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     

Fluoride‐Bridged {GdIII3MIII2} (M=Cr,Fe, Ga) Molecular Magnetic Refrigerants

The reaction of fac‐[M^IIIF₃(Me₃tacn)]?x H₂O with Gd(NO₃)₃?5H₂O affords a series of fluoride‐bridged, trigonal bipyramidal {Gd^III₃M^III₂} (M=Cr ( 1 ), Fe ( 2 ), Ga ( 3 )) complexes without signs of concomitant GdF₃ formation, thereby demonstrating the applicability even of labile fluoride‐complexes as precursors for 3d–4f systems. Molecular geometry enforces weak exchange interactions, which is rationalized computationally. This, in conjunction with a lightweight ligand sphere, gives rise to large magnetic entropy changes of 38.3 J kg^?1 K^?1 ( 1 ) and 33.1 J kg^?1 K^?1 ( 2 ) for the field change 7 T→0 T. Interestingly, the entropy change, and the magnetocaloric effect, are smaller in 2 than in 1 despite the larger spin ground state of the former secured by intramolecular Fe–Gd ferromagnetic interactions. This observation underlines the necessity of controlling not only the ground state but also close‐lying excited states for successful design of molecular refrigerants.     

Benchmarking of density functionals for a soft but accurate prediction and assignment of 1H and 13C NMR chemical shifts in organic and biological molecules

A number of programs and tools that simulate ¹H and ¹³C nuclear magnetic resonance (NMR) chemical shifts using empirical approaches are available. These tools are user‐friendly, but they provide a very rough (and sometimes misleading) estimation of the NMR properties, especially for complex systems. Rigorous and reliable ways to predict and interpret NMR properties of simple and complex systems are available in many popular computational program packages. Nevertheless, experimentalists keep relying on these “unreliable” tools in their daily work because, to have a sufficiently high accuracy, these rigorous quantum mechanical methods need high levels of theory. An alternative, efficient, semi‐empirical approach has been proposed by Bally, Rablen, Tantillo, and coworkers. This idea consists of creating linear calibrations models, on the basis of the application of different combinations of functionals and basis sets. Following this approach, the predictive capability of a wider range of popular functionals was systematically investigated and tested. The NMR chemical shifts were computed in solvated phase at density functional theory level, using 30 different functionals coupled with three different triple–ζ basis sets. © 2016 Wiley Periodicals, Inc.     

Systematic studies on the computation of nuclear magnetic resonance shielding constants and chemical shifts: the density functional models

We present a systematic density functional investigation on the prediction of the 13C, 15N, 17O, and 19F NMR properties of 23 molecules with 21 density functionals. Extensive comparisons are made for both 13C magnetic shieldings and chemical shifts with respect to the gas phase experimental data and the best CCSD(T) results. We find that the OPBE and OPW91 exchange-correlation functionals perform significantly better than some popular functionals such as B3LYP and PBE1PBE, even surpassing, in many cases, the standard wavefunction-based method MP2. Further analysis has been performed to explore the individual role played by various exchange and correlation functionals. We find that the B88 and PBE exchange functionals have a too strong tendency of deshielding, leading to too deshielded magnetic shielding constants; whereas the OPTX exchange functional performs remarkably well. We claim that the main source of error arises from the exchange functional, but correlation functional also makes important contribution. We find that the correlation functionals may be grouped into two classes. class A, such as LYP and B98, leads to deshielded NMR values, deteriorating the overall performance; whereas class B, such as PW91 and PBE, generally increases the absolute shieldings, which complements the exchange functionals, leading to improved results in the calculation of NMR data.     

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     

荷电(±1)对二十面体X_(13)(X=Cr,Mn,Fe,Co)团簇的稳定性与磁性的影响

采用基于密度泛函理论的计算方法,对正二十面体金属X13(X=Cr,Mn,Fe,Co)中性和荷电团簇进行了全面的结构优化计算,研究了荷电对团簇的稳定性和磁性的影响.结果表明:荷负电能够使团簇的稳定性增强;荷电对不同团簇的原子间距离的影响不同;同时荷电对不同团簇磁性的影响也是不一样的,尤其是荷负电能够使Fe13和Co13团簇的磁性大大增强;荷电对不同团簇磁性的影响不是通过原子间距离的变化来实现的,而是受到原子内部电荷的转移和杂化程度的影响.     

Cyano-bridged Ln^3＋-Cr^3＋ Binuclear Complexes [Ln（L）x（H2O）y^- Cr（CN）6]·mL·nH2O （Ln=La-Nd,x=5, y=2, m=1 or 2, n=2 or 2.5; Ln-Sm-Dy,Er, x=4, y=3, m=0, n=1.5 or 2.0; L= 2-pyrrolidinone）： Structure,Magnetism and Spin Density Map

In order to shed light upon the nature and mechanism of 4f-3d magnetic exchange interactions, a series of binuclear complexes of lanthanide（3＋） and chromium（3＋） with the general formula [Ln（L）5（H2O）2Cr（CN）6]·mL· nH2O （Ln=La （1）, Ce （2）, Pr （3）, Nd （4）; x=5, y=2, m=1 or 2, n=2 or 2.5; L=2-pyrrolidinone） and [Ln（L）4（H2O）3Cr（CN）6] ·nH2O （Ln=Sm （5）, Eu （6）, Gd （7）, Tb （8）, Dy （9）, Er （10）; x=4, y=3, m=0, n= 1.5 or 2.0; L=2-pyrrolidinone） were prepared and the X-ray crystal structures of complexes 2, 6 and 7 were determined. All the compounds consist of a Ln-CN-Cr unit, in which Ln^3＋ in a square antiprism environment is bridged to an octahedral coordinated Cr^3＋ ion through a cyano group. The magnetic properties of the complexes 3 and 6-10 show an overall antiferromagnetic behavior. The fitting to the experimental magnetic susceptibilities of 7 give g= 1.98, J=0.40 cm^-1, zJ＇= -0.21 cm^-1 on the basis of a binuclear spin system （Scd=7/2, Scr=3/2）, revealing an intra-molecular Gd^3＋-Cr^3＋ ferromagnetic interaction and an inter-molecular antiferromagnetic interaction. For 7 the calculation of quantum chemical density functional theory （DFT）, combined with the broken symmetry approach, showed that the calculated spin coupling constant was 20.3 cm^-1, supporting the observation of weak ferromagnetic intra-molecular interaction in 7. The spin density distributions of 7 in both the high spin ground state and the broken symmetry state were obtained, and the spin coupling mechanism between Gd^3＋ and Cr^3＋ was discussed.     

Systematic investigation on the geometric dependence of the calculated nuclear magnetic shielding constants

We perform a systematic examination on the dependence of the calculated nuclear magnetic shielding constants on the chosen geometry for a selective set of density functional methods of B3LYP, PBE0, and OPBE. We find that the OPBE exchange-correlation functional performs remarkably well when either the optimized geometries or the experimental geometries are used. The popular B3LYP and PBE0 functionals have a clear tendency of deshielding, giving shieldings that are usually too low and shifts that are usually too high, at the experimental geometries. Combined with the Hartree-Fock geometries, however, much improved magnetic constants are obtained for B3LYP and PBE0, due to the compensation effect from the systematic underestimation of bond lengths by the Hartree-Fock method.     

Electronic properties and 1/3 magnetization plateau of the S=1/2 magnetism Cu3(P2O6OH)2

First, the geometrical structure, energy band structure, density of states, and overlap population of the copper hydroxydiphosphate ( ) are investigated systematically using the first‐principles density functional method. The generalized gradient approximations (GGA)+U method is adopted to consider the on‐site coulomb repulsion on Cu 3d orbits. The theoretical structural results obtained by the geometry optimization agree well with the experimental data. Energy band structures show that the belongs to a semiconductor. It is found that the on‐site Coulomb repulsion plays a key role in the opening of the energy gap. The uppest valence band is found to be mainly contributed from O 2p and Cu 3d states, but the lowest conduction band is characterized by Cu 3d state. Furthermore, a strong hybridization between O‐2p and Cu‐3d orbits is observed. Then, the magnetization, bipartite entanglement, and the nearest‐neighbor correlations in such a cuprate are calculated by the infinite time‐evolving block decimation algorithm. Distinctive magnetization plateaus accompanied with some interesting bipartite entanglement and correlation plateaus are observed at T=0 k in the thermodynamic limit. © 2014 Wiley Periodicals, Inc.     

Magnetic Relaxation in Single‐Electron Single‐Ion Cerium(III) Magnets: Insights from Ab Initio Calculations

Detailed ab initio calculations were performed on two structurally different cerium(III) single‐molecule magnets (SMMs) to probe the origin of magnetic anisotropy and to understand the mechanism of magnetic relaxations. The complexes [Ce^III{Zn^II(L)}₂(MeOH)]BPh₄ ( 1 ) and [Li(dme)₃][Ce^III(cot′′)₂] ( 1 ; L=N,N,O,O‐tetradentate Schiff base ligand; 2 ; DME=dimethoxyethane, COT′′=1,4‐bis(trimethylsilyl)cyclooctatetraenyldianion), which are reported to be zero‐field and field‐induced SMMs with effective barrier heights of 21.2 and 30 K respectively, were chosen as examples. CASSCF+RASSI/SINGLE_ANISO calculations unequivocally suggest that m_J|±5/2〉 and |±1/2〉 are the ground states for complexes 1 and 2 , respectively. The origin of these differences is rooted back to the nature of the ligand field and the symmetry around the cerium(III) ions. Ab initio magnetisation blockade barriers constructed for complexes 1 and 2 expose a contrasting energy‐level pattern with significant quantum tunnelling of magnetisation between the ground state Kramers doublet in complex 2 . Calculations performed on several model complexes stress the need for a suitable ligand environment and high symmetry around the cerium(III) ions to obtain a large effective barrier.     

Density functional study of magnetic exchange of dinuclear manganese complexes with the heteropoly-molyanion:[Mn~(II)_2(X~(n )Mo_9O_(33))_2]~(2(n-10)-) (X=P~V, As~V, Se~VI)

The magnetic exchange interactions between the dimanganese(II)-substituted complexes and the het-eropolymolyanion, [MnII2(Xn Mo9O33)2]2(n-10)-(X = PV(I), AsV(II) and SeVI(III)), are investigated by using density functional theory combined with broken-symmetry approach (DFT-BS) method. The calculated magnetic exchange coupling constant (J) of complex II is in reasonable agreement with the responding experimental value and the negative J values indicate that antiferromagnetic exchange interactions exist in these complexes. Furthermore, the influence of the central heteroatom on the exchange cou-pling within the dimanganese core unit is studied from standpoints of geometry, spin density and fron-tier orbitals. It demonstrates that the change of the heteroatom X via PV-AsV-SeVI elongates the dis-tances of Mn1···Mn2 and shortens the distances of Ob···Ob, and reduces the effectiveness of the super-exchange pathways, consequently, decreasing the magnitude of the antiferromagnetic coupling constant, J, of these species.     

A dissected ring current model for assessing magnetic aromaticity: a general approach for both organic and inorganic rings

A model based on classical electrodynamics is used to measure the strength of ring currents of different molecular orbitals, i.e., σ- and π-orbitals, and characteristics of ring current loops, i.e., ring current radii and height of current loops above/below the ring planes, among a number of organic as well as inorganic molecules. For the π-current, the present model represents an improvement of previous approaches to determine ring current intensity. It is proven that the present model is more precise than previous models as they could not explain presence of the minimum in the plot of NICS(πzz) versus distance close to the ring plane. Variations in the charge of molecules and the types of constituent atoms of each species affect the ring current radii of both σ- and π-current loops as well as the height of π-current loops above/below the ring plane. It is suggested that variation in the distribution of the one-electron density in different systems is the main source of differences of the ring current characteristics.     

Organic-inorganic hybrids based on novel bimolecular [Si2W22Cu2O78(H2O)]12- polyoxometalates and the polynuclear complex cations [Cu(ac)(phen)(H2O)]n n+ (n=2, 3)

The reaction of a monosubstituted Keggin polyoxometalate (POM) generated in situ with copper-phenanthroline complexes in excess ammonium or rubidium acetate led to the formation of the hybrid metal organic-inorganic compounds A7[Cu2(ac)2(phen)2(H2O)2][Cu3(ac)3(phen)3(H2O)3][Si2W22Cu2O78(H2O)].approximately 18 H2O (A=NH4+ (1), Rb+ (2); ac=acetate; phen=1,10-phenanthroline). These compounds are constructed from inorganic and metalorganic interpenetrated sublattices containing the novel bimolecular Keggin POM, [Si2W22Cu2O78(H2O)]12-, and Cu-ac-phen complexes, [Cu(ac)(phen)(H2O)]n n+ (n=2, 3). The packing of compound 1 can be viewed as a stacking of open-framework layers parallel to the xy plane built of hydrogen-bonded POMs, and zigzag columns of pi-stacked Cu-ac-phen complex cations running along the [111] direction. Magnetic and EPR results are discussed with respect to the crystal structure of the compounds. DFT calculations on [Cu(ac)(phen)(H2O)]n n+ cationic complexes have been performed, to check the influence of packing in the complex geometry and determine the magnetic exchange pathways.     

Density functional study of magnetic exchange of dinuclear manganese complexes with the heteropolymolyanion: [MnII2(X n +Mo9O33)2]2( n ?10)? (X = PV, AsV, SeVI)

The magnetic exchange interactions between the dimanganese(II)-substituted complexes and the heteropolymolyanion, [Mn^II ₂(X ⁿ⁺Mo₉O₃₃)₂]^2(n−10)− (X = P^V(I), As^V(II) and Se^VI(III)), are investigated by using density functional theory combined with broken-symmetry approach (DFT-BS) method. The calculated magnetic exchange coupling constant (J) of complex II is in reasonable agreement with the responding experimental value and the negative J values indicate that antiferromagnetic exchange interactions exist in these complexes. Furthermore, the influence of the central heteroatom on the exchange coupling within the dimanganese core unit is studied from standpoints of geometry, spin density and frontier orbitals. It demonstrates that the change of the heteroatom X via P^V-As^V-Se^VI elongates the distances of Mn₁...Mn₂ and shortens the distances of O_b...O_b, and reduces the effectiveness of the superexchange pathways, consequently, decreasing the magnitude of the antiferromagnetic coupling constant, J, of these species. Supported by the National Natural Science Foundation of China (Grant No. 20703008) and Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT0714)     

A New Quantum Chemical Approach to the Magnetic Properties of Oligonuclear Transition‐Metal Complexes: Application to a Model for the Tetranuclear Manganese Cluster of Photosystem II

Broken‐symmetry DFT calculations on transition‐metal clusters with more than two centers allow the hyperfine coupling constants to be extracted. Application of the proposed theoretical scheme to a tetranuclear manganese complex that models the S₂ state of the oxygen‐evolving complex of photosystem II yields hyperfine parameters that can be directly compared with experimental data. The picture shows the metal–oxo core of the model and the following parameters; exchange coupling constant J_ij, the expectation value of the site‐spin operator , and the isotropic hyperfine coupling parameters.

     

Probing the Local Magnetic Structure of the [FeIII(Tp)(CN)3]− Building Block Via Solid-State NMR Spectroscopy,Polarized Neutron Diffraction,and First-Principle Calculations

The local magnetic structure in the [Fe^III(Tp)(CN)₃]⁻ building block was investigated by combining paramagnetic Nuclear Magnetic Resonance (pNMR) spectroscopy and polarized neutron diffraction (PND) with first-principle calculations. The use of the pNMR and PND experimental techniques revealed the extension of spin-density from the metal to the ligands, as well as the different spin mechanisms that take place in the cyanido ligands: Spin-polarization on the carbon atoms and spin-delocalization on the nitrogen atoms. The results of our combined density functional theory (DFT) and multireference calculations were found in good agreement with the PND results and the experimental NMR chemical shifts. Moreover, the ab-initio calculations allowed us to connect the experimental spin-density map characterized by PND and the suggested distribution of the spin-density on the ligands observed by NMR spectroscopy. Interestingly, significant differences were observed between the pseudo-contact contributions of the chemical shifts obtained by theoretical calculations and the values derived from NMR spectroscopy using a simple point-dipole model. These discrepancies underline the limitation of the point-dipole model and the need for more elaborate approaches to break down the experimental pNMR chemical shifts into contact and pseudo-contact contributions.     

Ring Currents in Benzo‐ and Benzocyclobutadieno‐Annelated Biphenylene Derivatives

The effect of benzo and benzocyclobutadieno annelation on the current density induced in a series of biphenylene derivatives is examined at the B3LYP/cc‐pVDZ level of theory, by using the CTOCD‐DZ method. Angular benzo annelation increases, whereas linear benzo annelation decreases the intensity of paratropic (antiaromatic) current density along the four‐membered ring of biphenylene. The opposite effect is found for benzocyclobutadieno annelation. It is shown that the extent of local aromaticity of the four‐membered ring in biphenylene congeners can vary from highly antiaromatic to nonaromatic, as a result of different modes of annelation.     

Impact of Tube Curvature on the Ground‐State Magnetism of Axially Confined Single‐Walled Carbon Nanotubes of the Zigzag‐Type

The magnetic properties of axially confined, hydrogenated single‐walled carbon nanotubes (SWCNTs) of the (n,0)‐type with n=5–24 are systematically explored by density functional theory. Emphasis is placed on the relation between the ground‐state magnetic moments of SWCNTs and zigzag graphene nanoribbons (ZGNRs). Comparison between the SWCNTs considered here and ZGNRs of equal length gives rise to two basic questions: 1) how does the nanotube curvature affect the antiferromagnetic order known to prevail for ZGNRs, and 2) to what extent do the magnetic moments localized at the SWCNT edges deviate from the zero‐curvature limit of n/3 μ_B? In response to these questions, it is found that systems with n≥7 display preference for antiferromagnetic order at any length investigated, whereas for n=5, 6 the magnetic phase varies with tube length. Furthermore, elementary patterns are identified that describe the progression of the magnitude of the magnetic moment with n for the longest tubes explored in this work. The spin densities of the considered SWCNTs are analyzed as a function of the tube length L, with L ranging from 3 to 11 transpolyene rings for n≥7 and from 3 to 30 rings for n=5 and 6.