Insufficient description of dispersion in B3LYP and large basis set superposition errors in MP2 calculations can hide peptide conformers

Basis Set Superposition Errors Are Partly Basis Set Imbalances

When calculating fragment interaction energies by electronic structure methods employing medium-sized atom-centered basis sets, it is often observed that the effect is systematically overestimated. The common interpretation is that the systematic error arises because the basis set for the complex is more complete than for the isolated fragments, and this is denoted basis set superposition errors. It has been observed, however, that the interaction energy in some cases is underestimated, which defies the interpretation in terms of basis set completeness, and instead suggests that the effect partly is due to basis set imbalance. The imbalance can be removed by explicit optimization of the basis sets for each structure, and it is shown that this to a significant extent reduces the systematic overestimation attributed to basis set superposition error.

Quantifying Intramolecular Basis Set Superposition Errors

We show that medium-sized Gaussian basis sets lead to significant intramolecular basis set superposition errors at Hartree-Fock and density functional levels of theory, with artificial stabilization of compact over extended conformations for a 186 atom deca-peptide. Errors of ∼80 and ∼10 kJ/mol are observed, with polarized double zeta and polarized triple zeta quality basis sets, respectively. Two different procedures for taking the basis set superposition error into account are tested. While both reduce the error, it appears that polarized quadruple zeta basis sets are required to reduce the error below a few kJ/mol. Alternatively, the basis set superposition error can be eliminated using multiresolution methods based on Multiwavelets.

A benchmark study of aromaticity indexes for benzene, pyridine and the diazines - I. Ground state aromaticity

Five different aromaticity indexes are benchmarked for benzene, pyridine and the diazines in their ground states. A basis set study was performed using the Pople style, Karlsruhe and Dunning's correlation consistent basis sets. Ten different DFT functionals, including LSDA, PBE, PBE0, B3LYP, CAM-B3LYP, wB97XD, M06-2X, SOGGA11X, M11 and MN15 were benchmarked by comparison with CCSD, CASSCF and MP2. Large out-of-plane imaginary frequencies were observed for some of the optimized structures at the correlated wavefunction level of theory. It was found that the DFT functionals in general predict the para-delocalization index, multicenter index and aromatic fluctuation index to be approximately 70%, 50% and 45% larger, respectively, compared to the CCSD method. Comparisons of the DFT functionals showed that the wB97XD, CAM-B3LYP and M06-2X functionals performed the best. Furthermore, the basis set dependence of the DFT functionals was found to be large for the electron sharing indexes. Based on these findings, it is recommended to perform ground state calculations of aromaticity indexes at the wB97XD, CAM-B3LYP or M06-2X level of theory utilizing a simple basis set of triple-ζ quality.

Five different aromaticity indexes are benchmarked for benzene, pyridine and the diazines in their ground states.

Nature of intermolecular interaction in squaraine dimers

Squaraine dyes are known for their particular optical properties. They exhibit intense photochemically stable fluorescence in usually (near) infra red region that can be quenched by intermolecular interactions. Moreover, even the centrosymmetric dyes feature non-zero second harmonic generation upon aggregation. Therefore, the detailed knowledge of the squaraine dye interaction nature both in homogenic aggregates and with other species present in the environment can be of importance for the design of new materials of desired properties. In the present study, interaction in squaraine dimers is investigated with quantum chemistry tools. Four structures: two stacked and two hydrogen-bonded are analyzed in terms of supermolecular approach and symmetry-adapted perturbation theory. MP2C/aug-cc-pVTZ supermolecular calculations confirm the particular stability of the stacked dimers and the favoured dispersion attraction for the long-displaced system.

Neutral Peptides in the Gas Phase: Conformation and Aggregation Issues

Combined IR and UV laser spectroscopic techniques in molecular beams merged with theoretical approaches have proven to be an ideal tool to elucidate intrinsic structural properties on a molecular level. It offers the possibility to analyze structural changes, in a controlled molecular environment, when successively adding aggregation partners. By this, it further makes these techniques a valuable starting point for a bottom-up approach in understanding the forces shaping larger molecular systems. This bottom-up approach was successfully applied to neutral amino acids starting around the 1990s. Ever since, experimental and theoretical methods developed further, and investigations could be extended to larger peptide systems. Against this background, the review gives an introduction to secondary structures and experimental methods as well as a summary on theoretical approaches. Vibrational frequencies being characteristic probes of molecular structure and interactions are especially addressed. Archetypal biologically relevant secondary structures investigated by molecular beam spectroscopy are described, and the influences of specific peptide residues on conformational preferences as well as the competition between secondary structures are discussed. Important influences like microsolvation or aggregation behavior are presented. Beyond the linear α-peptides, the main results of structural analysis on cyclic systems as well as on β- and γ-peptides are summarized. Overall, this contribution addresses current aspects of molecular beam spectroscopy on peptides and related species and provides molecular level insights into manifold issues of chemical and biochemical relevance.

Fantasy versus reality in fragment-based quantum chemistry

Since the introduction of the fragment molecular orbital method 20 years ago, fragment-based approaches have occupied a small but growing niche in quantum chemistry. These methods decompose a large molecular system into subsystems small enough to be amenable to electronic structure calculations, following which the subsystem information is reassembled in order to approximate an otherwise intractable supersystem calculation. Fragmentation sidesteps the steep rise (with respect to system size) in the cost of ab initio calculations, replacing it with a distributed cost across numerous computer processors. Such methods are attractive, in part, because they are easily parallelizable and therefore readily amenable to exascale computing. As such, there has been hope that distributed computing might offer the proverbial "free lunch" in quantum chemistry, with the entrée being high-level calculations on very large systems. While fragment-based quantum chemistry can count many success stories, there also exists a seedy underbelly of rarely acknowledged problems. As these methods begin to mature, it is time to have a serious conversation about what they can and cannot be expected to accomplish in the near future. Both successes and challenges are highlighted in this Perspective.

Effect of the sulfur atom on S2 and S4 positions of the uracil ring in different DNA:RNA hybrid microhelixes with three nucleotide base pairs

The effect of the sulphur atom on the uracil ring was analyzed in different DNA:RNA microhelixes with three nucleotide base-pairs, including uridine, 2-thiouridine, 4-thiouridine, 2,4-dithiouridine, cytidine, adenosine and guanosine. Distinct backbone and helical parameters were optimized at different density functional (DFT) levels. The Watson-Crick pair with 2-thiouridine appears weaker than with uridine, but its interaction with water molecules appears easier. Two types of microhelixes were found, depending on the H-bond of H2' hydroxyl atom: A-type appears with the ribose ring in ³ E-envelope C_3' -endo, and B-type in ² E-envelope C_2' -endo. B-type is less common but it is more stable and with higher dipole-moment. The sulphur atoms significantly increase the dipole-moment of the microhelix, as well as the rise and propeller twist parameters. Simulations with four Na atoms H-bonded to the phosphate groups, and further hydration with explicit water molecules were carried out. A re-definition of the numerical value calculation of several base-pair and base-stacking parameters is suggested.

Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms

We present an innovative method for predicting the dynamic electron correlation energy of an atom or a bond in a molecule utilizing topological atoms. Our approach uses the machine learning method Kriging (Gaussian Process Regression with a non-zero mean function) to predict these dynamic electron correlation energy contributions. The true energy values are calculated by partitioning the MP2 two-particle density-matrix via the Interacting Quantum Atoms (IQA) procedure. To our knowledge, this is the first time such energies have been predicted by a machine learning technique. We present here three important proof-of-concept cases: the water monomer, the water dimer, and the van der Waals complex H₂···He. These cases represent the final step toward the design of a full IQA potential for molecular simulation. This final piece will enable us to consider situations in which dispersion is the dominant intermolecular interaction. The results from these examples suggest a new method by which dispersion potentials for molecular simulation can be generated.

A DFT study of 2-aminopurine-containing dinucleotides: prediction of stacked conformations with B-DNA structure

The fluorescence properties of dinucleotides incorporating 2-aminopurine (2AP) suggest that the simplest oligonucleotides adopt conformations similar to those found in duplex DNA. However, there is a lack of structural data for these systems. We report a density functional theory (DFT) study of the structures of 2AP-containing dinucleotides (deoxydinucleoside monophosphates), including full geometry optimisation of the sugar-phosphate backbone. Our DFT calculations employ the M06-2X functional for reliable treatment of dispersion interactions and include implicit aqueous solvation. Dinucleotides with 2AP in the 5'-position and each of the natural bases in the 3'-position are examined, together with the analogous 5'-adenine-containing systems. Computed structures are compared in detail with typical B-DNA base-step parameters, backbone torsional angles and sugar pucker, derived from crystallographic data. We find that 2AP-containing dinucleotides adopt structures that closely conform to B-DNA in all characteristic parameters. The structures of 2AP-containing dinucleotides closely resemble those of their adenine-containing counterparts, demonstrating the fidelity of 2AP as a mimic of the natural base. As a first step towards exploring the conformational heterogeneity of dinucleotides, we also characterise an imperfectly stacked conformation and one in which the bases are completely unstacked.

Exploring short intramolecular interactions in alkylaromatic substrates

From proteins and peptides to semiconducting polymers, aliphatic chains on aromatic groups are recurring motifs in macromolecules from very diverse application fields. Fields in which molecular folding and packing determine the macroscopic physical properties that make such advanced materials appealing in the first place. Within each macromolecule, the intrinsic structure of each unit defines how it interacts with its neighbours, ultimately opening up or denying certain backbone conformations. This eventually also determines how macromolecules interact with each other. This account deals specifically with the conformational problem of many common alkylaromatic units, examining the features of an intramolecular interaction involving a side chain with as few as three methylene groups. A set of 23 model compounds featuring an intramolecular interaction between an aliphatic X-H (X = C, N, O, and S) bond and an aromatic ring was considered. Quantitative computational analysis was made possible, thanks to complete basis set extrapolated CCSD(T) calculations and NCI topological analysis, the latter of which revealed an elaborate network of dispersive and steric interactions leading to somewhat unintuitive and unexpected results, such as the higher energetic stability of certain twisted conformational isomers over those with extended side chains. Vicinal covalent effects from polarizing groups and various heteroatoms, along with the occurrence of non-dispersive phenomena, were also investigated. The conclusions drawn from the investigation include a comprehensive set of guidelines intended to aid in the prediction of the most stable conformation for this class of building blocks. Our findings affect a variety of different research fields, including the tailoring of functional materials for organic electronics and photovoltaics, with insights into a rational treatment of conformational disorder, and the study of protein- and peptide-folding preferences, putting an emphasis on peculiar interactions between the backbone and aromatic residues.

A DFT study on the role of long range correlation interaction and solvent effects in homochiral and heterochiral cyclic trimerization of imidazole based heterocyclic amino acids

Using B3LYP and B97D functionals of density functional theory (DFT), homochiral and heterochiral cyclic trimerization of imidazole based heterocyclic amino acids are studied in gas phase and solvent phase, i. e., Acetonitrile. Both the functionals show that formation of homochiral cyclic tripeptide is thermodynamically and kinetically favorable over its heterochiral counterpart in gas phase. The functional, B97D, decreases the height of reaction barriers significantly compared to those predicted by the functional B3LYP. The reaction pathways explored using PCM implicit solvent model show reduced kinetic favorability for formation of the homochiral cyclic tripeptide over its heterochiral counterpart. The results are substantiated by structural aspects.

Small Atomic Orbital Basis Set First-Principles Quantum Chemical Methods for Large Molecular and Periodic Systems: A Critical Analysis of Error Sources

In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.

Conformational Interconversions of Amino Acid Derivatives

Exhaustive conformational interconversions including transition structure analyses of N-acetyl-l-glycine-N-methylamide as well as its alanine, serine, and cysteine analogues have been investigated at the MP2/6-31G** level, yielding a total of 142 transition states. Improved estimates of relative energies were obtained by separately extrapolating the Hartree-Fock and MP2 energies to the basis set limit and adding the difference between CCSD(T) and MP2 results with the cc-pVDZ basis set to the extrapolated MP2 results. The performance of eight empirical force fields (AMBER94, AMBER14SB, MM2, MM3, MMFFs, CHARMM22_CMAP, OPLS_2005, and AMOEBAPRO13) in reproducing ab initio energies of transition states was tested. Our results indicate that commonly used class I force fields employing a fixed partial charge model for the electrostatic interaction provide mean errors in the ∼10 kJ/mol range for energies of conformational transition states for amino acid conformers. Modern reparametrized versions, such as CHARMM22_CMAP, and polarizable force fields, such as AMOEBAPRO13, have slightly lower mean errors, but maximal errors are still in the 35 kJ/mol range. There are differences between the force fields in their ability for reproducing conformational transitions classified according to backbone/side-chain or regions in the Ramachandran angles, but the data set is likely too small to draw any general conclusions. Errors in conformational interconversion barriers by ∼10 kJ/mol suggest that the commonly used force field may bias certain types of transitions by several orders of magnitude in rate and thus lead to incorrect dynamics in simulations. It is therefore suggested that information for conformational transition states should be included in parametrizations of new force fields.

Multi-conformer molecules in solutions: an NMR-based DFT/MP2 conformational study of two glucopyranosides of a vitamin E model compound

Overall geometries of both glucosyl derivatives of PMC were found on the basis of their NMR spectra in CDCl₃and relatedδ_H,C/ⁿJ_HHIEF-PCM(UFF,CHCl₃)/DFT calculational results.

An Atomic Counterpoise Method for Estimating Inter- and Intramolecular Basis Set Superposition Errors

An atomic counterpoise method is proposed to calculate estimates of inter- and intramolecular basis set superposition errors. The method estimates the basis set superposition error as a sum of atomic contributions and can be applied for both independent particle and electron correlation models. It is shown that the atomic counterpoise method provides results very similar to the molecular counterpoise method for intermolecular basis set superposition errors at both the HF and MP2 levels of theory with a sequence of increasingly larger basis sets. The advantage of the atomic counterpoise method is that it can be applied with equal ease to estimate intramolecular basis set superposition errors, for which few other methods exist. The atomic counterpoise method is computationally quite efficient, requiring typically double the amount of computer time as required for calculating the uncorrected energy.

Gas Phase Detection of the NH-P Hydrogen Bond and Importance of Secondary Interactions

We have observed the NH···P hydrogen bond in a gas phase complex. The bond is identified in the dimethylamine-trimethylphosphine complex by a red shift of the fundamental NH-stretching frequency observed using Fourier transform infrared spectroscopy (FT-IR). On the basis of the measured NH-stretching frequency red shifts, we find that P is a hydrogen bond acceptor atom similar in strength to S. Both are stronger acceptors than O and significantly weaker acceptors than N. The hydrogen bond angle, ∠NHP, is found to be very sensitive to the functional employed in density functional theory (DFT) optimizations of the complex and is a possible parameter to assess the quality of DFT functionals. Natural bonding orbital (NBO) energies and results from the topological methods atoms in molecules (AIM) and noncovalent interactions (NCI) indicate that the sensitivity is caused by the weakness of the hydrogen bond compared to secondary interactions. We find that B3LYP favors the hydrogen bond and M06-2X favors the secondary interactions leading to under- and overestimation, respectively, of the hydrogen bond angle relative to a DF-LCCSD(T)-F12a calculated angle. The remaining functionals tested, B3LYP-D3, B3LYP-D3BJ, CAM-B3LYP, and ωB97X-D, as well as MP2, show comparable contributions from the hydrogen bond and the secondary interactions and are close to DF-LCCSD(T)-F12a results.

Isolated neutral peptides

This chapter examines the structural characterisation of isolated neutral amino-acids and peptides. After a presentation of the experimental and theoretical state-of-the-art in the field, a review of the major structures and shaping interactions is presented. Special focus is made on conformationally-resolved studies which enable one to go beyond simple structural characterisation; probing flexibility and excited-state photophysics are given as examples of promising future directions.

Experimental and theoretical evaluation on the conformational behavior of l-aspartic acid dimethyl ester and its N-acetylated derivative

The AspOMe and AcAspOMe conformational preferences and their corresponding intramolecular interactions were studied through spectroscopic and theoretical methodologies.

Assignment of O–O and Mo=O Stretching Frequencies of Molybdenum/Tungsten Complexes Revisited

The assignment of peroxo stretching frequencies for Molybdenum and Tungsten complexes is studied by DFT and MP2 calculations. We found that M06 functional is unsuitable for assignment of Mo=O and O–O stretches in CpMo(η2-O2)OCH3and we found that MP2 and even the def2-TZVP do not give accurate order of asymmetric and symmetric Mo=O stretching. We recommend the M06L, which is a good compromise between speed and accuracy, for works involving these complexes. For a series of ten Molybdenum and Tungsten complexes studied we found that, for Mo/W=O stretching frequencies at M06L/def2-TZVP, after scaling, a small RMSD of 15 cm−1could be obtained. However peroxo stretching frequencies RMSD remains high at 40 cm−1after scaling. This could potentially point out the need for reassignment of experimental peroxo frequencies in some of the works cited in this report.

Density functional theory based study on cis-trans isomerism of the amide bond in homodimers of β(2,3)- and β(3)-substituted homoproline

Preference for a cis/trans peptide bond between residues of dipeptides formed by substituted β(2,3) (I) and β(3) (II) homoproline is investigated using density functional theory (DFT). Potential energy surfaces for monomer and linear dimers are explored at the B3LYP/6-31G(d,p) level of theory. Minimum energy conformations of the dipeptides are optimized using B3LYP, PBE1PBE, B97D, and M06-2X functionals at the 6-31G(d,p) level of basis set in both the gas phase and solvent phase. The relative free energy difference between the selected conformations is marginal. Results obtained using the functionals M06-2X and B97D on dimers of I and II, respectively, agree with experimental results. The lowest energy conformations predicted by B97D/6-31G(d,p) and M06-2X/6-31G(d,p) levels of theory show greater relative MP2 correlation energy. Dipeptides of I with hydrophilic substituents show preference for a trans peptide bond. Support for cis/trans isomerism in dimers of I with hydrophobic substituents comes from potential energy surfaces and free energy data. Although dipeptides of II with hydrophilic substituents show preference for cis peptide bond, the dipeptides with hydrophobic substituent prefer trans bond.

On the Relevance of Considering the Intermolecular Interactions on the Prediction of the Vibrational Spectra of Isopropylamine

The effects of implicitly considering the effects of hydrogen bonding on the molecular properties, such as vibrational frequencies, were inferred on the basis of DFT calculations. Several clusters of isopropylamine were assembled and theoretically characterized. The results showed that maximum H-bond cooperativity is achieved when the amine group acts simultaneously as donor and acceptor. The effect of H-bond cooperativity manifests itself in the relative cluster stability and on the structural and vibrational frequency predictions. Referring to the vibrational frequencies it was found that theNH2stretching and torsion vibrational modes are the most affected by the amine involvement in hydrogen bonding. Both stretching modes were found to be significantly redshifted relative to the monomer. TheNH2torsional mode, on the other hand, was found to be blueshifted up to 350 cm-1. Finally, the comparative study between the theory levels performed allows to conclude that the small 6-31G* basis set is able to stabilize weakC–H⋯Ninteractions as long as the new dispersion corrected DFT methods are considered. The impairments observed with conventional DFT methods for describing weak interactions may be overcome with the improvement of basis set, but the associated increase of computational costs may turn the calculations unfeasible.

Analysis of the basis set superposition error in molecular dynamics of hydrogen-bonded liquids: application to methanol

An efficient protocol is presented to compensate for the basis set superposition error (BSSE) in DFT molecular dynamics (MD) simulations using localized Gaussian basis sets. We propose a classical correction term that can be added a posteriori to account for BSSE. It is tested to what extension this term will improve radial distribution functions (RDFs). The proposed term is pairwise between certain atoms in different molecules and was calibrated by fitting reference BSSE data points computed with the counterpoise method. It is verified that the proposed exponential decaying functional form of the model is valid. This work focuses on hydrogen-bonded liquids, i.e., methanol, and more specific on the intermolecular hydrogen bond, but in principle the method is generally applicable on any type of interaction where BSSE is significant. We evaluated the relative importance of the Grimme-dispersion versus BSSE and found that they are of the same order of magnitude, but with an opposite sign. Upon introduction of the correction, the relevant RDFs, obtained from MD, have amplitudes equal to experiment.