Theoretical investigation on 1H and 13C NMR chemical shifts of small alkanes and chloroalkanes

Using density functional theory (DFT) with the B3LYP, PBE, and PBE0 exchange-correlation functionals as well as the Moller-Plesset second-order perturbation theory (MP2) combined with a series of rather extended basis sets, 1H and 13C chemical shifts of small alkanes and chloroalkanes (with different numbers of chlorine atoms on specific positions) have been simulated and compared to experimental data. For the 1H chemical shifts, theory tends to reproduce experiment within the limits of the experimental errors. In the case of 13C chemical shift, the differences between theory and experiment increase monotonically with the number of chlorine atoms and exhibit a deviation from additivity. This behavior is related to the saturation of the experimental 13C chemical shifts with the number of chlorine atoms, whereas the evolution is mostly linear at both DFT and MP2 levels of approximation. This difference has been traced back to the relativistic spin-orbit coupling effects, which are exalted as a result of the enhancement of the s character of the C atom when increasing the number of linked Cl atoms. Thus, it was demonstrated that not only electron correlation but also relativistic effects have to be considered for estimating the 13C chemical shifts when several Cl atoms are directly attached to the C atom. Linear (theory/experiment) regressions have then been performed for the different types of C atoms, i.e., bearing one, two, and three Cl atoms, with excellent correlation coefficients. The linear correlation relationships so obtained can then serve to predict and facilitate the interpretation of the nuclear magnetic resonance spectra of more complex compounds. Furthermore, by investigating the basis set effects, the correlation between the chemical shifts calculated using the 6-311 + G(2d,p) basis set and the more extended 6-311 + G(2df,p) and aug-cc-pvtz basis sets is excellent, demonstrating that the choice of the 6-311 + G(2d,p) basis set for calculating the 1H and 13C chemical shifts is relevant.     

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.     

The heat of formation of the uranyl dication: theoretical evaluation based on relativistic density functional calculations

By using a set of model reactions, we estimated the heat of formation of gaseous UO2(2+) from quantum-chemical reaction enthalpies and experimental heats of formation of reference species. For this purpose, we performed relativistic density functional calculations for the molecules UO2(2+), UO2, UF6, and UF5. We used two gradient-corrected exchange-correlation functionals (revised Perdew-Burke-Ernzerhof (PBEN) and Becke-Perdew (BP)) and we accounted for spin-orbit interaction in a self-consistent fashion. Indeed, spin-orbit interaction notably affects the energies of the model reactions, especially if compounds of U(IV) are involved. Our resulting theoretical estimates for delta fH(o)0 (UO2(2+)), 365+/-10 kcal mol(-1) (PBEN) and 370+/-12 kcal mol(-1) (BP), are in quantitative agreement with a recent experimental result, 364+/-15 kcal mol(-1). Agreement between the results of the two different exchange-correlation functionals PBEN and BP supports the reliability of our approach. The procedure applied offers a general means to derive unknown enthalpies of formation of actinide species based on the available well-established data for other compounds of the element in question.     

Scaling factors for vibrational frequencies and zero-point vibrational energies of some recently developed exchange-correlation functionals

The scaling factors for the vibrational frequencies and zero-point vibrational energies evaluated at various combinations of recently developed exchange-correlation functionals and various basis sets are reported. The exchange-correlation functionals considered are B972, B98, HCTH, OLYP, O3LYP, G96LYP, PBE0 and VSXC functionals; the basis sets employed are 3-21G, 6-31G*, 6-31G**, 6-31+G, 6-311G*, 6-311G**, 6-311G(df,p), 6-311+G(df,p), cc-pVDZ and aug-cc-pVDZ. The experimental harmonic frequencies of 122 small molecules and the zero-point vibrational energies of 39 small molecules are used to determine the scaling factors through the least-square fitting procedure. It was found that the scaling factors do not depend significantly on the basis sets considered. The vibrational frequency scaling factors evaluated by using the B98 and PBE0 functionals are recommended on the basis of smallest root mean square error. The zero-point vibrational energy scaling factors evaluated from the B972 functional with Pople's double-zeta basis set and the HCTH functional with Pople's triple-zeta basis set are recommended on the basis of smallest root mean square error.     

Low-lying isomers of the B9(-) boron cluster: the planar molecular wheel versus three-dimensional structures

The B(9)(-) cluster was found previously to be an unprecedented molecular wheel containing an octacoordinate planar boron with D(8h) symmetry in a combined photoelectron spectroscopy (PES) and theoretical study [H. J. Zhai et al., Angew. Chem., Int. Ed. 42, 6004 (2003)]. However, the PES spectra of B(9)(-) exhibit minor features that cannot be explained by the global minimum D(8h) structure, suggesting possible contributions from low-lying isomers at finite temperatures. Here we present Car-Parrinello molecular dynamics with simulated annealing simulations to fully explore the potential energy surface of B(9)(-) and search for low-lying isomers that may account for the minor PES features. We performed density functional theory (DFT) calculations with different exchange-correlation functionals and ab initio calculations at various levels of theory with different basis sets. Two three-dimensional low-lying isomers were found, both of C(s) symmetry, 6.29 (C(s)-2) and 10.23 (C(s)-1) kcal/mol higher in energy than the D(8h) structure at the highest CCSD(T) level of theory. Calculated detachment transitions from the C(s)-2 isomer are in excellent agreement with the minor features observed in the PES spectra of B(9)(-). The B(9)(-) cluster proves to be a challenge for most DFT methods and the calculated relative energies strongly depend on the exchange-correlation functionals, providing an excellent example for evaluating the accuracies of various DFT methods.     

Comparative theoretical investigation of the vertical excitation energies and the electronic structure of [MoVOCl4]-: influence of basis set and geometry

The electronic structures, geometries, and vibration frequencies of the open-shell molybdenum(V) ion, [MoOCl(4)](-), have been calculated at the extended Hückel, semiempirical ZINDO/1, ZINDO/S, and PM3(tm), as well as ab initio and DFT theoretical levels. Electronic structure calculations suggest that the expected metal-fold orbital order can be satisfied only at the DFT level. The time-dependent density functional theory (TDDFT) approach has been used for the calculation of the vertical excitation energies in the UV-vis region with different basis sets, starting geometries, and exchange-correlation functionals. A good agreement between the predicted and the experimental electronic absorption and MCD spectra of the complex, [MoOCl(4)](-), was observed when the B3LYP and B3P86 exchange-correlation functionals were used with a full electron valence double-zeta with polarization basis set for the molybdenum and 6-311G(d) for all other atoms. Similar results were obtained when the LANL2DZ effective core potential for molybdenum atom and 6-31G(d) for all other atoms were used. The best absolute deviation of 0.13 and mean deviation of 0.01 eV were calculated for the bands in the UV-vis region by B3P86, while the results for the B3LYP exchange-correlation functional were less satisfactory. Compared to polarization functions, the inclusion of diffuse functions resulted in little improvement. The calculated excitations energies and charge-transfer band intensities are found to be sensitive to the Mo=O distance and O-Mo-Cl angle.     

A dual-level approach to density-functional theory

An efficient approximate scheme for density-functional theory (DFT) calculations, which eliminates the time-consuming self-consistent-field (SCF) procedure, is proposed using a dual-level DFT approach. In this approach, dual levels of basis sets and exchange-correlation functionals are adopted. The dual-level DFT approach is based on the idea that the total electron density in the ground state can be represented in terms of the density evaluated using the low-quality basis set and the low-cost exchange-correlation functional. Since the SCF procedure is avoided in the total energy evaluation, the dual-level DFT approach drastically reduces the computational cost. The applications of several dual-level DFT calculations to molecular systems show that our approach is more efficient than the self-consistent DFT approach with a moderate accuracy.     

Theoretical predictions of nuclear magnetic resonance parameters in a novel organo-xenon species: chemical shifts and nuclear quadrupole couplings in HXeCCH

We calibrate the methodology for the calculation of nuclear magnetic resonance (NMR) properties in novel organo-xenon compounds. The available state-of-the-art quantum-chemical approaches are combined and applied to the HXeCCH molecule as the model system. The studied properties are (129)Xe, (1)H, and (13)C chemical shifts and shielding anisotropies, as well as (131)Xe and (2)H nuclear quadrupole coupling constants. The aim is to obtain, as accurately as currently possible, converged results with respect to the basis set, electron correlation, and relativistic effects, including the coupling of relativity and correlation. This is done, on one hand, by nonrelativistic correlated ab initio calculations up to the CCSD(T) level and, on the other hand, for chemical shifts and shielding anisotropies by the leading-order relativistic Breit-Pauli perturbation theory (BPPT) with correlated ab initio and density-functional theory (DFT) reference states. BPPT at the uncorrelated Hartree-Fock level as well as the corresponding fully relativistic Dirac-Hartree-Fock method are found to be inapplicable due to a dramatic overestimation of relativistic effects, implying the influence of triplet instability in this multiply bonded system. In contrast, the fully relativistic second-order Moller-Plesset perturbation theory method can be applied for the quadrupole coupling, which is a ground-state electric property. The performance of DFT with various exchange-correlation functionals is found to be inadequate for the nonrelativistic shifts and shielding anisotropies as compared to the CCSD(T) results. The relativistic BPPT corrections to these quantities can, however, be reasonably predicted by DFT, due to the improved triplet excitation spectrum as compared to the Hartree-Fock method, as well as error cancellation within the five main BPPT contributions. We establish three computationally feasible models with characteristic error margins for future calculations of larger organo-xenon compounds to guide forthcoming experimental NMR efforts. The predicted (129)Xe chemical shift in HXeCCH is in a novel range for this nucleus, between weakly bonded or solvated atomic xenon and xenon in the hitherto characterized molecules.     

The chemical Hamiltonian approach in density functional theory

The chemical Hamiltonian approach (CHA) for handling the basis set superposition error problem in intermolecular interactions has been implemented within density functional theory (DFT) using Gaussian atomic basis sets. As test examples, the potential curves of the water dimer were calculated using the Vosko-Wilk-Nusair, Becke-Perdew and Perdew exchange-correlation functionals. Comparisons with the counterpoise correction method show that CHA within DFT performs as well as previously for Hartree-Fock.     

Interaction of lead atom with atmospheric hydroxyl radical. An ab initio and density functional theory study of the resulting complexes PbOH and HPbO

The two potential hypersurfaces 2A' (ground state) and 2A" (excited state) have been studied through ab initio and density functional theory (DFT) methods for the Pb(OH) complex. Two processes have been identified. The first one concerns the hydrogen inversion process in the coordination of PbOH and the second one the isomerization of PbOH into HPbO. Eight stationary points have been found; four of them correspond to the stable structures with symmetries PbOH(2A'), PbOH(2A"), HPbO(2A'), and HPbO(2Pi), and four correspond to transition states [TS] with the symmetries 2Pi, 2A', 2Sigma+, and 2A". The hydrogen inversion process in PbOH exhibits the so-called Renner-Teller effect with a rather low barrier, whereas the isomerization process PbOH-->HPbO exhibits a rather high barrier. The energetic, structural, spectroscopy, and thermodynamics results obtained at various levels through, e.g., DFT with BLYP, B3LYP exchange-correlation functionals, coupled clusters methods, namely CCSD (single and double excitations) and CCSD(T) (with triple excitations, by perturbation) are presented for the whole sets of the stationary points and their dissociation products. The relativistic effects, as well as spin-orbit interaction, taken into account in the case of the BLYP exchange-correlation functional, have been estimated and discussed in order to measure their importance in the case of system including heavy metals such as Pb. Reactions of lead (Pb) with oxidizing atmospheric molecules (OH, HO2, O2, and O3) have been studied at various levels of approximation in order to study the possible existence of PbOH in the atmosphere.     

Density functional investigation of high-spin XY (X = Cr, Mo, W and Y = C, N, O) molecules

The performance of a density functional theory approach in calculating the equilibrium bond length, dipole moment, and harmonic vibrational frequency in a series of group 6 (Cr, Mo, W) transition metal-containing diatomic molecules is evaluated. Using flexible basis sets comprised of Slater type functions, a wide range of exchange-correlation functionals is investigated. Comparing with known experimental values and published results from high-level theoretical calculations, the most suitable functional form is selected. The importance of relativistic effects is checked, and predictions are made for several unknown dipole moments. The best agreement with experimental parameters is obtained when using a general gradient approximation, while special and hybrid functional forms give less accurate results.     

Numerical examination of performance of some exchange-correlation functionals for molecules containing heavy elements

The performance of 17 exchange-correlation functionals for molecules containing heavy elements are numerically examined through four-component relativistic density DFT calculations. The examined functionals show the similar accuracy as they do for the molecules containing light elements only except for bond lengths. LDA and OP86 produce good results for bond lengths and frequencies but bad bond energies. Different functionals do not show much different performance for bond energies except LDA. BP86 and GP86 produce results with average accuracy while LYP does not perform well. Although encouraging results are obtained with functional B97GGA-1, other heavily parameterized and meta-GGA functionals do not produce impressive results.     

Vibrational and electron paramagnetic resonance properties of free and MgO supported AuCO complexes

The bonding, spin density related properties, and vibrational frequency of CO bound to single Au atom in the gas-phase or supported on MgO surfaces have been investigated with a variety of computational methods and models: periodic plane waves calculations have been compared with molecular approaches based on atomic orbital basis sets; pseudopotential methods with all electron fully relativistic calculations; various density functional theory (DFT) exchange-correlation functionals with the unrestricted coupled-cluster singles and doubles with perturbative connected triples [CCSD(T)]. AuCO is a bent molecule but the potential for bending is very soft, and small changes in the bond angle result in large changes in the CO gas-phase vibrational frequency. At the equilibrium geometry the DFT calculated vibrational shift of CO with respect to the free molecule is about -150 cm(-1), whereas smaller values -60-70 cm(-1) are predicted by the more accurate CCSD(T) method. These relatively large differences are due to the weak and nonclassic bonding in this complex. Upon adsorption on MgO, the CO vibrational shift becomes much larger, about -290 cm(-1), due to charge transfer from the basic surface oxide anion to AuCO. This large redshift is predicted by all methods, and is fully consistent with that measured for MgOAuCO complexes. The strong influence of the support on the AuCO bonding is equally well described by all different approaches.     

甲烷晶体的晶格能和弹性性质: 不同方法及泛函的评估

通过对甲烷晶体进行结构、晶格能和弹性特性的研究, 评估了不包含和包含色散能量修正的密度泛函理论的性能. 我们分别利用不包含色散能量修正的密度泛函理论(DFT) (包含不同的标准泛函和杂化泛函)和包含色散能量修正的密度泛函理论(DFT-D)计算了甲烷晶体特性, 并与实验作对比. 尽管DFT-D 与传统密度泛函理论及杂化密度泛函理论相比, 修正了甲烷晶体中的范德华(vdW)相互作用, 但是一些修正方案过分修正了这种相互作用. 因此, 人们在使用DFT-D方法时务必谨慎.     

Unambiguous optimization of effective potentials in finite basis sets

The optimization of effective potentials is of interest in density-functional theory (DFT) in two closely related contexts. First, the evaluation of the functional derivative of orbital-dependent exchange-correlation functionals requires the application of optimized effective potential methods. Second, the optimization of the effective local potential that yields a given electron density is important both for the development of improved approximate functionals and for the practical application of embedding schemes based on DFT. However, in all cases this optimization turns into an ill-posed problem if a finite basis set is introduced for the Kohn-Sham orbitals. So far, this problem has not been solved satisfactorily. Here, a new approach to overcome the ill-posed nature of such finite-basis set methods is presented for the optimization of the effective local potential that yields a given electron density. This new scheme can be applied with orbital basis sets of reasonable size and makes it possible to vary the basis sets for the orbitals and for the potential independently, while providing an unambiguous potential that systematically approaches the numerical reference.     

Theoretical investigation of substituted anthraquinone dyes

We have investigated with computational chemistry techniques the visible spectra of substituted anthraquinones. A wide panel of theoretical methods has been used, with various basis sets and density functional theory (DFT) functionals, in order to assess a level of theory that would lead to converged excitation energies. It turns out that the hybrid Becke-Lee-Yang-Parr and Perdew-Burke-Erzenrhof functionals with the 6-31G (d,p) atomic basis set provide reliable lambda(max) when the solvent effects are included in the model. Combining the results of both DFT schemes allows the prediction of lambda(max) with a standard deviation limited to 13 nm.     

Density functional theory and molecular clusters

Density functional theory (DFT) methods, including nonlocal density gradient terms in the exchange and correlation energy functionals, were applied to various types of molecular clusters: H-bonded, ionic, electrostatic, and London. Reliable results on the structure and stabilization energy were obtained for the first two types of cluster as long as Becke3LYP and Becke3P86 functionals and basis sets of at least DZ + P quality were used. DFT methods with currently available functionals failed completely, however, for London-type clusters, for which no minimum was found on the potential energy surfaces. DFT interaction energy exhibits the same basis set extension dependence as the Hartree-Fock (HF) interaction energy. Therefore, the Boys-Bernardi function counterpoise procedure should be employed for elimination of the DFT basis set superposition error. © 1995 John Wiley & Sons, 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.