Elisa Liberatore

Free energy methods in coupled electron ion Monte Carlo

Recent progress in simulation methodologies and in computer power allow first-principles simulations of condensed systems with Born–Oppenheimer electronic energies obtained by quantum Monte Carlo methods. Computing free energies and therefore getting a quantitative determination of phase diagrams is one step more demanding in terms of computer resources. In this paper we derive a general relation to compute the free energy of an ab initio model with Reptation Quantum Monte Carlo (RQMC) energies from the knowledge of the free energy of the same ab initio model in which the electronic energies are computed by the less demanding but less accurate Variational Monte Carlo (VMC) method. Moreover we devise a procedure to correct transition lines based on the use of the new relation. In order to illustrate the procedure, we consider the liquid–liquid phase transition in hydrogen, a first-order transition between a lower pressure, molecular and insulating phase and a higher pressure, partially dissociated and conducting phase. We provide new results along the T = 600 K isotherm across the phase transition and find good agreement between the transition pressure and specific volumes at coexistence for the model with RQMC accuracy between the prediction of our procedure and the values that can be directly inferred from the observed plateau in the pressure–volume curve along the isotherm. This work paves the way for future use of VMC in first-principles simulations of high-pressure hydrogen, an essential simplification when considering larger system sizes or quantum proton effects by Path Integral Monte Carlo methods.

Charge migration and charge transfer in molecular systems

The transfer of charge at the molecular level plays a fundamental role in many areas of chemistry, physics, biology and materials science. Today, more than 60 years after the seminal work of R. A. Marcus, charge transfer is still a very active field of research. An important recent impetus comes from the ability to resolve ever faster temporal events, down to the attosecond time scale. Such a high temporal resolution now offers the possibility to unravel the most elementary quantum dynamics of both electrons and nuclei that participate in the complex process of charge transfer. This review covers recent research that addresses the following questions. Can we reconstruct the migration of charge across a molecule on the atomic length and electronic time scales? Can we use strong laser fields to control charge migration? Can we temporally resolve and understand intramolecular charge transfer in dissociative ionization of small molecules, in transition-metal complexes and in conjugated polymers? Can we tailor molecular systems towards specific charge-transfer processes? What are the time scales of the elementary steps of charge transfer in liquids and nanoparticles? Important new insights into each of these topics, obtained from state-of-the-art ultrafast spectroscopy and/or theoretical methods, are summarized in this review.

Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

In situ parameterisation of SCC-DFTB repulsive potentials by iterative Boltzmann inversion

The parameterisation of accurate and transferable repulsive potentials is a key ingredient for the self-consistent-charge density functional tight-binding method (SCC-DFTB). In the conventional parameterisation scheme the balanced description of different chemical environments involves significant human effort and chemical intuition. In this work, we propose an in situ parameterisation method with reduced transferability but maximal accuracy for the chemical and physical environment under investigation. Starting from an initial guess, we used iterative Boltzmann inversion to successively improve the repulsive potentials. The corrections were extracted iteratively from the differences in the radial distribution functions with respect to a density functional reference calculation. With this protocol convergence was reached within a few iterations involving only minimal human input. We applied this new scheme to liquid water at ambient conditions, a particularly challenging case for conventional SCC-DFTB. The newly determined parameters lead to a clear improvement of both the structural and dynamical properties of liquid water.

Liquid-solid transition in fully ionized hydrogen at ultra-high pressures.

We study the phase diagram of an effective ion model of fully ionized hydrogen at ultra-high pressure. We assume that the protons interact with a screened Coulomb potential derived from a static linear response theory. This model accurately reproduces the physical properties of hydrogen for densities greater than g/ρ(m)=10 cm(3) corresponding to the range of the coupling parameter r(s) ≲ 0.6. The pressure range, P ≳ 20 TPa, is well beyond present experimental limitations. Assuming classical protons, we find that the zero temperature enthalpy of the perfect bcc crystal is slightly lower than for other structures at g/ρ(m)=12.47 cm(3) while the fcc structure gains stability at higher density. Using Monte Carlo calculations, we compute the free energy of various phases and locate the melting transition versus density. We find that on melting, bcc is energetically favored with respect to fcc over the entire range investigated. In the solid phase the system undergoes a structural transition from bcc at higher temperature to fcc at lower temperature. The free energy difference between these two structures is very small so that obtaining a quantitative estimate of this second transition line requires accuracy beyond that provided by our method. We estimate the effect of proton zero point motion on the bcc melting line for hydrogen, deuterium, and tritium by a path integral Monte Carlo method. Although zero point effects on hydrogen are large, since the two competing phases (bcc and liquid) have locally similar environments, the effect on the melting line is small; the melting temperature for hydrogen is lowered by about 10% with respect to the classical value.

Ultrafast Relaxation Dynamics of the Ethylene Cation C2H4

We present a combined experimental and computational study of the relaxation dynamics of the ethylene cation. In the experiment, we apply an extreme-ultraviolet-pump/infrared-probe scheme that permits us to resolve time scales on the order of 10 fs. The photoionization of ethylene followed by an infrared (IR) probe pulse leads to a rich structure in the fragment ion yields reflecting the fast response of the molecule and its nuclei. The temporal resolution of our setup enables us to pinpoint an upper bound of the previously defined ethylene-ethylidene isomerization time to 30 ± 3 fs. Time-dependent density functional based trajectory surface hopping simulations show that internal relaxation between the first excited states and the ground state occurs via three different conical intersections. This relaxation unfolds on femtosecond time scales and can be probed by ultrashort IR pulses. Through this probe mechanism, we demonstrate a route to optical control of the important dissociation pathways leading to separation of H or H2.

Photoemission and photoionization time delays and rates

Ionization and, in particular, ionization through the interaction with light play an important role in fundamental processes in physics, chemistry, and biology. In recent years, we have seen tremendous advances in our ability to measure the dynamics of photo-induced ionization in various systems in the gas, liquid, or solid phase. In this review, we will define the parameters used for quantifying these dynamics. We give a brief overview of some of the most important ionization processes and how to resolve the associated time delays and rates. With regard to time delays, we ask the question: how long does it take to remove an electron from an atom, molecule, or solid? With regard to rates, we ask the question: how many electrons are emitted in a given unit of time? We present state-of-the-art results on ionization and photoemission time delays and rates. Our review starts with the simplest physical systems: the attosecond dynamics of single-photon and tunnel ionization of atoms in the gas phase. We then extend the discussion to molecular gases and ionization of liquid targets. Finally, we present the measurements of ionization delays in femto- and attosecond photoemission from the solid–vacuum interface.

Nonadiabatic effects in electronic and nuclear dynamics

Due to their very nature, ultrafast phenomena are often accompanied by the occurrence of nonadiabatic effects. From a theoretical perspective, the treatment of nonadiabatic processes makes it necessary to go beyond the (quasi) static picture provided by the time-independent Schrödinger equation within the Born-Oppenheimer approximation and to find ways to tackle instead the full time-dependent electronic and nuclear quantum problem. In this review, we give an overview of different nonadiabatic processes that manifest themselves in electronic and nuclear dynamics ranging from the nonadiabatic phenomena taking place during tunnel ionization of atoms in strong laser fields to the radiationless relaxation through conical intersections and the nonadiabatic coupling of vibrational modes and discuss the computational approaches that have been developed to describe such phenomena. These methods range from the full solution of the combined nuclear-electronic quantum problem to a hierarchy of semiclassical approaches and even purely classical frameworks. The power of these simulation tools is illustrated by representative applications and the direct confrontation with experimental measurements performed in the National Centre of Competence for Molecular Ultrafast Science and Technology.

A Versatile Multiple Time Step Scheme for Efficient ab Initio Molecular Dynamics Simulations

We present here our implementation of a time-reversible, multiple time step (MTS) method for full QM and hybrid QM/MM Born-Oppenheimer molecular dynamics simulations. The method relies on a fully flexible combination of electronic structure methods, from density functional theory to wave function-based quantum chemistry methods, to evaluate the nuclear forces in the reference and in the correction steps. The possibility of combining different electronic structure methods is based on the observation that exchange and correlation terms only contribute to low frequency modes of nuclear forces. We show how a pair of low/high level electronic structure methods that individually would lead to very different system properties can be efficiently combined in the reference and correction steps of this MTS scheme. The current MTS implementation makes it possible to perform highly accurate ab initio molecular dynamics simulations at reduced computational cost. Stable and accurate trajectories were obtained with time steps of several femtoseconds, similar to and even exceeding the ones usually adopted in classical molecular dynamics, in particular when using a generalized Langevin stochastic thermostat. Compared to the standard Velocity Verlet integration, the present MTS scheme allows for a 5- to 6-fold overall speedup, at an unaltered level of accuracy.