell. The method reproduces with reasonable accuracy geometry and spin states of the Fe(II) complexes with monodentate and polydentate aromatic ligands with nitrogen donor atoms. In this setting a single set of MM parameters set is shown to be sufficient for handling all spin states of the complexes under consideration.