On the mass of atoms in molecules: Beyond the Born-Oppenheimer approximation

Describing the dynamics of nuclei in molecules requires a potential energy surface, which is traditionally provided by the Born-Oppenheimer or adiabatic approximation. However, we also need to assign masses to the nuclei. There, the Born-Oppenheimer picture does not account for the inertia of the electrons and only bare nuclear masses are considered. Nowadays, experimental accuracy challenges the theoretical predictions of rotational and vibrational spectra and requires to include the participation of electrons in the internal motion of the molecule. More than 80 years after the original work of Born and Oppenheimer, this issue still is not solved in general. Here, we present a theoretical and numerical framework to address this problem in a general and rigorous way. Starting from the exact factorization of the electron-nuclear wave function, we include electronic effects beyond the Born-Oppenheimer regime in a perturbative way via position-dependent corrections to the bare nuclear masses. This maintains an adiabatic-like point of view: the nuclear degrees of freedom feel the presence of the electrons via a single potential energy surface, whereas the inertia of electrons is accounted for and the total mass of the system is recovered. This constitutes a general framework for describing the mass acquired by slow degrees of freedom due to the inertia of light, bounded particles. We illustrate it with a model of proton transfer, where the light particle is the proton, and with corrections to the vibrational spectra of molecules. Inclusion of the light particle inertia allows to gain orders of magnitude in accuracy

a solvent triggered molecular switch

We present a computational investigation of the conformational response of phycocyanobilin (PCB) to the ability of solvents to form hydrogen bonds. PCB is the chromophore of several proteins in light harvesting complexes. We determine the conformational distributions in different solvents (methanol and hexamethylphosphoramide HMPT) by means of ab initio molecular dynamics simulations and characterize them via ab initio calculations of NMR chemical shift patterns. The computed trajectories and spectroscopic fingerprints illustrate that the energy landscape is very complex and exhibits various conformations of similar energy. We elucidate the strong influence of the solvent characteristics on the structural and spectroscopic parameters. Specifically, we predict a cis–trans isomerization of phycocyanobilin upon switching from the aprotic to the protic solvent, which explains an experimentally observed change in the NMR patterns. In the context of technological molecular recognition, solvent induced conformational switching can be considered a precursor mechanism to the recognition of single molecules

Alpha-C-phycocyanobilin in vitro

We present hybrid ab initio QM/MM MD simulations and theoretical NMR chemical shift calculations of the bilin chromophore phycocyanobilin (PCB) in the binding pocket of the α-subunit of C-phycocyanin (α-C-PC). The good overall agreement between the computed NMR chemical shifts and the experimental values confirm the overall structural picture. A particular discrepancy is observed for the pyrrole nitrogen and hydrogen on ring A, which points to a disagreement between the reported X-ray structure and the experimental solution-state NMR spectrum. Our results suggest that in the solution-state, the binding pocket of α-C-PC slightly opens up allowing one water molecule to form a stable bridge between ring A in PCB and the protein backbone at the ASN73 residue. With this modified solution-state structure, the computed NMR chemical shifts are in excellent agreement with experimental values. For proteins still lacking a fully-resolved solution-state NMR-based structure, this approach of combining ab initio MD/NMR provides a very sensitive probe for local geometries at the sub-Ångstrom range that can be utilized to compare/reconcile simple experimental one- and two-dimensional NMR data with X-ray structures

Electronic density response to molecular geometric changes from explicit electronic susceptibility calculations

We present a first principles approach to compute the response of the molecular electronic charge distribution to a geometric distortion. The scheme is based on an explicit representation of the linear electronic susceptibility. The linear electronic susceptibility is a tensor quantity which directly links the first-order electronic response density to the perturbation potential, without requiring self-consistency. We first show that the electronic susceptibility is almost invariant to small changes in the molecular geometry. We then compute the dipole moments from the response density induced by the geometrical changes. We verify the accuracy by comparing the results to the corresponding values obtained from the self- consistent calculations of the ground-state densities in both geometries

First principles calculation of inhomogeneous broadening in solid-state cw-EPR spectroscopy

We present a scheme for the first-principles calculation of EPR lineshapes for continuous-wave-EPR spectroscopy (cw-EPR) of spin centers in complex chemical environments. We specifically focus on poorly characterized systems, e.g. powders and frozen glasses with variable microsolvation structures. Our approach is based on ab initio molecular dynamics simulations and ab initio calculations of the ensemble of g- and A-tensors along the trajectory. The method incorporates temperature effects as well as the full anharmonicity of the intra- and intermolecular degrees of freedom of the system. We apply this scheme to compute the lineshape of a prototypical spin probe, the nitrosodisulfonate dianionic radical (Fremy's salt), dissolved in a 50 : 50 mixture of water and methanol. We are able to determine the specific effect of variations of local solvent composition and microsolvation structure on the cw-EPR lineshape. Our molecular dynamics reveal a highly anisotropic solvation structure with distinct spatial preferences for water and methanol around Fremy's salt that can be traced back to a combination of steric and polar influences. The overall solvation structure and conformational preferences of Fremy's salt as found in our MD simulations agree very well with the results obtained from EPR and orientation-selective ENDOR spectroscopy performed on the frozen glass. The simulated EPR lineshapes show good agreement with the experimental spectra. When combined with our MD results, they characterize the lineshape dependence on local morphological fluctuations

Reverse mapping of coarse grained polyglutamine conformations from PRIME20 sampling

An inverse coarse-graining protocol is presented for generating and validating atomistic structures of large (bio-) molecules from conformations obtained via a coarse-grained sampling method. Specifically, the protocol is implemented and tested based on the (coarse-grained) PRIME20 protein model (P20/SAMC), and the resulting all-atom conformations are simulated using conventional biomolecular force fields. The phase space sampling at the coarse-grained level is performed with a stochastical approximation Monte Carlo approach. The method is applied to a series of polypeptides, specifically dimers of polyglutamine with varying chain length in aqueous solution. The majority (>70 %) of the conformations obtained from the coarse-grained peptide model can successfully be mapped back to atomistic structures that remain conformationally stable during 10 ns of molecular dynamics simulations. This work can be seen as the first step towards the overarching goal of improving our understanding of protein aggregation phenomena through simulation methods

First Principles Calculations of NMR Chemical Shifts of Liquid Water at an Amorphous Silica Interface

We investigate the anomalous structure and hydrogen bond network of water molecules confined inside a silica nanopore (MCM-41 type). In addition to geometric data, we use proton NMR chemical shifts as a measure for the strength of the H-bonding network. We compute the 1H NMR shifts of confined water based on a first principle approach in the framework of density functional perturbation theory under periodic boundary conditions. The hydrophilic character of the silica is well manifested in the water density profile. Our calculations illustrate both the modifications of the 1H NMR chemical shifts of the water with respect to bulk water and a considerable slowing down of water diffusion. In the vicinity of silanols, weakly hydrogen bonded liquid water is observed, while at the center region of the pore, the hydrogen bonding network is enhanced with respect to bulk water

a swarm intelligence-based optimizer for molecular geometry

We present a stochastic, swarm intelligence-based optimization algorithm for the prediction of global minima on potential energy surfaces of molecular clusterstructures. Our optimization approach is a modification of the artificial bee colony (ABC) algorithm which is inspired by the foraging behavior of honey bees. We apply our modified ABC algorithm to the problem of global geometryoptimization of molecular clusterstructures and show its performance for clusters with 2–57 particles and different interatomic interaction potentials