Evaluation of the intramolecular basis set superposition error in the calculations of larger molecules: [n]helicenes and Phe-Gly-Phe tripeptide

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 theoretical study on the strain energy of helicene-containing carbon nanobelts

In this study, the theoretical analysis of the strain energy of helicene-containing carbon nanobelts is reported. It was found that the combined method of linear regression analysis and suitable homodesmotic reactions can successfully estimate the strain energies of various helicene-containing carbon nanobelts including previously synthesized chiral (18,12) carbon nanobelts.

Structural analysis of helicene molecules adsorbed on symmetric surfaces

Helicenes are chiral polyaromatic hydrocarbon molecules which self-assemble into ordered monolayers on solid substrates, and are of current interest in the study of supramolecular systems and the development of smart materials. In this work we investigate the geometry of helicene monomers and stacked dimers on (111) facets of coinage metals. The geometry of the adsorbed molecules is shaped by the coupling of intermolecular dispersive forces, intramolecular steric repulsion between end rings and surface-molecule interactions. Thus, binding and stereospecificity outcomes vary broadly depending on the identity of molecule/surface pair. Overall, homochiral interactions are found to be more effective than heterochiral stacking, due to a better fit between the helical structures in like dimers. On a surface, this effect is enhanced by the flattening of surface-proximal molecular rings. However, our results show that the "sandwich" effect of the second molecular layer increases molecular footprints in the first layer, with potentially large implications in monolayer organization and surface commensuration.

Single-Stranded DNA Oligonucleotides Retain Rise Coordinates Characteristic of Double Helices

The structures of single-stranded DNA oligonucleotides from dimeric to hexameric sequences have been thoroughly investigated. Computations performed at the density functional level of theory including dispersion forces and solvation show that single-stranded helices adopt conformations very close to crystallographic B-DNA, with rise coordinates amounting up to 3.3 Å. Previous results, suggesting that single strands should be shorter than double helices, largely originated from the incompleteness of the adopted basis set. Although sensible deviations with respect to standard B-DNA are predicted, computations indicate that sequences rich in stacked adenines are the most ordered ones, favoring the B-DNA pattern and inducing regular arrangements also on flanking nucleobases. Several structural properties of double helices rich in adenine are indeed already reflected by the corresponding single strands.

Assessment of Density Functional Methods for Geometry Optimization of Bimolecular van der Waals Complexes

We explore the suitability of three popular density functionals (B97-D3, B3LYP-D3, M05-2X) for producing accurate equilibrium geometries of van der Waals (vdW) complexes with diverse binding motifs. For these functionals, optimizations using Dunning's aug-cc-pVDZ basis set best combine accuracy and a reasonable computational expense. Each DFT/aug-cc-pVDZ combination produces optimized equilibrium geometries for 21 small vdW complexes of organic molecules (up to four non-hydrogen atoms total) that agree with high-level CCSD(T)/CBS reference geometries to within ±0.1 Å for the averages of the center-of-mass displacement and the mean least root-mean-squared displacement. The DFT/aug-cc-pVDZ combinations are also able to reproduce the optimal center-of-mass displacements interpolated from CCSD(T)/CBS radial potential energy surfaces in both NBC7x and HBC6 test sets to within ±0.1 Å. We therefore conclude that each of these denisty functional methods, together with the aug-cc-pVDZ basis set, is suitable for producing equilibrium geometries of generic nonbonded complexes.

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.

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.

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.

Base-Pairing Energies of Proton-Bound Dimers and Proton Affinities of 1-Methyl-5-Halocytosines: Implications for the Effects of Halogenation on the Stability of the DNA i-Motif

(CCG)(n)•(CGG)(n) trinucleotide repeats have been found to be associated with fragile X syndrome, the most widespread inherited cause of mental retardation in humans. The (CCG)(n)•(CGG)(n) repeats adopt i-motif conformations that are preferentially stabilized by base-pairing interactions of noncanonical proton-bound dimers of cytosine (C(+)•C). Halogenated cytosine residues are one form of DNA damage that may be important in altering the structure and stability of DNA or DNA-protein interactions and, hence, regulate gene expression. Previously, we investigated the effects of 5-halogenation and 1-methylation of cytosine on the base-pairing energies (BPEs) using threshold collision-induced dissociation (TCID) techniques. In the present study, we extend our work to include proton-bound homo- and heterodimers of cytosine, 1-methyl-5-fluorocytosine, and 1-methyl-5-bromocytosine. All modifications examined here are found to produce a decrease in the BPEs. However, the BPEs of all of the proton-bound dimers examined significantly exceed those of Watson-Crick G•C, neutral C•C base pairs, and various methylated variants such that DNA i-motif conformations should still be preserved in the presence of these modifications. The proton affinities (PAs) of the halogenated cytosines are also obtained from the experimental data by competitive analysis of the primary dissociation pathways that occur in parallel for the proton-bound heterodimers. 5-Halogenation leads to a decrease in the N3 PA of cytosine, whereas 1-methylation leads to an increase in the N3 PA. Thus, the 1-methyl-5-halocytosines exhibit PAs that are intermediate.

Base-pairing energies of protonated nucleobase pairs and proton affinities of 1-methylated cytosines: model systems for the effects of the sugar moiety on the stability of DNA i-motif conformations

Expansion of (CCG)n·(CGG)n trinucleotide repeats leads to hypermethylation of cytosine residues and results in Fragile X syndrome, the most common cause of inherited intellectual disability in humans. The (CCG)n·(CGG)n repeats adopt i-motif conformations that are preferentially stabilized by base-pairing interactions of noncanonical protonated nucleobase pairs of cytosine (C(+)·C). Previously, we investigated the effects of 5-methylation of cytosine on the base-pairing energies (BPEs) using threshold collision-induced dissociation (TCID) techniques. In the present work, we extend our investigations to include protonated homo- and heteronucleobase pairs of cytosine, 1-methylcytosine, 5-methylcytosine, and 1,5-dimethylcytosine. The 1-methyl substituent prevents most tautomerization processes of cytosine and serves as a mimic for the sugar moiety of DNA nucleotides. In contrast to permethylation of cytosine at the 5-position, 1-methylation is found to exert very little influence on the BPE. All modifications to both nucleobases lead to a small increase in the BPEs, with 5-methylation producing a larger enhancement than either 1-methyl or 1,5-dimethylation. In contrast, modifications to a single nucleobase are found to produce a small decrease in the BPEs, again with 5-methylation producing a larger effect than 1-methylation. However, the BPEs of all of the protonated nucleobase pairs examined here significantly exceed those of canonical G·C and neutral C·C base pairs, and thus should still provide the driving force stabilizing DNA i-motif conformations even in the presence of such modifications. The proton affinities of the methylated cytosines are also obtained from the TCID experiments by competitive analyses of the primary dissociation pathways that occur in parallel for the protonated heteronucleobase pairs.

Base-pairing energies of proton-bound heterodimers of cytosine and modified cytosines: implications for the stability of DNA i-motif conformations

The DNA i-motif conformation was discovered in (CCG)•(CGG)n trinucleotide repeats, which are associated with fragile X syndrome, the most widespread inherited cause of mental retardation in humans. The DNA i-motif is a four-stranded structure whose strands are held together by proton-bound dimers of cytosine (C(+)•C). The stronger base-pairing interactions in C(+)•C proton-bound dimers as compared to Watson-Crick G•C base pairs are the major forces responsible for stabilization of i-motif conformations. Methylation of cytosine results in silencing of the FMR1 gene and causes fragile X syndrome. However, the influence of methylation or other modifications such as halogenation of cytosine on the base-pairing energies (BPEs) in the i-motif remains elusive. To address this, proton-bound heterodimers of cytosine and 5-methylcytosine, 5-fluorocytosine, 5-bromocytosine, and 5-iodocytosine are probed in detail. Experimentally, the BPEs of proton-bound heterodimers of cytosine and modified cytosines are determined using threshold collision-induced dissociation (TCID) techniques. All modifications at the 5-position of cytosine are found to lower the BPE and therefore would tend to destabilize DNA i-motif conformations. However, the BPEs in these proton-bound heterodimers still significantly exceed those of the Watson-Crick G•C and neutral C•C base pairs, suggesting that C(+)•C mismatches are still energetically favored such that i-motif conformations are preserved. Excellent agreement between TCID measured BPEs and B3LYP calculated values is found with the def2-TZVPPD and 6-311+G(2d,2p) basis sets, suggesting that calculations at these levels of theory can be employed to provide reliable energetic predictions for related systems.

Base-pairing energies of proton-bound homodimers determined by guided ion beam tandem mass spectrometry: application to cytosine and 5-substituted cytosines

Base-pairing interactions in proton-bound dimers of cytosine (C(+)·C) are the major forces responsible for stabilization of DNA i-motif conformations. Permethylation of cytosine in extended (CCG)·(CGG)n trinucleotide repeats has been shown to cause fragile-X syndrome, the most widespread inherited cause of mental retardation in humans. Oligonucleotides containing 5-bromo- or 5-fluorocytosine can bind to proteins that selectively bind methylated DNA, suggesting that halogenated cytosine damage products can potentially mimic methylation signals. However, the influence of methylation or halogenation on the base-pairing energies (BPEs) of proton-bound dimers of cytosine and their impact on the stability of DNA i-motif conformations is presently unknown. To address this, proton-bound homodimers of cytosine and 5-methyl-, 5-fluoro-, 5-bromo-, and 5-iodocytosine are investigated in detail both experimentally and theoretically. The BPEs of proton-bound homodimers of cytosine and the modified cytosines are measured by threshold collision-induced dissociation (TCID) techniques. 5-Methylation of cytosine is found to increase the BPE and would therefore tend to stabilize DNA i-motif conformations. In contrast, 5-halogenation lowers the BPE. However, the BPEs of the proton-bound 5-halocytosine homodimers examined here still significantly exceed that of Watson-Crick G·C base pairs, such that DNA i-motif conformations should be preserved in the presence of these modifications. Excellent agreement between TCID measured and B3LYP calculated BPEs is found, suggesting that B3LYP calculations can be used to provide reliable energetic predictions for related systems.

New parameterization scheme of DFT-D for graphitic materials

A new parametrization scheme of DFT-D is proposed with the aim of devising a methodology for the study of graphitic material. The main feature of the new system is the geometry optimization within the fitting scheme. The DFT-D parameters are obtained for the benzene dimer, a good model molecule for graphitic systems. Very accurate CCSD(T) results are used as reference data for the benzene dimer, and the new method is shown to reproduce accurately its binding energies with small basis sets. After geometry optimization our new scheme performs better than the other methods. This approach generates proper geometries and accurate binding energies, even with small basis sets. We can expect this method to give similarly good results for larger graphitic systems.

Ring opening polymerization of mannosyl tricyclic orthoesters: rationalising the stereo and regioselectivity of glycosidic bond formation using quantum chemical calculations

Quantum chemical methods have been used to assess the physico-chemical origin of the stereo and regio-selectivity during glycosyl tricyclic orthoester polymerization. The subtle modulation of steric and electronic factors dramatically influences the reaction.

The DNA and RNA sugar-phosphate backbone emerges as the key player. An overview of quantum-chemical, structural biology and simulation studies

Knowledge of geometrical and physico-chemical properties of the sugar-phosphate backbone substantially contributes to the comprehension of the structural dynamics, function and evolution of nucleic acids. We provide a side by side overview of structural biology/bioinformatics, quantum chemical and molecular mechanical/simulation studies of the nucleic acids backbone. We highlight main features, advantages and limitations of these techniques, with a special emphasis given to their synergy. The present status of the research is then illustrated by selected examples which include classification of DNA and RNA backbone families, benchmark structure-energy quantum chemical calculations, parameterization of the dihedral space of simulation force fields, incorporation of arsenate into DNA, sugar-phosphate backbone self-cleavage in small RNA enzymes, and intricate geometries of the backbone in recurrent RNA building blocks. Although not apparent from the current literature showing limited overlaps between the QM, simulation and bioinformatics studies of the nucleic acids backbone, there in fact should be a major cooperative interaction between these three approaches in studies of the sugar-phosphate backbone.

Refinement of the Cornell et al. Nucleic Acids Force Field Based on Reference Quantum Chemical Calculations of Glycosidic Torsion Profiles

We report a reparameterization of the glycosidic torsion χ of the Cornell et al. AMBER force field for RNA, χ(OL). The parameters remove destabilization of the anti region found in the ff99 force field and thus prevent formation of spurious ladder-like structural distortions in RNA simulations. They also improve the description of the syn region and the syn-anti balance as well as enhance MD simulations of various RNA structures. Although χ(OL) can be combined with both ff99 and ff99bsc0, we recommend the latter. We do not recommend using χ(OL) for B-DNA because it does not improve upon ff99bsc0 for canonical structures. However, it might be useful in simulations of DNA molecules containing syn nucleotides. Our parametrization is based on high-level QM calculations and differs from conventional parametrization approaches in that it incorporates some previously neglected solvation-related effects (which appear to be essential for obtaining correct anti/high-anti balance). Our χ(OL) force field is compared with several previous glycosidic torsion parametrizations.