Computational NMR coupling constants: Shifting and scaling factors for evaluating 1JCH

Optimized shifting and/or scaling factors for calculating one‐bond carbon–hydrogen spin–spin coupling constants have been determined for 35 combinations of representative functionals (PBE, B3LYP, B3P86, B97‐2 and M06‐L) and basis sets (TZVP, HIII‐su3, EPR‐III, aug‐cc‐pVTZ‐J, ccJ‐pVDZ, ccJ‐pVTZ, ccJ‐pVQZ, pcJ‐2 and pcJ‐3) using 68 organic molecular systems with 88 ¹J_CH couplings including different types of hybridized carbon atoms. Density functional theory assessment for the determination of ¹J_CH coupling constants is examined, comparing the computed and experimental values. The use of shifting constants for obtaining the calculated coupling improves substantially the results, and most models become qualitatively similar. Thus, for the whole set of couplings and for all approaches excluding those using the M06 functional, the root‐mean‐square deviations lie between 4.7 and 16.4 Hz and are reduced to 4–6.5 Hz when shifting constants are considered. Alternatively, when a specific rovibrational contribution of 5 Hz is subtracted from the experimental values, good results are obtained with PBE, B3P86 and B97‐2 functionals in combination with HIII‐su3, aug‐cc‐pVTZ‐J and pcJ‐2 basis sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Performance of range‐separated hybrid exchange–correlation functionals for the calculation of magnetic exchange coupling constants of organic diradicals

The prediction of magnetic behavior is important for the design of new magnetic materials. Kohn–Sham density functional theory is popular for this purpose, although one should be careful about choosing the right exchange–correlation functional. Here, we perform a statistical analysis to test different range‐separated hybrid density functionals for the calculation of magnetic exchange coupling constants J of fourteen organic diradicals. Our analysis suggests that in absolute terms the MN12SX functional performs best among the series of twelve functionals studied here (including the popular B3LYP), followed by N12SX functionals along with Scuseria's HSE series of functionals. LC‐ PBE was found to be the least accurate, which is in contrast with its good performance for calculating J for transition metal complexes. The HSE family of functionals and B3LYP are the only functionals to reproduce the qualitative trends of the coupling constants correctly for the ferromagnetically coupled diradicals under study. © 2017 Wiley Periodicals, Inc.     

Which density functional is close to CCSD accuracy to describe geometry and interaction energy of small noncovalent dimers? A benchmark study using Gaussian09

A benchmark study on all possible density functional theory (DFT) methods in Gaussian09 is done to locate functionals that agree well with CCSD/aug‐cc‐pVTZ geometry and Ave‐CCSD(T)/(Q‐T) interaction energy (E_int) for small non‐covalently interacting molecular dimers in “dispersion‐dominated” (class 1), “dipole‐induced dipole” (class 2), and “dipole‐dipole” (class 3) classes. A DFT method is recommended acceptable if the geometry showed close agreement to CCSD result (RMSD < 0.045) and E_int was within 80–120% accuracy. Among 382 tested functionals, 1–46% gave good geometry, 13–44% gave good E_int, while 1–33% satisfied geometry and energy criteria. Further screening to locate the best performing functionals for all the three classes was made by counting the acceptable values of energy and geometry given by each functionals. The meta‐generalized gradient approximation (GGA) functional M06L was the best performer with total 14 hits; seven acceptable energies and seven acceptable geometries. This was the only functional “recommended” for at least two dimers in each class. The functionals M05, B2PLYPD, B971, mPW2PLYPD, PBEB95, and CAM‐B3LYP gave 11 hits while PBEhB95, PW91B95, Wb97x, BRxVP86, BRxP86, HSE2PBE, HSEh1PBE, PBE1PBE, PBEh1PBE, and PW91TPSS gave 10 hits. Among these, M05, B971, mPW2PLYPD, Wb97x, and PW91TPSS were among the “recommended” list of at least one dimer from each class. Long‐range correction (LC) of Hirao and coworkers to exchange‐correlation functionals showed massive improvement in geometry and E_int. The best performing LC‐functionals were LC‐G96KCIS and LC‐PKZBPKZB. Our results predict that M06L is the most trustworthy DFT method in Gaussian09 to study small non‐covalently interacting systems. © 2013 Wiley Periodicals, Inc.     

Assessing the performance of density functional theory for the dynamic polarizabilities of amino acids: Treatment of correlation and role of exact exchange

The theoretical determination of electric response properties of the biological systems is a field where the application of density functional theory (DFT) appears to be quite promising. In this work, the performance of 41 density functional methods is evaluated in predicting dynamic polarizabilities of an experimental benchmark set of 20 proteinogenic amino acids. The behavior of a large number of density functionals, including various types of the local spin density approximation (LSDA), generalized gradient approximation (GGA), meta‐GGA (m‐GGA), hybrid‐GGA (h‐GGA), hybrid meta‐GGA (hm‐GGA), and range‐separated hybrid‐GGA (rsh‐GGA), has been assessed for the purpose. Analyzing the results of our DFT benchmarking, we found that these computationally economical methods show very diverse predictive capability and a careful selection of DFT functionals is very important in the polarizability calculations. Considering the role of exchange, correlation, dispersion and long‐range corrections, it turned out that in the LSDA class, SVWN3 gives better results than SPL and SVWN5 toward the reference values. Of the GGA methods, OPBE outperforms all other functionals. The M06‐L is the best method of m‐GGA class. The B3LYP and TPSSh are the best functionals of h‐GGA and hm‐GGA lineages, respectively. Finally, CAM‐B3LYP is the best method of rsh‐GGA functionals that predicts the most accurate polarizability for amino acids by a large margin with respect to others. Overall, the best performing functionals turn out to be hm‐GGAs TPSSh, TPSS1KCIS, M05, tau‐HCTHhyb, and h‐GGA B3LYP. Hopefully, the results of this investigation might provide the useful guidance to propose a new exchange‐correlation functional for calculating the optical properties of biomolecular materials. © 2013 Wiley Periodicals, Inc.     

Effect of Inter‐Porphyrin Distance on Spin‐State in Diiron(III) μ‐Hydroxo Bisporphyrins

The synthesis, structure, and properties of bischloro, μ‐oxo, and a family of μ‐hydroxo complexes (with BF₄^?, SbF₆^?, and PF₆^? counteranions) of diethylpyrrole‐bridged diiron(III) bisporphyrins are reported. Spectroscopic characterization has revealed that the iron centers of the bischloro and μ‐oxo complexes are in the high‐spin state (S=⁵/₂). However, the two iron centers in the diiron(III) μ‐hydroxo complexes are equivalent with high spin (S=⁵/₂) in the solid state and an intermediate‐spin state (S=³/₂) in solution. The molecules have been compared with previously known diiron(III) μ‐hydroxo complexes of ethane‐bridged bisporphyrin, in which two different spin states of iron were stabilized under the influence of counteranions. The dimanganese(III) analogues were also synthesized and spectroscopically characterized. A comparison of the X‐ray structural parameters between diethylpyrrole and ethane‐bridged μ‐hydroxo bisporphyrins suggest an increased separation, and hence, less interactions between the two heme units of the former. As a result, unlike the ethane‐bridged μ‐hydroxo complex, both iron centers become equivalent in the diethylpyrrole‐bridged complex and their spin state remains unresponsive to the change in counteranion. The iron(III) centers of the diethylpyrrole‐bridged diiron(III) μ‐oxo bisporphyrin undergo very strong antiferromagnetic interactions (J=?137.7 cm^?1), although the coupling constant is reduced to only a weak value in the μ‐hydroxo complexes (J=?42.2, ?44.1, and ?42.4 cm^?1 for the BF₄, SbF₆, and PF₆ complexes, respectively).     

Performance of six functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in the simulation of vibrational and dielectric properties of crystalline compounds. The case of forsterite Mg2SiO4

The performance of six different density functionals (LDA, PBE, PBESOL, B3LYP, PBE0, and WC1LYP) in describing the infrared spectrum of forsterite, a crystalline periodic system with orthorhombic unit cell (28 atoms in the primitive cell, Pbmn space group), is investigated by using the periodic ab initio CRYSTAL09 code and an all‐electron Gaussian‐type basis set. The transverse optical (TO) branches of the 35 IR active modes are evaluated at the equilibrium geometry together with the oscillator strengths and the high‐frequency dielectric tensor ?_∞. These quantities are essential to compute the dielectric function ?(ν), and then the reflectance spectrum R(ν), which is compared with experiment. It turns out that hybrid functionals perform better than LDA and GGA, in general; that B3LYP overperforms WC1LYP and, in turn, PBE0; that PBESOL is better than PBE; that LDA is the worst performing functional among the six under study. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

聚合物{[CuII(Hpb) (mal)]H2O}n :单体的量子化学计算和磁性研究

{[Cu^Ⅱ（Hpb）（mal）]H=O}n （Hpb=2-2＇-pyridylbenzimidazole, mal=maleic acid） is a helical chain-like polymer complex. In order to investigate the electronic structure of the complex, the monomer Cu^Ⅱ（Hpb）（mal） was obturated with different functional groups respectively. For these selective segments, the geometry optimizations were conducted by using hybrid DFT （B3LYP）methods to find that the structure obturated with H2O was better consistent with the experiment, and then this model would be used to latter calculations, such as the frontier molecular orbital and the NBO charge population analysis. In addition the magnetic behaviors of this complex were analyzed by experiments and the weak antiferromagnetic couple between copper（Ⅱ） ions was observed. The exchange coupling constant was calculated by DFT based on the spin broken symmetry formalism. The calculated coupling constants were in good agreement with the experimental data.     

Role of nonlocal exchange in molecular crystals: The case of two proton‐ordered phases of ice

We present a periodic density functional theory investigation of twoproton‐ordered phases of ice. Their equilibrium lattice parameters,relative stabilities, formation energies, and densities of states havebeen evaluated. Nine exchange‐correlation functionals, representativeof the generalized gradient approximation (GGA), global hybrids,range‐separated hybrids, meta‐GGA, and hybrid meta‐GGA families havebeen taken into account, considering two oxygen basis sets. Althoughthe hydrogen‐bond network of ice is well reproduced at the B3LYP,M06‐L, or LC‐ wPBE levels, formation energies are only correctlyevaluated with the two former functionals. Band gaps on the other handare only quantitatively reproduced at the B3LYP level. These resultsindicate that this last functional, a de facto reference formolecular calculations, gives in average the most accurate results forthe considered ice properties. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Wolves in Sheep's Clothing: μ‐Oxo‐Diiron Corroles Revisited

For well over 20 years, μ‐oxo‐diiron corroles, first reported by Vogel and co‐workers in the form of μ‐oxo‐bis[(octaethylcorrolato)iron] (Mössbauer δ 0.02 mm s^?1, ΔE_Q 2.35 mm s^?1), have been thought of as comprising a pair antiferromagnetically coupled low‐spin Fe^IV centers. The remarkable stability of these complexes, which can be handled at room temperature and crystallographically analyzed, present a sharp contrast to the fleeting nature of enzymatic, iron(IV)‐oxo intermediates. An array of experimental and theoretical methods have now shown that the iron centers in these complexes are not Fe^IV but intermediate‐spin Fe^III coupled to a corrole^.2?. The intramolecular spin couplings in {Fe[TPC]}₂(μ‐O) were analyzed via DFT(B3LYP) calculations in terms of the Heisenberg–Dirac–van Vleck spin Hamiltonian H=J_Fe–corrole(S_Fe?S_corrole)+J_Fe–Fe′(S_Fe?S_Fe′)+J_{Fe′–corrole}(S_Fe′?S_corrole′), which yielded J_Fe–corrole=J_{Fe′–corrole′}=0.355 eV (2860 cm^?1) and J_Fe–Fe′=0.068 eV (548 cm^?1). The unexpected stability of μ‐oxo‐diiron corroles thus appears to be attributable to charge delocalization via ligand noninnocence.     

Theoretical study of the magnetic exchange coupling behavior substituting Cr(III) with Mo(III) in cyano‐bridged transition metal complexes

Molecular magnetism in a series of cyano‐bridged first and second transition metal complexes has been investigated using density functional theory (DFT) combined with the broken‐symmetry (BS) approach. Several exchange‐correlation (XC) functionals in the ADF package were used to investigate complexes I [?(Me₃tacn)₂(cyclam)NiMo₂(CN)₆]²⁺, II [?(Me₃tacn)₂(cyclam)Ni‐Cr₂(CN)₆]²⁺, III [(Me₃tacn)₆MnMo₆(CN)₁₈]²⁺, and IV [(Me₃tacn)₆MnCr₆(CN)₁₈]²⁺ (Me₃tacn = N,N′,N?‐trimethyl‐1,4,7‐triazacyclononane). For models A (the molded structure of complex I) and B (the modeled structure of complex II), all the XCs given qualitatively reasonable results and predict ferromagnetic coupling character between M (M = Mo^III for A or Cr^III for B) and Ni^II in coincidence with the experimental results (see Tables I and II ). The calculated using Operdew, OPBE, O3LYP, and B3LYP functionals and experimental J values show that substituting Cr^III with Mo^III will enhance the ferromagnetic exchange coupling interactions. But VWN, PW91, PBE, VSXC, and tau‐HCTH functionals have no way to differentiate the relative strength of the intramolecular magnetic exchange coupling interactions of A and B correctly. For models C (the modeled structure of complex III) and D (the modeled structure of complex IV), all the XCs in ADF and B3LYP in Gaussian 03 with several basis sets show that substituting Cr^III with Mo^III will enhance the antiferromagnetic exchange coupling interactions. From the above calculations, the substitution of Cr^III by Mo^III will enhance the magnetic coupling interactions, whether the magnetic coupling interactions are ferro‐ or antiferromagnetic. Moreover, Kahn's model was applied to investigate the above facts. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Three‐Axis Anisotropic Exchange Coupling in the Single‐Molecule Magnets NEt4[MnIII2(5‐Brsalen)2(MeOH)2MIII(CN)6] (M=Ru,Os)

We have investigated the single‐molecule magnets [Mn^III₂(5‐Brsalen)₂(MeOH)₂M^III(CN)₆]NEt₄ (M=Os ( 1 ) and Ru ( 2 ); 5‐Brsalen=N,N′‐ethylenebis(5‐bromosalicylidene)iminate) by frequency‐domain Fourier‐transform terahertz electron paramagnetic resonance (THz‐EPR), inelastic neutron scattering, and superconducting quantum interference device (SQUID) magnetometry. The combination of all three techniques allows for the unambiguous experimental determination of the three‐axis anisotropic magnetic exchange coupling between Mn^III and Ru^III or Os^III ions, respectively. Analysis by means of a spin‐Hamiltonian parameterization yields excellent agreement with all experimental data. Furthermore, analytical calculations show that the observed exchange anisotropy is due to the bent geometry encountered in both 1 and 2 , whereas a linear geometry would lead to an Ising‐type exchange coupling.     

Benchmarking of density functionals for the kinetics and thermodynamics of the hydrolysis of glycosidic bonds catalyzed by glycosidases

In recent years, there has been an increased interest in understanding the enzymatic mechanism of glycosidases resorting mostly to DFT and DFT/MM calculations. However, the performance of density functionals (DFs) is well known to be system and property dependent. Trends drawn from general studies, despite important to evaluate the quality of the DFs and to pave the way for the development of new DFs, may be misleading when applied to a single specific system/property. To overcome this issue, we carried out a benchmarking study of 40 DFs applied to the geometry optimization and to the electronic barrier height (E _Barrier) and electronic energy of reaction (E _R) of prototypical glycosidase‐catalyzed reactions. Additionally, we report calculations with SCC‐DFTB and four semiempirical MO methods applied to the same problem. We have used a universal molecular model for retaining glycosidases, comprising only a 22‐atoms system that mimics the active site and substrate. High accuracy reference geometries and energies were calculated at the CCSD(T)/CBS//MP2/aug‐cc‐pVTZ level of theory. Most DFs reproduce the reference geometries extremely well, with mean unsigned errors (MUE) smaller than 0.05 Å for bond lengths and 3° for bond angles. Among the DFs, wB97X‐D, CAM‐B3LYP, B3P86, and PBE1PBE have the best performance in geometry optimizations (MUE = 0.02 Å). Conversely, semiempirical MO and SCC‐DFTB methods yielded less accurate geometries (MUE between 0.09 and 0.17 Å). The inclusion of D3 correction has a small, but still relevant, influence in the geometry predicted by some DFs. Regarding E _Barrier, 11 DFs (MPW1B95, CAM‐B3LYP, M06 ‐ 2X, PBE1PBE, wB97X ‐ D, B1B95, BMK, MN12 – SX, M05, M06, and M11) presented errors below 1 kcal.mol^?1, in relation to the reference energy. Most of these functionals belong to the family of hybrid functionals (H‐GGA, HH‐GGA, and HM‐GGA), which shows a positive influence of HF exchange in the determination of E _Barrier. The inclusion of D3 correction has not affected significantly the E _Barrier and E _R. The use of geometries at the accurate but expensive MP2/aug‐cc‐pVTZ level of theory has a small, albeit not insignificant, influence in the E _Barrier when compared with energies calculated with geometries determined with the DFs (usually a few tenths of kcal.mol^?1, with exceptions). In general, semiempirical MO methods and DFTB are associated with larger errors in the determination of E _Barrier, with unsigned errors from 6.9 to 24.7 kcal.mol^?1.     

Magnetic exchange interactions in cyano‐bridged MoIII binuclear complexes: Broken‐symmetry and density functional theory calculations

Molecular magnetism in cyano‐bridged Mo^III binuclear complexes [Mo₂(CN)₁₁]^5? and [(Me₃tacn)₂Mo₂(CN)₅]⁺ (Me₃tacn?N, N′, N″‐trimethyl‐1,4,7‐triazacyclononane) has been calculated using Becke's three‐parameter exchange functional and the gradient‐corrected functional of Lee, Yang, and Parr (B3LYP), a hybrid density functional theory (DFT), combined with a modified broken symmetry (BS) approach and the post–Hartree‐Fock (post‐HF) method difference‐dedicated configuration interaction (DDCI). We find B3LYP combined with broken‐symmetry approach (DFT‐BS) give the similar J values to those calculated by DDCI. So we use B3LYP combined with BS approach to investigate the magnetism above two molecules. Through calculations, we find that the absolute J values decrease with the increase of r (the Mo(2)‐C_brid and Mo(1)‐N_brid distances) and are linearly related to the differences of the squared spin populations [(ρ ? ρ)] on Mo^III atoms between the highest‐spin (HS) state and the broken symmetry (BS) state. Moreover, the absolute J values are linearly related to the sum of the square of the difference in energy of the unpaired electrons (ξ) with a limited variation of the r distance. We conclude that ξ can be used to scale the degree of the antiferromagnetic coupling interactions. At the end of the paper, the spin density distributions and the mechanisms of magnetic coupling interactions are analyzed by us. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

基于顺丁烯二酸和N,N螯合配体构筑的两个新型三维氢键型超分子体系: 结构、磁性质与理论化学研究

通过调变辅助配体,设计合成了两个新的Cu(II)化合物Cu(mal)(tap)(H2O)]n(1) 和 [Cu2(mal)2(bpym)2(H2O)2]·2H2O(2) (其中H2mal =顺丁烯二酸, tap=1,4,5,8-四氮杂菲,bpym=2,2′-联嘧啶),并用X-射线单晶衍射技术对其进行了结构表征。化合物1是一维弓背状配位聚合链通过氢键和π–π 堆积作用拓展形成的三维超分子体系;化合物2 展现一个具有六连接α-Po(46)拓扑的3D→3D二重穿插结构。此外根据晶体结构,利用Gaussian 03W中的DFT方法对化合物1和2进行几何构型优化,同时,用DFT-BS方法研究了两个化合物的磁性,结果表明计算结果与实验结果吻合,它们均具有弱的反铁磁相互作用。     

Protonation of an Oxo‐Bridged Diiron Unit Gives Two Different Iron Centers: Synthesis and Structure of a New Class of Diiron(III)‐μ‐hydroxo Bisporphyrins and the Control of Spin States by Using Counterions

Reported herein is a hitherto unknown family of diiron(III)‐μ‐hydroxo bisporphyrins in which two different spin states of Fe are stabilized in a single molecular framework, although both cores have identical molecular structures. Protonation of the oxo‐bridged dimer ( 2 ) by using strong Brønsted acids, such as HI, HBF₄, and HClO₄, produce red μ‐hydroxo complexes with I₃^? ( 3 ), BF₄^? ( 4 ), and ClO₄^? ( 5 ) counterions, respectively. The X‐ray structure of the molecule reveals that the Fe? O bond length increases on going from the μ‐oxo to the hydroxo complex, whereas the Fe‐O(H)‐Fe unit becomes more bent, which results in the smallest known Fe‐O(H)‐Fe angles of 142.5(2) and 141.2(1)° for 3 and 5 , respectively. In contrast, the Fe‐O(H)‐Fe angle remains unaltered in 4 from the corresponding μ‐oxo complex. The close approach of two rings in a molecule results in unequal core deformations in 3 and 4 , whereas the cores are deformed almost equally but to a lesser extent in 5 . Although 3 was found to have nearly high‐spin and admixed intermediate Fe spin states in cores I and II, respectively, two admixed intermediate spin states were observed in 4 . Even though the cores have identical chemical structures, crucial bond parameters, such as the Fe? N_p, Fe? O, and Fe???Ct_p bond lengths and the ring deformations, are all different between the two Fe^III centers in 3 and 4 , which leads to an eventual stabilization of two different spin states of Fe in each molecule. In contrast, the two Fe centers in 5 are equivalent and assigned to high and intermediate spin states in the solid and solution states, respectively. The spin states are thus found to be dependent on the counterions and can also be reversibly interconverted. Upon protonation, the strong antiferromagnetic coupling in the μ‐oxo dimer (J, ?126.6 cm^?1) is attenuated to almost zero in the μ‐hydroxo complex with the I₃^? counterion, whereas the values of J are ?36 and ?42 cm^?1, respectively, for complexes with BF₄^? and ClO₄^? counterions.     

Comparative theoretical study of small Rhn nanoparticles (2 ≤ n ≤ 8) using DFT methods

This work is aimed at identifying some key characteristics (energy, geometry, and spin) concerning Rh_n particles (2 = n ≤ 8) to perform further studies on adsorption and coadsorption sites of pollutants (CO and NO). The DFT methods of the Gaussian 03 program with the LANL2DZ basis set and the LANL2 potential are used. With the purpose to obtain a better nanoparticles definition, five different functionals were tested: B3LYP, O3LYP, BPW91, BP86, and HCTH; and the corresponding results are used to determine which of them best describes distances, spin, and gives acceptable highest vibration frequency and binding energy values, by comparing these results with values measured or calculated by many other authors. For the structure optimization process of the particles, the initial geometric shape was taken mainly from the literature, using the Rh–Rh distance: 2.67 Å, known for the bulk; and doing a complete optimization. We also considered flat nanoparticles structures, which most of them display three‐dimensional structures after the optimization process. The few flat shapes are mainly higher in energy than those of three‐dimensional structure. For some Rh_n particles for different n values, the spin of the ground state present degeneration. In some cases, the optimization process changes the initial geometry, but in most cases, there are only minor changes in bonds and geometry. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010