A comparative relativistic DFT and ab initio study on the structure and thermodynamics of the oxofluorides of uranium(IV), (V) and (VI)

All the possible uranium(VI, V, IV) oxides, fluorides and oxofluorides were studied theoretically by using density functional theory (DFT) in the generalised gradient approximation (GGA), and three different relativistic methods (all-electron scalar four component Dyall RESC method (AE), relativistic small-core ECPs, and zeroth order regular approximation ZORA). In order to test different correlation methods, for the two former relativistic methods hybrid DFT, and, for the AE method, MP2 molecular orbital calculations were performed as well. Single-point AE-CCSD(T) energies were calculated on MP2 geometries as well. Energies of the uranium(VI) and (V) oxofluorides dissociation, uranium(VI) fluoride hydrolysis and oxofluoride disproportionation were calculated and compared against the available experimental thermochemical data. AE-CCSD(T) energies were the closest to the experiment. For GGA DFT methods, all the relativistic methods used yield similar results. For thermochemistry, the best quantitative agreement with the experimental and CCSD(T) values for both U=O and U-F bond strengths was obtained with hybrid DFT methods, provided that a reliable basis set was used. Both the GGA DFT and MP2 MO methods show overbinding of these bonds; moreover, this overbinding was found to be not uniform but strongly dependent on the coordination environment of the uranium atom in each case. U=O vibrational frequencies given by hybrid DFT, however, are systematically overestimated, and are better reproduced by GGA DFT; MP2 values usually fall in-between. Reaction enthalpies, U=O frequencies and complex geometries given by the PBE, MPBE, BPBE, BLYP and OLYP GGA functionals are quite similar, with OLYP performing slightly better than the others but still not as good as hybrid DFT. The geometries of the molecules are found to be influenced by the following factors: the inverse transinfluence (ITI) of the oxygen ligand and, for U(V), and U(IV), the Jahn-Teller distortion.     

van der Waals corrections to density functional theory calculations: Methane,ethane, ethylene,benzene, formaldehyde,ammonia, water,PBE, and CPMD

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.     

Barrier heights of hydrogen‐transfer reactions with diffusion quantum monte carlo method

Hydrogen‐transfer reactions are an important class of reactions in many chemical and biological processes. Barrier heights of H‐transfer reactions are underestimated significantly by popular exchange–correlation functional with density functional theory (DFT), while coupled‐cluster (CC) method is quite expensive and can be applied only to rather small systems. Quantum Monte‐Carlo method can usually provide reliable results for large systems. Performance of fixed‐node diffusion quantum Monte‐Carlo method (FN‐DMC) on barrier heights of the 19 H‐transfer reactions in the HTBH38/08 database is investigated in this study with the trial wavefunctions of the single‐Slater–Jastrow form and orbitals from DFT using local density approximation. Our results show that barrier heights of these reactions can be calculated rather accurately using FN‐DMC and the mean absolute error is 1.0 kcal/mol in all‐electron calculations. Introduction of pseudopotentials (PP) in FN‐DMC calculations improves efficiency pronouncedly. According to our results, error of the employed PPs is smaller than that of the present CCSD(T) and FN‐DMC calculations. FN‐DMC using PPs can thus be applied to investigate H‐transfer reactions involving larger molecules reliably. In addition, bond dissociation energies of the involved molecules using FN‐DMC are in excellent agreement with reference values and they are even better than results of the employed CCSD(T) calculations using the aug‐cc‐pVQZ basis set. © 2017 Wiley Periodicals, Inc.     

等电子三原子铀化物OUO2+、NUN和NUO+的结构和谐振频率的CCSD(T)计算研究

用小核相对论有效势和CCSD(T)方法计算了三原子铀化物OUO²⁺, NUN和NUO⁺的平衡键长和谐振频率. 计算结果显示U原子内层5s5p5d 电子相关能对这些化合物性质的影响非常小. 除NUN的弯曲振动频率,旋轨耦合效应对这些化合物的结构和频率的影响并不明显. 本文的计算结果与其他研究组的计算结果以及已有的实验值相比符合较好, 这表明作为单参考态方法, CCSD(T)能够对这些体系的键长和频率给出较精确的计算结果. 与此前密度泛函理论(DFT)的计算结果相比, CCSD(T)方法与PBE0泛函的结果吻合最好. 本文的工作有助于在用密度泛函方法研究这些体系时选择合适的交换相关泛函, 也为今后的实验研究提供了新的理论数据.     

Accuracy of geometries: influence of basis set,exchange–correlation potential,inclusion of core electrons,and relativistic corrections

The geometries of a set of small molecules were optimized using eight different exchange–correlation (xc) potentials in a few different basis sets of Slater-type orbitals, ranging from a minimal basis (I) to a triple-zeta valence basis plus double polarization functions (VII). This enables a comparison of the accuracy of the xc potentials in a certain basis set, which can be related to the accuracies of wavefunction-based methods such as Hartree–Fock and coupled cluster. Four different checks are done on the accuracy by looking at the mean error, standard deviation, mean absolute error and maximum error. It is shown that the mean absolute error decreases with increasing basis set size, and reaches a basis set limit at basis VI. With this basis set, the mean absolute errors of the xc potentials are of the order of 0.7–1.3 pm. This is comparable to the accuracy obtained with CCSD and MP2/MP3 methods, but is still larger than the accuracy of the CCSD(T) method (0.2 pm). The best performing xc potentials are found to be Becke–Perdew, PBE and PW91, which perform as well as the hybrid B3LYP potential. In the second part of this paper, we report the optimization of the geometries of five metallocenes with the same potentials and basis sets, either in a nonrelativistic or a scalar relativistic calculation using the zeroth-order regular approximation approach. For the first-row transition-metal complexes, the relativistic corrections have a negligible effect on the optimized structures, but for ruthenocene they improve the optimized Ru–ring distance by some 1.4–2.2 pm. In the largest basis set used, the absolute mean error is again of the order of 1.0 pm. As the wavefunction-based methods either give a poor performance for metallocenes (Hartree–Fock, MP2), or the size of the system makes a treatment with accurate methods such as CCSD(T) in a reasonable basis set cumbersome, the good performance of density functional theory calculations for these molecules is very promising; even more so as density functional theory is an efficient method that can be used without problems on systems of this size, or larger.     

Density functional investigations of the properties and thermochemistry of UF6 and UF5 using valence-electron and all-electron approaches

The structural properties and thermochemistry of UF6 and UF5 have been investigated using both Hartree-Fock and density functional theory (DFT) approximations. Within the latter approach, the local spin-density approximation, the generalized gradient approximation, and hybrid density functionals were considered. To describe the uranium atom we employed small-core (60 electrons) and large-core (78 electrons) relativistic effective core potentials (RECPs), as well as the all-electron approximation based on the two-component third-order Douglas-Kroll-Hess Hamiltonian. For structural properties, we obtained very good agreement with experiment with DFT and both large and small-core RECPs. The best match with experiment is given by the hybrid functionals with the small-core RECP. The bond dissociation energy (BDE) was obtained from the relative energies of the fragments [UF6 --> UF5 + F], corrected for zero-point energy and spin-orbit interaction. Very good agreement was found between the BDE obtained from all-electron calculations and those calculated with the small-core RECP, while those from the large-core RECP are off by more than 50%. In order to obtain good agreement with experiment in the BDE it is imperative to work with hybrid density functionals and a small-core RECP.     

Molecular structures,bond energies,and bonding analysis of group 11 cyanides TM(CN) and isocyanides TM(NC) (TM = Cu,Ag, Au)

We report on quantum chemical calculations at the DFT (BP86/TZP) and ab initio (CCSD(T)/III+) levels of the title compounds. The geometries, vibrational spectra, heats of formation, and homolytic and heterolytic bond dissociation energies are given. The calculated bond length of Cu-CN is in reasonable agreement with experiment. The theoretical geometries for CuNC and the other group 11 cyanides and isocyanides which have not been measured as isolated species provide a good estimate for the exact values. The theoretical bond dissociation energies and heats of formation should be accurate with an error limit of +/-5 kcal/mol. The calculation of the vibrational spectra shows that the C-N stretching mode of the cyanides, which lies between 2170 and 2180 cm(-)(1), is IR inactive. The omega(1)(C-N) vibrations of the isocyanides are shifted by approximately 100 cm(-)(1) to lower wavenumbers. They are predicted to have a very large IR intensity. The nature of the metal-ligand interactions was investigated with the help of an energy partitioning analysis in two different ways using the charged fragments TM(+) + CN(-) (TM = transition metal) and the neutral fragments TM(*) + CN(*) as bonding partners. The calculations suggest that covalent interactions are the driving force for the formation of the TM-CN and TM-NC bonds, but the finally formed bonds are better described in terms of interactions between TM(+) and CN(-), which have between 73% and 80% electrostatic character. The contribution of the pi bonding is rather small. The lower energy of the metal cyanides than that of the isocyanides comes from the stronger electrostatic interaction between the more diffuse electron density at the carbon atom of the cyano ligand and the positively charged nucleus of the metal.     

羰基镍簇Ni(CO)n(n=1-4)的结构和Ni-CO键解离性质的密度泛函理论研究

在密度泛函理论框架下, 应用不同泛函计算了配合物Ni(CO)n(n=1~4)的平衡几何构型和振动频率. 考察了泛函和基组重叠误差对预测Ni—CO键解离能的影响. 计算结果表明, 用杂化泛函能得到与实验一致的优化几何构型和较合理的振动频率. 对Ni(CO)n(n=2~4)体系, 用“纯”泛函, 如BP86和BPW91, 可得到与CCSD(T)更符合、 并与实验值接近的解离能. 当解离产物出现单个金属原子或离子(如金属羰基配合物的完全解离)时, BSSE校正项的计算中应保持金属部分的电子结构一致. 只有考虑配体基组和不考虑配体基组两种情况下金属的电子构型与配合物中金属的构型一致时, 才能得到合理的BSSE校正, 从而预测合理的解离能.     

Pyrrolizidine alkaloids necine bases: Ab initio,semiempirical, and molecular mechanics approaches to molecular properties

The structural stabilities of endo and exo conformations of retronecine and heliotridine molecules were analyzed using different ab initio, semiempirical, and molecular mechanics methods. All electron and pseudopotential ab initio calculations at the Hartree-Fock level of theory with 6-31G* and CEP-31G* basis sets provided structures in excellent agreement with available experimental results obtained from X-ray crystal structure and ¹H-NMR (nuclear magnetic resonance) studies in D₂O solutions. The exo conformations showed a greater stability for both molecules. The most significant difference between the calculations was found in the ring planarity of heliotridine, whose distortion was associated with the interaction between the O(11)H group and the C(1)-C(2) double bond as well as with a hydrogen bond between O(11)H and N(4). The discrepancy between pseudopotential and all-electron optimized geometries was reduced after inclusion of the innermost electrons of C(1), C(2), and N(4) in the core potential calculation. The MNDO, AM1, and PM3 semiempirical results showed poor agreement with experimental data. The five-membered rings were observed to be planar for AM1 and MNDO calculations. The PM3 calculations for exo-retronecine showed a greater stability than the endo conformer, in agreement with ab initio results. A good agreement was observed between MM3 and ab initio geometries, with small differences probably due to hydrogen bonds. While exo-retronecine was calculated to be more stable than the endo conformer, the MM3 calculations suggested that endo-heliotridine was slightly more stable than the exo form. © 1996 by John Wiley & Sons, Inc.     

Theoretical investigation of CO interaction with copper sites in zeolites: periodic DFT and hybrid quantum mechanical/interatomic potential function study

Periodic DFT and combined quantum mechanics/interatomic potential function (QM-pot) models were used to describe the interaction of CO with the Cu+ sites in FER. The CO stretching frequencies were calculated using omega(CO)(CCSD(T))/r(CO)(DFT) scaling method relating frequencies determined using a high-level quantum-chemical (coupled clusters) method for simple model carbonyls to CO bond lengths calculated using periodic DFT and QM-pot methods for the Cu+-zeolite system. Both periodic DFT and QM-pot models together with omega(CO)/r(CO) scaling describe the CO stretching dynamics with the "near spectroscopic accuracy", giving nu(CO) = 2156 cm(-1) in excellent agreement with experimental data. Calculations for various Cu+ sites in FER show that both types of Cu+ sites in FER (channel-wall sites and intersection sites) have the same CO stretching frequencies. Thus, the CO stretching frequencies are not site-specific in the CO/Cu+/FER system. The convergence of the results with respect to the model size was analyzed. When the same exchange-correlation functional is used the adsorption energies from periodic DFT and QM-pot are in good agreement (about 2 kcal/mol difference) but substantially larger than those of the experiment. The adsorption energy calculated with the B3LYP functional agrees with available experimental data. The overestimation of the adsorption energy in DFT calculations (periodic or QM-pot) is related to a red-shift of the CO stretching mode, both result from an underestimation of the HOMO(5sigma)-LUMO(2pi) gap of CO and the consequent overestimation of the Cu(+)(d)-CO(2pi*) back-donation. For the adsorption energy, this can be overcome by the use of hybrid B3LYP exchange-correlation functional. For the frequency calculations, the DFT problem can be overcome by the use of the omega(CO)(CCSD(T))/r(CO)(DFT) correlation.     

Self-interaction artifacts on structural features of uranyl monohydroxide from Kohn�CSham calculations

Invoking a DFT?+?U approach, we explored self-interaction artifacts in results from Kohn?CSham (KS) density functional calculations on the geometry and the vibrational frequencies of uranyl monohydroxide and the corresponding tetra-aqua complex. Exchange?Ccorrelation functionals based on the local density approximation (LDA) and the generalized-gradient approximation (GGA) predict equilibrium geometries for [UO₂(OH)]⁺ that deviate from the results of hybrid DFT calculations and high-level wavefunction-based methods such as CCSD(T). LDA?+?U and GGA?+?U functionals with corrections for the insufficient localization of the U 5f shell yield better agreement, in particular for the angle U-O_h-H. At the LDA level, a linear coordination of the OH ligand results; with the +U correction, the angle U-O_h-H is reduced by ~35°, in good agreement with CCSD(T) results. At the GGA level, the bending angle is changed by ~20°. This relatively strong self-interaction artifact is traced back to a spurious ?? interaction between U 5f and O(p) orbitals which is less pronounced in the presence of further (aqua) ligands.     

M(CO)4~(2+)(M=Ni,Pd,Pt)的几何结构与自旋态的理论研究

对标题化合物的几何结构和可能的自旋态在密度泛函DFT-BP86和从头算的水平上进行了研究.计算结果表明:作为16电子配合物阳离子,Pd(CO)_4~(2+)和Pt(CO)~(2+)都以低自旋态平面四边形构型存在,这与实验事实相符,计算得到的键长Pd-C和Pt-C相对趋势也与实验数据一致.而对于Ni(CO)_4~(2+)阳离子计算,在低自旋态平面四边形构型和高自旋态的(扭曲)四面体之间无法给出明确的答案,因为CCSD(T)//BP86和CCSD(T)//MP2水平下得到的两种结构之间的能量差几乎可以忽略.     

Benchmark calculations on the electron detachment energies of MO3* and M2O6* (M = Cr, Mo, W)

Neutral and anionic molecules of the monomers and dimers of the group VIB transition metal oxides (MO3 and M2O6) were studied with density functional theory (DFT) and coupled cluster CCSD(T) theory. Franck-Condon simulations of the photoelectron spectra were carried out for the transition from the ground state of the anion to that of the neutral molecule. Molecular structures from the DFT and CCSD(T) methods are compared. Electron detachment energies reported in the literature were evaluated. The calculated adiabatic and vertical electron detachment energies (ADEs and VDEs) were compared with the experimental results. CCSD(T) gives results within 0.12 eV for the ADEs. CCSD(T) predicts VDEs that are in error by as much as 0.3 eV for M = Cr. DFT hybrid functionals were found to give poor results for the ADEs and VDEs for M = Cr due to the substantial amount of multireference character in the wavefunction, whereas the pure DFT functionals give superior results. For M = Mo and W, excellent agreement was found for both CCSD(T) and many DFT fucntionals. The BP86 functional yields the best overall results for the VDEs of all the metal oxide clusters considered. Heats of formation calculated at the CCSD(T) level extrapolated to the complete basis set limit are also in good agreement with available experimental data.     

Intermolecular pi-pi interactions in solids

A parameter-free DFT/CCSD(T) correction scheme is proposed for precise calculations (close to CCSD(T) accuracy) of weakly bound molecular solids. The correction scheme has been tested for solid benzene and graphite. The CCSD(T)/CBS correction to planewave DFT calculations reproduces the experimentally determined lattice constants for solid benzene. The calculated cohesive energy of benzene (457 meV per molecule) compares well with the experimental values of the heat of sublimation (460-560 meV per molecule). For graphite, the correction yields structural parameters (a = 2.46 A, c = 6.60 A) in good agreement with experiment (a = 2.46 A, c = 6.67 A). The calculated exfoliation energy of 54 meV per atom agrees fairly well with the most recent experimental value of 52 +/- 5 meV per atom.     

Quantum Monte Carlo calculations of the dissociation energies of three-electron hemibonded radical cationic dimers

We report variational and diffusion quantum Monte Carlo (VMC and DMC) calculations of the dissociation energies of the three-electron hemibonded radical cationic dimers of He, NH3, H2O, HF, and Ne. These systems are particularly difficult for standard density-functional methods such as the local-density approximation and the generalized gradient approximation. We have performed both all-electron (AE) and pseudopotential (PP) calculations using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. Our results are in good agreement with coupled-cluster CCSD(T) calculations. We have also studied the relative stability of the hemibonded and hydrogen-bonded water radical dimer isomers. Our calculations indicate that the latter isomer is more stable, in agreement with post-Hartree-Fock methods. The excellent agreement between our AE and PP results demonstrates the high quality of the PPs used within our VMC and DMC calculations.     

Conformations and energetics of sulfur and selenium diimides

The geometries and energetics of different conformations of sulfur and selenium diimides E(NR)(2) (E = S, Se; R = H, Me, (t)Bu, C(6)H(3)Me(2)-2,6, SiMe(3)) have been studied by using various ab initio and DFT molecular orbital techniques. The syn,syn conformation is found to be most stable for parent E(NH)(2), but in general, the preferred molecular conformation for substituted chalcogen diimides is syn,anti. In the case of E(NH)(2) the present calculations further confirm that syn,syn and syn,anti conformations lie energetically close to each other. From the three different theoretical methods used, B3PW91/6-31G proved to be the most suitable method for predicting the geometries of chalcogen diimides. The optimized geometrical parameters are in a good agreement with all available experimental data. While qualitative energy ordering of the different conformations is independent of the level of theory, the quantitative energy differences are dependent on the method used. The performance and reliability of higher level ab initio calculations and DFT methods using large basis sets were tested and compared with experimental information where available. All of the higher level ab inito methods give very similar results, but the use of large basis sets with the B3PW91 method does not increase the reliability of the results. The combination of CCSD(T)/cc-pVDZ with the B3PW91/6-31G-optimized geometries is found to be the method of choice to study energetic properties of chalcogen diimides.     

Density functional theory and CCSD(T) evaluation of ionization potentials,redox potentials,and bond energies related to zirconocene polymerization catalysts

Quantum-mechanical-based computational design of molecular catalysts requires accurate and fast electronic structure calculations to determine and predict properties of transition-metal complexes. For Zr-based molecular complexes related to polyethylene catalysis, previous evaluation of density functional theory (DFT) and wavefunction methods only examined oxides and halides or select reaction barrier heights. In this work, we evaluate the performance of DFT against experimental redox potentials and bond dissociation enthalpies (BDEs) for zirconocene complexes directly relevant to ethylene polymerization catalysis. We also examined the ability of DFT to compute the fourth atomic ionization potential of zirconium and the effect the basis set selection has on the ionization potential computed with CCSD(T). Generally, the atomic ionization potential and redox potentials are very well reproduced by DFT, but we discovered relatively large deviations of DFT-calculated BDEs compared to experiment. However, evaluation of BDEs with CCSD(T) suggests that experimental values should be revisited, and our CCSD(T) values should be taken as most accurate.     

Quantum Chemical Study of the Preferred Conformations,Molecular Geometries,and Relative Thermodynamic Stabilities of 2-Substituted 4-Methylene-1,3-Dioxolanes and 4-Methyl-1,3-Dioxoles

The preferred conformations, molecular geometries, and relative stabilities of carbon–carbon double-bond exo–endo isomeric 2-substituted 4-methylene-1,3-dioxolanes (a) and 4-methyl-1,3-dioxoles (b) have been studied by DFT calculations at the B3LYP/6-31G* level of theory. The main interest of this work was devoted to the contribution of alkoxy substituents on the relative thermodynamic stabilities of these isomeric unsaturated acetals. Comparison of the computational data with previous experimental findings shows both the enthalpies and entropies of the a b isomerization to be accurately predictable by the DFT calculations. Most importantly, the good agreement between experiment and theory proved also to be applicable to the previously observed unexpectedly large effect of 2-alkoxy substitution on the isomer equilibria.     

Study of the formamide–methanol dimer with ab initio and density functional theory methods

For the first time, the structures and energies for the hydrogen bonding of a 1:1 complex formed between formamide and methanol molecules have been computed with various pure and hybrid density functional theory (DFT) and ab initio methods at varied basis set levels from 6‐31g to 6‐31+g(d,p). Five reasonable geometries on the potential energy surface of methanol and formamide system are considered and their relative stability is discussed. The infrared (IR) spectrum frequencies, IR intensities, and vibrational frequency shifts are reported. From the systematic studies, it is found that all the DFT methods selected here correctly compute the dimerization energies and geometries, with the B3P86 method predicting the hydrogen bond lengths relatively shorter and BPW91 yielding the interaction energies relatively lower. Finally, the solvent effects on the geometries of the formamide–methanol complexes have also been investigated using self‐consistent reaction field (SCRF) calculations with five different DFT methods at the 6‐31+g(d,p) basis set level. The results indicate that the polarity of the solvent has played an important role on the structures and relative stabilities of different isomers. Moreover, the basis set superposition error correction is critical to the interaction energies in the polar solvents. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004