Ab initio molecular dynamics with quantum Monte Carlo

Quantum Monte Carlo (QMC) is one of the most accurate electronic structure methods for ab initio many-body calculations in a broad range of electronic systems. Thanks to fast evolving massively parallel computers, much larger simulations of realistic systems become affordable. We have developed an ab initio simulation scheme at finite temperature based on molecular dynamics (MD) and QMC during the past few years. In this approach, a second order Langevin MD is employed by using a statistical evaluation of the forces acting on each atom by means of QMC. Moreover, the corresponding statistical noise is also used to drive and accelerate the dynamics of ions. The accuracy and the reliability of our ab initio MD have been studied systematically and it has been already successfully applied to study the molecular and atomic phases of liquid hydrogen under pressure and liquid water at ambient conditions. Since this ab initio method provides a better resolution of the thermodynamic properties of materials, we believe that it represents a very promising tool for the most challenging applications in physics, chemistry, and biology. Since the Car-Parrinello molecular dynamics (Car and Parrinello, 1985) was proposed three decades ago, ab initio molecular dynamics (MD) based on the density functional theory (DFT) has been widely accepted as an accurate and powerful tool to study the thermodynamic properties of systems at ambient and extreme conditions in the fields of physics, chemistry, and biology. Even though DFT is in principle exact, its accuracy, in practice, is affected by the quality of the approximation used in the exchange correlation functional term whose universal exact expression is not accessible, as the simplest approximate functionals, such as LDA, PBE, BLYP, and several other ones, so far cannot be systematically improved in a computationally efficient way. Quantum Monte Carlo (QMC) is the most promising successor of DFT in ab initio molecular dynamics. Indeed, the scaling behavior of QMC with the number of electrons is very good, from the second power (Ceperley et al., 1977) for thermodynamic properties – e.g., energy per electron, because in this case the number of samples to obtain a fixed accuracy in this quantity can be decreased when increasing the number Ne of electrons, implying N3e/Ne=N2e scaling with the standard algorithm – to the fourth power of the number of electrons when chemical accuracy in the total energy is required – in this case, instead the number of samples required for fixed accuracy has to increase with Ne, yielding N3e×Ne=N4e scaling. For this reason (a cost similar to DFT, albeit with a considerably larger pre-factor), QMC is also by far more efficient compared with other quantum chemistry methods based on multi-determinant expansions or many-body perturbation theory around the Hartree–Fock, such as, for instance, configuration interaction and coupled cluster theory, respectively. These methods provide a similar or even better accuracy than QMC for systems consisting of a few atoms, but they become computationally prohibitive when the system sizes increase. Another very important reason favoring the QMC algorithm is its well established efficient parallelization in current and upcoming supercomputers. QMC codes can be easily adapted to millions of CPU cores while DFT codes are still struggling with its parallel performance over several thousand cores. For the above reasons, it is probably not too far from reality to claim that QMC represents the rising star in the ab initio MD simulations. This opinion paper focuses on the construction of the QMC-based MD by showing the key ingredients and the main recent developments of the building blocks necessary for the efficient implementation of this method. There are four main components: the basics of QMC, the wavefunction optimization, the evaluation of forces, and the molecular dynamics scheme. The last three ingredients were efficiently developed within only 10 years, with substantial contribution given also by us (Casula et al., 2004; Sorella et al., 2007; Umrigar et al., 2007; Attaccalite and Sorella, 2008; Sorella and Capriotti, 2010; Luo et al., 2014; Mazzola et al., 2014; Zen et al., 2014). Thus, the QMC-based MD is no longer a dream. © 2015 AIP Publishing LLC.