Pople Basis Sets Research Articles

Role of dispersion corrected hybrid GGA class in accurately calculating the bond dissociation energy of carbon halogen bond: A benchmark study

Benchmark study has been carried out to find a cost effective and accurate method for bond dissociation energy (BDE) of carbon halogen (CX) bond. BDE of C-X bond plays a vital role in chemical reactions, particularly for kinetic barrier and thermochemistry etc. The compounds (1–16, Fig. 1) with CX bond used for current benchmark study are important reactants in organic, inorganic and bioorganic chemistry. Experimental data of CX bond dissociation energy is compared with theoretical results. The statistical analysis tools such as root mean square deviation (RMSD), standard deviation (SD), Pearson's correlation (R) and mean absolute error (MAE) are used for comparison. Overall, thirty-one density functionals from eight different classes of density functional theory (DFT) along with Pople and Dunning basis sets are evaluated. Among different classes of DFT, the dispersion corrected range separated hybrid GGA class along with 6-31G(d), 6-311G(d), aug-cc-pVDZ and aug-cc-pVTZ basis sets performed best for bond dissociation energy calculation of C-X bond. ωB97XD show the best performance with less deviations (RMSD, SD), mean absolute error (MAE) and a significant Pearson's correlation (R) when compared to experimental data. ωB97XD along with Pople basis set 6–311g(d) has RMSD, SD, R and MAE of 3.14 kcal mol−1, 3.05 kcal mol−1, 0.97 and −1.07 kcal mol−1, respectively.▪

Effects of CO/CO2/NO on elemental lead adsorption on carbonaceous surfaces.

The adsorption processes of elemental lead on carbonaceous surfaces which adsorbed CO/CO2/NO flue gases were investigated to understand the effects of CO/CO2/NO on elemental lead adsorption on carbonaceous surfaces with density functional theory. All calculations including optimizations, energies, and frequencies were conducted at B3PW91 density functional theory level, utilizing SDD basis set for lead and 6-31G(d) Pople basis set for other atoms. The results indicate that CO, CO2, and NO can promote the adsorption of elemental lead on the carbonaceous surface, but probably compete for adsorption sites with elemental lead. The promotion effects on adsorption can be attributed to active sites on the carbonaceous surface rather than flue gas adsorption on the carbonaceous surface. In addition, the adsorption order of three kinds of flue gas on the carbonaceous surface is CO2 > NO > CO > Pb on average. Furthermore, the enhancement order of three kinds of flue gas on the elemental lead adsorption on carbonaceous surfaces is CO-CS > CO2-CS > NO-CS > CS in general. In particular, atomic charge and adsorption energy have good linear relationship in the process of elemental lead adsorption. Graphical Abstract Competitive adsorption between flue gas and elemental lead on carbonaceous surfaces.

A comparative examination of density functional performance against the ISOL24/11 isomerization energy benchmark

The isomerization energy (ΔisomE) performance of a wide range of density functionals was tested against the set of 24 individual intramolecular reactions collectively comprising the ISOL24/11 benchmark database. Among 50 non-dispersion corrected functionals examined, the M06-2X single-component density functional offered the best estimation capacity, yielding a mean unsigned error (MUE) of 2.4kcal/mol. The addition of molecular mechanics dispersion-like terms to the M06-2X functional offers minimal improvement in its capacity to reliably estimate isomerization energies, whereas the choice of basis set played a significant role. Triple zeta Dunning, Ahlrichs, and Pople basis sets offer effectively equivalent ΔisomE performance, modestly better than double zeta equivalent basis sets, with ΔisomE performance subsequently rapidly declining at basis set sizes below this level. Among a reduced set of dispersion corrected functionals considered, the APFD functional displayed ΔisomE performance (MUE=1.8kcal/mol) superior to both the non-dispersion corrected M06-2X functional and the wB97X-D and PBE0-D3 dispersion corrected functionals (1.9kcal/mol). At this accuracy, the APFD functional is competitive with computationally expensive high-accuracy methods such as MC3MPWB and MC3MPW and nearing that of composite methods and dispersion corrected double-hybrid density functionals.

Unravelling Protein-DNA Interactions at Molecular Level: A DFT and NCI Study.

Histone-DNA interactions were probed computationally at a molecular level, by characterizing the bimolecular clusters constituted by selected amino acid derivatives with polar (asparagine and glutamine), nonpolar (alanine, valine, and isoleucine), and charged (arginine) side chains and methylated pyrimidinic (1-methylcytosine and 1-methylthymine) and puric (9-methyladenine and 9-methylguanine) DNA bases. The computational approach combined different methodologies: a molecular mechanics (MMFFs forced field) conformational search and structural and vibrational density-functional calculations (M06-2X with double and triple-ζ Pople's basis sets). To dissect the interactions, intermolecular forces were analyzed with the Non-Covalent Interactions (NCI) analysis. The results for the 24 different clusters studied show a noticeable correlation between the calculated binding energies and the propensities for protein-DNA base interactions found in the literature. Such correlation holded even for the interaction of the selected amino acid derivatives with Watson and Crick pairs. Therefore, the balance between hydrogen bonds and van der Waals interactions (specially stacking) in the control of the final shape of the investigated amino acid-DNA base pairs seems to be well reproduced in dispersion-corrected DFT molecular models, reinforcing the idea that the specificity between the amino acids and the DNA bases play an important role in the regulation of DNA.

Predicting the structure and vibrational frequencies of ethylene using harmonic and anharmonic approaches at the Kohn-Sham complete basis set limit.

In this work, regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limit are demonstrated for the first time. The performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with two Pople basis sets (6-311++G** and 6-311++G(3df,2pd)), the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, 6) was tested.The BLYP-calculated harmonic frequencies were found to be markedly closer than the B3LYP-calculated harmonic frequencies to the experimentally derived values, while the calculated anharmonic frequencies consistently underestimated the observed wavenumbers. The different basis set families gave very similar estimated values for the CBS parameters. The anharmonic frequencies calculated with B3LYP/aug-pc-3 were consistently significantly higher than those obtained with the pc-3 basis set; applying the aug-pcseg-n basis set family alleviated this problem. Utilization of B3LYP/aug-pcseg-n basis sets instead of B3LYP/aug-cc-pVXZ, which is computationally less expensive, is suggested for medium-sized molecules. Harmonic BLYP/pc-2 calculations produced fairly accurate ethylene frequencies.Graphical In this study, the performance of the VPT2 scheme implemented using density functional theory (DFT-BLYP and DFT-B3LYP) in combination with the polarization-consistent basis sets pc-n, aug-pc-n, and pcseg-n (n = 0, 1, 2, 3, 4), and the correlation-consistent basis sets cc-pVXZ and aug-cc-pVXZ (X = D, T, Q, 5, and 6) was tested. For the first time, we demonstrated regular convergence patterns of the structural, harmonic, and VPT2-calculated anharmonic vibrational parameters of ethylene towards the Kohn–Sham complete basis set (KS CBS) limitElectronic supplementary materialThe online version of this article (doi:10.1007/s00894-015-2902-z) contains supplementary material, which is available to authorized users.

Stereochemical analysis of (+)-limonene using theoretical and experimental NMR and chiroptical data

Using limonene as test molecule, the success and the limitations of three chiroptical methods (optical rotatory dispersion (ORD), electronic and vibrational circular dichroism, ECD and VCD) could be demonstrated. At quite low levels of theory (mpw1pw91/cc-pvdz, IEFPCM (integral equation formalism polarizable continuum model)) the experimental ORD values differ by less than 10 units from the calculated values. The modelling in the condensed phase still represents a challenge so that experimental NMR data were used to test for aggregation and solvent–solute interactions. After establishing a reasonable structural model, only the ECD spectra prediction showed a decisive dependence on the basis set: only augmented (in the case of Dunning's basis sets) or diffuse (in the case of Pople's basis sets) basis sets predicted the position and shape of the ECD bands correctly. Based on these result we propose a procedure to assign the absolute configuration (AC) of an unknown compound using the comparison between experimental and calculated chiroptical data.

Accurate Electron Densities at Nuclei Using Small Ramp-Gaussian Basis Sets.

Electron densities at nuclei are difficult to calculate accurately with all-Gaussian basis sets because they lack an electron-nuclear cusp. The newly developed mixed ramp-Gaussian basis sets, such as R-31G, possess electron-nuclear cusps due to the presence of ramp functions in the basis. The R-31G basis set is a general-purpose mixed ramp-Gaussian basis set modeled on the 6-31G basis set. The prediction of electron densities at nuclei using R-31G basis sets for Li-F outperforms Dunning, Pople, and Jensen general purpose all-Gaussian basis sets of triple-ζ quality or lower and the cc-pVQZ basis set. It is of similar quality to the specialized pcJ-0 basis set which was developed with partial decontraction of core functions and extra high exponent s-Gaussians to predict electron density at the nucleus. These results show significant advantages in the properties of mixed ramp-Gaussian basis sets compared to all-Gaussian basis sets.

Density Functional Theory Study of Cyanoetheneselenol: A Molecule of Astrobiological Interest.

The interstellar medium has a rich chemistry which involves a wide variety of molecules. Of particular interest are molecules that have a link to prebiotic chemistry which hold the key to understanding of our origins. On the basis of suggestions that selenium may have been involved in the origin and evolution of life, we have studied the selenium analogue of cyanoethenethiol, namely the novel cyanoetheneselenol. Cyanoetheneselenol exhibits conformational and geometrical isomerism. This theoretical work deals with the study of four forms of cyanoetheneselenol in terms of their structural, spectroscopic and thermodynamic parameters. All computations were performed using density functional theory method with the B3LYP functional and the Pople basis set, 6-311 + G(d,p), for all atoms. The relative stability of the four isomers of cyanoetheneselenol was obtained and interpreted. The infrared spectra were generated and assignment of the normal modes of vibration was performed. Probable regions of detection, proposed on the basis of parameters obtained from this study for the four isomers, include comets, the molecular cloud: Sagittarius B2(N), and planetary atmospheres. The molecular and spectroscopic parameters should be useful for future identification of the astrobiological molecule cyanoetheneselenol and the development of the Square Kilometre Array. Graphical Abstract E and Z isomers of cyanoetheneselenol.

Benchmarking of Density Functionals for the Accurate Description of Thiol-Disulfide Exchange.

A set of 92 density functionals was employed to accurately characterize thiol-disulfide exchange. The properties we have benchmarked throughout the study include the geometry of a 15 atoms model system, the potential energy surface, the activation barrier, and the energy of reaction for thiol-disulfide exchange. Reference energies were determined at the CCSD(T)/CBS//MP2/aug-cc-pVDZ level of theory, and reference geometries were calculated at the MP2/aug-cc-pVTZ level. M11-L, M06-2X, M06-HF, N12-SX, PBE1PBE, PBEh1PBE, and OHSE2PBE described better the geometry of the model system, with average deviations of 0.06 Å in bond lengths (0.06 Å in bond-breaking lengths) and 1.9° in bond angles. On the other hand, the potential energy surface and its gradient were more accurately described by the hybrid density functional BHandH, closely followed by mPW1N, mPW1K, and mPWB1K. The barrier height and energy of reaction were better reproduced by the BMK and M06-2X functionals (deviations of 0.17 and 0.07 kcal·mol(-1), respectively) for a set of 10 Pople's basis sets. MN12-SX and M11-L showed very good results for the widely used 6-311++G(2d,2p) basis set, with deviations of 0.02 and 0.05 kcal·mol(-1), respectively. We studied the effect of the split-valence, diffuse, and polarized functions in the activation barrier of thiol-disulfide exchange, for a set of 10 Pople's basis sets. While increasing the splitting and polarization may increase the activation barrier in approximately 1 kcal·mol(-1), diffuse functions generally contribute to decreasing it no more than 0.10 kcal·mol(-1). In general, 13 functionals provided energies within 1 kcal·mol(-1) of the reference value. The BB1K density functional is one of the best density functionals to characterize thiol-disulfide exchange reactions; however, several density functionals with modified Perdew-Wang exchange and about 40% Hartree-Fock exchange, such as mPW1K, mPW1N, and mPWB1K, show a good performance, too.

Mind the correct basis set: A case study for predicting gas phase acidities of small compounds using calculations from first principles

Some of the most popular computational methods have been utilized to determine a dependency of the acidity trend of the first‐row hydrides on a choice of basis set. For about three decades, methyl anion ( ) was known as the strongest base but after Tian et al. were able to produce the gas phase lithium monoxide anion (LiO–) they discovered it was a stronger base than (Tian et al., Proc Natl Acad Soc USA 2008, 105, 7647). Furthermore, the authors confirmed their experimental results using high‐level ab initio methods, namely W1 and W2C composite methods, as well as complete active space‐averaged quadratic coupled cluster and Brueckner Doubles with triple excitation contribution (BD(T)) within the aug‐cc‐pVQZ basis set. These methods are highly demanding in terms of the computational effort as well as a level of expertise needed from the user to correctly conduct such calculations. We have shown that the proper acidity trend, that is, , can be obtained with less expensive, ”black‐box” type methods if only the basis set is properly chosen. Our results prove that the diffuse augmented basis sets are absolutely necessary for appropriate predictions of acidities. Our calculations show that the correct order of is achieved by augmenting relatively small cc‐pVXZ (X = D,T) basis sets. A similar effect is observed for the family of Pople's basis sets. Our estimate for with CCSD(T)/aug‐cc‐pVTZ was 423.8 kcal/mol, which agrees very well with the experimental value 425.7 ± 6.1 kcal/mol. An important finding is that the proper acidity trend may be reversed if the basis sets are not correctly selected. © 2014 Wiley Periodicals, Inc.

On the Use of Locally Dense Basis Sets in the Calculation of EPR Hyperfine Couplings: A Study on Model Systems for Bio-Inorganic Fe and Co Complexes

The usage of locally dense basis sets in the calculation of Electron Paramagnetic Resonance (EPR) hyperfine coupling constants is investigated at the level of Density Functional Theory (DFT) for two model systems of biologically important transition metal complexes: One for the active site in the compound 0 intermediate of cytochrome P450cam, [Fe(OOH)(SH)(en)2]+, and one for the active site in coenzyme B12, [Co(NH3)(CN)(en)2]+. The Fermi contact, spin-dipolar and second order paramagnetic spin-orbit coupling contributions to the hyperfine coupling tensors of the metal and the ligating ethylenediamine N atoms are calculated, and their dependence on the basis set for the remaining atoms are investigated. Core property basis sets are employed for the metals (aug-cc-pVTZ-Juc) and their equatorially coordinating N atoms (aug-cc-pVTZ-J or 6-31G-Juc analogues to the Pople style basis sets used for the remaining atoms), while smaller correlation-consistent or Pople style basis sets are used for the remaining, so-called “non-coupled'', atoms. Most of the investigated basis set combinations are found to give results which differ by less than 1% from the results obtained with core property basis sets on all atoms. We find thus for the cytochrome model system that using the small 6-31G(d) basis set on the non-coupled atoms together with core property basis sets on the Fe and N atoms gives essentially converged results. It is found to be mostly the second order paramagnetic spin-orbit interaction that demands the use of larger basis sets on the non-coupled atoms. If, however, an error of less than 0.5MHz is sufficient any basis set can be used for the noncoupled atoms. For the cobalt containing model system the 6-31G(2d) basis set generally gives results within 1% of the reference value.

UV-vis spectra of singlet state cationic polycyclic aromatic hydrocarbons: time-dependent density functional theory study.

A theoretical study of singlet state cations of polycyclic aromatic hydrocarbons is performed. Appropriate symmetry suitable for further calculations is chosen for each of the systems studied. The excitation states of such species are obtained by the time dependent density functional theory (TD-DFT) method. The computations are performed using both Pople and electronic response properties basis sets. The results obtained with the use of different basis sets are compared. The electronic transitions are described and the relationships for the lowest-lying transitions states of different species are found. The properties of in-plane and out-of-plane transitions are also delineated. The TD-DFT results are compared with the experimental data available.

Probing theoretical level effect on fluorine chemical shielding calculations

The extensive quantum‐chemical calculations are assessed for prediction of the 19F nuclear magnetic shielding constants. The methods within domain of density functional theory (DFT) and ab initio, Hartree–Fock (HF), and second‐order Møller–Plesset perturbation theory (MP2) are employed for calculation of the 19F chemical shielding constants for a series of 30 small fluorine‐containing molecules. The importance of inclusion of four factors, namely, electron correlation treatment, triple‐ξ valence shell, diffuse function, and polarization function on calculating the fluorine NMR chemical shieldings for a variety of Pople's standard basis sets at gauge invariant atomic orbital (GIAO) and continuous set of gauge transformation (CSGT) conditions are discussed by employing the linear regression analysis. The systematic investigation performed here on the influence of the method, level of theory, and basis set size on the accuracy of 19F chemical shielding demonstrates that the presence of a high level of electron correlation factor in level as well as the polarization function in basis set leads to an accurate wave function to compute the reliable fluorine chemical shielding. The results analysis illustrates that the polarization function has a significant effect on the basis sets to minimize the difference between theoretical and experimental values in several fluorine molecules. An additional comparison of the GIAO and CSGT results is used as a supplementary study to confirm the validity of the results. The basis set dependence of fluorine chemical shielding constants verifies that GIAO provides results that are often more accurate than those that are calculated with CSGT approach at the same basis set size, as expected. © 2013 Wiley Periodicals, Inc. Concepts Magn Reson Part A 42A: 140‐153, 2013.

Selecting DFT methods for use in optimizations of enzyme active sites: applications to ONIOM treatments of DNA glycosylases

When using a hybrid methodology to treat an enzymatic reaction, many factors contribute to selecting the method for the high-level region, which can be complicated by the presence of dispersion-driven interactions such as π–π stacking. In addition, the proper treatment of the reaction center often requires a large number of heavy atoms to be included in the high-level region, precluding the use of ab initio methods such as MP2 as well as large basis sets, in the optimization step. In the present work, popular DFT methods were tested to identify an appropriate functional for treating the high-level region in ONIOM optimizations of reactions catalyzed by nonmetalloenzymes. Eight different DFT methods (B3LYP, B97-2, MPW1K, MPWB1K, BB1K, B1B95, M06-2X, and ωB97X-D) in combination with four double-ζ quality Pople basis sets were tested for their ability to optimize noncovalent interactions (hydrogen bonding and π–π) and characterize reactions (proton transfer, SN2 hydrolysis, and unimolecular cleavage). Although the primary focus of this study is accurate structure determination, energetics were also examined at both the optimization level of theory, and with triple-ζ quality basis set and select (M06-2X or ωB97X-D) methods. If dispersion-driven interactions exist within the active site, then MPWB1K/6-31G(d,p) or M06-2X/6-31+G(d,p) are recommended for the optimization step with subsequent triple-ζ quality single-point energies. However, since dispersion-corrected functionals (M06-2X and ωB97X-D) generally require diffuse functions to yield appropriate geometries, the possible size of the high-level region is greatly limited with these methods. In contrast, if the model is large enough to recover steric constraints on π–π interactions, then B3LYP with a small basis set performs comparatively well for the optimization step and is significantly less computationally expensive. Interestingly, the functionals that afford the best geometries often do not yield the best energetics, which emphasizes the importance of structural benchmark studies.

Comparative analysis of the performance of commonly available density functionals in the determination of geometrical parameters for copper complexes

In this study, a set of 50 transition-metal complexes of Cu(I) and Cu(II), were used in the evaluation of 18 density functionals in geometry determination. In addition, 14 different basis sets were considered, including four commonly used Pople's all-electron basis sets; four basis sets including popular types of effective-core potentials: Los Alamos, Steven-Basch-Krauss, and Stuttgart-Dresden; and six triple-ζ basis sets. The results illustrate the performance of different methodological alternatives for the treatment of geometrical properties in relevant copper complexes, pointing out Double-Hybrid (DH) and Long-range Correction (LC) Generalized Gradient Approximation (GGA) methods as better descriptors of the geometry of the evaluated systems. These however, are associated with a computational cost several times higher than some of the other methods employed, such as the M06 functional, which has also demonstrated a comparable performance. Regarding the basis sets, 6-31+G(d) and 6-31+G(d,p) were the best performing approaches. In addition, the results show that the use of effective-core potentials has a limited impact, in terms of the accuracy in the determination of metal-ligand bond-lengths and angles in our dataset of copper complexes. Hence, these could become a good alternative for the geometrical description of these systems, particularly CEP-121G and SDD basis sets, if one is considering larger copper complexes where the computational cost could be an issue.

1H-Pyrrolo[3,2-h]quinoline: A Benchmark Molecule for Reliable Calculations of Vibrational Frequencies, IR Intensities, and Raman Activities

Reliable assignment of 55 out of 57 vibrational modes has been achieved for 1H-pyrrolo[3,2-h]quinoline using IR, Raman, and fluorescence spectroscopy combined with quantum chemical calculations. The experiments provided a data set for assessing the performance of different models/basis sets for predicting the vibrational frequencies, as well as IR and Raman intensities for a molecule with 13 heavy atoms. Among six different tested DFT functionals, the hybrid B3LYP used with Pople's split-valence basis sets is suggested as the best choice for accurate and cost-effective IR/Raman spectral simulations. Neither HF nor MP2 methods can satisfactorily describe the vibrational structure. Increasing the basis set size from double to triple-ζ and by adding polarization and diffuse functions does not necessarily improve the results, especially regarding the predictions of vibrational frequencies. With respect to the intensities, extending the basis set helps, with the accuracy increasing systematically for the Raman spectra, and in a less regular fashion for the IR. A large difference in accuracy is observed while comparing the spectral parameters predicted for in-plane and out-of-plane normal modes. The former are reliably computed with modest basis sets, whereas for the out-of-plane vibrations, larger basis sets are necessary, but even in this case, the out-of-plane vibrations are reproduced with much less accuracy than in-plane modes. This effect is general, as it has been observed using different functionals and basis sets.

Electronic and Vibrational Nonlinear Optical Properties of Five Representative Electrides.

The electrides have a very special electronic structure with diffuse excess electrons not localized on any specific atom. Such systems are known to have huge electronic nonlinear optical (NLO) properties. Here, we determine and analyze the vibrational, as compared to the electronic, NLO properties for a representative set of electrides: Li@Calix, Na@Calix, Li@B10H14, Li2(•+)TCNQ(•-), and Na2(•+)TCNQ(•-). The static and dynamic vibrational (hyper)polarizabilities are computed by the nuclear relaxation method (with field-induced coordinates and the infinite optical frequency approximation) at the UB3LYP level using a hybrid Pople basis set. In general, the static vibrational βvec and γ∥ exceed the corresponding static electronic property values by up to an order of magnitude. The same comparison for dynamic vibrational hyperpolarizabilities shows a smaller ratio. For the intensity-dependent refractive index (IDRI) and dc-Kerr processes, the ratio is on the order of unity or somewhat larger; it is less for the dc-Pockels and the electric field induced second harmonic (EFISH) effects (as well as the static α̅) but still important. The role of anharmonicity, motion of the alkali atoms, and substitution of Na for Li is discussed along with specific aspects of the charge distribution associated with the excess electron.

The analysis of polarization effects on the interelectronic separations in the atoms and molecules of the G1 test set

AbstractWe have calculated the differences between kinetic, nuclear attraction, and two‐electron energies as well as the position intracules, P(u), for 56 molecules and 17 atoms contained in the G1 test set, using basis sets differing in their degree of polarization. The calculations were performed using an unrestricted Hartree–Fock wave function that was expanded using the 6‐31G, 6‐31G(d,p), 6‐31G(3d,3p), 6‐31G(3df,3pd), 6‐311G, 6‐311G(d,p), 6‐311G(3d,3p), 6‐311G(3df,3pd), 6‐311++G, 6‐311++G(d,p), 6‐311++G(3d,3p), and 6‐311++G(3df,3pd) basis sets. In addition to these Pople basis sets, the Dunning's cc‐pVDZ and cc‐pVTZ bases as well as the non‐polarized portions of these basis sets were used. We observe a consistent contraction of electron pairs (as measured by the distribution in P(u)) as the number of polarization functions is increased beyond zero in molecular systems. This contraction is related to an increase in the electron density in the internuclear bonding regions of molecules as the wave functions are polarized. We note that the increased flexibility in the polarized basis set allows for a more accurate description of the chemical bond and is energetically favorable due to an increased level of attraction to the nuclei (despite the obvious increase in electronic repulsion energy). Because of the increase in electron density in internal regions of the molecule (at the expense of electron density depletions in outer regions), the probability of observing electrons closer together (i.e., at smaller u) increases due to the relationship between P(u) and its Coulomb component, J(u). © 2012 Wiley Periodicals, Inc.

Stability and Reactivity of Methane Clathrate Hydrates: Insights from Density Functional Theory

The sI methane clathrate hydrate consists of methane gas molecules encapsulated as dodecahedron (5(12)CH(4)) and tetrakaidecahedron (5(12)6(2)CH(4)) water cages. The characterization of the stability of these cages is crucial to an understanding of the mechanism of their formation. In the present work, we perform calculations using density functional theory to calculate interaction energies, free energies, and reactivity indices of these cages. The contributions from polarization functions to interaction energies is more than diffuse functions from Pople basis sets, though both functions from the correlation-consistent basis sets contribute significantly to interaction energies. The interaction energies and free energies show that the formation of the 5(12)CH(4) cage (from the 5(12) cage) is more favored compared to the 5(12)6(2)CH(4) cage (from the 5(12)6(2) cage). The pressure-dependent study shows a spontaneous formation of the 5(12)CH(4) cage at 273 K (P ≥ 77 bar) and the 5(12)6(2)CH(4) cage (P = 100 bar). The reactivity of the 5(12)CH(4) cage is similar to that of the 5(12) cage, but the 5(12)6(2)CH(4) cage is more reactive than the 5(12)6(2) cage.

Quantum-mechanical computations on the electronic structure of trans-resveratrol and trans-piceatannol: a theoretical study of the stacking interactions in trans-resveratrol dimers

Accurate quantum-chemical calculations based on the second-order Møller-Plesset perturbation method (MP2) and density functional theory (DFT) were performed for the first time to investigate the electronic structures of trans-resveratrol and trans-piceatannol, as well as to study the stacking interaction between trans-resveratrol molecules. Ab initio MP2 calculations performed with using standard split-valence Pople basis sets led us to conclude that these compounds have structures that deviate strongly from planarity, whereas the DFT computations for the same basis sets revealed that the equilibrium geometries of these bioactive polyphenols are planar. Furthermore, the results obtained at the MP2(full)/aug-cc-pVTZ and B3LYP/aug-cc-pVTZ levels indicated that the geometries of trans-resveratrol and trans-piceatannol are practically planar at their absolute energy minima. The relative energies of the equilibrium geometries of trans-resveratrol on its potential energy surface were computed at the MP2(full)/aug-cc-pVTZ level. According to the results obtained, a T-shaped (edge-to-phase) conformer of trans-resveratrol dimer is the most stable in vacuum. This T-shaped conformer is mainly stabilized by strong hydrogen bonding and weak C-H...π interactions. Stacked structures with parallel-displaced trans-stilbene skeletons were also found to be energetically stable. The vertical separation and twist angle dependencies of the stacking energy were investigated at the MP2(full)/aug-cc-pVTZ, B3LYP/aug-cc-pVTZ, and HF/aug-cc-pVTZ levels. The standard B3LYP functional and the Hartree-Fock method neglect long-range attractive dispersion interactions. The MP2 computations revealed that the London dispersion energy cannot be neglected at long or short distances. The stacked model considered here may be useful for predicting the quantum nature of the interactions in π-stacked systems of other naturally occurring stilbenoids, and can help to enhance our understanding of the antioxidant and anticancer activities of trans-resveratrol.