Invariance of multipole polarisabilities of nuclear magnetic shielding within the approach of continuous transformation of the origin of the current density

Electric multipole polarisabilities of nuclear magnetic shielding of a molecule in the presence of external fields—a uniform magnetic and a non-uniform electric field—calculated via the approach of continuous transformation of the origin of the current density, are shown to be invariant in a translation of the gauge of the vector potential. However, multipole polarisabilities depend upon the origin of the coordinate system for multipole higher than dipole, because of the intrinsic origin dependence of the related operators.     

On expectation value calculations of one-electron properties using the coupled cluster wave functions

The ability of various approximate coupled cluster (CC) methods to provide accurate first-order one-electron properties calculated as expectation values is theoretically analysed and computationally examined for BH and CO. For actual calculations the infinite number of terms of the expectation value expansion (O=¦exp (T ⁺)O exp (T)¦_c) was truncated so that T ₁ T ₂, T ₃, and (1/2) T ₂T₂ clusters were retained on both sides of O. The role of individual clusters is carefully discussed. Inclusion of T ₁, is unavoidable, but if triples are essential in the energy evaluation, they may play an even more important role in the property expansion, as shown in the case of CO. It is shown that the CC wave function, which is exact to second order, effectively satisfies the Hellmann-Feynman theorem.     

Fe2 and Fe4 clusters encapsulated in vacant polyoxotungstates: hydrothermal synthesis, magnetic and electrochemical properties, and DFT calculations

While the reaction of [PW(11)O(39)](7-) with first row transition-metal ions M(n+) under usual bench conditions only leads to monosubstituted {PW(11)O(39)M(H(2)O)} anions, we have shown that the use of this precursor under hydrothermal conditions allows the isolation of a family of novel polynuclear discrete magnetic polyoxometalates (POMs). The hybrid asymmetric [Fe(II)(bpy)(3)][PW(11)O(39)Fe(2) (III)(OH)(bpy)(2)]12 H(2)O (bpy=bipyridine) complex (1) contains the dinuclear {Fe(micro-O(W))(micro-OH)Fe} core in which one iron atom is coordinated to a monovacant POM, while the other is coordinated to two bipyridine ligands. Magnetic measurements indicate that the Fe(III) centers in complex 1 are weakly antiferromagnetically coupled (J=-11.2 cm(-1), H=-JS(1)S(2)) compared to other {Fe(micro-O)(micro-OH)Fe} systems. This is due to the long distances between the iron center embedded in the POM and the oxygen atom of the POM bridging the two magnetic centers, but also, as shown by DFT calculations, to the important mixing of bridging oxygen orbitals with orbitals of the POM tungsten atoms. The complexes [Hdmbpy](2)[Fe(II)(dmbpy)(3)](2)[(PW(11)O(39))(2)Fe(4) (III)O(2)(dmbpy)(4)]14 H(2)O (2) (dmbpy=5,5'-dimethyl-2,2'-bipyridine) and H(2)[Fe(II)(dmbpy)(3)](2)[(PW(11)O(39))(2)Fe(4) (III)O(2)(dmbpy)(4)]10 H(2)O (3) represent the first butterfly-like POM complexes. In these species, a tetranuclear Fe(III) complex is sandwiched between two lacunary polyoxotungstates that are pentacoordinated to two Fe(III) cations, the remaining paramagnetic centers each being coordinated to two dmbpy ligands. The best fit of the chi(M)T=f(T) curve leads to J(wb)=-59.6 cm(-1) and J(bb)=-10.2 cm(-1) (H=-J(wb)(S(1)S(2)+S(1)S(2*)+S(1*)S(2)+S(1*)S(2*))-J(bb)(S(2)S(2*))). While the J(bb) value is within the range of related exchange parameters previously reported for non-POM butterfly systems, the J(wb) constant is significantly lower. As for complex 1, this can be justified considering Fe(w)--O distances. Finally, in the absence of a coordinating ligand, the dimeric complex [N(CH(3))(4)](10)[(PW(11)O(39)Fe(III))(2)O]12 H(2)O (4) has been isolated. In this complex, the two single oxo-bridged Fe(III) centers are very strongly antiferromagnetically coupled (J=-211.7 cm(-1), H=-JS(1)S(2)). The electrochemical behavior of compound 1 both in dimethyl sulfoxide (DMSO) and in the solid state is also presented, while the electrochemical properties of complex 2, which is insoluble in common solvents, have been studied in the solid state.     

Vorticity: Simplifying the analysis of the current density

The induced current density ( J ( r )) provides useful information about the electronic structure of molecules under a magnetic field ( B ). However, the analysis of its topology is cumbersome because of its vectorial nature. We show that its tropicity (direction of rotation) and its strength can be compressed in the triple product B ⋅ ∇ × J ( r ) (tp J ( r )) that is a scalar field. The topology of tp J ( r ) has clear similarities to the Laplacian of the electron density. Additionally, the topology of aromatic and antiaromatic compounds is notoriously different. The vorticity of J ( r ) is helpful to define the circulation of the current density, C, that contrary to other methods, can be easily defined for individual rings in polycyclic molecules. This allows tp J ( r ) to clearly reproduce the Clar's structure of polycyclic aromatic hydrocarbons. © 2019 Wiley Periodicals, Inc.     

Electronic structure,magnetic properties,and mixed valence character of Ce2Ni3Si5 from first principles calculations

Cerium intermetallic compounds exhibit anomalous physical properties such as heavy fermion and Kondo behaviors. Here, an ab initio study of the electronic structure, magnetic properties, and mixed valence character of Ce₂Ni₃Si₅ using density functional theory (DFT) is presented. Two theoretical methods, including pure Perdew–Burke–Ernzerhof (PBE) and PBE + U , are used. In this study, Ce³⁺ and Ce⁴⁺ are considered as two different constituents in the unit cell. The formation energy calculations on the DFT level propose that Ce is in a stable mixed valence of 3.379 at 0 K. The calculated electronic structure shows that Ce₂Ni₃Si₅ is a metallic compound with a contribution at the Fermi level from Ce 4f and Ni 3d states. With the inclusion of the effective Hubbard parameter (U _eff), the five valence electrons of 5 Ce³⁺ ions are distributed only on Ce³⁺ 4f orbitals. Therefore, the occupied Ce³⁺ 4f band is located in the valence band (VB) while Ce⁴⁺ 4f orbitals are empty and Located at the Fermi level. The calculated magnetic moment in Ce₂Ni₃Si₅ is only due to cerium (Ce³⁺) in good agreement with the experimental results. The U _eff value of 5.4 eV provides a reasonable magnetic moment of 0.981 for the unpaired electron per Ce³⁺ ion. These results may serve as a guide for studying present mixed valence cerium‐based compounds. © 2017 Wiley Periodicals, Inc.     

Novel method of self‐interaction corrections in density functional calculations

It is demonstrated that the commonly applied self‐interaction correction (SIC) used in density functional theory does not remove all self‐interaction. We present as an alternative a novel method that, by construction, is totally free from self‐interaction. The method has the correct asymptotic 1/r dependence. We apply the new theory to localized f electrons in praseodymium and compare with the old version of SIC, the local density approximation (LDA) and with an atomic Hartree–Fock calculation. The results show a lowering of the f level, a contraction of the f electron cloud and a lowering of the total energy by 13 eV per 4 f electron compared to LDA. The equilibrium volume of the new SIC method is close to the ones given by LDA and the older SIC method and is in good agreement with experiment. The experimental cohesive energy is in better agreement using the new SIC method, both compared to LDA and another SIC method. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 247–252, 2001     

Gauge invariant calculations of nuclear magnetic shielding constants using the continuous transformation of the origin of the current density approach. II. Density functional and coupled cluster theory

The quantum mechanical current density induced in a molecule by an external magnetic field is invariant to translations of the coordinate system. This fundamental symmetry is exploited to formally annihilate the diamagnetic contribution to the current density via the approach of "continuous transformation of the origin of the current density-diamagnetic zero" (CTOCD-DZ). The relationships obtained by this method for the magnetic shielding at the nuclei are intrinsically independent of the origin of the coordinate system for any approximate computational scheme relying on the algebraic approximation. The authors report for the first time an extended series of origin-independent estimates of nuclear magnetic shielding constants using the CTOCD-DZ approach at the level of density functional theory (DFT) with four different types of functionals and unrelaxed coupled cluster singles and doubles linear response (CCSD-LR) theory. The results obtained indicate that in the case of DFT the procedure employed is competitive with currently adopted computational methods allowing for basis sets of gauge-including atomic orbitals, whereas larger differences between CTOCD-DZ and common origin CCSD-LR results are observed due to the incomplete fulfillment of hypervirial relations in standard CCSD-LR theory. It was found furthermore that the unrelaxed CCSD-LR calculations predict larger correlation corrections for the shielding constants of almost all nonhydrogen atoms in their set of molecules than the usual relaxed energy derivative CCSD calculations. Finally the results confirm the excellent performance of Keal and Tozer's third functional, in particular, for the multiply bonded systems with a lot of electron correlation, but find also that the simple local density functional gives even better results for the few singly bonded molecules in their study where correlation effects are small.     

Analytical formulas for the magnetic field produced by a spin or a paramagnetic current density in the case of Gaussian basis functions

We present a derivation of simple formulas for the evaluation at any point of space of the magnetic field produced by a spin or a paramagnetic orbital current when Cartesian Gaussian basis functions are used, as is often the case in quantum chemistry. These formulas can be useful to plot the magnetic field vector density obtained from ab initio calculations or from a density operator fitted on experimental data. The magnetic field density is the observable probed in polarized neutron diffraction (PND) experiment, for it is, in fact, with this quantity that the neutron spins interact and not with the spin or magnetization density. The formulas make extensive use of the confluent hypergeometric function. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 11–15, 2001     

Experimental and theoretical studies on the magnetic properties of manganese(II) compounds with mixed isocyanate and carboxylate bridges

Two manganese(II) isocyanate complexes with different flexible zwitterionic dicarboxylate ligands, [Mn(2)(bcpp)(NCO)(4)](n) (1; bcpp=1,3-bis(N-carboxylatomethyl-4-pyridinio)propane) and [Mn(2)(bcp)(NCO)(4)](n) (2; bcp=bis(N-carboxylatomethyl)-4,4'-bipyridinium, have been synthesized and characterized by X-ray crystallography and magnetic measurements. Both compounds consist of two-dimensional coordination layers in which uniform anionic chains with mixed (NCO)(2)(COO) triple bridges are cross-linked by flexible cationic 4,4'-trimethylenedipyridinium spacers. Magnetic studies revealed antiferromagnetic interactions through the triple bridges (J=-8.0 cm(-1) (1) and J=-8.6 cm(-1) (2)), which are stronger than those in the isoelectronic analogue (N(3))(2)(COO). To complement the experimental data, periodic and finite-cluster DFT and CASPT2 calculations were performed on the dimeric units of the (NCO)(2)(COO) and (N(3))(2)(COO) mixed-bridged systems to support the Heisenberg picture and stress the relative efficiency of the magnetic couplers. It was found that the isocyanate ligand plays a greater role in the conveyance of antiferromagnetic behavior than the azide counterpart, and that both pseudohalide bridges function cooperatively with the carboxylate group.     

Origin‐independent sum over states simulations of magnetic and electronic circular dichroism spectra via the localized orbital/local origin method

Although electronic and magnetic circular dichroism (ECD, MCD) spectra reveal valuable details about molecular geometry and electronic structure, quantum‐chemical simulations significantly facilitate their interpretation. However, the simulated results may depend on the choice of coordinate origin. Previously (?těpánek and Bou?, J. Comput. Chem. 2013, 34, 1531), the sum‐over‐states (SOS) methodology was found useful for efficient MCD computations. Approximate wave functions were “resolved” using time‐dependent density functional theory, and the origin‐dependence was avoided by placing the origin to the center of mass of the investigated molecule. In this study, a more elegant way is proposed, based on the localized orbital/local origin (LORG) formalism, and a similar approach is also applied to generate ECD intensities. The LORG‐like approach yields fully origin‐independent ECD and MCD spectra. The results thus indicate that the computationally relatively cheap SOS simulations open a new way of modeling molecular properties, including those involving the origin‐dependent magnetic dipole moment operator. © 2015 Wiley Periodicals, Inc.     

Predicting the redox properties of uranyl complexes using electronic structure calculations

A plethora of chemical reactions is redox driven processes. The conversion of toxic and highly soluble U(VI) complexes to nontoxic and insoluble U(IV) form are carried out through proton coupled electron transfer by iron containing cytochromes and mineral surfaces such as machinawite. This redox process takes place through the formation of U(V) species which is unstable and immediately undergo the disproportionation reaction. Thus, theoretical methods are extremely useful to understand the reduction process of U(VI) to U(V) species. We here have carried out the structures and reduction properties of several U(VI) to U(V) complexes using a variety of electronic structure methods. Due to the lack of experimental ionization energies for uranyl (UO₂(V)‐UO₂(VI)) couple, we have benchmarked the current and popularly used density functionals and cost effective ab initio methods against the experimental electron detachment energies of [UO₂F₄]^1‐/2‐ and [UO₂Cl₄]^1‐/2‐. We find that electron detachment energy of U(VI) predicted by RI‐MP2 level on the BP86 geometries correlate nicely with the experimental and CCSD(T) data. Based on our benchmark studies, we have predicted the structures and electron detachment energies of U(V) to U(VI) species for a series of uranium complexes at the RI‐MP2//BP86 level which are experimentally inaccessible till date. We find that the redox active molecular orbital is ligand centered for the oxidation of U(VI) species, where it is metal centered (primarily f‐orbital) for the oxidation of U(V) species. Finally, we have also calculated the detachment energies of a known uranyl [UO₂]¹⁺ complex whose X‐ray crystal structures of both oxidation states are available. The large bulky nature of the ligand stabilizing the uncommon U(V) species which cannot be routinely studied by present day CCSD(T) methods as the system size are more than 20–30 atoms. The success of our efficient computational strategy can be experimentally verified in the near future for the complex as the structures are stable in gas phase which can undergo oxidation.     

On the magnetic properties of Lithium Vanadium Bronzes LixV2O5

Magnetic susceptibility of V₂O₅ and of the α-, ?-, δ- and γ-Li_xV₂O₅ bronzes prepared either at high or at room temperature has been measured between liquid helium and ambient temperature. The results are representative of the localized character of the V⁴⁺ ion d-electron and, for high enough x-values, of the existence of antiferromagnetic interactions in a low dimensional system. The intrachain exchange integral J has been determined using the Bonner/Fischer model for Heisenberg chains with S = 1/2 spin. It is larger for the γ- than for the δ-phase. This result as well as the occurrence of long range ordering below T_N ≈ 130 K in the γ-phase may be ascribed to ordering of V⁴⁺ and V⁵⁺ ions in the former bronze and to the random distribution of V⁴⁺ ions in the latter one.     

Theoretical study of the magnetic behavior of ferric wheels.

Calculations of exchange coupling constants (J) based on density functional theory for eight complete, nonmodeled ferric wheels have been performed, and a comparison with the values obtained from magnetic susceptibility data is presented. The calculated J values obtained with a generalized-gradient approximation (GGA) functional are in good agreement with the experiment probably because the inclusion of pseudopotentials partially compensates the overestimation of the spin delocalization. The magnetostructural correlation obtained shows a strong dependence of the exchange coupling on both the Fe-O-Fe bond angle and the Fe-O bond distance. This correlation holds for both the ferric wheels and the alkoxo-bridged Fe(III) dinuclear complexes reported in the literature.     

Electron delocalization and electrostatic repulsion at the origin of the strong spin coupling in mixed-valence keggin polyoxometalates: ab initio calculations of the one- and two-electron processes

We present here a general theoretical procedure to treat the problem of electron delocalization and magnetic interactions in high-nuclearity mixed valence clusters based on polyoxometalates. The main interactions between the delocalized electrons of mixed-valence polyoxometalate anions are extracted from valence spectroscopy ab initio calculations on embedded fragments. Electron transfer, magnetic coupling and exchange transfer parameters between nearest and next-nearest-neighbor metal ions, as well as the value of the electrostatic repulsion between pairs of metal ions are determined. These parameters are introduced in a model Hamiltonian that considers the whole anion. It thus provides macroscopic properties that should be compared with the experimental data. This method is applied to a two-electron-reduced polyoxowolframate Keggin anion. The results demonstrate that the electron transfer processes, combined with the Coulombic repulsion between the "extra" electrons, induce a strong antiferromagnetic coupling between the two delocalized spins providing a definite explanation of the diamagnetic properties of these high nuclearity mixed-valence clusters.     

The ring current model of the pentaprismane molecule

Three-dimensional models of the quantum-mechanical current density J(B) , induced in the electron cloud of the C(10)H(10) pentaprismane molecule by a magnetic field B applied along the C(5) (a C(2)) symmetry axis, orthogonal to the pentagonal (a rectangular) face, and denoted by B(‖) (B(⊥)), have been constructed. Predictions of near Hartree-Fock quality are reported for the diagonal components of magnetic tensors, magnetizability (ξ), nuclear shielding of carbon (σ(C)) and hydrogen (σ(H)), and virtual shielding at the center of mass (σ(CM)). The complicated spatial features of the induced electronic current-density field have been rationalized and compactly described via stagnation graphs that elucidate the details of its topological structure. A representation of J(B) is obtained by three-dimensional perspective plots and by planar maps visualizing phase portraits of electron flow in a series of molecular domains. Both streamline J(B) /|J(B) | and modulus |J(B) | are analyzed. These graphic tools illustrate the competition between diatropic and paratropic regimes which determine the magnitude of various components of magnetizability and magnetic shielding of hydrogen and carbon nuclei. Shielding density maps show that the differential Biot-Savart law explains magnetic shielding at hydrogen and carbon nuclei, and virtual shielding at ring and cage centers. Similarities and/or contrasting ring current effects on magnetotropicity are discussed by a comparison with triprismane C(6)H(6) and cubane C(8)H(8) .     

反式-双(二甲基苯膦)铂配合物二阶非线性光学性质的密度泛函理论研究

采用密度泛函理论B3LYP方法,在6-31G(d)的水平上对两种反式-双(二甲基苯膦)铂配合物的几何构型进行优化,在获得稳定构型基础上,利用TD-B3LYP方法得到体系的UV-Vis吸收光谱,并用有限场(FF/B3LYP)方法探讨体系的二阶非线性光学性质(NLO).结果表明,此类铂配合物具有较大的二阶极化率,以及在可见光范围内透明等优点,是具有很好应用前景的非线性光学材料.     

DFT description of the electronic structure and spectromagnetic properties of strongly correlated electronic systems: NiII, CuII and ZnII o-dioxolene complexes

The spectroscopic and magnetic properties of dioxolene complexes of zinc, copper and nickel were studied by DFT calculations on model complexes of formulas [(NH(3))(4)M(II)(SQ)](+) (M=Zn, Ni; SQ=semiquinonato) and [(NH(3))(2)Cu(II)(SQ)](+). Standard approaches such as time-dependent DFT (TDDFT), the Slater transition state (STS), and broken symmetry (BS) were found to be unable to completely account for the physical properties of the systems, and complete active space-configuration interaction (CAS-CI) calculations based on the Kohn-Sham (KS) orbitals was applied. The CAS-CI energies, properly corrected with multireference perturbation theory (MR-PT), were found to be in good agreement with experimental data. We present here a calculation protocol that has a low CPU cost/accuracy ratio and seems to be very promising for interpreting the properties of strongly correlated electronic systems in complexes of real chemical size.