Accurate quantum chemical energies for tetrapeptide conformations: why MP2 data with an insufficient basis set should be handled with caution

Abstract

Understanding the structure-function relationship in polypeptides and proteins is a crucial step in the elucidation of biochemical processes. In this regard, constantly improving hardware architectures and program codes have allowed the in silico treatment of proteins to become an important partner in related investigations. Due to the immense size of proteins, their computational study has generally been carried out with molecular mechanics (MM) force-field methods, such as CHARMM or GROMOS. 1 At the other extreme, high-level quantum mechanical (QM) methods, such as coupled-cluster with perturbative triples 2 [CCSD(T)] or composite methods like Gn 3 or Wn, 4 provide results with much higher accuracy. However, due to their computational cost, their applicability has been restricted to smaller systems such as amino acids, and di-and tripeptides. 5,6 Tetrapeptides are the smallest model systems that are able to mimic the typical hydrogen-bond pattern in a-helices. They are therefore of particular biological interest, and QM treatments of them have been reported since the late 1990s. 7 The highest levels of theory used in such studies were often conventional or local second-order Møller-Plesset perturbation theory (MP2) with a triple-z basis set. These levels are still popular in recent similar investigations. 8 Of particular relevance to the present work is the extensive study of 100 tetrapeptides by Jiang et al., 9 who evaluated the performance of a large number of QM and MM methods based on MP2/cc-pVTZ reference values.In the present article, we will demonstrate where potential problems of the MP2 approach combined with finite basis sets might lie when applied to conformers of polypeptides. For this purpose, we selected two systems from the study by Jiang et al. 9 that have the sequence ACE-ALA-X-ALA-NME. ALA is alanine, X is either glycine (GLY) or serine (SER), and ACE and NME stand for acetyl and methylamide groups, respectively (see Fig. 1a). For each peptide, five conformers have been examined, whose backbone dihedral angles (see ESI †) have been fixed such that they resemble those typically found in parallel (b) and antiparallel (b a ) b-sheets, in right-handed (a R ) and left-handed (a L ) a-helices, and in the common polyproline-II (PP-II) helix. We note that while the two a-helical conformers are stabilised by hydrogen bonds, the backbones of the other three conformers are not (see for example Fig. 1).

Reaction barrier heights for cycloreversion of heterocyclic rings: An Achilles’ heel for DFT and standard ab initio procedures

“…It is of interest to assess the performance of the CCSD(T) method using an additivity-based approach in which the CCSD(T)/CBS energy is estimated from the CCSD(T)/A 0 VDZ energy and an MP2-based basis-set-correction term (DMP2 = MP2/A 0 V{T,Q}Z À MP2/A 0 VDZ, where the MP2/A 0 V{T,Q}Z energy is extrapolated to the basis-set limit with an extrapolation exponent of 3) [93]. This cost-effective approach, which is denoted here by CCSD(T)/CBS(MP2), has been widely used for obtaining noncovalent interaction energies at the CCSD(T)/CBS limit [5,[94][95][96][97]. More recently; this method has also been found to give good performance for reaction energies [98][99][100] and barrier heights [6].…”

“…At present, the only validation for a given DFT approximation is benchmarking against accurate theoretical or experimental reference data. Ideally, the benchmark data should: (i) have well-defined error bars that are much smaller (preferably, by an order of magnitude or more) than the intrinsic error of the method being evaluated, and (ii) be as large and chemically diverse as reasonably possible [3][4][5][6].…”

Estimating the CCSD basis-set limit energy from small basis sets: basis-set extrapolations vs additivity schemes

“…In this context, it is worth mentioning the work of Bakowies, 36 which highlights the limitations of conventional extrapolations and proposes an empirically motivated extrapolation formula for MP2 and CCSD correlation energies. The scaling factors in this extrapolation depend on the number of hydrogen atoms and the number of correlated electrons in each system.The second approach is anadditivity scheme in which the CCSD energy is calculated with a relatively small basis set and an MP2-based basis-set-correction term is added in order to approximate the CCSD/CBS energy.This cost-effective approach, which is widely used in conjunction with the correlation-consistent basis sets for obtaining noncovalent interaction energies at the CCSD(T)/CBS limit, [42][43][44][45] has been recently shown to give good performance for reaction energies 46,47 and barrier heights. 48 …”

Conformational Preferences in Small Peptide Models: The Relevance of cis/trans‐Conformations

“…[51][52] The frequency calculations were performed at the same level of theory and all minima were confirmed with all-positive frequencies. [56][57] For CCSD(T)/CBS, extrapolations to the complete-basis-set (CBS) limit were carried out based on the MP2 single-point energies by the two-point extrapolation scheme using cc-pVTZ and cc-pVQZ basis set (see the Supporting Information for ad etailed description). [56][57] For CCSD(T)/CBS, extrapolations to the complete-basis-set (CBS) limit were carried out based on the MP2 single-point energies by the two-point extrapolation scheme using cc-pVTZ and cc-pVQZ basis set (see the Supporting Information for ad etailed description).…”