Vibrationally averaged magnetizabilities and rotational g tensors of the water molecule

Mixed-valence nickel-iron dithiolate models of the [NiFe]-hydrogenase active site

A series of mixed-valence nickel-iron dithiolates is described. Oxidation of (diphosphine)Ni(dithiolate)Fe(CO)(3) complexes 1, 2, and 3 with ferrocenium salts affords the corresponding tricarbonyl cations [(dppe)Ni(pdt)Fe(CO)(3)](+) ([1](+)), [(dppe)Ni(edt)Fe(CO)(3)](+) ([2](+)) and [(dcpe)Ni(pdt)Fe(CO)(3)](+) ([3](+)), respectively, where dppe = Ph(2)PCH(2)CH(2)PPh(2), dcpe = Cy(2)PCH(2)CH(2)PCy(2), (Cy = cyclohexyl), pdtH(2) = HSCH(2)CH(2)CH(2)SH, and edtH(2) = HSCH(2)CH(2)SH. The cation [2](+) proved unstable, but the propanedithiolates are robust. IR and EPR spectroscopic measurements indicate that these species exist as C(s)-symmetric species. Crystallographic characterization of [3]BF(4) shows that Ni is square planar. Interaction of [1]BF(4) with P-donor ligands (L) afforded a series of substituted derivatives of type [(dppe)Ni(pdt)Fe(CO)(2)L]BF(4) for L = P(OPh)(3) ([4a]BF(4)), P(p-C(6)H(4)Cl)(3) ([4b]BF(4)), PPh(2)(2-py) ([4c]BF(4)), PPh(2)(OEt) ([4d]BF(4)), PPh(3) ([4e]BF(4)), PPh(2)(o-C(6)H(4)OMe) ([4f]BF(4)), PPh(2)(o-C(6)H(4)OCH(2)OMe) ([4g]BF(4)), P(p-tol)(3) ([4h]BF(4)), P(p-C(6)H(4)OMe)(3) ([4i]BF(4)), and PMePh(2) ([4j]BF(4)). EPR analysis indicates that ethanedithiolate [2](+) exists as a single species at 110 K, whereas the propanedithiolate cations exist as a mixture of two conformers, which are proposed to be related through a flip of the chelate ring. Mössbauer spectra of 1 and oxidized S = 1/2 [4e]BF(4) are both consistent with a low-spin Fe(I) state. The hyperfine coupling tensor of [4e]BF(4) has a small isotropic component and significant anisotropy. DFT calculations using the BP86, B3LYP, and PBE0 exchange-correlation functionals agree with the structural and spectroscopic data, suggesting that the SOMOs in complexes of the present type are localized in an Fe(I)-centered d(z(2)) orbital. The DFT calculations allow an assignment of oxidation states of the metals and rationalization of the conformers detected by EPR spectroscopy. Treatment of [1](+) with CN(-) and compact basic phosphines results in complex reactions. With dppe, [1](+) undergoes quasi-disproportionation to give 1 and the diamagnetic complex [(dppe)Ni(pdt)Fe(CO)(2)(dppe)](2+) ([5](2+)), which features square-planar Ni linked to an octahedral Fe center.

Gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster level

An implementation of the gauge-origin independent calculation of magnetizabilities and rotational g tensors at the coupled-cluster (CC) level is presented. The properties of interest are obtained as second derivatives of the energy with respect to the external magnetic field (in the case of the magnetizability) or with respect to magnetic field and rotational angular momentum (in the case of the rotational g tensor), while gauge-origin independence and fast basis-set convergence are ensured by using gauge-including atomic orbitals (London atomic orbitals) as well as their extension to treat rotational perturbations (rotational London atomic orbitals). The implementation within our existing CC analytic second-derivative code is described, focusing on the required modifications concerning integral evaluation and treatment of the unperturbed and perturbed two-particle density matrices. An extensive set of test calculations for LiH and BH (up to the full configuration-interaction limit), for a series of simple hydrides (HF, H(2)O, NH(3), and CH(4)) as well as the more challenging molecules CO, N(2), and O(3) [employing the CC singles and doubles (CCSD) and the CCSD approximation augmented by a perturbative treatment of triple excitations] demonstrates the importance of electron correlation for high-accuracy predictions of magnetizabilities and rotational g tensors.

Calculation of static and dynamic linear magnetic response in approximate time-dependent density functional theory

We report implementations and results of time-dependent density functional calculations (i) of the frequency-dependent magnetic dipole-magnetic dipole polarizability, (ii) of the (observable) translationally invariant linear magnetic response, and (iii) of a linear intensity differential (LID) which includes the dynamic dipole magnetizability. The density functional calculations utilized density fitting. For achieving gauge-origin independence we have employed time-periodic magnetic-field-dependent basis functions as well as the dipole velocity gauge, and have included explicit density-fit related derivatives of the Coulomb potential. We present the results of calculations of static and dynamic magnetic dipole-magnetic dipole polarizabilities for a set of small molecules, the LID for the SF6 molecule, and dispersion curves for M-hexahelicene of the origin invariant linear magnetic response as well as of three dynamic polarizabilities: magnetic dipole-magnetic dipole, electric dipole-electric dipole, and electric dipole-magnetic dipole. We have also performed comparison of the linear magnetic response and magnetic dipole-magnetic dipole polarizability over a wide range of frequencies for H2O and SF6.

Gauge-origin-independent magnetizabilities of solvated molecules using the polarizable continuum model

We present an implementation of the polarizable continuum model in its integral equation formulation for the calculation of the magnetizabilities of solvated molecules. The gauge-origin independence of the calculated magnetizabilities and the fast basis set convergence are ensured through the use of London atomic orbitals. Our implementation can use Hartree-Fock and multiconfigurational self-consistent-field (MCSCF) wave functions as well as density-functional theory including hybrid functionals such as B3LYP. We present the results of dielectric continuum effects on water and pyridine using MCSCF wave functions, as well as dielectric medium effects on the magnetizability of the aromatic amino acids as a model for how a surrounding protein environment affects the magnetizability of these molecules. It is demonstrated that the dielectric medium effects on the magnetizability anisotropies of the aromatic amino acids may be substantial, being as large as 25% in the case of tyrosine.

On equilibrium structures of the water molecule

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born-Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [ ibid. 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born-Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3 x 10(-5) A and 0.02 degrees for water. The mass-independent [Born-Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is r(e) (BO)=0.957 82 A and theta e (BO)=104.48(5) degrees , respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2 (16)O is r(e) (ad)=0.957 85 A and theta e (ad)=104.50(0) degrees , respectively, while those of D2 (16)O are r(e) (ad)=0.957 83 A and theta e (ad)=104.49(0) degrees . Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002 cm(-1) for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05 cm(-1) (or the lower ones to better than 0.0035 cm(-1)) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born-Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2 16O, obtained from experimentally determined A'0 and B'0 rotational constants corrected empirically to obtain equilibrium rotational constants, are r(e) (sp)=0.957 77 A and theta e (sp)=104.48 degrees .