A new database and benchmark of the bond energies of noble-gas-containing molecules

We have developed a new database of structures and bond energies of 59 noble-gas-containing molecules. The structures were calculated by CCSD(T)/aug-cc-pVTZ methods and the bond energies were obtained using the CCSD(T)/complete basis set method. Many wavefunction-based and density functional theory methods have been benchmarked against the 59 accurate bond energies. Our results show that the MPW1B95, B2GP-PLYP, and DSD-BLYP functionals with the aug-cc-pVTZ basis set excel in predicting the bond energies of noble-gas molecules with mean unsigned errors (MUEs) of 2.0 to 2.1 kcal/mol. When combinations of Dunning's basis sets are used, the MPW1B95, B2GP-PLYP, DSD-BLYP, and BMK functionals give significantly lower MUEs of 1.6 to 1.9 kcal/mol. Doubly hybrid methods using B2GP-PLYP and DSD-BLYP functionals and MP2 calculation also provide satisfactory accuracy with MUEs of 1.4 to 1.5 kcal/mol. If the Ng bond energies and the total atomization energies of a group of 109 main-group molecules are considered at the same time, the MPW1B95/aug-cc-pVTZ single-level method (MUE = 2.7 kcal/mol) and the B2GP-PLYP and DSD-PLYP functionals with combinations of basis sets or using the doubly hybrid method (MUEs = 1.9-2.2 kcal/mol) give the overall best result.     

Microwave spectrum of 3-butyne-1-thiol: evidence for intramolecular S-H...pi hydrogen bonding

The microwave spectrum of 3-butyne-1-thiol has been studied by means of Stark-modulation microwave spectroscopy and quantum-chemical calculations employing the B3LYP/6-311++G(3df,2pd), MP2/aug-cc-pVTZ, MP2/6-311++G(3df,2pd), and G3 methods. Rotational transitions attributable to two conformers of this molecule were assigned. One of these conformers possesses an antiperiplanar arrangement of the atoms S-C1-C2-C3, while the other is synclinal and stabilized by the formation of an intramolecular hydrogen bond between the H-atom of the thiol group and the pi-electrons of the C[triple bond]C triple bond. The energy difference between these conformers was estimated to be 1.7(4) kJ mol(-1) by relative intensity measurements, with the hydrogen-bonded conformer being lower in energy. The spectra of five vibrationally excited states of the synclinal conformer were observed, and an assignment of these states to particular vibrational modes was made with the aid of a density functional theory (DFT) calculation of the vibrational frequencies at the B3LYP/6-311++G(3df,2pd) level of theory.     

Basis set and method dependence in quantum theory of atoms in molecules calculations for covalent bonds

The influence of various small- and medium-size basis sets used in Hartree-Fock (HF) and density functional theory (DFT)/B3LYP calculations on results of quantum theory of atoms in molecules based (QTAIM-based) analysis of bond parameters is investigated for several single, double, and triple covalent bonds. It is shown that, in general, HF and DFT/B3LYP methods give very similar QTAIM results with respect to the basis set. The smallest 6-31G basis set and DZ-quality basis sets of Dunning type lead to poor results in comparison to those obtained by the most reliable aug-cc-pVTZ. On the contrary, 6-311++G(2df,2pd) and in a somewhat lesser extent 6-311++G(3df,3pd) basis sets give satisfactory values of QTAIM parameters. It is also demonstrated that QTAIM calculations may be sensitive for the method and basis set in the case of multiple and more polarized bonds.     

An assessment of theoretical procedures for predicting the thermochemistry and kinetics of hydrogen abstraction by methyl radical from benzene

The reaction enthalpy (298 K), barrier (0 K), and activation energy and preexponential factor (600-800 K) have been examined computationally for the abstraction of hydrogen from benzene by the methyl radical, to assess their sensitivity to the applied level of theory. The computational methods considered include high-level composite procedures, including W1, G3-RAD, G3(MP2)-RAD, and CBS-QB3, as well as conventional ab initio and density functional theory (DFT) methods, with the latter two classes employing the 6-31G(d), 6-31+G(d,p) and/or 6-311+G(3df,2p) basis sets, and including ZPVE/thermal corrections obtained from 6-31G(d) or 6-31+G(d,p) calculations. Virtually all the theoretical procedures except UMP2 are found to give geometries that are suitable for subsequent calculation of the reaction enthalpy and barrier. For the reaction enthalpy, W1, G3-RAD, and URCCSD(T) give best agreement with experiment, while the large-basis-set DFT procedures slightly underestimate the endothermicity. The reaction barrier is slightly more sensitive to the choice of basis set and/or correlation level, with URCCSD(T) and the low-cost BMK method providing values in close agreement with the benchmark G3-RAD value. Inspection of the theoretically calculated rate parameters reveals a minor dependence on the level of theory for the preexponential factor. There is more sensitivity for the activation energy, with a reasonable agreement with experiment being obtained for the G3 methods and the hybrid functionals BMK, BB1K, and MPW1K, especially in combination with the 6-311+G(3df,2p) basis set. Overall, the high-level G3-RAD composite procedure, URCCSD(T), and the cost-effective DFT methods BMK, BB1K, and MPW1K give the best results among the methods assessed for calculating the thermochemistry and kinetics of hydrogen abstraction by the methyl radical from benzene.     

Thermochemistry, bond energies, and internal rotor potentials of dimethyl tetraoxide

Thermochemical properties of dimethyl tetraoxide (CH(3)OOOOCH(3)), the dimer of the methylperoxy radical, are studied using ab initio and density functional theory methods. Methylperoxy radicals are known to be important intermediates in the tropospheric ozone cycle, and the self-reaction of methylperoxy radicals, which is thought to proceed via dimethyl tetraoxide, leads to significant chain radical termination in this process. Dimethyl tetraoxide has five internal rotors, three of them unique; the potential energy profiles are calculated for these rotors, as well as for those in the CH(3)OO, CH(3)OOO, and CH(3)OOOO radicals. The dimethyl tetraoxide internal rotor profiles show barriers to rotation of 2-8 kcal mol(-1). Using B3LYP/6-31(d) geometries, frequencies, internal rotor potentials, and moments of inertia, we determine entropy and heat capacity values for dimethyl tetraoxide and its radicals. Isodesmic work reactions with the G3B3 and CBS-APNO methods are used; we calculate this enthalpy as -9.8 kcal mol(-1). Bond dissociation energies (BDEs) are calculated for all C-O and O-O bonds in dimethyl tetraoxide, again with the G3B3 and CBS-APNO theoretical methods, and we suggest the following BDEs: 46.0 kcal mol(-1) for CH(3)-OOOOCH(3), 20.0 kcal mol(-1) for CH(3)O-OOOCH(3), and 13.9 kcal mol(-1) for CH(3)OO-OOCH(3). From the BDE calculations and the isodesmic enthalpy of formation for dimethyl tetraoxide, we suggest enthalpies of 2.1, 5.8, and 1.4 kcal mol(-1) for the CH(3)OO, CH(3)OOO, and CH(3)OOOO radicals, respectively. We evaluate the suitability of 10 different density functional theory (DFT) methods for calculating thermochemical properties of dimethyl tetraoxide and its radicals with the 6-31G(d) and 6-311++G(3df,3pd) basis sets, using a variety of work reaction schemes. Overall, the best-performed DFT methods of those tested were TPSSh, BMK, and B1B95. Significant improvements in accuracy were made by moving from atomization to isodesmic work reactions, with most DFT methods yielding errors of less than 2 kcal mol(-1) with the 6-311++G(3df,3pd) basis set for isodesmic calculations on the dimethyl tetraoxide enthalpy. These isodesmic calculations were basis set consistent, with a considerable reduction in error found by using the 6-311++G(3df,3pd) basis set over the 6-31G(d) basis set. This was not the case, however, for atomization and bond dissociation work reactions, where the two basis sets returned similar results. Improved group additivity terms for the O-O-O moiety (O/O2 central atom group) are also determined.     

Theoretical Studies on Structures and Stabilities of C4H2+ Isomers

The structures, energies, stabilities and spectroscopies of doublet C₄H₂⁺ cations were explored at the DFT/B3LYP/6-311G(d,p), CCSD(T)/6-311+G(2df,2pd)(single-point), and G3B3 levels. Ten minimum isomers including the chainlike, three-member-ring, and four-member-ring structures are interconverted by means of 15 interconversion transition states. The potential energy surface was investigated. At the CCSD(T)/6-311+G(2df,2pd) and G3B3 levels, the global minimum isomer was found to be a linear HCCCCH. The structures of the stable isomer and its relevant transition state are further optimized at the QCISD/6-311G(d,p) level. The bonding nature and structure of isomer HCCCCH were analyzed.     

Performance of density functionals for calculation of reductive ring-opening reaction energies of Li<Superscript>+</Superscript>-EC and Li<Superscript>+</Superscript>-VC

Reaction energies were determined for reductive ring-opening reactions of Li⁺-coordinated ethylene carbonate (EC) and vinylene carbonate (VC) by using various density functional theory (DFT) and ab-initio methods applying the basis sets up to Dunnings aug-cc-pVQZ. The methods examined include the local density functional (SVWN), the pure gradient-corrected density functionals (BLYP and BPW91), and the hybrid density functionals (B3LYP, B1LYP, B3PW91, and mPW1PW91). Comparison of the DFT results with ab-initio results indicates that the mPW1PW91 approach introduced by Adamo and Barone, is superior to all the other DFT methods (including B3LYP). The performance of more cost-effective Pople-type basis sets ranging from 6-31G(d,p) to 6-311++G(3df,3pd) was assessed at DFT levels of theory by calibrating them with the aug-cc-pVQZ results     

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.     

An evaluation of harmonic vibrational frequency scale factors

Scale factors for obtaining fundamental vibrational frequencies, low-frequency vibrational frequencies, zero-point vibrational energies (ZPVEs), and thermal contributions to enthalpy and entropy have been derived through a least-squares approach from harmonic frequencies determined at more than 100 levels of theory. Wave function procedures (HF, MP2, QCISD, QCISD(T), CCSD, and CCSD(T)) and a large and representative range of density functional theory (DFT) approaches (B3-LYP, BMK, EDF2, M05-2X, MPWB1K, O3-LYP, PBE, TPSS, etc.) have been examined in conjunction with basis sets such as 6-31G(d), 6-31+G(d,p), 6-31G(2df,p), 6-311+G(d,p), and 6-311+G(2df,p). The vibrational frequency scale factors were determined by a comparison of theoretical harmonic frequencies with the corresponding experimental fundamentals utilizing a standard set of 1066 individual vibrations. ZPVE scale factors were generally obtained from a comparison of the computed ZPVEs with experimental ZPVEs for a smaller standard set of 39 molecules, though the effect of expansion to a 48 molecule data set was also examined. In addition to evaluating the scale factors for a wide range of levels of theory, we have also probed the effect on scale factors of varying the percentage of incorporated exact exchange in hybrid DFT calculations using a modified B3-LYP functional. This has revealed a near-linear relationship between the magnitude of the scale factor and the proportion of exact exchange. Finally, we have investigated the effect of basis set size on HF, MP2, B3-LYP, and BMK scale factors by deriving values with basis sets ranging from 6-31G(d) up to 6-311++G(3df,3pd) as well as with basis sets in the cc-pVnZ and aug-cc-pVnZ series and with the TZV2P basis.     

Density functional theory and post-Hartree-Fock studies on molecular structure and harmonic vibrational spectrum of formaldehyde

Density functional theory (DFT) with the Becke's three-parameter exchange correlation functional and the functional of Lee, Yang and Parr, gradient-corrected functionals of Perdew, and Perdew and Wang [the DFT(B3LYP), DFT(B3P86) and DFT(B3PW91) methods, respectively], and several levels of conventional ab initio post-Hartree-Fock theory (second- and fourth-order perturbation theory M?ller-Plesset MP2 and MP4(SDTQ), coupled cluster with the single and double excitations (CCSD), and CCSD with perturbative triple excitation [CCSD(T)], configuration interaction with the single and double excitations [CISD], and quadratic configuration interaction method [QCISD(T)], using several basis sets [ranging from a simple 6-31G(d,p) basis set to a 6-311+ +G(3df, 2pd) one], were applied to study of the molecular structure (geometrical parameters, rotational constants, dipole moment) and harmonized infrared (IR) spectrum of formaldehyde (CH₂O). High-level ab initio methods CCSD(T) and QCISD(T) with the 6-311+ +G(3df, 2pd) predict correctly molecular parameters, vibrational harmonic wavenumbers and the shifts of the harmonic IR spectrum of ¹²CH₂ ¹⁶O upon isotopic substitution. Received: 30 January 1997 / Accepted: 7 May 1997     

High-level ab initio versus DFT calculations on (H2O2)2 and H2O2–H2O complexes as prototypes of multiple hydrogen bond systems

The performance of B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91 density functionals to describe multiple hydrogen bond systems was studied. For this purpose we have chosen the dimers of hydrogen peroxide and the hydrogen peroxide–water complexes. The geometries and vibrational frequencies obtained with a 6-311+G(d,p) basis set were compared with those obtained at the MP2 level using the same basis set expansion. The corresponding dimerization energies were obtained using a 6-311+G(3df,2p) basis set and compared with those obtained using the G2(MP2) theory. Red shiftings of the OH donor stretching frequencies were predicted by all approaches investigated; however, in all cases, the DFT values were sizably larger than the MP2 ones. Similarly, the blue shifting of the torsion of the hydrogen peroxide subunit was larger when evaluated at the DFT level. All functionals reproduced the G2(MP2) relative stabilities of the different local minima quite well. With the exception of the B-LYP and B3-PW91 approaches, all functionals yielded binding energies which deviated from the G2(MP2) values by less than 0.5 kcal/mol, provided that G2-type basis sets were used and that the corresponding BSSE corrections were included. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1124–1135     

Computational study of hydrogen-bonded complexes of HOCO with acids: HOCO⋯HCOOH, HOCO⋯H(2)SO(4), and HOCO⋯H(2)CO(3)

Quantum chemistry calculations at the density functional theory (DFT) (B3LYP), MP2, QCISD, QCISD(T), and CCSD(T) levels in conjunction with 6-311++G(2d,2p) and 6-311++G(2df,2p) basis sets have been performed to explore the binding energies of open-shell hydrogen bonded complexes formed between the HOCO radical (both cis-HOCO and trans-HOCO) and trans-HCOOH (formic acid), H(2)SO(4) (sulfuric acid), and cis-cis-H(2)CO(3) (carbonic acid). Calculations at the CCSD(T)∕6-311++G(2df,2p) level predict that these open-shell complexes have relatively large binding energies ranging between 9.4 to 13.5 kcal∕mol and that cis-HOCO (cH) binds more strongly compared to trans-HOCO in these complexes. The zero-point-energy-corrected binding strengths of the cH?Acid complexes are comparable to that of the formic acid homodimer complex (～13-14 kcal∕mol). Infrared fundamental frequencies and intensities of the complexes are computed within the harmonic approximation. Infrared spectroscopy is suggested as a potential useful tool for detection of these HOCO?Acid complexes in the laboratory as well as in various planetary atmospheres since complex formation is found to induce large frequency shifts and intensity enhancement of the H-bonded OH stretching fundamental relative to that of the corresponding parent monomers. Finally, the ability of an acid molecule such as formic acid to catalyze the inter-conversion between the cis- and trans-HOCO isomers in the gas phase is also discussed.     

Theoretical Study on the Structures and Isomerization of Germylenoid GeH2LiCl

Using geometrical optimization and DFT method at the B3LYP/6-311++G (3df,3pd) level, four equilibrium geometries and one transition state of GeH2LiCl were identified, and the structures at the MP2/6-311++G(3df,3pd) level were calculated simultaneously. We also studied the solvent effects on the structures of Germylenoid GeH2LiCl at the B3LYP/6-311++G (3df,3pd) level. The two more stable forms are suggested to be the p-complex and three-membered ring. The vibrational frequencies and infrared intensities were computed at the B3LYP/6-311++G (3df,3pd) level.     

Intermolecular potentials of the silane dimer calculated with Hartree-Fock theory, Møller-Plesset perturbation theory, and density functional theory

We have calculated the intermolecular interaction potentials of the silane dimer at the D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order M?ller-Plesset (MP2) perturbation theory, and the density functional theory (DFT) with 108 functionals chosen from the combinations of 9 exchange and 12 correlation functionals. Single-point coupled cluster [CCSD(T)] calculations have also been carried out to calibrate the correlation effect. The HF calculations yield unbound potentials largely because of the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. We have employed basis sets from the Slater type orbitals fitted with Gaussian functions (STO-nG, n = 3 approximately 6), Pople's medium size basis sets [up to 6-311++G(3df,3pd)], to Dunning's correlation consistent basis sets (cc-pVXZ and aug-cc-pVXZ, X = D, T, Q). With increasing basis size, the repulsion exponent and the equilibrium bond length converge at the 6-31G** basis set and the 6-311++G(3d,3p) basis set, respectively, while a large basis set (aug-cc-pVTZ) is required to converge the binding energy at a chemical accuracy ( approximately 0.05 kcal/mol). Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the expected C6 value from molecular polarizability calculations. We attribute the slow convergence partly to the inefficacy of using the MP2 calculations with Gaussian type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the expected potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, from purely unbound to strongly bound, underestimating or overestimating the binding energy. The binding energies calculated using the OPTXHCTH147, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals and the equilibrium bond lengths calculated using the MPWHCTH93, TPSSHCTH, PBEVP86, PBEP86, PW91TPSS, PW91PBE, and PW91PW91 functionals are close to the MP2 results using the 6-311++G(3df,3pd) basis set. A correlation between the calculated DFT potentials and the exchange and correlation enhancement factors at the low-density region has been elucidated. The asymptotic behaviors of the DFT potentials are also analyzed.     

F原子与瞬态自由基CH_2SH反应的理论研究

用量子化学从头算和密度泛函理论（DFT）对F原子与自由基CH_2SH在势能面上 的反应进行了研究。在B3LYP/6-311G水平上计算出了各物种的优化构型、振动频率 和零点振动能(ZPVE);各物种的总能量由B3LYP/6-311 + G(2df, pd)//B3LYP/6- 311G计算,另外对反应物和产物还计算了其G3能量。结果表明：首先F通过与C或S 结合的两种途径与CH_2SH相配位,再通过H（4）原子转移形成甲基,然后甲基再旋 转,甲基中H（4）原子最终与F结合,反应产物为HF和CH_2S。反应为放热反应,分 别为ΔH_r = -370.7 kJ/mol (DFT)和-396.94 kJ/mol (G3)。此外依据计算出的反 应热,可得自由基·CH_2SH的生成热Δ_fH°_(298.15) = 146.44 kJ/mol (DFT), 而Δ_fH°_0 = 167.36 kJ/mol (G3)。它们与以前的实验和理论值是一致的。     

The observed and calculated 1H and 13C chemical shifts of tertiary amines and their N-oxides

A series of model tertiary amines were oxidized in situ in an NMR tube to amine N-oxides and their (1)H and (13)C NMR spectra were recorded. Next, the chemical shifts induced by oxidation (Δδ) were calculated using different GIAO methods investigating the influence of the method [Hartree-Fock (HF), Moeller-Plesset perturbation, density functional theory (DFT)], the functional applied in the DFT (B3LYP, BPW, OPBE, OPW91) and the basis set used [6-31G*, 6-311G**, 6-311 + + G** and 6-311 + + G(3df,3pd)]. The best results were obtained with the HF/6-311 + + G** and OPBE/6-311 + + G** methods. The computation/experiment comparison approach was used for the configuration prediction of chiral amine N-oxides-(R) and (S)-agroclavine-6-N-oxide.     

An Ab Initio Study of the Complexes Formed by the Positive Acetylene Ion with the Hydrogen and Nitrogen Molecules and the Argon Atom

The complexes formed by the positive acetylene ion with the hydrogen molecule, the nitrogen molecule, and the argon atom are investigated with ab initio calculations using the 6-311G** and the 6-31+G(2df,2pd) basis sets. MP2/6-311G** energies and optimum geometries are obtained, as well as single-point MP3, MP4, and QCISD(T) energies with the MP2/6-311G** optimized geometries. Single-point calculations are performed with the 6-31+G(2df,2pd) basis set at MP2/6-311G** optimized geometries.     

Barrier heights for H‐atom abstraction by HȮ2 from n‐butanol—A simple yet exacting test for model chemistries?

The barrier heights involved in the abstraction of a hydrogen atom from n‐butanol by the hydroperoxyl radical have been computed with both compound (CBS‐QB3, CBS‐APNO, G3) and coupled cluster methods. In particular, the benchmark computations CCSD(T)/cc‐pVTZ//MP2/6‐311G(d,p) were used to determine that the barrier heights increase in the order α <γ < β < δ < OH. Two prereaction hydrogen‐bonded complexes are formed, one of which connects the TGt conformer of n‐butanol to the α and β transition states and the other connects to the γ and OH channels from the TGg conformer. Four postreaction complexes were also found which link the transition states to the products, hydrogen peroxide + C₄H₉O radical. Abstraction from the terminal δ carbon atom does not involve either a pre or postreaction complex. A number of DFT functionals—B3LYP, BMK, MPWB1K, BB1K, MPW1K, and M05‐2X—were tested to see whether the correct ranking could be obtained with computationally less expensive methods. Only the later functional predicts the correct order but requires a basis set of 6‐311++G(df,pd) to achieve this. However, the absolute values obtained do not agree that well with the benchmarks; the composite G3 method predicts the correct order and comes closest (≤ 2 kJ, mol ^?1) in absolute numerical terms for H‐abstraction from carbon. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Design of density functionals that are broadly accurate for thermochemistry, thermochemical kinetics, and nonbonded interactions

This paper develops two new hybrid meta exchange-correlation functionals for thermochemistry, thermochemical kinetics, and nonbonded interactions. The new functionals are called PW6B95 (6-parameter functional based on Perdew-Wang-91 exchange and Becke-95 correlation) and PWB6K (6-parameter functional for kinetics based on Perdew-Wang-91 exchange and Becke-95 correlation). The resulting methods were comparatively assessed against the MGAE109/3 main group atomization energy database, against the IP13/3 ionization potential database, against the EA13/3 electron affinity database, against the HTBH38/4 and NHTBH38/04 hydrogen-transfer and non-hydrogen-transfer barrier height databases, against the HB6/04 hydrogen bonding database, against the CT7/04 charge-transfer complex database, against the DI6/04 dipole interaction database, against the WI7/05 weak interaction database, and against the new PPS5/05 pi-pi stacking interaction database. From the assessment and comparison of methods, we draw the following conclusions, based on an analysis of mean unsigned errors: (i) The PW6B95, MPW1B95, B98, B97-1, and TPSS1KCIS methods give the best results for a combination of thermochemistry and nonbonded interactions. (ii) PWB6K, MPWB1K, BB1K, MPW1K, and MPW1B95 give the best results for a combination of thermochemical kinetics and nonbonded interactions. (iii) PWB6K outperforms the MP2 method for nonbonded interactions. (iv) PW6B95 gives errors for main group covalent bond energies that are only 0.41 kcal (as measured by mean unsigned error per bond (MUEPB) for the MGAE109 database), as compared to 0.56 kcal/mol for the second best method and 0.92 kcal/mol for B3LYP.