High-spin versus broken symmetry-Effect of DFT spin density representation on the geometries of three diiron (III) model compounds

Unrestricted density functional theory calculations have been conducted on three diiron(III) synthetic model compounds containing antiferromagnetically coupled high-spin (HS) irons for which crystallographic structures and Raman spectral data are available. Three density functionals have been employed: BPW91, PWC, and BOP. The study compares the effects on optimized geometries and harmonic vibrational frequencies of spin-paired (SP) low-spin, HS, and broken symmetry antiferromagnetically coupled singlet representations of the spin density distribution. The geometries around the diiron centers in the HS and broken symmetry (BS) representations are found to be similar, both markedly different from those arising from the SP representation. Small differences between the HS and BS results are seen in bond lengths, angles, Raman frequencies, and spin densities associated with oxo and peroxo bridges between the irons.     

Magnetic and optical properties of Cu(II)-bis(oxamato) complexes: combined quantum chemical density functional theory and vibrational spectroscopy studies

Vibrational spectroscopies are shown to be highly sensitive to the structural modifications of paramagnetic mono- and trinuclear Cu(II)-bis(oxamato) complexes. The vibrational bands are assigned using density functional theory (DFT) calculations. Moreover, Raman spectroscopy investigations for different temperatures of thin films show that the onset of superexchange interactions at low temperatures does not involve a modification of the structural parameters. The influence of packing effects, however, on the magnetic properties is significant, as demonstrated by means of DFT using the broken symmetry approach.     

端接配体原子的电负性对磁耦合作用的影响

应用微扰理论，分析了端接配体原子的电负性对体系磁耦合作用的影响。研究 表明，随着端接配体原子电负性的增大，磁中心间的耦合作用减弱。应用密度泛函 理论和对称性破损方法对双核铜（II）模型体系进行了计算，计算结果验证了上述 结论。     

Magnetic and redox properties in hydroxo‐ and alkoxo‐bridged Fe(III) binuclear complexes: A density functional study

DFT calculations were carried out in order to deduce the dependence of magnetic coupling on the structure of doubly hydroxide/alkoxide‐bridged diiron(III) dimers. The broken‐symmetry formalism was employed to calculate the magnetic exchange parameter J. The potential surfaces of the ground state display a geometrical minimum at an Fe O(H) Fe angle of 105° and FeFe distance of 3.2 Å, in good agreement with experimental values. The calculated correlation between the magnetic coupling with the geometrical structure agrees well with the experimental literature data, although always overestimated. Electrochemical measurements show that a one‐electron reduction is likely to cause dissociation into pseudooctahedral, monomeric subunits, and, consequently, no calculations were made for the reduced dimeric species. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 61–71, 1999     

A structural, spectroscopic and computational study of the molecular and electronic structure of a [bis(alpha-diiminato)manganese(II)] pi radical complex

The synthesis, molecular and electronic structure of the first bis(alpha-diiminato)manganese(II) complex are reported, [Mn(II)(L )(2)] (S(t) = (3)/(2)) where (L )(1-) represents the one-electron reduced form of N,N'-bis(2,6-isopropylphenyl)-1,4-diaza-1,3-diene; density functional theoretical calculations using the B3LYP functional and the broken symmetry approach BS(5,2) corroborate the presence of a high-spin Mn(II) ion and two ligand pi radical monoanions.     

Spin densities in two-component relativistic density functional calculations: noncollinear versus collinear approach

With present day exchange-correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar-relativistic calculations, the spin density can be defined conventionally, but if spin-orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the "spin density" is. In many applications, a fixed quantization axis is used to define the spin density ("collinear approach"), but one can also use the length of the local spin magnetization vector without any reference to an external axis ("noncollinear approach"). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange-correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn-Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I+2 and PbF indicate that the error introduced by the collinear approximation is approximately 0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort.     

On the photomagnetism of nitronyl nitroxide, imino nitroxide, and verdazyl-substituted azobenzene

The cis- and trans-azobenzenes are known as photochromic isomers with the trans- converting into the cis-form and vice versa upon irradiation with specific wavelengths. We have quantum chemically investigated the cis- and trans-forms of substituted azobenzene diradicals, with two nitronyl nitroxides, imino nitoxides, or verdazyls at para positions and serving as monoradical centers, to determine whether they can exhibit a photoassisted magnetic crossover. Geometries of both substituted and unsubstituted molecules have been optimized by density functional (DF) method UB3LYP using the 6-311G(d,p) basis set. Optimization of the geometry of the cis isomers has required special care. Single point singlet, triplet, and broken symmetry calculations have been done using 6-311++G(3df, 3pd) basis set. The magnetic exchange coupling constants have been estimated from the broken symmetry calculations. Absorption wavelengths have been estimated for both substituted and unsubstituted species from time-dependent DF treatment using restricted spin-polarized methodology RB3LYP and 6-311++G(3df, 3pd) basis set. From the similarity in the calculated absorption wavelengths for the unsubstituted and substituted azobenzenes, and the increased oscillator strengths (f) for the substituted species, we predict that the diradical isomers would be strongly photochromic. From our triplet state and broken symmetry calculations, we predict that both the cis- and the trans-diradicals are antiferromagnetically coupled. This prediction is consistent with the spin alternation rule, and the possibility of a magnetic crossover is nonexistent for these species.     

Performance of the elongation method with larger basis sets

The elongation method proposed by Imamura serves as a theoretical model for polymerization processes. It can now be used together with larger basis sets, Hartree–Fock and density functional methods from the Gaussian 94 package with direct self‐consistent field (SCF). This allows electronic structure calculation of elongating clusters with an efficiency superior to full cluster calculations and a precision superior to previous versions of our elongation method. Performance and accuracy compared with full cluster calculations on a regular polymer using the BLYP/6‐31G(d, p) method. Interaction energies of water and hydrogen fluoride polymers of increasing length are compared between HF, BLYP methods and 4‐31G, 6‐31G(d, p) basis sets: Diffuse and polarization functions have a large influence on the interaction energy on both polymers. Local density of states are calculated for different cluster lengths. They are in good agreement with full cluster calculations. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 35–47, 1999     

CAS–SCF and density functional calculations of second hyperpolarizabilities for a nitronyl nitroxide radical

In this study, we investigated a multireference‐based nondynamical electron correlation dependence of the second hyperpolarizability, γ. We performed complete active space self‐consistent‐field (CAS–SCF) calculations including the effect of π electrons. Although the sign of γ obtained by CAS–SCF calculation was found to be negative, the magnitude of γ was found to be much larger than that at the CCSD(T) level. We also applied density functional (DF) methods with different exchange–correlation functionals (BLYP and B3LYP) to the calculation of γ. Although the B3LYP method is found to provide negative γ, its magnitude is much smaller than that at the CCSD(T) level. This feature is discussed in detail by using γ density plots. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 329–336, 1999     

Calculating the electron paramagnetic resonance parameters of exchange coupled transition metal complexes using broken symmetry density functional theory: application to a MnIII/MnIV model compound

The capability of the density functional broken symmetry approach for the calculation of various EPR parameters of exchange coupled metal clusters is demonstrated by studying the experimentally well-investigated [Mn(III)Mn(IV)(mu-O)(2)(mu-OAc)DTNE](2+) complex. Geometry optimizations of the complex in its broken symmetry and high spin states yielded structures with two distinct manganese sites and geometrical parameters in good agreement with the X-ray structure. Exchange coupling constants were calculated from the energy differences between the high spin and broken symmetry states using the Heisenberg spin Hamiltonian. Very good agreement between theory and experiment was achieved with the B3LYP hybrid functional. The g-tensor calculations were performed employing the coupled perturbed Kohn-Sham equations. A strategy for the computation of g-tensor site values is presented and provides single-site g-tensors that are in good agreement with the expectations for Mn(III) and Mn(IV), respectively. Spin projection gave the g-tensor of the coupled manganese complex in very good agreement with the experimental results. Complete (55)Mn hyperfine tensors, including spin-orbit contributions, were calculated and spin-projected. The source of anisotropy in this system could be traced back to the Mn(III) ion in line with the experimental results. The isotropic manganese hyperfine coupling constants were underestimated by factors between 1.4 and 2.5. It is shown that this deficiency is systematic in character and not anchored in the broken symmetry approach. Nuclear quadrupole splitting of the (55)Mn nuclei is shown to be small in this system. In addition, (14)N and (1)H ligand hyperfine data were calculated and compared well with the experimental results. The quality of the extended point-dipole model was demonstrated in application to (1)H anisotropic hyperfine coupling constants.     

Structural and static electric response properties of highly symmetric lithiated silicon cages: Theoretical predictions

It is shown by density functional theory calculations that high symmetry silicon cages can be designed by coating with Li atoms. The resulting highly symmetric lithiated silicon cages (up to D_5d symmetry) are low‐lying true minima of the energy hypersurface with binding energies of the order of 4.6 eV per Si atom and moderate highest occupied molecular orbital–lowest unoccupied molecular orbital gaps. Moreover, relying on a systematic study of the electric response properties obtained by ab initio (Hartree–Fock, MP2, and configuration interaction singles (CIS)) and density functional (B3LYP, B2PLYP, and CAM‐B3LYP) methods, it is shown that lithium coating has a large impact on the magnitude of their second hyperpolarizabilities resulting to highly hyperpolarizable species. Such hyperpolarizable character is directly connected to the increase in the density of the low‐lying excited states triggered by the interaction between the Si cage and the surrounding Li atoms. © 2012 Wiley Periodicals, Inc.     

Quantum Chemical Spin Densities for Radical Cations of Photosynthetic Pigment Models

The spin densities of radical cations of magnesium porphyrin, magnesium chlorine and a truncated chlorophyll a model are calculated with density‐functional theory and multiconfigurational quantum chemical methods. The latter serve as a reference for approximate density‐functional theory which yields spin densities that may suffer from the self‐interaction error. We carried out complete active space self‐consistent field calculations with increasing active orbital spaces to systematically converge qualitatively correct spin densities. In particular, for the magnesium chlorine and chlorophyll a model radical cations, this is not easy to achieve because of the lower symmetry compared to magnesium porphyrin. Strategies had to be employed which allowed us to consider very large active orbital spaces. We explored restricted active space self‐consistent field and density‐matrix renormalization group calculations. Based on these reference data, we assessed the accuracy of different density‐functional approximations. We show that in particular, exchange–correlation model potentials with correct asymptotic behavior yield good spin densities, and we find, in agreement with previous studies on different classes of compounds, that hybrid functionals systematically increase spin‐polarization effects with increasing amounts of exact exchange. Our results provide a starting point for investigations of spin densities of more complex systems such as the hinge model for the primary electron donor in photosystem II.     

Useful parameter describing magnetic interactions in extended bis‐bidentate bridged dimers

A useful parameter describing magnetic coupling interactions has been inspected in transition metal dimers, in which two transition metal ions are bridged by extended bis‐bidentate ligands. This parameter is the square of overlap integral between the spatial parts of magnetic orbitals in the broken symmetry state. The oxalato‐bridged Cu (II) dimers, in which the Cu (II) atom is either in tetrahedral or square pyramid coordination environment, have been calculated with the density functional theory coupling the broken symmetry approach. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Theoretical Vibrational Raman and Surface‐Enhanced Raman Scattering Spectra of Water Interacting with Silver Clusters

In this study, we analyzed the Raman spectrum of a water molecule adsorbed on a cluster of 20 silver atoms, and the plasmonic electromagnetic effect of the silver surface was also considered to give a theoretical prediction of the surface‐enhanced Raman scattering spectrum. The calculations were performed at the density functional theory (DFT) level by using both frozen and unfrozen silver clusters. Two different models were used to consider the plasmonic enhancement; one of them was a modified classical (dipole) model and the other was the coupled perturbed Hartree–Fock method with excitation frequencies obtained from time‐dependent DFT calculations and with proper detuning of these frequencies. The importance of small geometrical distortions of the silver surface in the orientation of the adsorbed water was shown. Moreover, it was shown how the symmetry of the transition dipole moment and the symmetry of the vibrational modes influence the Raman intensities of the SERS spectrum.     

X-ray diffraction, magnetochemical, and quantum chemical study of the structure and properties of binuclear copper(II) complexes

The binuclear chelates of copper(II) based on the tridentate azomethine ligands were synthesized and characterized by elemental analysis, IR, ¹H NMR spectroscopy, X-ray absorption spectroscopy (XANES and EXAFS), and magnetic measurements. The quantum-chemical study of the structure and calculation of magnetic properties of the obtained metal-chelates was performed using the density functional theory with the broken symmetry technique. The performed magnetochemical studies in the temperature range 2?C300 K suggest the existence of antiferromagnetic exchange interaction in all obtained complexes. The parameters of the exchange interaction ?2J > 260 cm^?1 were determined experimentally for all compounds, the experimental data is in a good agreement with the results of quantum-chemical calculations.     

Phase Equilibria of Hydrogen Bonding Fluid in a Slit Pore with Broken Symmetry

Phase equilibria of hydrogen bonding (HB) fluid confined in a slit pore with broken symmetry were investigated by the density functional theory incorporated with modified fundamental measure theory, where the symmetry breaking originated from the distinct interactions between fluid molecules and two walls of the slit pore. In terms of adsorption-desorption isotherms and the corresponding grand potentials, phase diagrams of HB fluid under various conditions are presented. Furthermore, through phase coexistences of laying transition and capillary condensation, the effects of HB interaction, pore width, fluid-pore interaction and the broken symmetry on the phase equilibrium properties are addressed. It is shown that these factors can give rise to apparent influences on the phase equilibria of confined HB fluid because of the competition between intermolecular interaction and fluid-pore interaction. Interestingly, a significant influence of broken symmetry of the slit pore is found, and thus the symmetry breaking can provide a new way to regulate the phase behavior of various confined fluids.     

Atomic multiplet energies from density functional calculations

Atomic multiplet term energies for dⁿ configurations have been estimated within density functional theory (DFT) exploiting symmetry to the largest possible extent. The electrostatic two-electron integrals, as well as term energies, are expressed in function of only three non-redundant single determinants (NRSDs), each of them being obtained from density functional calculations. The influence of correlation effects described with a gradient-corrected functional (GGA) is examined and discussed. Comparison with experimental data shows the reliability of this symmetry-based density functional approach.     

A comparative study of DFT and traditional ab initio methodologies on the OsO4 molecule

The performance of different conventional ab initio methodologies and density functional procedures is compared through its application to the theoretical calculation of the bond distance and harmonic vibrational frequencies of the OsO₄ molecule. The problem of the basis set is first considered, with up to nine different basis sets being tested in calculations using the hybrid Becke3LYP density functional, and the most appropriate basis set is used in the comparison of Hartree–Fock, post‐Hartree–Fock, and density functional methods. The post‐Hartree–Fock methods analyzed are MP2, CISD, and CCSD(T), and the density functionals tested are SVWN, BLYP, BPW91, and Becke3LYP. The results show that for this particular system density functional methods perform better than do HF‐based methods with the exception of CCSD(T), which gives the best overall results. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 544–551, 2000     

Plane-wave calculations applied to conjugated polymers

Density functional calculations using pseudopotentials and a plane-wave basis set are applied to study the geometry and the electronic structure of conjugated polymers consisting of heterocyclic aromatic rings. This article focuses on the computational methods. The influence of the pseudopotentials on the structural and electronic properties is studied. The rates of convergence of these properties with respect to the basis set size and the density of sampling points for the Brillouin zone integration are considered. The effects of using different exchange–correlation potentials (local density or generalized gradient approximations) are examined. It is shown that smooth norm-conserving pseudopotentials used for calculations on conjugated polymers lead to converged results with a moderately sized basis set. Received: 20 August 1999 / Accepted: 23 November 1999 / Published online: 19 April 2000     

Multi‐zinc‐expanded graphene patches: Tetraradical versus diradical character

Three classes of multi‐Zn‐expanded graphene patches in different shapes are computationally designed through introducing a Zn chain into the corresponding middle benzenoid chain. Both density functional theory and complete active space self‐consistent field calculations predict that molecules of nnn‐quasi‐linear and nnn‐slightly bent series have the open‐shell broken‐symmetry (BS) singlet diradical ground states, whereas those of n(n+1)n species possess quintet tetraradical as their ground state and become open‐shell BS singlet tetraradicals when they are in a higher energy state. These results offer the first theoretical attempt to introduce multi‐Zn into the small graphene patches to form Zn‐expanded graphene patches, leading them to polyradical structures. This work provides an executable strategy to yield molecules which have stable polyradicaloid character and enhanced electronic properties of multi‐Zn‐expanded graphene patches. © 2012 Wiley Periodicals, Inc.