Assessment of density functionals with long‐range and/or empirical dispersion corrections for conformational energy calculations of peptides

Density functionals with long‐range and/or empirical dispersion corrections, including LC‐ωPBE, B97‐D, ωB97X‐D, M06‐2X, B2PLYP‐D, and mPW2PLYP‐D functionals, are assessed for their ability to describe the conformational preferences of Ac‐Ala‐NHMe (the alanine dipeptide) and Ac‐Pro‐NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22–0.40 kcal/mol in conformational energy and 2.0–3.2° in torsion angles ? and ψ using these functionals with the 6‐311++G(d,p) basis set against the reference values calculated at the MP2/aug‐cc‐pVTZ//MP2/aug‐cc‐pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP‐D ≈ mPW2PLYP‐D > ωB97X‐D ≈ M06‐2X > MP2 > LC‐ωPBE > B3LYP with the 6–311++G(d,p) basis set. The SMD model at the M06‐2X/6‐31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP‐D/6‐311++G(d,p)//SMD M06‐2X/6‐31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Complexation of Phenol and Thiophenol by Amine N‐Oxides: Isothermal Titration Calorimetry and ab Initio Calculations

To develop a new solvent‐impregnated resin (SIR) system for removal of phenols from water, the complex formation of dimethyldodecylamine N‐oxide (DMDAO), trioctylamine N‐oxide (TOAO), and tris(2‐ethylhexyl)amine N‐oxide (TEHAO) with phenol (PhOH) and thiophenol (PhSH) is studied. To this end we use isothermal titration calorimetry (ITC) and quantum chemical modeling (on B3LYP/6‐311G(d,p)‐optimized geometries: B3LYP/6‐311+G(d,p), B3LYP/6‐311++G(2d,2p), MP2/6‐311+G(d,p), and spin component scaled (SCS) MP2/6‐311+G(d,p); M06‐2X/6‐311+G(d,p)//M06‐2X/6‐311G(d,p), MP2 with an extrapolation to the complete basis set limit (MP2/CBS), as well as CBS‐Q). The complexes are analyzed in terms of structural (e.g., bond lengths) and electronic elements (e.g., charges). Furthermore, complexation and solvent effects (in benzene, toluene, and mesitylene) are investigated by ITC measurements, yielding binding constants K, enthalpies ΔH⁰, Gibbs fre energies ΔG⁰, and entropies ΔS⁰ of complex formation, and stoichiometry N. The ITC measurements revealed strong 1:1 complex formation between both DMDAO–PhOH and TOAO–PhOH. The binding constant (K=1.7–5.7×10⁴ M ^?1) drops markedly when water‐saturated toluene was used (K=5.8×10³ M ^?1), and π–π interaction with the solvent is shown to be relevant. Quantum mechanical modeling confirms formation of stable 1:1 complexes with linear hydrogen bonds that weaken on attachment of electron‐withdrawing groups to the amine N‐oxide moiety. Modeling also showed that complexes with PhSH are much weaker than those with PhOH, and in fact too weak for ITC determination. CBS‐Q incorrectly predicts equal or even higher binding enthalpies for PhSH than for PhOH, which invalidates it as a benchmark for other calculations. Data from the straightforward SCS‐MP2 method without counterpoise correction show very good agreement with the MP2/CBS values.     

The Rearrangement of 2,2‐Diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane to 3,4,4‐Triphenylcyclopent‐1‐ene: a DFT Analysis

A computational study on the rearrangement of 2,2‐diphenyl‐1‐[(E)‐2‐phenylethenyl]cyclopropane ( 1 ) is presented, using density functional theory (DFT), (U)B3LYP with the 6‐31G* basis set (DFT1) and (U)M05‐2X with the 6‐311+G** basis set (DFT2). In agreement with a biradical character of the transition structure (TS) or intermediate, the potential‐energy hypersurface is lowered by the influence of three conjugated Ph groups. Surprisingly, two conformations of the geminal diphenyl group (different twist angles) induce two different minimum‐energy pathways for the rearrangement. Independent of the functional used, the first hypersurface harbors true biradical intermediates, whereas the second energy surface is a flat, slightly ascending slope from the starting material to the TS. The functional (U)M05‐2X with the basis set 6‐311+G** provides realistic energies which seem to be close to experiment. The activation energy for racemization of enantiomers of 1 is lower than that of rearrangement by 2.5 kcal mol^?1, in agreement with experiment.     

Hydrogen Bonding in Phosphine Oxide/Phosphate–Phenol Complexes

To develop a new solvent‐impregnated resin (SIR) system for the removal of phenols and thiophenols from water, complex formation by hydrogen bonding of phosphine oxides and phosphates is studied using isothermal titration calorimetry (ITC) and quantum chemical modeling. Six different computational methods are used: B3LYP, M06‐2X, MP2, spin component‐scaled (SCS) MP2 [all four with 6‐311+G(d,p) basis set], a complete basis set extrapolation at the MP2 level (MP2/CBS), and the composite CBS‐Q model. This reveals a range of binding enthalpies (ΔH) for phenol–phosphine oxide and phenol–phosphate complexes and their thio analogues. Both structural (bond lengths/angles) and electronic elements (charges, bond orders) are studied. Furthermore, solvent effects are investigated theoretically by the PCM solvent model and experimentally via ITC. From our calculations, a trialkylphosphine oxide is found to be the most promising extractant for phenol in SIRs, yielding ΔH=?14.5 and ?9.8 kcal mol^?1 with phenol and thiophenol, respectively (MP2/CBS), without dimer formation that would hamper the phenol complexation. In ITC measurements, the ΔH of this complex was most negative in the noncoordinating solvent cyclohexane, and slightly less so in π–π interacting solvents such as benzene. The strongest binding is found for the dimethyl phosphate–phenol complex [?15.1 kcal mol^?1 (MP2/CBS)], due to the formation of two H‐bonds (P?O???H‐O‐ and P‐O‐H???O‐H); however, dimer formation of these phosphates competes with complexation of phenol, and would thus hamper their use in industrial extractions. CBS‐Q calculations display erroneous trends for sulfur compounds, and are found to be unsuitable. Computationally relatively cheap SCS‐MP2 and M06‐2X calculations did accurately agree with the much more elaborate MP2/CBS method, with an average deviation of less than 1 kcal mol^?1.     

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.     

Adsorption of polycyclic aromatic hydrocarbons and inversion barriers of curved conjugated systems inside the molecular cage ExCage6+

We investigated the hosting of planar and curved π systems by ExCage⁶⁺. The M06‐2X/6‐311G* method and including basis set superposition error (BSSE) corrections showed good agreement with the experimental free energy changes in solution. The mean absolute deviation (MAD) with respect to experiment was 1.3 kcal/mol. The M06‐2X/6‐31G* method exhibited a MAD of 2.1 kcal/mol, so it may be useful to investigate large systems. The good agreement between the M06‐2X/6‐311G*+BSSE results and the M06‐2X/6‐31G* ones was due to a fortuitous error cancelation between basis set incompleteness and BSSE. The interaction energies decreased linearly with the number of CC double bonds present in the PAH, but the shape of the PAH is an important factor in determining the binding strength. Finally, we studied how effective is ExCage⁶⁺ in reducing the inversion barriers of buckybowls. For corannulene, sumanene and dibenzo[a,g]corannulene they are reduced by 2.0, 2.7, and 2.0 kcal/mol, respectively. Although these values indicate an induced fit catalysis by ExCage⁶⁺, they are far from those values calculated inside bilayer graphene. Therefore, much work is necessary to replicate the reduction of inversion barriers observed for graphene.     

A theoretical study on three conformational structures of 2,6‐distyrylpyridine

Ab initio methods at the levels HF/cc‐pVDZ, HF/6‐31G(d,p), MP2/cc‐pVDZ, and MP2/6‐31G(d,p), as well as methods based on density functional theory (DFT) employing the hybrid functional B3LYP with the basis sets cc‐pVDZ and 6‐31G(d,p), have been applied to study the conformers of 2,6‐distyrylpyridine. Bond distances, bond angles, and dihedral angles have been calculated at the B3LYP level. The calculated values were in good agreement with those measured by X‐ray diffraction analysis of 2,6‐distyrylpyridine. The values calculated using the Hartree‐Fock method and second‐order perturbation theory (MP2) were inconsistent. The optimized lowest‐energy geometries were calculated from the reported X‐ray structural data by the B3LYP/cc‐pVDZ method. Three conformations, A, B, and C, were proposed for 2,6‐distyrylpyridine. Calculations at the three levels of theory indicated that conformation A was the most stable structure, with conformations C and B being higher in energy by 1.10 and 2.57 kcal/mol, respectively, using the same method and basis function. The same trend in the relative energies of the three possible conformations was observed at the two levels of theory and with the different basis sets employed. The reported X‐ray data were utilized to optimize total molecular energy of conformation A at the different calculation levels. The bond lengths, bond angles, and dihedral angles were then obtained from the optimized geometries by ab initio methods and by applying DFT using the two basis functions cc‐pVDZ and 6‐31G(d,p). The values were analyzed and compared. The calculated total energies, the relative energies of the molecular orbitals, the gap between them, and the dipole moment for each conformational structure proposed for 2,6‐distyrylpyridine are also reported. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Theoretical study for the HNSi–HSiN isomerization: ab initio and DFT calculations

Ab initio and density functional theory (DFT) calculations using the GAUSSIAN 94 program have been performed to investigate the molecular structures of HNSi and HSiN in the ground state as well as the transition state for the HNSi–HSiN isomerization reaction at the 6-311G(d,p), 6-311+G(2d,p) and 6-311+G(2df,p) basis sets. The results show that DFT calculations at higher levels of theory reproduce experimental vibrational frequencies of both HNSi and HSiN better than ab initio methods including electron correlation effects. Those calculated geometries are accurate enough to predict the rotational constant of HNSi. The barrier height for the isomerization reaction is found to be about 10 kcal/mol.     

Symmetric ring puckering potential in thietane‐1,1‐dioxide compared with experiment and analysis of theoretical vibrational spectra

We studied the ring puckering potential in thietane‐1,1‐dioxide with different methods, using a suitable basis set, 6‐311+G**. We obtained a barrier to ring puckering of 153 cal/mol with the DFT/B3LYP (Becke3 exchange–Lee, Yang, Parr correlation functional) method, ～60% too small compared with experiment. However, using MP2, MP3, and MP4 we obtained values around 200% too large. The MP series turned out to converge far too slowly to the experimental barrier value, showing no sign of convergence even at MP4, while higher orders are out of our reach for such a system. Obviously, of all methods used, DFT worked best despite some shortcomings. The barrier corresponds to 77 K; thus, there should be rapid interconversion over the barrier at room temperature, a phenomenon actually observed at room temperature, the measured barrier corresponding to 201 K. Thus, we decided to use the DFT/6‐311+G** calculations to predict reasonable vibrational spectra and assignments of the lines found. The ring puckering mode is found at 80 cm^?1 in DFT in good agreement with the experimental value of 78.3 cm^?1 for this vibration. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Highly Accurate CCSD(T) and DFT–SAPT Stabilization Energies of H‐Bonded and Stacked Structures of the Uracil Dimer

The CCSD(T) interaction energies for the H‐bonded and stacked structures of the uracil dimer are determined at the aug‐cc‐pVDZ and aug‐cc‐pVTZ levels. On the basis of these calculations we can construct the CCSD(T) interaction energies at the complete basis set (CBS) limit. The most accurate energies, based either on direct extrapolation of the CCSD(T) correlation energies obtained with the aug‐cc‐pVDZ and aug‐cc‐pVTZ basis sets or on the sum of extrapolated MP2 interaction energies (from aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets) and extrapolated ΔCCSD(T) correction terms [difference between CCSD(T) and MP2 interaction energies] differ only slightly, which demonstrates the reliability and robustness of both techniques. The latter values, which represent new standards for the H‐bonding and stacking structures of the uracil dimer, differ from the previously published data for the S22 set by a small amount. This suggests that interaction energies of the S22 set are generated with chemical accuracy. The most accurate CCSD(T)/CBS interaction energies are compared with interaction energies obtained from various computational procedures, namely the SCS–MP2 (SCS: spin‐component‐scaled), SCS(MI)–MP2 (MI: molecular interaction), MP3, dispersion‐augmented DFT (DFT–D), M06–2X, and DFT–SAPT (SAPT: symmetry‐adapted perturbation theory) methods. Among these techniques, the best results are obtained with the SCS(MI)–MP2 method. Remarkably good binding energies are also obtained with the DFT–SAPT method. Both DFT techniques tested yield similarly good interaction energies. The large magnitude of the stacking energy for the uracil dimer, compared to that of the benzene dimer, is explained by attractive electrostatic interactions present in the stacked uracil dimer. These interactions force both subsystems to approach each other and the dispersion energy benefits from a shorter intersystem separation.     

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     

Hetero‐π‐systems from 2 + 2 cycloreversion,part 2.1Ab initio thermochemical study of heterocyclobutanes 2 + 2 cycloreversion to form heteroethenes H2C=X (X=NH,O, SiH2, PH,S)

Ab initio and DFT thermochemical study of diradical mechanism of 2 + 2 cycloreversion of parent heterocyclobutanes and 1,3‐diheterocyclobutanes, cyclo‐(CH₂CH₂CH₂X), and cyclo‐(CH₂XCH₂X), where X = NH, O, SiH₂, PH, S, was undertaken by calculating closed‐shell singlet molecules at three levels of theory: MP4/6‐311G(d)//MP2/6‐31G(d)+ZPE, MP4/6‐311G(d,p)//MP2/6‐31G (d,p)+ZPE, and B3LYP/6‐311+G(d,p)+ZPE. The enthalpies of 2 + 2 cycloreversion decrease on going from group 14 to group 16 elements, being substantially higher for the second row elements. Normally endothermic 2 + 2 cycloreversion is predicted to be exothermic for 1,3‐diazetidine and 1,3‐dioxtane. Strain energies of the four‐membered rings were calculated via the appropriate homodesmic reactions. The enthalpies of ring opening via the every possible one‐bond homolysis that results in the formation of the corresponding 1,4‐diradical were found by subtracting the strain energies from the central bond dissociation energies of the heterobutanes CH₃CH₂—CH₂XH, CH₃CH₂—XCH₃, and HXCH₂—XCH₃. The latter energies were determined via the enthalpies of the appropriate dehydrocondensation reactions, using C—H and X—H bond energies in CH₃XH calculated at G2 level of theory. Except 1,3‐disiletane, in which ring‐opening enthalpy attains 69.7 kcal/mol, the enthalpies of the most economical ring openings do not exceed 60.7 kcal/mol. The 1,4‐diradical decomposition enthalpies found as differences between 2 + 2 cycloreversion and ring‐opening enthalpies were negative, the least exothermicity was calculated for ⋅ CH₂SiH₂CH₂CH₂. The only exception was 1,3‐disiletane, which being diradical, CH₂SiH₂CH₂SiH₂, decomposed endothermically. Since decomposition of the diradical containing two silicon atoms required extra energy, raising the enthalpy of the overall reaction to 78.9 kcal/mol, 1,3‐disiletane was predicted to be highly resisting to 2 + 2 cycloreversion. © 2007 Wiley Periodicals, Inc. Heteroatom Chem 18:704–720, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20377     

The shape of gaseous n-butylbenzene: assessment of computational methods and comparison with experiments

Conformational landscape of neutral and ionized n-butylbenzene has been examined. Geometries have been optimized at the B3LYP/6-31G(d), B3LYP/6-31+G(d,p), B3LYP-D/6-31+G(d,p), B2PLYP/6-31+G(d,p), B2PLYP-D/6-31+G(d,p), B97-D/6-31+G(d,p), and M06-2X/6-31+G(d,p) levels. This study is complemented by energy computations using 6-311++G(3df,2p) basis set and CBS-QB3 and G3MP2B3 composite methods to obtain accurate relative enthalpies. Five distinguishable conformers have been identified for both the neutral and ionized systems. Comparison with experimentally determined rotational constants shows that the best geometrical parameters are provided by B3LYP-D and M06-2X functionals, which include an explicit treatment of dispersion effects. Composite G3MP2B3 and CBS-QB3 methods, and B2PLYP-D, B3LYP-D, B97-D, and M06-2X functionals, provide comparable relative energies for the two sets of neutral and ionized conformers of butyl benzene. An exception is noted however for conformer V(+) the stability of which being overestimated by the B3LYP-D and B97-D functionals. The better stability of neutral conformers I, III, and IV, and of cation I(+) , demonstrated by our computations, is in perfect agreement with conclusions based on micro wave, fluorescence, and multiphoton ionization experiments.     

Coordination of methanol clusters to benzene: a computational study

Benzene-methanol cluster structures were investigated with theoretical chemistry methods to describe the microsolvation of benzene and the benzene-methanol azeotrope. Benzene-methanol (MeOH) clusters containing up to six methanol molecules have been calculated by ab initio [MP2/6-311++G(d,p)//MP2/6-31+G(d,p) + BSSE correction] method. The BSSE was found quite large with this basis set, hence, different extrapolation schemes in combination with the aug-cc-pVxZ basis sets have been used to estimate the complete basis set limit of the MP2 interaction energy [ΔE(MP2/CBS)]. For smaller clusters, n ≤ 3, DFT procedures (DFTB+, MPWB1K, M06-2X) have also been applied. Geometries obtained for these clusters by M06-2X and MP2 calculations are quite similar. Based on the MP2/CBS results, the most stable C(6)H(6)(MeOH)(3) cluster is characterized by a hydrogen bonded MeOH trimer chain interacting with benzene via π···H-O and O···H-C(benzene) hydrogen bonds. Larger benzene-MeOH clusters with n ≥ 4 consist of cyclic (MeOH)(n) subclusters interacting with benzene by dispersive forces, to be denoted by C(6)H(6) + (MeOH)(n). Interaction energies and cooperativity effects are discussed in comparison with methanol clusters. Besides MP2/CBS calculations, for selected larger clusters the M06-2X/6-311++G(d,p)//M06-2X/6-31+G(d,p) procedure including the BSSE correction was also used. Interaction energies obtained thereby are usually close to the MP2/CBS limit. To model the benzene-MeOH azeotrope, several structures for (C(6)H(6))(2)(MeOH)(3) clusters have been calculated. The most stable structures contain a tilted T-shaped benzene dimer interacting by π···H-O and O···H-C (benzene) hydrogen bonds with a (MeOH)(3) chain. A slightly less negative interaction energy results for a parallel displaced benzene sandwich dimer with a (MeOH)(3) chain atop of one of the benzene molecules.     

Transition states for deactivation reactions in the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy‐mediated free‐radical polymerization of acrylonitrile

The geometries and energetics of transition states (TS) for radical deactivation reactions, including competitive combination and disproportionation reactions, have been studied for the modeled 2,2,6,6‐tetramethyl‐1‐piperidinyloxy (TEMPO)‐mediated free‐radical polymerization of acrylonitrile with quantum mechanical calculations at the DFT/UB3‐LYP/6‐311+G(3df,2p)//(U)AM1 level of theory (where DFT is density functional theory, AM1 is Austin model 1, and UAM1 is unrestricted Austin model 1). A method providing reasonable starting geometries for an effective search for TS between the TEMPO radical and 1‐cyanopropyl radical mimicking the growing polyacrylonitrile macroradical is shown. For the hydrogen atom abstraction reaction by the TEMPO radical from the 1‐cyanopropyl radical, practically one TS has been found, whereas for the combination reaction of the radicals, several TS have been found, mainly differing in out‐of‐plane angle α of the N? O bond in the TEMPO structure. α in the TS is correlated with the activation energy, ΔE, determined from the single‐point calculation at the DFT UB3‐LYP/6‐311+G(3df, 2p)//UAM1 level for the combination reaction of CH₃AN· with the TEMPO radical. The theoretical activation energy for the coupling reaction from DFT UB3‐LYP/6‐311+G(3df, 2p)//UAM1 calculations has been estimated to be 11.6 kcal mol^?1, that is, only about 4.5 times smaller than ΔE for the disproportionation reaction obtained with the DFT UB3‐LYP/6‐311+G(3df, 2p)//(U)AM1 approach. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 914–927, 2006     

Accurate prediction of heats of formation by a combined method of B3LYP and neural network correction

Recently, we proposed the X1 method which combines the B3LYP/6‐311+G(3df,2p)//B3LYP/6‐311+G(d,p) method with a neural network correction for an accurate yet efficient prediction of heats of formation (Wu and Xu, J Chem Phys 2007, 127, 214105). In this contribution, we discuss in detail how to set up the X1 neural network. We give examples, showing how to apply the X1 method and how the applicability of X1 can be extended. The overall mean absolute deviation of the X1 method from experiment for the 488 heats of formation is 1.52 kcal/mol compared with 9.44 kcal/mol for the original B3LYP results. © 2008 Wiley Periodicals, Inc. J Comput Chem 2009