Density Functional Theory Optimization Research Articles

Mechanism and Stereoselectivity of a Dual Amino-Catalyzed Robinson Annulation: Rare Duumvirate Stereocontrol

Computational study of the mechanisms and stereoselectivities of a dual amino-catalyzed synthesis of cyclohexenones containing all-carbon γ-quaternary and ∂-tertiary stereocenters is reported. Extensive conformational search with density functional theory optimizations, the high-accuracy SCS-MP2/cc-pV∞Z energies, and PCM solvation corrections were used to characterize all intermediates and transition states. Six mechanisms were considered, all consistent with available experiments. The reaction proceeds via sequential Michael and Mannich conjugate additions whereby the primary amine activates the aldehyde and the catalyst activates the pentenone. We have discovered a rare duumvirate stereocontrol: the Michael reaction sets the enantioselectivity, but both the Michael and the Mannich reactions control the diastereoselectivity.

An Empirically Optimized Classical Force-Field for Molecular Simulations of 2,4,6-Trinitrotoluene (TNT) and 2,4-Dinitrotoluene (DNT)

An empirical classical all-atom specific force-field for use in molecular dynamics simulations (MD) has been developed to reproduce the experimental densities and structures of trinitrotoluene (TNT) in its crystalline and liquid phases at six different temperatures, as well as its enthalpies of sublimation and fusion. The average structural parameters and partial charges were obtained from density functional theory optimizations of single molecules at the B3LYP/6-311+G** level. The other constants for the potential were adjusted in order to obtain a classical force-field, which is able to reproduce the aforementioned properties for TNT with a high degree of accuracy. This force-field was also found to predict closely the experimental densities and structures of 2,4-dinitrotoluene (2,4-DNT) in its crystalline and liquid phases as well as its enthalpy of sublimation. It was a bit less successful for its enthalpy of fusion, but it still remained reasonable, and the model mechanical properties were of the right order of magnitude. As such, this fairly simple force-field can be used for MD simulations of both TNT and 2,4-DNT nitroaromatic compounds.

LiCe(BH4)3Cl, a New Lithium-Ion Conductor and Hydrogen Storage Material with Isolated Tetranuclear Anionic Clusters

Mechanochemical synthesis using CeCl3-MBH4 (M = Li, Na or K) mixtures are investigated and produced a new compound, LiCe(BH4)3Cl, which crystallizes in a cubic space group I4̅3m, a = 11.7204(2) Å. The structure contains isolated tetranuclear anionic clusters [Ce4Cl4(BH4)12]4– with a distorted cubane Ce4Cl4 core, charge-balanced by Li+ cations. Each Ce atom coordinates three chloride ions and three borohydride groups via the η3–BH3 faces, thus completing the coordination environment to an octahedron. Combination of synchrotron radiation powder X-ray diffraction (SR-PXD), powder neutron diffraction and density functional theory (DFT) optimization show that Li cations are disordered, occupying 2/3 of the 12d Wyckoff site. DFT calculation indicates that LiCe(BH4)3Cl is stabilized by higher entropy rather than lower enthalpy, in accord with the disorder in Li positions. The structural model also agrees well with the very high lithium ion conductivity measured for LiCe(BH4)3Cl of 1 × 10–4 Scm–1 at T = 20 °C. In situ SR-PXD reveals that the decomposition products consist of LiCl, CeB6 and CeH2. The Sieverts measurements show that 4.7 wt % H2 is released during heating to 500 °C. After rehydrogenation at 400 °C and p(H2) = 100 bar for 24 h an amount of 1.8 wt % H2 is released in the second dehydrogenation. The 11B MAS NMR spectra of the central and satellite transitions for LiCe(B(D/H)4)3Cl reveal highly asymmetric manifolds of spinning sidebands from a single 11B site, reflecting dipolar couplings of the 11B nuclear spin with the paramagnetic electron spin of the Ce3+ ions.

A mixed-cation mixed-anion borohydride NaY(BH4)2Cl2

A new sodium-yttrium borohydride-chloride, NaY(BH4)2Cl2, is obtained by a combination of mechanochemical synthesis and annealing of NaBH4–YCl3 mixtures and is characterized by in-situ synchrotron radiation X-ray powder diffraction, density functional theory, thermal analysis and vibrational spectroscopy. Several simultaneous and coupled reactions occur during the synthesis, also yielding Na3YCl6 and Na(BH4)1−xClx besides the title compound. The polymeric pseudo-orthorhombic crystal structure of NaY(BH4)2Cl2 (space group P2/c) is built of edge- and corner-sharing octahedral coordination polyhedra of yttrium (4Cl + 2BH4) and sodium (2Cl + 4BH4). The structure is isomorphous to the high temperature polymorph of NaYCl4. The BH4 units in NaY(BH4)2Cl2 are located only on the larger of the two independent anion sites in NaYCl4. Density functional theory optimization of the experimental structure suggests that the BH4 units act as η3-ligands (face-sharing) towards yttrium and η1-ligands (corner-sharing) towards sodium. Raman spectroscopy confirms this BH4 configuration. NaY(BH4)2Cl2 decomposes at ∼300 °C under formation of Na3YCl6, while the latter compound at higher temperatures reacts with Na(BH4)1−xClx to form NaCl and possibly amorphous products. The reactions are associated with mass losses of 2.62 and 3.78 wt% for the NaBH4–YCl3 (3:1) and (4:1) samples, respectively.

Theoretical study of different substituent benzenes and benzene dimers blue-shifted hydrogen bonds

Density functional theory (DFT) optimizations at M06-2X/6-31++G (d,p) level had been performed in the T-shaped structures of C6H5R (R=NO2, F, H, OH, CH3, and NH2) with benzene complexes. The interaction energies were calculated by counterpoise (CP)-corrected methods. Among the six dimers, we can see that the C–H⋯π bonded of C6H5NO2⋯benzene complex is the most stable one. Furthermore, the C–H⋯π blue-shifted hydrogen bonds in the dimers were studied. All the C–H bonds of the proton donors showed behavior of the contraction. And the different substituent groups had some effect on the contraction of the C–H bond. In addition, the natural bond orbital (NBO) and atoms in molecules (AIMs) analysis were investigated the origin of C–H⋯π blue-shifted hydrogen bond. From the NBO analysis, it was found that a negligible increase of electron density (ED) on the σ* (C–H) orbital and an increase of an s character of the C–H bond upon complexation were responsible for contraction and strengthening of this C–H bond. The AIM analysis showed that all studied dimers in this paper satisfied the indicative criteria of hydrogen bonding interactions and it was necessary to supplement those criteria with information on the changes in the electron density of the donor X–H bond occurring upon complexation to differentiate between H bonding and anti-H bonding.

Structures, Theoretical Vibrational Frequency and <sup>1</sup>H-NMR Spectral Analysis of Pyrazine-Dibenzylsulfoxide Platinum(II) Complexes

Mixed-ligand Pt(II) complexes containing pyrazine (C4N2H4, pz) and dibenzyl sulfoxide [C6H5CH2)2SO, DBzSO] ligands have been studied using density functional theory (DFT) methods with a particular emphasis on the theoretical1H-NMR spectra of the methylene protons. The DFT optimization calculations on Pt(DBzSO)Cl2(pz) and {Pt(DBzSO)Cl2}2(pz) predicted the structure parameters, vibrational frequency and1H-NMR spectra. Different structures of DBzSO will affect the bond lengths and angles in the complexes, except for the pz ligands. The [shift(Pt(II)complex)-shift(sulfoxide)] values of trans-Pt(DBzSO)(pz)Cl2were smaller than those for cis-Pt(DBzSO)(pz)Cl2and the calculation results appear to be reasonable. The1H-NMR spectra of the methylene protons of cis- and trans-{Pt(DBzSO)Cl2}2(pz) indicate that these two structures have high symmetry.

Nanocatalyst structure as a template to define chirality of nascent single-walled carbon nanotubes

Chirality is a crucial factor in a single-walled carbon nanotube (SWCNT) because it determines its optical and electronic properties. A chiral angle spanning from 0° to 30° results from twisting of the graphene sheet conforming the nanotube wall and is equivalently expressed by chiral indexes (n,m). However, lack of chirality control during SWCNT synthesis is an obstacle for a widespread use of these materials. Here we use first-principles density functional theory (DFT) and classical molecular dynamics (MD) simulations to propose and illustrate basic concepts supporting that the nanocatalyst structure may act as a template to control the chirality during nanotube synthesis. DFT optimizations of metal cluster (Co and Cu)∕cap systems for caps of various chiralities are used to show that an inverse template effect from the nascent carbon nanostructure over the catalyst may exist in floating catalysts; such effect determines a negligible chirality control. Classical MD simulations are used to investigate the influence of a strongly interacting substrate on the structure of a metal nanocatalyst and illustrate how such interaction may help preserve catalyst crystallinity. Finally, DFT optimizations of carbon structures on stepped (211) and (321) cobalt surfaces are used to demonstrate the template effect imparted by the nanocatalyst surface on the growing carbon structure at early stages of nucleation. It is found that depending on the step structure and type of building block (short chains, single atoms, or hexagonal rings), thermodynamics favor armchair or zigzag termination, which provides guidelines for a chirality controlled process based on tuning the catalyst structure and the type of precursor gas.

Crystal structure of the mineral strontiodresserite from laboratory powder diffraction data

The crystal structure of the mineral strontiodresserite, (Sr,Ca)Al2(CO3)2(OH)4⋅H2O, from the Francon Quarry, Montreal, Quebec, Canada, has been solved from laboratory powder diffraction data using a combination of charge-flipping and simulated annealing methods. The structure is orthorhombic in space group Pnma with a=16.0990(7), b=5.6133(3), and c=9.1804(4) Å (Z=4) and the framework of the mineral is isostructural with that of dundasite. The strontium has a coordination number of 9 and the carbonate anions form a bridge between the SrO9 polyhedra and AlO6 octahedra. The water molecule lies in a channel that runs parallel to the b axis. An ordered network of hydrogen atoms could be uniquely determined from crystal-chemical principles in the channels of strontiodresserite. Ab initio density functional theory (DFT) energy minimization of the whole structure gave results in full agreement with X-ray refinement results for nonhydrogen atoms. The stability of this model (as well as that of the corresponding model of dundasite) in the proposed Pnma space group was tested by DFT optimization in space group P1 of random small distortions of this structure. This test confirms that both minerals are isostructural, including their hydrogen-bond networks.

Intramolecular Hydrogen Bond-Controlled Prolyl Amide Isomerization in Glucosyl 3(S)-Hydroxy-5-hydroxymethylproline Hybrids: A Computational Study

Peptide mimics containing spirocyclic glucosyl-(3(S)-hydroxy-5(S)-hydroxymethyl)proline (1) and glucosyl-(3(S)-hydroxy-5(R)-hydroxymethyl)proline (2) hybrids differing in the stereochemistry of the polar hydroxymethyl substitutent at the C-5- or (C(delta))-position have been investigated computationally. A computational "build and search" protocol of molecular mechanics systematic search/Monte Carlo search, followed by density functional theory (DFT), has been developed to ensure complete coverage of the large conformational space. Gas-phase DFT optimizations at the B3LYP level of theory lead to a strong preference for the cis conformation in the prolyl amide bond for both compounds 1 and 2. However, inclusion of the solvent water by means of continuum solvation (PCM) results in a reduction of the prolyl amide cis population in both compounds, leading to good agreement with previous experimental observations. Intramolecular hydrogen bonding involving the C-5-hydroxymethyl substitutent is seen to play a crucial role to tune the thermodynamics of prolyl amide cis/trans isomerization and is responsible for the high cis prolyl amide population in compound 2. Our results indicate that H-bond-forming substituents like the hydroxymethyl group at the C-5-position in proline can be used to control cis/trans prolyl amide isomerization. High cis prolyl amide conformer populations can be achieved by proper choice of the stereochemistry at the C-5-position.

Interaction of brassinolide with essential amino acid residues: A theoretical approach

The interaction of the most active natural brassinosteroid, brassinolide, with the twenty natural amino acids is studied applying the multiple minima hypersurface method to model the molecular interactions explicitly. The resulting thermodynamic data gives useful information about the amino acids with the greatest association for brassinolide and the stabilities of such complexes. Density functional theory (DFT) optimizations were further carried out to test the performance of semiempirical calculations. Additional calculations with a more accurate DFT method were performed to explore the formation of this type of molecular complexes. The semiempirical geometries and stability order of these complexes are in good agreement with the DFT calculations. Each group of amino acids possesses a preferential zone of interaction with brassinolide, forming the polar-charged amino acids the most stable complexes. This study could contribute to future investigations of the interaction of brassinosteroids with the receptor protein in plants.

Adsorption and Diffusion of Light Gases in ZIF-68 and ZIF-70: A Simulation Study

We have computed the adsorption and diffusion of CO2, N2, CH4, and H2 in zeolitic imidazolate framework (ZIF) materials ZIF-68 and ZIF-70 from atomistic simulations. These simulations were performed using geometries obtained from density functional theory (DFT) optimization of the experimental crystal structure of ZIF-68 and on four structures of ZIF-70, one based on the experimental crystal structure and three having different imidazole/nitroimidazole substitution ratios. The framework charges for charge−quadrupole interaction (CQI) terms in our simulations were parametrized with charges obtained from Bader charge decomposition (periodic DFT calculations) and ChelpG charges (cluster DFT calculations). The adsorption and diffusion of the quadrupolar fluids can be dramatically different when using the Bader and ChelpG charges. Agreement between simulations and experiments for the N2 adsorption isotherms in ZIF-68 and 70 is very good when CQI terms are included. In contrast, simulations overpredict the amou...

Systematic conformational search analysis of the SRR and RRR epimers of 7‐hydroxymatairesinol

AbstractAn extensive and systematic conformational search was performed on the two epimers of the natural lignan 7‐hydroxymatairesinol (HMR), by means of a home‐made Systematic Conformational Search Analysis (SCSA) code, designed to select more and more stable conformers through sequential geometry optimization of trial structures at increasing levels of calculation theory. In the present case, the starting molecular structures were selected by the semi‐empirical AM1 method and filtered – i.e. decreased in number by choosing the more stable species – on the basis of their energy calculated by the HF method and the 6‐31G(d) basis set. The geometries obtained were further refined by performing density functional theory (DFT) optimizations, using the B3LYP functional and the 6‐31G(d,p) basis set, both in vacuo and in ethanol solution. This procedure allowed us to isolate, at a high level of theory, three groups of epimer conformers characterized by open, semi‐folded, and folded conformations. Moreover, the SCSA allowed us to describe a conformational space made‐up by about 20 species for each of the two epimers. The corresponding energy content of these species was within 27 kJ mol−1 from the absolute minimum found, both in vacuo and in ethanol solution. The conformational analysis, followed by the inspection of the stereochemistry of the two most stable conformers of both epimers, provides support in rationalizing the proposed reaction mechanism of the catalytic hydrogenolysis of the HMR to matairesinol (MAT). Copyright © 2009 John Wiley & Sons, Ltd.

NMR elucidation of novel ligands derived from (R)-(+)-camphor

The complete NMR elucidation of five camphor-derived ligands is reported. 2D NMR techniques such as NOESY are used to assist in the determination of the orientation of the donor groups in space. The compounds were synthesized as ligands to be used in asymmetric catalysis. They represent the first instance where both donor groups are pendant on the C3 position of the camphor skeleton. The single crystal X-ray structure of one of the ligands was obtained and was helpful in determining the potential NOESY interactions within the molecule. For the other ligands, density functional theory (DFT) optimizations was performed [B3LYP/6-31+g(d)] to visualize possible NOE interactions.

Computational modeling of the dizinc–ferroxidase complex of human H ferritin: direct comparison of the density functional theory calculated and experimental structures

Density functional theory optimizations of structures of dizinc(II) complexes with a six-residue model of the ferroxidase center of human H ferritin have been performed and the results compared with the crystallographically determined structure of the complex as presented in Protein Data Bank file 2CEI. The model employs the full structures of Glu27, Glu62, His65, Glu107, Gln141, and Ala144, and the structural effect of Tyr34 is also examined. The mean absolute deviation from experiment of atomic positions in the best calculated structures is less than 0.3 A. The experimental structure is reproduced well enough to determine the coordination environment of the metal ions. Each zinc(II) center is pentacoordinate with a single water ligand, and the two centers are bridged by a hydroxide ion. Ala144 interacts weakly and repulsively with the rest of the complex. Tyr34 displays a weak attraction through a hydrogen bond to Glu107 that affects the orientation of that group.

Optimization of Spin-Unrestricted Density Functional Theory for Redox Properties of Rubredoxin Redox Site Analogues

Quantum chemical calculations of metal clusters in proteins for redox studies require both computational feasibility as well as accuracies of at least ∼50 mV for redox energies but only ∼0.05 Å for bond lengths. Thus, optimization of spin-unrestricted density functional theory (DFT) methods, especially the hybrid generalized gradient approximation functionals, for energies while maintaining good geometries is essential. Here, different DFT functionals with effective core potential (ECP) and full core basis sets for [Fe(SCH(3))(4)](2-/1-) and [Fe(SCH(3))(3)](1-/0), which are analogs of the iron-sulfur protein rubredoxin, are investigated in comparison to experiment as well as other more computationally intensive electron correlation methods. In particular, redox energies are calibrated against gas-phase photoelectron spectroscopy data so no approximations for the environment are needed. B3LYP gives the best balance of accuracy in energy and geometry compared B97gga1 and BHandH and is better for energies than Møller-Plesset perturbation theory series (MP2, MP3, MP4SDQ) and comparable to coupled cluster [CCSD, CCSD(T)] methods. Of the full core basis sets tested, the 6-31G** basis sets give good geometries, and addition of diffuse functions to only the sulfur significantly improves the energies. Moreover, a basis set with an ECP on only the iron gives a less accurate but still reasonable geometries and energies.

Mössbauer and DFT Study of the Ferromagnetically Coupled Diiron(IV) Precursor to a Complex with an FeIV2O2 Diamond Core

Recently, we reported the reaction of the (mu-oxo)diiron(III) complex 1 ([Fe(III)(2)(mu-O)(mu-O(2)H(3))(L)(2)](3+), L = tris(3,5-dimethyl-4-methoxypyridyl-2-methyl)amine) with 1 equiv of H(2)O(2) to yield a diiron(IV) intermediate, 2 (Xue, G.; Fiedler, A. T.; Martinho, M.; Munck, E.; Que, L., Jr. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 20615-20). Upon treatment with HClO(4), complex 2 converted to a species with an Fe(IV)(2)(mu-O)(2) diamond core that serves as the only synthetic model to date for the diiron(IV) core proposed for intermediate Q of soluble methane monooxygenase. Here we report detailed Mossbauer and density functional theory (DFT) studies of 2. The Mossbauer studies reveal that 2 has distinct Fe(IV) sites, a and b. Studies in applied magnetic fields show that the spins of sites a and b (S(a) = S(b) = 1) are ferromagnetically coupled to yield a ground multiplet with S = 2. Analysis of the applied field spectra of the exchange-coupled system yields for site b a set of parameters that matches those obtained for the mononuclear [LFe(IV)(O)(NCMe)](2+) complex, showing that site b (labeled Fe(O)) has a terminal oxo group. Using the zero-field splitting parameters of [LFe(IV)(O)(NCMe)](2+) for our analysis of 2, we obtained parameters for site a that closely resemble those reported for the nonoxo Fe(IV) complex [(beta-BPMCN)Fe(IV)(OH)(OO(t)Bu)](2+), suggesting that a (labeled Fe(OH)) coordinates a hydroxo group. A DFT optimization performed on 2 yielded an Fe-Fe distance of 3.39 A and an Fe-(mu-O)-Fe angle of 131 degrees , in good agreement with the results of our previous EXAFS study. The DFT calculations reproduce the Mossbauer parameters (A-tensors, electric field gradient, and isomer shift) of 2 quite well, including the observation that the largest components of the electric field gradients of Fe(O) and Fe(OH) are perpendicular. The ferromagnetic behavior of 2 seems puzzling given that the Fe-(mu-O)-Fe angle is large but can be explained by noting that the orbital structures of Fe(O) and Fe(OH) are such that the unpaired electrons at the two sites delocalize into orthogonal orbitals at the bridging oxygen, rationalizing the ferromagnetic behavior of 2. Thus, inequivalent coordinations at Fe(O) and Fe(OH) define magnetic orbitals favorable for ferromagnetic ineractions.

DFT Comparison of Fe2+ Hydration in the Binding Sites of the Ferroxidase Center of Bullfrog M Ferritin

Density functional theory optimizations have been conducted on structures of complexes of Fe(2+) with (H(2)O)(n) (n = 0-3) in three-residue models of binding sites A and B of the ferroxidase center of bullfrog M ferritin. Each site is modeled by the full structures of its three active amino acids. The potential surface at each site in the presence of water molecules is complex; coordination numbers of iron from three to six are seen. Water contributes to the complexity through its ability to hydrogen bond, to coordinate to iron, and to displace the neutral ligands glutamine and histidine. Intrinsic differences are noted at each site; at site B, the most stable complexes are found to favor tetracoordinate iron, while pentacoordination is preferred at site A in the two- and three-water complexes. While each incremental addition of a water molecule results in increased stability, successive binding energies are found to decrease.

The structure of mixed H2O–OH monolayer films on Ru(0001)

Scanning tunneling microscopy (STM) and x-ray absorption spectroscopy (XAS) have been used to study the structures produced by water on Ru(0001) at temperatures above 140 K. It was found that while undissociated water layers are metastable below 140 K, heating above this temperature produces drastic transformations, whereby a fraction of the water molecules partially dissociate and form mixed H(2)O-OH structures. X-ray photoelectron spectroscopy and XAS revealed the presence of hydroxyl groups with their O-H bond essentially parallel to the surface. STM images show that the mixed H(2)O-OH structures consist of long narrow stripes aligned with the three crystallographic directions perpendicular to the close-packed atomic rows of the Ru(0001) substrate. The internal structure of the stripes is a honeycomb network of H-bonded water and hydroxyl species. We found that the metastable low temperature molecular phase can also be converted to a mixed H(2)O-OH phase through excitation by the tunneling electrons when their energy is 0.5 eV or higher above the Fermi level. Structural models based on the STM images were used for density functional theory optimizations of the stripe geometry. The optimized geometry was then utilized to calculate STM images for comparison with the experiment.

Structural transition of hexagonal tube to rocksalt for (MgO)3n, 2≤n≤10

The structures of (MgO)(3n) (2<or=n<or=10) clusters are studied using density functional theory (DFT). The starting structures are generated from empirical genetic algorithm simulations. The lowest-energy structures of (MgO)(3n) are then obtained from a number of structural isomers by using DFT optimization. It is found that when n<or=5 hexagonal tube is the most stable structure, and when n>or=6 (except 7) the rocksaltlike structure is favored, which is the same as that of the bulk. The n=7 is an interesting case, where the structure again is the hexagonal tube as the most stable structure. However, from the second order difference of the average atomization energy, we find that the n=7 case is thermodynamically unstable with respect to disproportionation to the smaller and larger clusters. The result may be the reason that it is not observed in the experiment. Therefore, we can conclude that the geometry transition really takes place at n=6. The rocksalt is the most stable structure for a large range of n numbers, from the (MgO)(3x6) cluster to bulk magnesium oxide. The result is different from Wilson's previous prediction because of the use of the ionic potential.

Assessment of the Accuracy of Density Functionals for Prediction of Relative Energies and Geometries of Low-Lying Isomers of Water Hexamers

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug'-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasi-perturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order Møller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.