Mariana Rossi

Dispersion Interactions with Density-Functional Theory: Benchmarking Semiempirical and Interatomic Pairwise Corrected Density Functionals.

We present a comparative assessment of the accuracy of two different approaches for evaluating dispersion interactions: interatomic pairwise corrections and semiempirical meta-generalized-gradient-approximation (meta-GGA)-based functionals. This is achieved by employing conventional (semi)local and (screened-)hybrid functionals, as well as semiempirical hybrid and nonhybrid meta-GGA functionals of the M06 family, with and without interatomic pairwise Tkatchenko-Scheffler corrections. All of those are tested against the benchmark S22 set of weakly bound systems, a representative larger molecular complex (dimer of NiPc molecules), and a representative dispersively bound solid (hexagonal boron nitride). For the S22 database, we also compare our results with those obtained from the pairwise correction of Grimme (DFT-D3) and nonlocal Langreth-Lundqvist functionals (vdW-DF1 and vdW-DF2). We find that the semiempirical kinetic-energy-density dependence introduced in the M06 functionals mimics some of the nonlocal correlation needed to describe dispersion. However, long-range contributions are still missing. Pair-wise interatomic corrections, applied to conventional semilocal or hybrid functionals, or to M06 functionals, provide for a satisfactory level of accuracy irrespectively of the underlying functional. Specifically, screened-hybrid functionals such as the Heyd-Scuseria-Ernzerhof (HSE) approach reduce self-interaction errors in systems possessing both localized and delocalized orbitals and can be applied to both finite and extended systems. Therefore, they serve as a useful underlying functional for dispersion corrections.

Isomer-Selective Detection of Hydrogen-Bond Vibrations in the Protonated Water Hexamer

The properties of hydrogen ions in aqueous solution are governed by the ability of water to incorporate ions in a dynamical hydrogen bond network, characterized by a structural variability that has complicated the development of a consistent molecular level description of H(+)(aq). Isolated protonated water clusters, H(+)(H2O)n, serve as finite model systems for H(+)(aq), which are amenable to highly sensitive and selective gas phase spectroscopic techniques. Here, we isolate and assign the infrared (IR) signatures of the Zundel-type and Eigen-type isomers of H(+)(H2O)6, the smallest protonated water cluster for which both of these characteristic binding motifs coexist, down into the terahertz spectral region. We use isomer-selective double-resonance population labeling spectroscopy on messenger-tagged H(+)(H2O)6·H2 complexes from 260 to 3900 cm(-1). Ab initio molecular dynamics calculations qualitatively recover the IR spectra of the two isomers and allow attributing the increased width of IR bands associated with H-bonded moieties to anharmonicities rather than excited state lifetime broadening. Characteristic hydrogen-bond stretching bands are observed below 400 cm(-1).

How to remove the spurious resonances from ring polymer molecular dynamics

Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.

Secondary Structure of Ac-Alan-LysH+ Polyalanine Peptides (n = 5,10,15) in Vacuo: Helical or Not?

The polyalanine-based peptide series Ac-Alan-LysH+ (n = 5−20) is a prime example that a secondary structure motif that is well-known from the solution phase (here: helices) can be formed in vacuo. Here we revisit the series members n = 5,10,15, using density functional theory (van der Waals corrected generalized gradient approximation) for structure predictions, which are then corroborated by room temperature gas-phase infrared vibrational spectroscopy. We employ a quantitative comparison based on Pendry’s reliability factor (popular in surface crystallography). In particular, including anharmonic effects into calculated spectra by way of ab initio molecular dynamics produces remarkably good experiment−theory agreement. We find the longer molecules (n = 10,15) to be firmly α-helical in character. For n = 5, calculated free-energy differences show different H-bond networks to still compete closely. Vibrational spectroscopy indicates a predominance of α-helical motifs at 300 K, but the lowest-energy conform...

Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase

Including quantum mechanical effects on the dynamics of nuclei in the condensed phase is challenging, because the complexity of exact methods grows exponentially with the number of quantum degrees of freedom. Efforts to circumvent these limitations can be traced down to two approaches: methods that treat a small subset of the degrees of freedom with rigorous quantum mechanics, considering the rest of the system as a static or classical environment, and methods that treat the whole system quantum mechanically, but using approximate dynamics. Here, we perform a systematic comparison between these two philosophies for the description of quantum effects in vibrational spectroscopy, taking the Embedded Local Monomer model and a mixed quantum-classical model as representatives of the first family of methods, and centroid molecular dynamics and thermostatted ring polymer molecular dynamics as examples of the latter. We use as benchmarks D2O doped with HOD and pure H2O at three distinct thermodynamic state points (ice Ih at 150 K, and the liquid at 300 K and 600 K), modeled with the simple q-TIP4P/F potential energy and dipole moment surfaces. With few exceptions the different techniques yield IR absorption frequencies that are consistent with one another within a few tens of cm(-1). Comparison with classical molecular dynamics demonstrates the importance of nuclear quantum effects up to the highest temperature, and a detailed discussion of the discrepancies between the various methods let us draw some (circumstantial) conclusions about the impact of the very different approximations that underlie them. Such cross validation between radically different approaches could indicate a way forward to further improve the state of the art in simulations of condensed-phase quantum dynamics.

Validation Challenge of Density-Functional Theory for Peptides - Example of Ac-Phe-Ala5-LysH+

We assess the performance of a group of exchange-correlation functionals for predicting the secondary structure of peptide chains, up to a new many-body dispersion corrected hybrid density functional, dubbed PBE0+MBD* by its original authors. For the purpose of validation, we first compare to published, high-level benchmark conformational energy hierarchies (coupled cluster at the singles, doubles, and perturbative triples level, CCSD(T)) for 73 conformers of small three-residue peptides, establishing that the van der Waals corrected PBE0 functional yields an average error of only ∼20 meV (∼0.5 kcal/mol). This compares to ∼40-50 meV for nondispersion corrected PBE0 and 40-100 meV for different empirical force fields (estimated for the alanine tetrapeptide). For longer peptide chains that form a secondary structure, CCSD(T) level benchmark data are currently unaffordable. We thus turn to the experimentally well studied Ac-Phe-Ala5-LysH(+) peptide, for which four closely competing conformers were established by infrared spectroscopy. For comparison, an exhaustive theoretical conformational space exploration yields at least 11 competing low energy minima. We show that (i) the many-body dispersion correction, (ii) the hybrid functional nature of PBE0+MBD*, and (iii) zero-point corrections are needed to reveal the four experimentally observed structures as the minima that would be populated at low temperature.

Role of methyl-induced polarization in ion binding

The chemical property of methyl groups that renders them indispensable to biomolecules is their hydrophobicity. Quantum mechanical studies undertaken here to understand the effect of point substitutions on potassium (K-) channels illustrate quantitatively how methyl-induced polarization also contributes to biomolecular function. K- channels regulate transmembrane salt concentration gradients by transporting K+ ions selectively. One of the K+ binding sites in the channel’s selectivity filter, the S4 site, also binds Ba2+ ions, which blocks K+ transport. This inhibitory property of Ba2+ ions has been vital in understanding K-channel mechanism. In most K-channels, the S4 site is composed of four threonine amino acids. The K channels that carry serine instead of threonine are significantly less susceptible to Ba2+ block and have reduced stabilities. We find that these differences can be explained by the lower polarizability of serine compared with threonine, because serine carries one less branched methyl group than threonine. A T→S substitution in the S4 site reduces its polarizability, which, in turn, reduces ion binding by several kilocalories per mole. Although the loss in binding affinity is high for Ba2+, the loss in K+ binding affinity is also significant thermodynamically, which reduces channel stability. These results highlight, in general, how biomolecular function can rely on the polarization induced by methyl groups, especially those that are proximal to charged moieties, including ions, titratable amino acids, sulfates, phosphates, and nucleotides.

Going clean: structure and dynamics of peptides in the gas phase and paths to solvation

The gas phase is an artificial environment for biomolecules that has gained much attention both experimentally and theoretically due to its unique characteristic of providing a clean room environment for the comparison between theory and experiment. In this review we give an overview mainly on first-principles simulations of isolated peptides and the initial steps of their interactions with ions and solvent molecules: a bottom up approach to the complexity of biological environments. We focus on the accuracy of different methods to explore the conformational space, the connections between theory and experiment regarding collision cross section evaluations and (anharmonic) vibrational spectra, and the challenges faced in this field.

Stability of Complex Biomolecular Structures: van der Waals, Hydrogen Bond Cooperativity, and Nuclear Quantum Effects

Biomolecules are complex systems stabilized by a delicate balance of weak interactions, making it important to assess all energetic contributions in an accurate manner. However, it is a priori unclear which contributions make more of an impact. Here, we examine stacked polyglutamine (polyQ) strands, a peptide repeat often found in amyloid aggregates. We investigate the role of hydrogen bond (HB) cooperativity, van der Waals (vdW) dispersion interactions, and quantum contributions to free energies, including anharmonicities through density functional theory and ab initio path integral simulations. Of these various factors, we find that the largest impact on structural stabilization comes from vdW interactions. HB cooperativity is the second largest contribution as the size of the stacked chain grows. Competing nuclear quantum effects make the net quantum contribution small but very sensitive to anharmonicities, vdW, and the number of HBs. Our results suggest that a reliable treatment of these systems can only be attained by considering all of these components.

Impact of vibrational entropy on the stability of unsolvated peptide helices with increasing length.

Helices are a key folding motif in protein structure. The question of which factors determine helix stability for a given polypeptide or protein is an ongoing challenge. Here we use van-der-Waals-corrected density functional theory to address a part of this question in a bottom-up approach. We show how intrinsic helical structure is stabilized with length and temperature for a series of experimentally well-studied unsolvated alanine-based polypeptides, Ac-Alan-LysH(+). By exhaustively exploring the conformational space of these molecules, we find that helices emerge as the preferred structure in the length range n = 4-8 not just due to enthalpic factors (hydrogen bonds and their cooperativity, van der Waals dispersion interactions, electrostatics) but importantly also by a vibrational entropic stabilization over competing conformers at room temperature. The stabilization is shown to be due to softer low-frequency vibrational modes in helical conformers than in more compact ones. This observation is corroborated by including anharmonic effects explicitly through ab initio molecular dynamics and generalized by testing different terminations and considering larger helical peptide models.