ABSTRACT
Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations, predominantly by density-functional theory. The energies of these configurations are interpreted in terms of the Heisenberg model, HÌ=∑i
ABSTRACT
We assess the calculation of hyperfine coupling (HFC) tensors by different variants of Projected Hartree-Fock (PHF) theory. For a set of small main-group S = 1/2 radicals (BO, CO+, CN, AlO, vinyl, methyl, ethynyl), spin-symmetry as well as complex-conjugation and point-group symmetry are first broken in a reference determinant, and then variationally restored, in the frame of the modern formulation of PHF theory. Historically, PHF theory was basically restricted to the restoration of spin symmetry from an unrestricted HF determinant (conserving Sz symmetry). This afforded unsatisfactory HFCs. We obtain far better results for isotropic (and anisotropic) HFCs when the variational energy is further lowered by working with generalized determinants that completely break spin symmetry, and when additional symmetries are used. Specifically, complex-conjugation projection recovers a substantial fraction of the dynamical correlation energy in small molecules, and the detailed equations for combined complex-conjugation, spin- and point-group projection in the density-matrix/diagonalization formulation of PHF theory are here reported for the first time. The compact representation of the PHF wave function allows for a straightforward evaluation of the spin-density matrix and of HFC tensors with little effort. The promising performance of PHF theory may motivate the application of post-PHF methods to the calculation of HFC tensors.
ABSTRACT
We present unrestricted and generalized Hartree-Fock solutions (UHF and GHF, respectively) for the single-band Hubbard model of an equilateral triangle. Spin-orbit coupling (SOC) is treated self-consistently, and HF stability and properties of different spin structures are studied in detail. The GHF solution switches from noncollinear to collinear when crossing a high-symmetry point in parameter space (spanned by the amplitudes of spin-conserving and spin-dependent hopping, i.e., kinetic energy and SOC, respectively). The collinear GHF solution represents a simple example to disprove the notion that a collinear vector spin density in a Slater determinant necessarily entails a defined spin projection. Spin Hamiltonian parameters for the anisotropic interaction between three spin-1/2 centers are extracted from HF energies and subsequently compared to exact results from effective Hamiltonian theory. This provides an unambiguous benchmark for interpreting broken-symmetry mean-field solutions in terms of spin configurations and puts this semiclassical approach (frequently applied in broken-symmetry density functional theory) on a firmer basis.
ABSTRACT
Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSHâGSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]4 ('Ni4 ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni4 , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSHâGSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.
ABSTRACT
We apply broken-symmetry density functional theory to determine isotropic exchange-coupling constants and local zero-field splitting (ZFS) tensors for the tetragonal Mn12(t)BuAc single-molecule magnet. The obtained parametrization of the many-spin Hamiltonian (MSH), taking into account all 12 spin centers, is assessed by comparing theoretical predictions for thermodynamic and spectroscopic properties with available experimental data. The magnetic susceptibility (calculated by the finite-temperature Lanczos method) is well approximated, and the intermultiplet excitation spectrum from inelastic neutron scattering (INS) experiments is correctly reproduced. In these respects, the present parametrization of the 12-spin model represents a significant improvement over previous theoretical estimates of exchange-coupling constants in Mn12, and additionally offers a refined interpretation of INS spectra. Treating anisotropic interactions at the third order of perturbation theory, the MSH is mapped onto the giant-spin Hamiltonian describing the S = 10 ground multiplet. Although the agreement with high-field EPR experiments is not perfect, the results clearly point in the right direction and for the first time rationalize the angular dependence of the transverse-field spectra from a fully microscopic viewpoint. Importantly, transverse anisotropy of the effective S = 10 manifold is explicitly shown to arise largely from the ZFS-induced mixing of exchange multiplets. This effect is given a thorough analysis in the approximate D2d spin-permutational symmetry group of the exchange Hamiltonian.
ABSTRACT
The ion-molecule reactions of dimethyl ether with cyclometalated [Pt(bipy-H)](+) were investigated in gas-phase experiments, complemented by DFT methods, and compared with the previously reported ion-molecule reactions with its sulfur analogue. The initial step corresponds in both cases to a platinum-mediated transfer of a hydrogen atom from the ether to the (bipy-H) ligand, and three-membered oxygen- and sulfur-containing metallacycles serve as key intermediates. Oxidative C--C bond coupling ("dehydrosulfurization"), which dominates the gas-phase ion chemistry of the [Pt(bipy-H)](+) ion with dimethyl sulfide, is practically absent for dimethyl ether. The competition in the formation of C(2)H(4) and CH(2)X (X=O, S) in the reactions of [Pt(bipy-H)](+) with (CH(3))(2)X (X=O, S) as well as the extensive H/D exchange observed in the [Pt(bipy-H)](+)/(CH(3))(2)O system are explained in terms of the corresponding potential-energy surfaces.
