Integrated computational approaches for spectroscopic studies of molecular systems in the gas phase and in solution: pyrimidine as a test case

An integrated computational approach built on quantum mechanical (QM) methods, purposely tailored inter-and intra-molecular force fields and continuum solvent models combined with time-independent and timedependent schemes to account for nuclear motion effects is applied to the spectroscopic investigation of pyrimidine in the gas phase as well as in aqueous and CCl4 solutions. Accurate post-Hartree-Fock methodologies are employed to compute molecular structure, harmonic vibrational frequencies, energies and oscillator strengths for electronic transitions in order to validate the accuracy of approaches rooted into density functional theory with emphasis also on hybrid QM/QM' models. Within the time-independent approaches, IR spectra are computed including anharmonicities through perturbative corrections while UV-vis line-shapes are simulated accounting for the vibrational structure; in both cases, the environmental effects are described by continuum models. The effects of conformational flexibility, including solvent dynamics, are described through time-dependent models based on purposely DFT-tailored force fields applied to molecular dynamics simulations and on QM computations of spectroscopic properties. Such procedures are exploited to simulate IR and UV-vis spectra of pyrimidine in the gas phase and in solutions, leading in all cases to good agreement with experimental observations and allowing to dissect different effects underlying spectral phenomena.

Peptide-Cation Systems: Conformational Search, Benchmark Evaluation, and Force Field Parameter Adjustment Using Regularized Linear Regression

Markus Schneider

Metal cations often play an important role in shaping the three-dimensional structure of peptides. As an example, the model system AcPheAla5LysH+ is investigated in order to fully understand the forces that stabilize its helical structure. In particular, the question of whether the local fixation of the positive charge at the peptide's C-terminus is a prerequisite for forming helices is addressed by replacing the protonated lysine residue by alanine and a sodium cation. The combination of gas-phase cold-ion vibrational spectroscopy with molecular simulations based on density-functional theory (DFT) revealed that the charge localization at the C-terminus is imperative for helix formation in the gas phase as this stabilizes the structure through a cation-helix dipole interaction. For sodiated AcPheAla6, globular rather than helical structures were found caused by the strong cation-backbone and cation-pi interactions. Interestingly, the global minimum-energy structure from simulation is not present in the experiment where the system remains kinetically trapped in a solution-state structure. Thereby calculated energies and IR spectra that are sufficiently accurate relied on DFT with computationally costly hybrid functionals, while for the structure search low-computational-cost force field (FF) models are crucial. This inspired a study where the goodness of commonly applied levels of theory, i.e. FFs, semi-empirical methods, density-functional approximations, composite methods, and wavefunction-based methods are being evaluated with respect to benchmark-grade coupled-cluster calculations. Acetylhistidine - either bare or in presence of a zinc cation - thereby serves as a molecular benchmark system. Neither FFs nor semi-empirical methods are reliable enough for a description of these systems within "chemical accuracy" of 1 kcal/mol. Accurate energetic description within chemical accuracy is achieved for all systems using the meta-GGA SCAN or computationally more demanding hybrid functionals. The double-hybrid functional B3LYP+XYG3 is best resembling the benchmark method DLPNO-CCSD(T). Despite poor energetic performances of conventional FFs for peptides in the gas phase, their low computational costs still render them appealing tools for large-scale structure searches. Consequently, a machine learning approach is presented where the torsional parameters and (if desired) van der Waals parameters in the potential-energy function of a particular FF are adjusted by fitting it against DFT energies using regularized regression models like LASSO or Ridge regression. For the peptide AcAla2NMe, this resulted in a significant improvement when comparing to standard OPLS-AA parameters. For more challenging peptide-cation systems, e.g. AcAla2NMe + Na+, this approach does not give satisfying results, which is caused by the formulation of the potential energy of the FF itself: While derived empirical partial charges using Hirshfeld partitioning or the electrostatic potential (ESP) decrease the accuracy, part of the energetic discrepancy can be "compensated" due to the flexibility of the torsional contributions in terms of the energetic description.

EPFL2018

Geometric Integrators for Nonadiabatic Molecular Quantum Dynamics Induced by the Interaction with the Electromagnetic Field

Aurélien Kevin Fabrice Patoz

Understanding the elementary steps involved in a chemical reaction forms the cornerstone of physical chemistry research. One way to deepen this understanding is by studying chemical and physical processes using linear and nonlinear spectroscopic techniques. However, the outcomes of such experiments can be difficult to decipher due to the interweaving of several effects. Therefore, in order to help experimentalists to disentangle such spectra, the role of theorists is to develop efficient tools that are able to accurately describe molecular systems. The starting point of such tools is solving the time-dependent Schrödinger equation. In this thesis, after implementing geometric integrators, which are based on a combination of the split-operator algorithm and Magnus expansion, for the exact nonadiabatic quantum dynamics of a molecule interacting with a time-dependent electromagnetic field, we derive and implement these geometric integrators for the time-dependent perturbation theory, the Condon, rotating-wave, and ultrashort-pulse approximations, as well as every possible combination thereof. As verified in several model systems, these integrators exactly preserve the geometric invariants, and achieve an arbitrary prescribed order of accuracy in the time step and an exponential convergence in the grid spacing. We also explore in more detail the ultrashort-pulse approximation and derive an analytical expression for the combination with the time-dependent perturbation theory; this expression significantly accelerates numerical calculations. We show that in the limit of the zero pulse width, the d-pulse approximation is recovered. We illustrate the performance of the introduced approximations, using a three-dimensional model of pyrazine, in which it is essential to go beyond the d-pulse limit in order to describe the dynamics correctly. The high-order algorithms are also applied to the photodissociation dynamics of iodomethane (CH3I), following its excitation to the A band. We implement a general split-operator with both discrete-variable and finite-basis representations that can treat one non-Cartesian, such as angular coordinate. To test the effect of various degrees of freedom and of the nonadiabatic dynamics, we apply these algorithms to one-, two-, and three-dimensional models of iodomethane, both in the presence and in the absence of nonadiabatic couplings. A full quantum calculation is, however, limited to problems with low dimensionality (approximately ten degrees of freedom). Beyond this, one must seek an affordable balance between computational efficiency and physical accuracy and can employ, for example, semiclassical methods that are based on classical trajectories. A simple semiclassical approximation that can treat larger systems and requires only local knowledge of the potential is the on-the-fly ab initio thawed Gaussian approximation. We implement a generalization of the method that goes beyond the Franck-Condon approximation and treats Herzberg-Teller active molecules. Our method is used to compute absorption spectra of phenyl radical and of benzene, for which the Herzberg-Teller contribution is essential.

EPFL2017

Bridging Static and Dynamical Descriptions of Chemical Reactions: An ab Initio Study of CO2 Interacting with Water Molecules

Wanda Andreoni, Fabio Pietrucci

Extracting reliable thermochemical parameters from molecular dynamics simulations of chemical reactions, although based on ab initio methods, is generally hampered by difficulties in reproducing the results and controlling the statistical errors. This is a serious drawback with respect to the quantum chemical description based on potential energy surfaces. This work is an attempt to fill this gap. We apply molecular dynamics, based on density functional theory (DFT) and empowered by path metadynamics (MTD), to simulate the reaction of CO2 with (one, two, and three) water molecules in the gas phase. This study relies on a strategy that ensures a precise control of the accuracy of the reaction coordinates and of the reconstructed free-energy surface on this space, namely, on (i) fully reversible MTD simulations, (ii) a committor probability analysis for the diagnosis of the collective variables, and (iii) a cluster analysis for the characterization of the reconstructed free energy surfaces. This robust procedure permits a meaningful comparison with more traditional calculations of the potential energy surfaces that we also perform within the same DFT computational scheme. This comparison shows in particular that the reactants and products of systems with only three water molecules can no longer be understood in terms of one structure but must be described as statistical configuration ensembles. Calculations carried out with different prescriptions for the exchange-correlation functionals also allow us to establish their quantitative effect on the activation barriers for the formation and the dissociation of carbonic acid. Their decrease induced by the addition of one water molecule (catalytic effect) is found to be largely independent of the specific functional.