Comparison of aromatic NH···π, OH···π, and CH···π interactions of alanine using MP2, CCSD, and DFT methods

A comparison of the performance of various density functional methods including long‐range corrected and dispersion corrected methods [MPW1PW91, B3LYP, B3PW91, B97‐D, B1B95, MPWB1K, M06‐2X, SVWN5, ωB97XD, long‐range correction (LC)‐ωPBE, and CAM‐B3LYP using 6‐31+G(d,p) basis set] in the study of CH···π, OH···π, and NH···π interactions were done using weak complexes of neutral (A) and cationic (A⁺) forms of alanine with benzene by taking the Møller–Plesset (MP2)/6‐31+G(d,p) results as the reference. Further, the binding energies of the neutral alanine–benzene complexes were assessed at coupled cluster (CCSD)/6‐31G(d,p) method. Analysis of the molecular geometries and interaction energies at density functional theory (DFT), MP2, CCSD methods and CCSD(T) single point level reveal that MP2 is the best overall performer for noncovalent interactions giving accuracy close to CCSD method. MPWB1K fared better in interaction energy calculations than other DFT methods. In the case of M06‐2X, SVWN5, and the dispersion corrected B97‐D, the interaction energies are significantly overrated for neutral systems compared to other methods. However, for cationic systems, B97‐D yields structures and interaction energies similar to MP2 and MPWB1K methods. Among the long‐range corrected methods, LC‐ωPBE and CAM‐B3LYP methods show close agreement with MP2 values while ωB97XD energies are notably higher than MP2 values. © 2010 Wiley Periodicals, Inc. J Comput Chem 2010     

Conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete

The conventional strain energies of 1,2-dihydroazete, 2,3-dihydroazete, 1,2-dihydrophosphete, and 2,3-dihydrophosphete are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero-point vibrational energies are computed for all pertinent molecular systems using SCF theory, second-order perturbation theory, and density functional theory and employing the correlation consistent basis sets cc-pVDZ, cc-pVTZ, and cc-pVQZ. Single-point fourth-order perturbation theory, CCSD, and CCSD(T) calculations employing the cc-pVTZ and the cc-pVQZ basis sets are computed using the MP2/cc-pVTZ and MP2/cc-pVQZ optimized geometries, respectfully, to ascertain the contribution of higher order correlation. Three DFT functionals, B3LYP, wB97XD, and M06-2X, are employed to determine whether they can yield results similar to those obtained at the CCSD(T) level.     

Assessment of ab initio MP2 and density functionals for characterizing the potential energy profiles of the SN2 reactions at N center

The potential energy profiles of five selected bimolecular nucleophilic substitution (S_N2) reactions at nitrogen (N) center have been reinvestigated with the CCSD(T), G3[MP2,CCSD(T)], MP2, and some density functional methods. The basis sets of 6‐31+G(d,p) and 6‐311+G(3d,2p) are used for the MP2 and density functional calculations. Taking the relative energies at the CCSD(T)/CBS level of theory as benchmarks, we recommend the MP2, B97‐K, B2K‐PLYP, BMK, ωB97X‐D, M06‐2X, M05‐2X, CAM‐B3LYP, M08‐SO, and ωB97X methods to generally characterize the potential energy profiles for the S_N2 reactions at N center. Furthermore, these recommended methods with the relatively small 6‐31+G(d,p) basis set may also be used to perform direct classical trajectory simulations to uncover the dynamic behaviors of the S_N2 reactions at N center. © 2012 Wiley Periodicals, Inc.     

Predictive power of long-range corrected functionals on the spectroscopic properties of tetrapyrrole derivatives for photodynamic therapy

Porphyrin and chlorin based compounds possess promising properties to be utilized as photosensitizers in photodynamic therapy (PDT). However, the photosensitizers available on the market today are not ideal for use in PDT, which has emphasized the need for new photosensitizers with improved photodynamic properties to be developed. Computational drug-design can be utilized in the search for improved pharmaceutical compounds, provided that the methods used are able to reproduce experimental data. In the present study we investigated, by the use of time-dependent density functional theory (TD-DFT), the performance of the long-range corrected functionals ωB97, ωB97X and ωB97XD on their ability to predict low-lying singlet excitations (>600 nm) of a set of well-known photosensitizing compounds. It was found that ωB97X reproduced the experimental red-most absorption band most satisfactorily. The use of either B3LYP, ωB97XD or M06 in geometry optimizations has a minor effect on the spectra in most cases. Calculated energy differences between the optimized singlet ground states and optimized first excited triplet states show consistent and overall higher triplet state energies for B3LYP, M06, and PBE0 compared with ωB97, ωB97X, and ωB97XD. The calculated triplet state energies are, however, sufficient to generate singlet oxygen in most cases.     

Conventional strain energies of azetidine and phosphetane: Can density functional theory yield reliable results?

The conventional strain energies for azetidine and phosphetane are determined within the isodesmic, homodesmotic, and hyperhomodesmotic models. Optimum equilibrium geometries, harmonic vibrational frequencies, and corresponding electronic energies and zero‐point vibrational energies are computed for all pertinent molecular systems using self‐consistent field theory, second‐order perturbation theory, and density functional theory and using the correlation consistent basis sets cc‐pVDZ, cc‐pVTZ, and cc‐pVQZ. Single point fourth‐order perturbation theory, CCSD, and CCSD(T) calculations using the cc‐pVTZ and the cc‐pVQZ basis sets are computed using the MP2/cc‐pVTZ and MP2/cc‐pVQZ optimized geometries, respectively, to ascertain the contribution of higher order correlation effects and to determine if the quadruple‐zeta valence basis set is needed when higher order correlation is included. In the density functional theory study, eight different functionals are used including B3LYP, wB97XD, and M06‐2X to determine if any functional can yield results similar to those obtained at the CCSD(T) level. © 2012 Wiley Periodicals, Inc.     

A DFT study of substituent effects in corannulene dimers

Corannulene dimers made up of corannulene monomers with different curvature and substituents were studied using M06-2X, B97D and ωB97XD functionals and 6-31+G* basis set. Corannulene molecules were substituted with five alternating Br, Cl, CH(3), C(2)H or CN units. Geometric results showed that substituents gave rise to small changes in the curvature of corannulene bowls. So, there was not a clear relationship between the curvature of bowls and the changes on interaction energy generated by addition of substituents in the bowl. Electron withdrawing substituents gave rise to a more positive molecular electrostatic potential (MEP) of the bowl, which was able to get a strong interaction with the negative MEP at the surface of a fullerene. Substitution with CN caused the largest effect, giving rise to the most positive MEP and to a large interaction energy of -24.64 kcal mol(-1), at the ωB97XD/6-31+G* level. Dispersive effects must be taken into account to explain the catching ability of the different substituted corannulenes. For unsubstituted dimers, calculations with DFT-D methods employing ωB97XD and B97D functionals led to similar results to those previously reported at the SCS-MP2/cc-pVTZ level for corannulene dimers (A. Sygula and S. Saeb?, Int. J. Quant. Chem., 2009, 109, 65). In particular, the ωB97XD functional led to a difference of only 0.35 kcal mol(-1), regarding MP2 interaction energy for corannulene dimers. On the other hand, the M06-2X functional showed a general considerable underestimation of interaction energies. This functional worked quite well to study trends, but not to obtain absolute interaction energies.     

Electronic structure and absorption spectra of supramolecular complexes of a fullerene crown ether with a π-extended TTF derivative

The present work is a theoretical investigation on supramolecular complexes of a fullerene crown ether (A and B isomers) with a derivative of π-extended tetrathiafulvalene (T). The geometry and the electronic structure of seven different conformers of the complex of dibenzo-18-crown-6 ether of fullero-N-methylpyrrolidine with a N-benzyl-N-(4-{[9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracen-2-yl]ethynyl}benzyl)ammonium cation were determined. We calculated the complexation energies and the absorption spectra, i.e., the lowest 50 excited electronic states of the complexes have been determined at the ground state optimum geometry. All calculations were carried out employing the density functional theory (DFT) and the time-dependent DFT, using the B3LYP, CAM-B3LYP, ωB97X-D, and M06-2X functionals in conjunction with the 6-31G(d,p) basis set. Various types of van der Waals interactions are observed in the complexes. Conformer complexation energies (CE) range from 2.54 to 2.14 eV in the gas phase and from 1.75 to 1.34 eV in CHCl(3) solvent at the ωB97X-D/6-31G(d,p)//M06-2X/6-31G(d,p) level of theory. There are three major features at about 390, 330, and 290 nm in the calculated absorption spectra of all the conformers. The major peaks correspond to T→T, T→T/F (electron density in both T and the fullerene F of B) and to T→F transitions, depending on the particular conformer. Other charge transfer T→F transitions are observed close to the T→T transition, indicating the possibility of photoinduced electron transfer in all these complexes.     

TD-CI simulation of the electronic optical response of molecules in intense fields II: comparison of DFT functionals and EOM-CCSD

Time-dependent configuration interaction (TD-CI) simulations can be used to simulate molecules in intense laser fields. TD-CI calculations use the excitation energies and transition dipoles calculated in the absence of a field. The EOM-CCSD method provides a good estimate of the field-free excited states but is rather expensive. Linear-response time-dependent density functional theory (TD-DFT) is an inexpensive alternative for computing the field-free excitation energies and transition dipoles needed for TD-CI simulations. Linear-response TD-DFT calculations were carried out with standard functionals (B3LYP, BH&HLYP, HSE2PBE (HSE03), BLYP, PBE, PW91, and TPSS) and long-range corrected functionals (LC-ωPBE, ωB97XD, CAM-B3LYP, LC-BLYP, LC-PBE, LC-PW91, and LC-TPSS). These calculations used the 6-31G(d,p) basis set augmented with three sets of diffuse sp functions on each heavy atom. Butadiene was employed as a test case, and 500 excited states were calculated with each functional. Standard functionals yield average excitation energies that are significantly lower than the EOM-CC, while long-range corrected functionals tend to produce average excitation energies slightly higher. Long-range corrected functionals also yield transition dipoles that are somewhat larger than EOM-CC on average. The TD-CI simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. The nonlinear response as indicated by the residual populations of the excited states after the pulse is far too large with standard functionals, primarily because the excitation energies are too low. The LC-ωPBE, LC-PBE, LC-PW91, and LC-TPSS long-range corrected functionals produce responses comparable to EOM-CC.     

Halogen bonds with benzene: An assessment of DFT functionals

The performance of an extensive set of density functional theory functionals has been tested against CCSD(T) and MP2 results, extrapolated to the complete basis set (CBS) limit, for the interaction of either DCl or DBr (D = H, HCC, F, and NC) with the aromatic system of benzene. It was found that double hybrid functionals explicitly including dispersion, that is, B2PLYPD and mPW2PLYPD, provide the better agreement with the CCSD(T)/CBS results on both energies and equilibrium geometry, indicating the importance of dispersive contributions in determining this interaction. Among the less expensive functionals, the better performance is provided by the ωB97X and M062X functionals, while the ωB97XD and B97D functionals are shown to work very well for bromine complexes but not so well for chlorine complexes. © 2013 Wiley Periodicals, Inc.     

A comparison of the behavior of functional/basis set combinations for hydrogen-bonding in the water dimer with emphasis on basis set superposition error

We evaluate the performance of ten functionals (B3LYP, M05, M05-2X, M06, M06-2X, B2PLYP, B2PLYPD, X3LYP, B97D, and MPWB1K) in combination with 16 basis sets ranging in complexity from 6-31G(d) to aug-cc-pV5Z for the calculation of the H-bonded water dimer with the goal of defining which combinations of functionals and basis sets provide a combination of economy and accuracy for H-bonded systems. We have compared the results to the best non-density functional theory (non-DFT) molecular orbital (MO) calculations and to experimental results. Several of the smaller basis sets lead to qualitatively incorrect geometries when optimized on a normal potential energy surface (PES). This problem disappears when the optimization is performed on a counterpoise (CP) corrected PES. The calculated interaction energies (ΔEs) with the largest basis sets vary from -4.42 (B97D) to -5.19 (B2PLYPD) kcal/mol for the different functionals. Small basis sets generally predict stronger interactions than the large ones. We found that, because of error compensation, the smaller basis sets gave the best results (in comparison to experimental and high-level non-DFT MO calculations) when combined with a functional that predicts a weak interaction with the largest basis set. As many applications are complex systems and require economical calculations, we suggest the following functional/basis set combinations in order of increasing complexity and cost: (1) D95(d,p) with B3LYP, B97D, M06, or MPWB1k; (2) 6-311G(d,p) with B3LYP; (3) D95++(d,p) with B3LYP, B97D, or MPWB1K; (4) 6-311++G(d,p) with B3LYP or B97D; and (5) aug-cc-pVDZ with M05-2X, M06-2X, or X3LYP.     

Topological phase transitions in the vibration–rotation dynamics of an isolated molecule

A computational investigation of anomeric effects in piperidine rings bearing fluoro and trifluoromethyl substituents shows for both compounds the most pronounced evidence of the anomeric effect, as expressed as hyperconjugative delocalization of the nitrogen lone pair, in structures with the substituent in the axial position and the N–H bond in the equatorial position. This structure is the lowest-energy structure in the fluoro case but not in the trifluoromethyl case where there is an increased axial penalty associated with the CF₃ group. The anomeric effect is characterized via geometrical evidence, natural bond orbital analysis, electrostatic effects, and energetic criteria. Computational results from a variety of levels of theory are presented including CCSD(T) with complete basis set extrapolation, B2PLYP-D, ωB97XD, B97-D, M06-2X, B3LYP, and MP2 allowing for a comparison of performance. The CCSD(T)/CBS results are very well represented by either B2PLYP-D or ωB97XD with moderate to large basis sets (aug-cc-pVTZ or aug-cc-pVDZ). Hyperconjugation, electrostatic effects, and steric effects play a role in the relative energetic ordering of the isomers considered.     

How accurate are electronic structure methods for actinoid chemistry?

The CASPT2, CCSD, and CCSD(T) levels of wave function theory and seven density functionals were tested against experiment for predicting the ionization potentials and bond dissociation energies of actinoid monoxides and dioxides with their cations. The goal is to guide future work by enabling the choice of an appropriate method when performing calculations on actinoid-containing systems. We found that four density functionals, namely MPW3LYP, B3LYP, M05, and M06, and three levels of wave function theory, namely CASPT2, CCSD, and CCSD(T), give similar mean unsigned errors for actinoid?Coxygen bond energies and for ionization potentials of actinoid oxides and their cations.     

Ferric complexes of 3-hydroxy-4-pyridinones characterized by density functional theory and Raman and UV-vis spectroscopies

Deferiprone and other 3-hydroxy-4-pyridinones are used in metal chelation therapy of iron overload. To investigate the structure and stability of these compounds in the natural aqueous environment, ferric complexes of deferiprone and amino acid maltol conjugates were synthesized and studied by computational and optical spectroscopic methods. The complexation caused characteristic intensity changes, a 300× overall enhancement of the Raman spectrum, and minor changes in UV-vis absorption. The spectra were interpreted on the basis of density functional theory (DFT) calculations. The CAM-B3LYP and ωB97XD functionals with CPCM solvent model were found to be the most suitable for simulations of the UV-vis spectra, whereas B3LYP, B3LYPD, B3PW91, M05-2X, M06, LC-BLYP, ωB97XD, and CAM-B3LYP functionals were all useful for simulation of the Raman scattering. Characteristic Raman band frequencies for 3-hydroxy-4-pyridinones were assigned to molecular vibrations. The computed conformer energies consistently suggest the presence of another isomer of the deferiprone-ferric complex in solution, in addition to that found previously by X-ray crystallography. However, the UV-vis and Raman spectra of the two species are similar and could not be resolved. In comparison to UV-vis, the Raman spectra and their combination with calculations appear more promising for future studies of iron sequestrating drugs and artificial metalloproteins as they are more sensitive to structural details.     

DFT calculations on the catalytic oxidation of CO over Si-doped (6,0) boron nitride nanotubes

The oxidation of carbon monoxide (CO) is important for a series of technological and environmental applications. In this work, the catalytic oxidation of CO on Si-doped (6,0) boron nitride nanotubes (BNNTs) is investigated by using density functional theory calculations. Reaction barriers and corresponding thermodynamic parameters were calculated using the M06-2X, B3LYP and wB97XD density functionals with 6-31G* basis set. Our results indicate that a vacancy defect in BNNT strongly stabilizes the Si adatom and makes it more positively charged. This charging enhances the adsorption of reaction gases (O₂ and CO) and results in the change of the electronic structure properties of the tube. The calculated barrier of the reaction CO + O₂ → CO₂ + O_ads on Si-doped BNNTs following the Langmuir–Hinshelwood is lower than that on the traditional noble metal catalysts. The second step of the oxidation would be the Eley–Rideal reaction (CO + O_ads → CO₂) with an energy barrier of about 1.8 and 10.1 kcal/mol at M06-2X/6-31G* level. This suggests that the CO oxidation catalyzed by the Si-doped BNNTs is likely to occur at the room temperature. The results also demonstrate that the activation energies and thermodynamic quantities calculated by M06-2X, B3LYP and wB97XD functionals are consistent with each other.     

Basis set convergence of indirect spin-spin coupling constants in the Kohn-Sham limit for several small molecules

The performance of more than 40 density functionals in predicting indirect spin-spin coupling constants (SSCCs) in the Kohn-Sham basis set limit was tested. For comparison, similar calculations were performed using the RHF, SOPPA, SOPPA(CC2), and SOPPA(CCSD) methods, and the results were estimated toward the complete basis set (CBS) limit. The SSCCs of nine small molecules (N(2), CO, CO(2), NH(3), CH(4), C(2)H(2), C(2)H(4), C(2)H(6), and C(6)H(6)) were calculated using the dedicated Jensen pcJ-n polarization-consistent basis sets and used for the CBS limit estimations within the Kohn-Sham limit. These CBS results were compared with calculations using the aug-cc-pVTZ-J basis set. Among the 41 studied DFT methods, the tHCTHhyb, HSEh1PBE, HSE2PBE, wB97XD, wB97, and wB97X functionals reproduced accurately the experimental (1)J(XH) SSCCs and (3)J(HH60) and (2)J(HH(gem)) in ethane. Similarly, the functionals HSEh1PBE, HSE2PBE, wB97XD, wB97, and wB97X predicted accurately (1)J(CC), and B98, B97-1, B97-2, PBE1PBE, B1LYP, and O3LYP provided accurate (1)J(CO) results in the CO molecule. A very good performance for the calculation of the SSCCs based on the use of the relatively small basis set aug-cc-pVTZ-J was observed.     

Assessment of density functionals and force field methods on anion–π interaction in heterocyclic calix complexes

The performance of ten density functionals and four force field methods in describing non-covalent interactions have been assessed by studying the interaction energies and structures of the four anion–π complexes involving tetraoxacalix[2]arene[2]triazine and various anions. Their structures are optimized at MP2/6-311++G(d,p) level, and interaction energies are obtained at DF-MP2-F12/aug-cc-pVDZ level. The result shows that the functional M06-2X predicts the most reliable interaction energy, followed by wB97XD and BHandH. B97D slightly overestimates the interaction energy. Other functionals and force field methods seriously overestimate the interaction energy. For the structures, three functionals M06-2X, wB97XD and BH and H predict the most reliable results, followed by B97D. The force field methods predict the largest deviations. The present work suggests that the functional M06-2X is a reliable method to describe energies and structural properties of the large molecules involving the anion–π interactions.     

A theoretical analysis of substituted aromatic compounds

The substituents ? CH₃, ? F, ? NO₂, ? OCH₃, and ? CH₂?CH₂ were placed at the ortho, meta, and para positions on the aromatic molecules aniline, benzaldehdye, nitrobenzene, and phenol. MMFF94, AM1, B3LYP, M06, M06‐2X, ωB97X, ωB97X‐d, and RI‐MP2 using cc‐pVDZ and cc‐pVTZ and CCSD(T) with cc‐pVDZ basis sets were used to calculate the geometries and energies of all regiomers of the molecules. Relative energies of the ortho and meta regiomers relative to the para regiomers were calculated and compared to the CCSD(T) values. A good basis set correlation between cc‐pVDZ and cc‐pVTZ was observed in RI‐MP2. Overall, RI‐MP2 gave the best correlation with the CCSD(T) results. All of the hybrid functionals showed similar accuracy and could effectively describe the intramolecular hydrogen‐bonding interactions of these compounds. The methoxy group at the para position in methoxyaniline, methoxyphenol, methoxynitrobenzene, and methoxybenzaldehyde was rotated around the phenyl‐O bond. HF, along with the cc‐pVDZ basis with the other methods, generated inaccurate energy profiles for p‐methoxyphenol. For the density functional theory methods, it was necessary to use improved grids to get smooth curves. © 2013 Wiley Periodicals, Inc.     

用GGA密度泛函及其长程、色散校正方法计算各类氢键的结合能

应用广义梯度近似(GGA) (PW91和PBE)、含动能密度的广义梯度近似(meta-GGA) (M06-L)、杂化泛函(hyper-GGA)(M06-2X、X3LYP和B3LYP)及其长程校正泛函LC-DFT(CAM-B3LYP、LC-ωPBE和ωB97X)和色散校正密度泛函(DFT-D)(ωB97X-D和B97-D),用多种基函数对15种不同强度的传统氢键和非传统氢键体系的结合能进行了系统的计算与分析.并与高精度的CCSD(T)/aug-cc-pVQZ结果比较发现:在上述各类泛函中,对于氢键结合能的计算M06-2X和ωB97X-D泛函较为精确与可靠,且没有必要使用过大的基函数,6-311++G(2d,2p)或aug-cc-pVDZ水平的基组就已足够,各类泛函所计算结合能的基组重叠误差(BSSE)均较小,除ωB97X和ωB97X-D外,其它9种泛函不经BSSE校正也能得到同样甚至更准确的结果.