Performance Of Density Functional Theory Research Articles

A computational study of CX (X = H, C, F, Cl) bond dissociation enthalpies (BDEs) in polyhalogenated methanes and ethanes

AbstractBond dissociation enthalpies (BDEs) play a significant role in the photolysis of Chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), which lead to the depletion of stratospheric ozone. In this work, we estimate the performance of Density Functional Theory (DFT) methods in calculating BDEs of CFCs and HCFCs, and find that DFTs are unreliable for this system. The reasons for the unreliability of DFT methods in this system are also concluded. Furthermore, composite ab initio methods G3 and G3B3 are demonstrated to accurately estimate BDEs of polyhalogenated lower alkanes. Eighty two experimental values from Comprehensive Handbook of Chemical Bond Energies (2007, 2nd edition) are re‐evaluated. Eight of them are doubted as having a deviation exceeding 20.0 kJ/mol between the theoretical and experimental values. We also systematically predict the BDEs in polyhalogenated methanes and ethanes. A further study is conducted on their relationships of structures and properties. Copyright © 2010 John Wiley & Sons, Ltd.

Performance of density functional theory on homogeneous gold catalysis

The performance of 32 density functionals to describe the homogeneous gold catalysis of propargyl esters has been tested. These catalytic reactions are very commonly rather complex, numerous intermediates can be found along the reaction profile and the individual reaction steps are often associated to very small barrier heights. In this scenario, the experimental kinetic study of the catalytic mechanisms is very challenging. A computational approach to this problem provides invaluable help to gain insight into these mechanisms. However the high accuracy needed to describe such highly branched paths with low energy transition states poses many practical problems for cost-efficient DFT methods. The lack of accurate experimental or high-level computational data to employ as validation sets for these methods is also an added difficulty. High-level computational data needed to validate these functionals have been obtained at the CCSD/def2-TZVPP//CCSD/def2-SVP level and, with such data, we aim to help discern the best density functional recipe for homogeneous gold catalysis

Benchmarks of electronically excited states: Basis set effects on CASPT2 results

Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.

Assessing the Performance of Density Functional Theory for the Electronic Structure of Metal−Salens: The M06 Suite of Functionals and the d4-Metals

We have systematically investigated the electronic structure of the d⁴ metal-salen complexes including the Cr(II)-, Mn(III)-, Fe(IV)-, Mo(II)-, Tc(III)-, and Ru(IV)-salen complexes. Density functional theory (DFT) has been employed, using the BP86 and B3LYP functionals, and the entire M05 and M06 suites of meta-generalized gradient functionals. These results are compared to robust complete active-space self-consistent field (CASSCF) optimized geometries and complete active-space third-order perturbation theory (CASPT3) energies for the lowest singlet, triplet, and quintet states. Although the M06 and M06-L DFT functionals have been generally recommended for computations on complexes that contain main group and transition metals, none of the M0-functionals appear statistically better than the B3LYP functional for the computation of spin-state energy gaps. DFT- and CASSCF-optimized geometries normally agree to within 0.3 Å least root mean squared deviation (LRMSD) for the singlet and triplet structures and less than 0.1 Å LRMSD for the quintet structures. It can be concluded that no DFT functional tested here can be considered reliable over all metal-salen complexes and it is highly recommended that the accuracy of any given DFT functional should be assessed on a case-by-case basis.

Systematic Theoretical Study of the Zero-Field Splitting in Coordination Complexes of Mn(III). Density Functional Theory versus Multireference Wave Function Approaches

This paper presents a detailed evaluation of the performance of density functional theory (DFT) as well as complete active space self-consistent field (CASSCF)-based methods (CASSCF and second-order N-electron valence state perturbation theory, NEVPT2) to predict the zero-field splitting (zfs) parameters for a series of coordination complexes containing the Mn(III) ion. The physical origin of the experimentally determined zfs's was investigated by studying the different contributions to these parameters. To this end, a series of mononuclear Mn(III) complexes was chosen for which the structures have been resolved by X-ray diffraction and the zfs parameters have been accurately determined by high-field EPR spectroscopy. In a second step, small models have been constructed to allow for a systematic assessment of the factors that dominate the variations in the observed zfs parameters and to establish magnetostructural correlations. Among the tested functionals, the best predictions have been obtained with B3LYP, followed by the nonhybrid BP86 functional, which in turn is more successful than the meta-hybrid GGA functional TPSSh. For the estimation of the spin-orbit coupling (SOC) part of the zfs, it was found that the coupled perturbed SOC approach CP is more successful than the Pederson-Khanna method. Concerning the spin-spin interaction (SS), the restricted open-shell Kohn-Sham (ROKS) approach led to a slightly better agreement with the experiment than the unrestricted KS (UKS) approach. The ab initio state-averaged CASSCF (SA-CASSCF) method with a minimal active space and the most recent implementation that treats the SOC and SS contributions on an equal footing provides the best predictions for the zfs. The analysis demonstrates that the major contribution to the axial zfs parameter (D) originates from the SOC interaction but that the SS part is far from being negligible (between 10 and 20% of D). Importantly, the various excited triplet ligand field states account for roughly half of the value of D, contrary to popular ligand field models. Despite covering dynamic correlation contributions to the transition energies, NEVPT2 does not lead to large improvements in the results as the excitation energies of the Mn(III) d-d transitions are already fairly accurate at the SA-CASSCF level. For a given type of coordination sphere (e.g., elongated or compressed octahedron), the magnetic anisotropy of the Mn(III) ion, D, does not appear to be highly sensitive to the nature of the ligands, while the E/D ratio is notably affected by all octahedral distortions. Furthermore, the introduction of different halides into the coordination sphere of Mn(III) only leads to small effects on D. Nevertheless, it appears that oxygen-based ligands afford larger D values than nitrogen-based ligands.

A density functional theory study of the zero-field splitting in high-spin nitrenes

This work presents a detailed evaluation of the performance of density functional theory (DFT) for the prediction of zero-field splittings (ZFSs) in high-spin nitrenes. A number of well experimentally characterized triplet mononitrenes, quartet nitrenoradicals, quintet dinitrenes, and septet trinitrenes have been considered. Several DFT-based approaches for the prediction of ZFSs have been compared. It is shown that the unrestricted Kohn-Sham and the Pederson-Khanna approaches are the most successful for the estimation of the direct spin-spin (SS) interaction and the spin-orbit coupling (SOC) parts, respectively, to the final ZFS parameters. The most accurate theoretical predictions (within 10%) are achieved by using the PBE density functional in combination with the DZ, EPR-II, and TZV basis sets. For high-spin nitrenes constituted from light atoms, the contribution of the SOC part to ZFS parameters is quite small (7%-12%). By contrast, for chlorine-substituted septet trinitrenes, the contribution of the SOC part is small only to D value but, in the case of E value, it is as large as the SS part and has opposite sign. Due to this partial cancellation of two different contributions, SS and SOC, the resulting values of E in heavy molecules are almost two times smaller than those predicted by analysis of the widely used semiempirical one-center spin-spin interaction model. The decomposition of D(SS) into n-center (n=1-4) interactions shows that the major contribution to D(SS) results from the one-center spin-spin interactions. This fact indicates that the semiempirical SS interaction model accurately predicts the ZFS parameters for all types of high-spin nitrenes with total spin S=2 and 3, if their molecules are constructed from the first-row atoms.

Prediction of Reliable Metal−PH3 Bond Energies for Ni, Pd, and Pt in the 0 and +2 Oxidation States

Phosphine-based catalysts play an important role in many metal-catalyzed carbon-carbon bond formation reactions yet reliable values of their bond energies are not available. We have been studying homogeneous catalysts consisting of a phosphine bonded to a Pt, Pd, or Ni. High level electronic structure calculations at the CCSD(T)/complete basis set level were used to predict the M-PH(3) bond energy (BE) for the 0 and +2 oxidation states for M = Ni, Pd, and Pt. The calculated bond energies can then be used, for example, in the design of new catalyst systems. A wide range of exchange-correlation functionals were also evaluated to assess the performance of density functional theory (DFT) for these important bond energies. None of the DFT functionals were able to predict all of the M-PH(3) bond energies to within 5 kcal/mol, and the best functionals were generalized gradient approximation functionals in contrast to the usual hybrid functionals often employed for main group thermochemistry.

Density functional theory study of the relative stability of the iron disulfide polymorphs pyrite and marcasite

The performance of density functional theory has been widely examined with regard to its ability to predict the properties of minerals, though less attention has been given to the correct determination of the relative stability of structurally similar polymorphs. Here a detailed examination is performed of the numerical and theoretical factors that may influence the structure and relative energetics of two such polymorphs of iron disulfide, namely, pyrite and marcasite, within density functional theory. Both the local-density approximation and commonly used generalized gradient approximation exchange-correlation functionals, such as Perdew, Burke and Ernzerhof (PBE), are found to predict that marcasite is more stable than pyrite, at variance with experiment. Allowing for the zero-point energy of vibration fails to remedy this discrepancy. While inclusion of a sufficiently large Hubbard $U$ parameter for iron is found to reverse the stability, this comes at the expense of a very poor description of other properties. Examination of three generalized gradient approximations developed specifically for the solid state, namely, AM05, Wu-Cohen and PBEsol, demonstrates that all of these functionals offer a superior description of the structures and relative energies of pyrite and marcasite through correctly predicting that the former is the ground-state phase at ambient conditions.

B3LYP calculations of cerium oxides

In this paper we evaluate the performance of density functional theory with the B3LYP functional for calculations on ceria (CeO(2)) and cerium sesquioxide (Ce(2)O(3)). We demonstrate that B3LYP is able to describe CeO(2) and Ce(2)O(3) reasonably well. When compared to other functionals, B3LYP performs slightly better than the hybrid functional PBE0 for the electronic properties but slightly worse for the structural properties, although neither performs as well as LDA+U(U=6 eV) or PBE+U(U=5 eV). We also make an extensive comparison of atomic basis sets suitable for periodic calculations of these cerium oxides. Here we conclude that there is currently only one type of cerium basis set available in the literature that is able to give a reasonable description of the electronic structure of both CeO(2) and Ce(2)O(3). These basis sets are based on a 28 electron effective core potential (ECP) and 30 electrons are attributed to the valence space of cerium. Basis sets based on 46 electron ECPs fail for these materials.

Performance of Density Functional Theory for 3d Transition Metal-Containing Complexes: Utilization of the Correlation Consistent Basis Sets

The performance of 44 density functionals used in conjunction with the correlation consistent basis sets (cc-pVnZ where n = T and Q) has been assessed for the gas-phase enthalpies of formation at 298.15 K of 3d transition metal (TM) containing systems. Nineteen molecules were examined: ScS, VO, VO(2), Cr(CO)(6), MnS, MnCl(2), Mn(CO)(5)Cl, FeCl(3), Fe(CO)(5), CoH(CO)(4), NiCl(2), Ni(CO)(4), CuH, CuF, CuCl, ZnH, ZnO, ZnCl, and Zn(CH(3))(2). Of the functionals examined, the functionals that resulted in the smallest mean absolute deviation (MAD, in parentheses, kcal mol(-1)) from experiment were B97-1 (6.9), PBE1KCIS (8.1), TPSS1KCIS (9.6), B97-2 (9.7), and B98 (10.7). All five of these functionals include some degree of Hartree-Fock (HF) exchange. The impact of increasing the basis set from cc-pVTZ to cc-pVQZ was found to be slight for the generalized gradient approximation (GGA) and meta-GGA (MGGA) functionals studied, indicating basis set saturation at the triple-zeta level. By contrast, for most of the generalized gradient exchange (GGE), hybrid GGA (HGGA), and hybrid meta-GGA (HMGGA) functionals considered, improvements in the average MAD of 2-3 kcal mol(-1) were seen upon progressing to a quadruple-zeta level basis set. Overall, it was found that the functionals that include Hartree-Fock exchange performed best overall, but those with greater than 40% HF exchange exhibit significantly poor performance for the prediction of enthalpies of formation for 3d TM complexes. Carbonyl-containing complexes, a mainstay in organometallic TM chemistry, are demonstrated to be exceedingly difficult to describe accurately with all but 2 of the 44 functionals considered. The most accurate functional, for both CO-containing and CO-free compounds, is B97-1/cc-pVQZ, which is shown to be capable of yielding results within 1 kcal mol(-1) of high-level ab initio composite methodologies.

Optical excitations of defects in realistic nanoscale silica clusters: Comparing the performance of density functional theory using hybrid functionals with correlated wavefunction methods

Optical excitations of low energy silica (SiO(2))(4) clusters obtained by global optimization, as opposed to constructed by hand, are studied using a range of theoretical methods. By focusing on the lowest energy silica clusters we hope to capture at least some of the characteristic ways by which the dry surfaces of silica nanosystems preferentially terminate. Employing the six lowest energy (SiO(2))(4) cluster isomers, we show that they exhibit a surprisingly wide range of geometries, defects, and associated optical excitations. Some of the clusters show excitations localized on isolated defects, which are known from previous studies using hydrogen-terminated versions of the defect in question. Other clusters, however, exhibit novel charge-transfer excitations in which an electron transfers between two spatially separated defects. In these cases, because of the inherent proximity of the constituent defects due to the small cluster dimensions, the excitation spectrum is found to be very different from that of the same defects in isolation. Excitation spectra of all clusters were calculated using time-dependent density functional theory (TD-DFT) and delta-SCF DFT (DeltaDFT) methods employing two different hybrid density functionals (B3LYP and BB1K) differing essentially in the amount of incorporated Hartree-Fock-like exchange (HFLE). In all cases the results were compared with CASPT2 calculated values which are taken as a benchmark standard. In line with previous work, the spatially localized excitations are found to be well described by TD-DFT/B3LYP but which gives excitation energies that are significantly underestimated in the case of the charge-transfer excitations. The TD-DFT/BB1K combination in contrast is found to give generally good excitation energies for the lowest excited states of both localized and charge-transfer excitations. Finally, our calculations suggest that the increased quality of the predicted excitation spectra by adding larger amounts of HFLE is mainly due to an increased localization of the excited state associated with the elimination of spurious self-interaction inherent to (semi-)local DFT functionals.

A Systematic Density Functional Study of the Zero-Field Splitting in Mn(II) Coordination Compounds

This work presents a detailed evaluation of the performance of density functional theory (DFT) for the prediction of zero-field splittings (ZFSs) in Mn(II) coordination complexes. Eighteen experimentally well characterized four-, five-, and six-coordinate complexes of the general formula [Mn(L)nL'2] with L' = Cl, Br, I, NCS, or N3 (L = an oligodentate ligand) are considered. Several DFT-based approaches for the prediction of the ZFSs are compared. For the estimation of the spin-orbit coupling (SOC) part of the ZFS, it was found that the Pederson-Khanna (PK) approach is more successful than the previously proposed quasi-restricted orbitals (QRO)-based method. In either case, accounting for the spin-spin (SS) interaction either with or without the inclusion of the spin-polarization effects improves the results. This argues for the physical necessity of accounting for this important contribution to the ZFS. On average, the SS contribution represents approximately 30% of the axial D parameters. In addition to the SS part, the SOC contributions of d-d spin flip (alphabeta) and ligand-to-metal charge transfer excited states (betabeta) were found to dominate the SOC part of the D parameter; the observed near cancellation between the alphaalpha and betaalpha parts is discussed in the framework of the PK model. The calculations systematically (correlation coefficient approximately 0.99) overestimate the experimental D values by approximately 60%. Comparison of the signs of calculated and measured D values shows that the signs of the calculated axial ZFS parameters are unreliable once E/D > 0.2. Finally, we find that the calculated D and E/D values are highly sensitive to small structural changes. It is observed that the use of theoretically optimized geometries leads to a significant deterioration of the theoretical predictions relative to the experimental geometries derived from X-ray diffraction. The standard deviation of the theoretical predictions for the D values almost doubles from approximately 0.1 to approximately 0.2 cm-1 upon using quantum chemically optimized structures. We do not find any noticeable improvement in considering basis sets larger than standard double- (SVP) or triple-zeta (TZVP) basis sets or using functionals other than the BP functional.

Xe 129 chemical shift by the perturbational relativistic method: Xenon fluorides

(129)Xe nuclear shielding tensor is calculated at the leading-order, one-electron Breit-Pauli perturbation theory (BPPT) level for the xenon fluorides XeF(+), XeF(2), XeF(3) (+), and XeF(4) that cover the large nuclear magnetic resonance chemical shift range of this nucleus. BPPT is found to improve the shift range and relative shifts as compared to the nonrelativistic (NR) theory. While the full BPPT expansion consists of 16 relativistic terms, 5 of them are responsible for the entire chemical shift and shielding anisotropy. The remaining terms are practically isotropic, corelike contributions that are significant for the absolute shielding constant but cancel for the relative chemical shifts. The five principal terms are due to the spin-orbit-modified wave function allowing the Fermi contact and spin-dipole hyperfine interactions to be coupled to the orbital Zeeman interaction, as well as three distinct scalar relativistic modifications of the NR paramagnetic shielding: wave function change due to mass-velocity and Darwin interactions and the relativistic modification of the orbital hyperfine interaction. A very good agreement with the experimental shifts is obtained for XeF(2) and the particularly challenging XeF(+) species when both the NR and the five main relativistic terms are calculated at electron-correlated ab initio levels of theory. The performance of density-functional theory (DFT) with different pure and hybrid exchange-correlation functionals (with increasing exact exchange admixture) is tested against the ab initio data for each individual contribution. It is shown that DFT has difficulties in the description of paramagnetic shielding, already and especially in the NR contribution, which causes a large discrepancy of DFT results with experiment for xenon fluorides. In contrast, the DFT errors for the relativistic terms cancel out to the extent that a fairly good approximation of the total relativistic shift and anisotropy contributions may be obtained. A combination of high-level ab initio NR calculation with hybrid DFT estimates of the five main BPPT terms is proposed for reasonable estimates of xenon chemical shift in molecules. For the difficult cases such as the present XeF(+) and XeF(3) (+) cations, correlated ab initio calculations are unavoidable throughout. None of the other currently available relativistic methods, either at the fully relativistic or a variationally stable quasirelativistic levels of theory, surpasses the quality of the present approach for Xe shifts in these systems.

Restricted Ensemble-Referenced Kohn-Sham versus Broken Symmetry Approaches in Density Functional Theory: Magnetic Coupling in Cu Binuclear Complexes.

The performance of density functional theory in estimating the magnetic coupling constant in a series of Cu(II) binuclear complexes is investigated by making use of two open shell formalisms: the broken symmetry and the spin-restricted ensemble-referenced Kohn-Sham methods. The strong dependence of the calculated magnetic coupling constants with respect to the exchange-correlation functional is confirmed and found to be independent of whether spin symmetry is imposed or not. The use of a method which guarantees the spin state does not improve the correlation with the experiment and indeed shows some worsening due to an overestimation of the ferromagnetic interactions. However, with the present exchange-correlation functionals, a rather systematic deviation is found. Therefore, it would be possible to develop improved density functionals which will allow for a rigorous treatment of open shell systems in density functional theory.

Benchmarking the performance of density functional theory based Green’s function formalism utilizing different self-energy models in calculating electronic transmission through molecular systems

Electronic transmission through a metal-molecule-metal system is calculated by employing a Green's function formalism in the scattering based scheme. Self-energy models representing the bulk and the potential bias are used to describe electron transport through the molecular system. Different self-energies can be defined by varying the partition between device and bulk regions of the metal-molecule-metal model system. In addition, the self-energies are calculated with different representations of the bulk through its Green's function. In this work, the dependence of the calculated transmission on varying the self-energy subspaces is benchmarked. The calculated transmission is monitored with respect to the different choices defining the self-energy model. In this report, we focus on one-dimensional model systems with electronic structures calculated at the density functional level of theory.

Comment on ‘Pople versus Dunning basis sets for group IA metal hydrides and some other second row hydrides: The case against a De Facto standard’ by R.A. Klein and M.A. Zottola [Chem. Phys. Lett. 419 (2006) 254–258

In their recent Letter, Klein and Zottola [Chem. Phys. Lett. 419 (2006) 254–258] emphasized the superior performance of density functional theory combined with the 6-311++G(2d, p) Pople-style basis set relative to conventional methods, such as second order perturbation theory and coupled cluster theory, with correlation consistent basis sets for the prediction of bond lengths. In this work, we present evidence that the former approach may be less capable of achieving uniformly accurate results for a variety of spectroscopic properties.

An Evaluation of Various Computational Methods for the Treatment of Organoselenium Compounds

A reliable computational method for the prediction of organoselenium geometries and bond dissociation energies (BDEs) has been determined on the basis of the performance of density functional theory (DFT: B3LYP and B3PW91) and ab initio molecular orbital procedures (Hartree-Fock (HF)) in conjunction with various Pople basis sets including (but not limited to) the 6-31G(d), 6-31G(d,p), 6-311G(d), 6-311G(d,p), 6-311G(2df,p), and 6-311G(3df,3pd) sets. Predicted geometries and BDEs are compared with available experimental data and quadratic configuration interaction including single and double substitutions (QCISD) results. The B3PW91/6-311G(2df,p) level of theory is recommended for the prediction of the geometries and energetics of organoselenium compounds.

Diels−Alder Reactions of Cyclopentadiene and 9,10-Dimethylanthracene with Cyanoalkenes: The Performance of Density Functional Theory and Hartree−Fock Calculations for the Prediction of Substituent Effects

The activation enthalpies for the reactions of cyclopentadiene with ethylene, acrylonitrile, fumaronitrile, maleonitrile, vinylidene cyanide, tricyanoethylene, and tetracyanoethylene have been computed with the Hartree-Fock quantum mechanical method and a variety of density functionals (B3LYP, BPW91, and MPW1K) and compared to classic experimental data obtained by Sauer, Wiest, and Mielert (Chem. Ber. 1964, 97, 3183). Some significant errors in B3LYP activation enthalpies involving cyano groups, especially 3 or 4 cyano groups, have been identified, whereas HF and MPW1K reproduce substituent effects quite accurately.

An Efficient a Posteriori Treatment for Dispersion Interaction in Density-Functional-Based Tight Binding.

The performance of density functional theory (DFT) (VWN-LDA, PBE-GGA, and B3LYP hybrid functionals), density-functional-based tight binding (DFTB), and ab initio methods [HF, MP2, CCSD, and CCSD(T)] for the treatment of London dispersion is investigated. Although highly correlated ab initio methods are capable of describing this phenomenon, if they are used with rather large basis sets, DFT methods are found to be inadequate for the description of H2/PAH (polycyclic aromatic hydrocarbon) interactions. As an alternative approach, an a posteriori addition of a van der Waals term to DFTB is proposed. This method provides results for H2/PAH interactions in close agreement with MP2 and higher-level ab initio methods. Bulk properties of graphite also compare well with the experimental data.

On the performance of density functional theory methods in the prediction of the electric polarizability and hyperpolarizability of ozone

We report a study of the performance of density functional theory (DFT) methods in the prediction of electric properties for the ozone molecule. We have used a large, flexible basis set for the calculation of the dipole moment and the dipole (hyper)polarizability with the B1LYP, B3LYP, B3P86, B3PW91, G96PW91 and MPW91PW91 methods. The results are compared to high-level, conventional ab initiomethods. We rely on a rigorous approach in order to evaluate the proximity and similarity of theoretical descriptions obtained via DFT and conventional ab initiomethods. We find that compared to the most accurate ab initio, DFT methods predict reliable dipole polarizabilities and second dipole hyperpolarizabilities for ozone. Agreement is less good for the dipole moment and the first dipole hyperpolarizability. Overall, the performance of the DFT is similar to that of the accurate ab initiomethods.