Extrapolation in quantum chemistry: Insights on energetics and reaction dynamics

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-[Formula: see text]J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

CBS extrapolation of Hartree-Fock energy: Pople and Dunning basis sets hand-to-hand on the endeavour

The Hartree-Fock (HF) energy is shown to be extrapolatable from subminimal, minimal, and extended basis sets. Unprecedentedly, it can be reliably extrapolated to the complete basis set limit (CBS) from as small as Pople's STO-2G up to the largest aug-cc-pVXZ basis sets of Dunning's correlation-consistent type and even more complete variants of such ansatzes. The approach is tested on a panoply of small, medium and large molecular systems. As a case study, extrapolation is shown to be particularly reliable and cost-effective (typically an order of magnitude more economical for similar accuracy) when employing a hybrid (STO-2G,extended) basis set pair. The additional cost relative to a single-point calculation with the extended basis set is of no significance. After training the novel scheme with a meager set of 18 systems (TS-18), four test sets covering from neutrals (TS-105) to neutrals plus cations (TS-26) and anions (TS-17), these involving up to third-row elements, as well as tetrapeptide conformers (TS-10) were utilized for its validation. Although the answer to the question of whether all basis sets converge to the same HF/CBS limit is a clear yes, that of whether they show the same convergence rate is open, an issue also examined in the present work. For systems involving atoms up to the second-row of the periodic table the answer seems to be a clear yes, at least when using correlation-consistent basis sets, but it is shown to be a no when the study is extended to anionic systems containing third-row elements. For the latter, augmented correlation consistent basis sets display a faster, perhaps optimal, convergence rate. The implications of this in practice can hardly be anticipated. For example, it cannot be predicted a priori which of such basis sets will yield the best relative energies for those anions, although a logical expectation suggests it to be the augmented ones which turn out to display the fastest convergence. As a blind-test type illustration, the novel scheme is applied to the conformational analysis of 2 tetrapeptides with 5 conformers each, using from subminimal up to extended basis sets as large as cc-pV5Z and aug-cc-pVQZ. The (STO-2G,extended) results so obtained are predicted to be in very good agreement with the best data reported thus far.

The influence of solvent on conformational properties of peptides with Aib residue-a DFT study

The conformational propensities of the Aib residue on the example of two model peptides Ac-Aib-NHMe (1) and Ac-Aib-NMe2 (2), were studied by B3LYP and M06-2X functionals, in the gas phase and in the polar solvents. To verify the reliability of selected functionals, we also performed MP2 calculations for the tested molecules in vacuum. Polarizable continuum models (PCM and SMD) were used to estimate the solvent effect. Ramachandran maps were calculated to find all energy minima. Noncovalent intramolecular interactions due to hydrogen-bonds and dipole attractions between carbonyl groups are responsible for the relative stabilities of the conformers. In order to verify the theoretical results, the available conformations of similar X-ray structures from the Cambridge Crystallographic Data Center (CCDC) were analyzed. The results of the calculations show that both derivatives with the Aib residue in the gas phase prefer structures stabilized by intramolecular N-H⋯O hydrogen bonds, i.e., C5 and C7 conformations, while polar solvent promotes helical conformation with φ, ψ values equal to +/-60°, +/-40°. In addition, in the case of molecule 2, the helical conformation is the only one available in the polar environment. This result is fully consistent with the X-ray data. Graphical abstract Effect of solvent on the Ramachandran maps of the model peptides with Aib residue.

Conformational preferences and synthesis of isomers Z and E of oxazole-dehydrophenylalanine

Dehydrophenylalanine, ΔPhe, is the most commonly studied α,β-dehydroamino acid. In nature, further modifications of the α,β-dehydroamino acids were found, for example, replacement of the C-terminal amide group by oxazole ring. The conformational properties of oxazole-dehydrophenylalanine residue (ΔPhe-Ozl), both isomers Z and E, were investigated. To determine all possible conformations, theoretical calculations were performed using Ac-(Z/E)-ΔPhe-Ozl(4-Me) model compounds at M06-2X/6-31++G(d,p) level of theory. Ac-(Z/E)-ΔPhe-Ozl-4-COOEt compounds were synthesized and the conformational preferences of each isomer, Z and E, were investigated using FTIR and NMR-NOE in solutions of increasing polarity (CHCl3 , DMSO-d6). The solid-state low-temperature structures of Ac-(Z)-ΔPhe-Ozl-4-COOEt and its intermediate analog Ac-(Z)-ΔPhe-Ozn(4-OH)-4-COOEt were also determined. In a weakly polar environment, the ΔPhe-Ozl residue has a tendency to adopt the conformation β2 with the calculated φ and ψ angles of -127° and 0° for the isomer Z and -170° and 26° for the isomer E. The increase of environment polarity favors the helical conformation α and the beta-turn like conformation β, but the conformation β2 seems to be still accessible. The (E)-ΔPhe-Ozl residue can be obtained from the isomer Z in photoisomerization reaction. However, hydroxyl-oxazoline-dehydrophenylalanine ΔPhe-Ozn(4-OH) decomposes in such conditions. Alternatively, (E)-ΔPhe-NH2 can be applied as a substrate in the Hantzsch reaction. © 2016 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 106: 283-294, 2016.

Toward engineering efficient peptidomimetics. Screening conformational landscape of two modified dehydroaminoacids

Effective peptidomimetics should posses structural rigidity and appropriate interaction pattern leading to potential spatial and electronic matching to the target receptor site. Rational design of such small bioactive molecules could push chemical synthesis and molecular modeling toward faster progress in medicinal chemistry. Conformational properties of N-t-butoxycarbonyl-glycine-(E/Z)-dehydrophenylalanine N',N'-dimethylamides (Boc-Gly-(E/Z)-ΔPhe-NMe2 ) in chloroform were studied by NMR and IR spectroscopy. The experimental findings were supported by extensive calculations at DFT(B3LYP, M06-2X) and MP2 levels of theory and the β-turn tendency for both isomers of the studied dipeptide were determined in vacuum and in solution. The theoretical data and experimental IR results were used as an additional information for the NMR-based determination of the detailed solution conformations of the peptides. The obtained results reveal that N-methylation of C-terminal amide group changes dramatically the conformational properties of studied dehydropeptides. Theoretical conformational analysis reveals that the tendency to adopt β-turn conformations is much weaker for the N-methylated Z isomer (Boc-Gly-(Z)-ΔPhe-NMe2 ), both in vacuum and in polar environment. On the contrary, N-methylated E isomer (Boc-Gly-(E)-ΔPhe-NMe2 ) can easily adopt β-turn conformation, but the backbone torsion angles (φ1, ψ1, φ2, ψ2) are off the limits for common β-turn types.

Conformational state of β-hydroxynaphthylamides: Barriers for the rotation of the amide group around CN bond and dynamics of the morpholine ring

Three β-hydroxynaphthylamides (morpholine, pyrrolidine and dimethylamine derivatives) have been synthesized and their conformational state was analyzed by NMR, X-ray and DFT calculations. In aprotic solution the molecules contain intramolecular OHO hydrogen bonds, which change into intermolecular ones in solid state. The energy barriers for the amide group rotation around the CN bond were estimated from the line shape analysis of (1)H and (13)C NMR signals. A tentative correlation between the barrier height and the strength of OHO bond was proposed. Calculations of the potential energy profiles for the rotations around CC and CN bonds were done. In case of morpholine derivative experimental indications of additional dynamics: chair-chair 'ring flip' in combination with the twisting around CC bond were obtained and confirmed by quantum chemistry calculations.

The effect of N-methylation of amino acids (Ac-X-OMe) on solubility and conformation: a DFT study

N-Methylation of amino acid derivatives (Ac-X-OMe, X = Gly, Val, Leu, Ile, Phe, Met, Cys, Ser, Asp and His) leads to an increase in aqueous solubility, lipophilicity and lowering of the cis/trans amide conformational energy barrier (E_A).