Energies Of Different Spin States Research Articles

Spin State Energetics in First-Row Transition Metal Complexes: Contribution of (3s3p) Correlation and Its Description by Second-Order Perturbation Theory.

This paper presents an in-depth study of the performance of multiconfigurational second-order perturbation theory (CASPT2, NEVPT2) in describing spin state energetics in first-row transition metal (TM) systems, including bare TM ions, TM ions in a field of point charges (TM/PC), and an extensive series of TM complexes, where the main focus lies on the (3s3p) correlation contribution to the relative energies of different spin states. To the best of our knowledge, this is the first systematic NEVPT2 investigation of TM spin state energetics. CASPT2 has been employed in several previous studies but was regularly found to be biased toward high spin states. The bias was attributed to a too low value of the so-called IPEA shift ϵ, an empirical correction in the CASPT2 zeroth-order Hamiltonian with a standard value of 0.25 hartree. Based on comparisons with experiment (TM ions) and calculations with the multireference configuration interaction (TM ions and TM/PC systems) and coupled-cluster (TM complexes) methods, we demonstrate in this work that standard CASPT2 works well for valence correlation and that its bias toward high-spin states is caused by an erratic description of (3s3p) correlation effects. The latter problem only occurs for spin transitions involving a ligand field (de)excitation, not in bare TM ions. At the same time the (3s3p) correlation contribution also becomes strongly ϵ dependent. The error can be reduced by increasing ϵ but only at the expense of deteriorating the CASPT2 description of valence correlation in the TM complexes. The alternative NEVPT2 method works well for bare TM and TM/PC systems, but its results for the TM complexes are disappointing, with large errors both for the valence and (3s3p) correlation contributions to the relative energies of different spin states.

Metaphenylene-Based Nitroxide Diradicals: A Protocol To Calculate Intermolecular Coupling Constant in a One-Dimensional Chain

Intramolecular magnetic exchange coupling constants are determined for seven isolated metaphenylene-based dinitroxide diradicals by unrestricted density functional methodology (UDFT) using a number of hybrid functionals such as B3LYP, B3LYP-D3, M06-2X, HSE, and LC-ωPBE. Geometry optimizations for both triplet and broken symmetry solutions are performed with the 6-311G(d,p) basis set for all the molecules. In all cases, B3LYP somewhat overestimates the coupling constant, and M06-2X produces a more realistic value. The range-separated HSE and LC-ωPBE functional yield large deviations from experiment. The nature of spin coupling agrees with the spin alternation rule and the calculated spin densities, in conjunction with the McConnell rule. It can also be explained in terms of the nondisjoint Single Occupied Molecular Orbital effect. Furthermore, it correlates with the calculated NICS(1) isotropic and zz and hyperfine coupling constants. We also put forward a method for the determination of the intramolecular (J) and intermolecular (J') coupling constants from quantum chemical calculations on a one-dimensional chain of weakly bound diradicals. Two expressions are derived for the energies of different spin states in terms of J and J'. Exemplary UDFT computations are done on the N-mers (N = 2-6) of two diradicals for which the crystal coordinates are available. The intramolecular and intermolecular coupling constants are determined from the calculated UDFT energies. These are indeed in general agreement with the measured coupling constants.

How Evenly Can Approximate Density Functionals Treat the Different Multiplicities and Ionization States of 4d Transition Metal Atoms?

The ability of density functional theory to predict the relative energies of different spin states, especially for systems containing transition metal atoms, is of great importance for many applications. Here, in order to sort out the key factors determining accuracy, we compare the predictions of 60 density functional approximations of 10 different types [local spin density approximation, generalized gradient approximation (GGA), nonseparable gradient approximation (NGA), global-hybrid GGA, range-separated hybrid GGA, range-separated hybrid GGA plus molecular mechanics, meta-GGA, meta-NGA, global-hybrid meta-GGA, and range-separated hybrid meta-GGA] for their ability to represent the spin-flip transitions of all 4d transition metal atoms of groups 3-10 (Y through Pd) and their singly positive cations. We consider all 16 excitation energies connecting the ground states (of the neutral atoms and the cations) to their first excited states of different multiplicities, and we also consider all eight ionization potentials. We also test the Hartree-Fock method. All density functional and Hartree-Fock calculations are converged to a stable solution, in which the spatial symmetry is allowed to be completely broken to achieve the lowest possible energy solution. By analyzing the fractional subshell occupancies and spin contaminations, we are able to sort out the effects of s orbital vs d orbital bias and high-spin vs low-spin bias. A reliable functional should have little or no bias of either type rather than succeeding for a limited subset of cases by cancellation of errors. We find that the widely used correlations of spin splittings to percentage of Hartree-Fock exchange are not borne out by the data, and the correlation functionals also play a significant role. We eventually conclude that SOGGA11-X, B1LYP, B3V5LYP, and MPW3LYP are the most consistently reliable functionals for balanced treatments of 4d transition metal atoms and their cations.

Metal Ion Dependent Adhesion Sites in Integrins: A Combined DFT and QMC Study on Mn2+

The theoretical study of relative energies of different spin states of Mn2+ has been carried out for the isolated cation and for structures in which the cation is coordinated to ligands that represent the first coordination shell in a protein environment that contains a metal ion dependent adhesion site (MIDAS, found in the ligand binding domain of protein LFA-1). The calculations determine whether the ligand field generated by a prototype protein environment affects the relative energies between high, intermediate, and low spin states. Geometry optimizations and vibrational frequency calculations were carried out at the B3LYP/SKBJ+* level of theory. Single point calculations were performed at the B3LYP/6-311++G(2df,2p) and diffusion monte carlo (DMC) levels for the refinement of the electronic energies. These calculations reveal important differences in the relative energies between high/low spin complexes obtained by B3LYP and DMC and show that although both DFT and DMC show similar trends, a higher level method such as DMC is necessary for a quantitative description of the interactions between Mn2+ and its natural ligands. (G)s of acetate-type ligand binding reactions were calculated that show that the higher the spin of the manganese complex, the lower the affinity for the ligand.

Parameter Calibration of Transition-Metal Elements for the Spin-Polarized Self-Consistent-Charge Density-Functional Tight-Binding (DFTB) Method: Sc, Ti, Fe, Co, and Ni.

Recently developed parameters for five first-row transition-metal elements (M = Sc, Ti, Fe, Co, and Ni) in combination with H, C, N, and O as well as the same metal (M-M) for the spin-polarized self-consistent-charge density-functional tight-binding (DFTB) method have been calibrated. To test their performance a couple sets of compounds have been selected to represent a variety of interactions and bonding schemes that occur frequently in transition-metal containing systems. The results show that the DFTB method with the present parameters in most cases reproduces structural properties very well, but the bond energies and the relative energies of different spin states only qualitatively compared to the B3LYP/SDD+6-31G(d) density functional (DFT) results. An application to the ONIOM(DFT:DFTB) indicates that DFTB works well as the low level method for the ONIOM calculation.

DommiMOE: An implementation of ligand field molecular mechanics in the molecular operating environment

The ligand field molecular mechanics (LFMM) model, which incorporates the ligand field stabilization energy (LFSE) directly into the potential energy expression of molecular mechanics (MM), has been implemented in the "chemically aware" molecular operating environment (MOE) software package. The new program, christened DommiMOE, is derived from our original in-house code that has been linked to MOE via its applications programming interface and a number of other routines written in MOE's native scientific vector language (SVL). DommiMOE automates the assignment of atom types and their associated parameters and popular force fields available in MOE such as MMFF94, AMBER, and CHARMM can be easily extended to provide a transition metal simulation capability. Some of the unique features of the LFMM are illustrated using MMFF94 and some simple [MCl)]2- and [Ni(NH3)n]2+ species. These studies also demonstrate how density functional theory calculations, especially on experimentally inaccessible systems, provide important data for designing improved LFMM parameters. DommiMOE treats Jahn-Teller distortions automatically, and can compute the relative energies of different spin states for Ni(II) complexes using a single set of LFMM parameters.

Theoretical study of magnetic coupling interaction in terephthalato‐bridged Ni(II) binuclear systems

AbstractThe density functional theory combined with broken‐symmetry approach has been successfully extended into the study of the long‐range weak coupling interaction in a binuclear Ni(II) complex bridged by terephthalate dianion. The calculated magnetic coupling constant (−0.27 cm−1) is well in agreement with the experimental one (−0.33 cm−1). The relative magnitude of the energies of different spin states has been obtained. The spin delocalization and spin polarization occur between two Ni(II) ions, based on the analysis of the spin density distribution. Weak antiferromagnetic behavior in such a system may result from the competition between spin delocalization and spin polarization where the former is dominant. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004