Andrea Zen

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature’s most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Static and Dynamical Correlation in Diradical Molecules by Quantum Monte Carlo Using the Jastrow Antisymmetrized Geminal Power Ansatz

Diradical molecules are essential species involved in many organic and inorganic chemical reactions. The computational study of their electronic structure is often challenging, because a reliable description of the correlation, and in particular of the static one, requires multireference techniques. The Jastrow correlated antisymmetrized geminal power (JAGP) is a compact and efficient wave function ansatz, based on the valence-bond representation, which can be used within quantum Monte Carlo (QMC) approaches. The AGP part can be rewritten in terms of molecular orbitals, obtaining a multideterminant expansion with zero-seniority number. In the present work we demonstrate the capability of the JAGP ansatz to correctly describe the electronic structure of two diradical prototypes: the orthogonally twisted ethylene, C2H4, and the methylene, CH2, representing respectively a homosymmetric and heterosymmetric system. In the orthogonally twisted ethylene, we find a degeneracy of π and π* molecular orbitals, as correctly predicted by multireference procedures, and our best estimates of the twisting barrier, using respectively the variational Monte Carlo (VMC) and the lattice regularized diffusion Monte Carlo (LRDMC) methods, are 71.9(1) and 70.2(2) kcal/mol, in very good agreement with the high-level MR-CISD+Q value, 69.2 kcal/mol. In the methylene we estimate an adiabatic triplet-singlet (X̃(3)B1-ã(1)A1) energy gap of 8.32(7) and 8.64(6) kcal/mol, using respectively VMC and LRDMC, consistently with the experimental-derived finding for Te, 9.363 kcal/mol. On the other hand, we show that the simple ansatz of a Jastrow correlated single determinant (JSD) wave function is unable to provide an accurate description of the electronic structure in these diradical molecules, both at variational level (VMC torsional barrier of C2H4 of 99.3(2) kcal/mol, triplet-singlet energy gap of CH2 of 13.45(10) kcal/mol) and, more remarkably, in the fixed-nodes projection schemes (LRDMC torsional barrier of 97.5(2) kcal/mol, triplet-singlet energy gap of 13.36(8) kcal/mol) showing that a poor description of the static correlation yields an inaccurate nodal surface. The suitability of JAGP to correctly describe diradicals with a computational cost comparable with that of a JSD calculation, in combination with a favorable scalability of QMC algorithms with the system size, opens new perspectives in the ab initio study of large diradical systems, like the transition states in cycloaddition reactions and the thermal isomerization of biological chromophores.

Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule

Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.

Finite-temperature electronic simulations without the Born-Oppenheimer constraint

The adiabatic approximation, typically assumed when performing standard Born-Oppenheimer (BO) molecular dynamics, can become unreliable at finite temperature, and specifically when the temperature is larger than the electronic energy gap between the ground state and the low-lying excited states. In this regime, relevant for many important chemical processes, the non-adiabatic couplings between the electronic energy states can produce finite temperature effects in several molecular properties, such as the geometry, the vibrational frequencies, the binding energy, and several chemical reactions. In this work, we introduce a novel finite-temperature non-adiabatic molecular dynamics based on a novel covariant formulation of the electronic partition function. In this framework, the nuclei are not constrained to move in a specific electronic potential energy surface. Then, by using a rigorous variational upper bound to the free energy, we are led to an approximate partition function that can be evaluated numerically. The method can be applied to any technique capable to provide an energy value over a given wave function ansatz depending on several variational parameters and atomic positions. In this work, we have applied the proposed method within a quantum Monte Carlo (QMC) scheme. In particular, we consider in this first application only classical ions, but we explicitly include an electronic correlation (Jastrow) term in the wave function, by extending in this way the standard variational QMC method, from ground state to finite temperature properties. We show that our approximation reduces correctly to the standard ground-state Born-Oppenheimer (gsBO) at zero temperature and to the correct high temperature limit. Moreover, at temperatures large enough, this method improves the upper bound of the free energy obtained with a single BO energy surface, since within our approach it is possible to estimate the electron entropy of a correlated ansatz in an efficient way. We test this new method on the simple hydrogen molecule, where at low temperature we recover the correct gsBO low temperature limit. Moreover, we show that the dissociation of the molecule is possible at a temperature much smaller than the one corresponding to the gsBO energy surface, in good agreement with experimental evidence. Several extensions of the proposed technique are also discussed, as for instance the inclusion of quantum effects for ions and the calculation of critical (magnetic, superconducting) temperatures.

Boosting the accuracy and speed of quantum Monte Carlo: size-consistency and time-step

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard for providing high-quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Greens function to avoid singularities near the nodal surface of the trial wave function. Here we show that these modifications affect the DMC energies in a way that is not size consistent, resulting in large time-step errors. Building on the modifications of Umrigar et al. and DePasquale et al. we propose a simple Greens function modification that restores size consistency to large values of the time step, which substantially reduces time-step errors. This algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.

Ab initio molecular dynamics with noisy forces: Validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties

We present a systematic study of a recently developed ab initio simulation scheme based on molecular dynamics and quantum Monte Carlo. In this approach, a damped Langevin molecular dynamics is employed by using a statistical evaluation of the forces acting on each atom by means of quantum Monte Carlo. This allows the use of an highly correlated wave function parametrized by several variational parameters and describing quite accurately the Born-Oppenheimer energy surface, as long as these parameters are determined at the minimum energy condition. However, in a statistical method both the minimization method and the evaluation of the atomic forces are affected by the statistical noise. In this work, we study systematically the accuracy and reliability of this scheme by targeting the vibrational frequencies of simple molecules such as the water monomer, hydrogen sulfide, sulfur dioxide, ammonia, and phosphine. We show that all sources of systematic errors can be controlled and reliable frequencies can be obtained with a reasonable computational effort. This work provides convincing evidence that this molecular dynamics scheme can be safely applied also to realistic systems containing several atoms.

Ice formation on kaolinite: Insights from molecular dynamics simulations

The formation of ice affects many aspects of our everyday life as well as important technologies such as cryotherapy and cryopreservation. Foreign substances almost always aid water freezing through heterogeneous ice nucleation, but the molecular details of this process remain largely unknown. In fact, insight into the microscopic mechanism of ice formation on different substrates is difficult to obtain even if state-of-the-art experimental techniques are used. At the same time, atomistic simulations of heterogeneous ice nucleation frequently face extraordinary challenges due to the complexity of the water-substrate interaction and the long time scales that characterize nucleation events. Here, we have investigated several aspects of molecular dynamics simulations of heterogeneous ice nucleation considering as a prototypical ice nucleating material the clay mineral kaolinite, which is of relevance in atmospheric science. We show via seeded molecular dynamics simulations that ice nucleation on the hydroxylated (001) face of kaolinite proceeds exclusively via the formation of the hexagonal ice polytype. The critical nucleus size is two times smaller than that obtained for homogeneous nucleation at the same supercooling. Previous findings suggested that the flexibility of the kaolinite surface can alter the time scale for ice nucleation within molecular dynamics simulations. However, we here demonstrate that equally flexible (or non flexible) kaolinite surfaces can lead to very different outcomes in terms of ice formation, according to whether or not the surface relaxation of the clay is taken into account. We show that very small structural changes upon relaxation dramatically alter the ability of kaolinite to provide a template for the formation of a hexagonal overlayer of water molecules at the water-kaolinite interface, and that this relaxation therefore determines the nucleation ability of this mineral.

Toward Accurate Adsorption Energetics on Clay Surfaces

Clay minerals are ubiquitous in nature, and the manner in which they interact with their surroundings has important industrial and environmental implications. Consequently, a molecular-level understanding of the adsorption of molecules on clay surfaces is crucial. In this regard computer simulations play an important role, yet the accuracy of widely used empirical force fields (FF) and density functional theory (DFT) exchange-correlation functionals is often unclear in adsorption systems dominated by weak interactions. Herein we present results from quantum Monte Carlo (QMC) for water and methanol adsorption on the prototypical clay kaolinite. To the best of our knowledge, this is the first time QMC has been used to investigate adsorption at a complex, natural surface such as a clay. As well as being valuable in their own right, the QMC benchmarks obtained provide reference data against which the performance of cheaper DFT methods can be tested. Indeed using various DFT exchange-correlation functionals yields a very broad range of adsorption energies, and it is unclear a priori which evaluation is better. QMC reveals that in the systems considered here it is essential to account for van der Waals (vdW) dispersion forces since this alters both the absolute and relative adsorption energies of water and methanol. We show, via FF simulations, that incorrect relative energies can lead to significant changes in the interfacial densities of water and methanol solutions at the kaolinite interface. Despite the clear improvements offered by the vdW-corrected and the vdW-inclusive functionals, absolute adsorption energies are often overestimated, suggesting that the treatment of vdW forces in DFT is not yet a solved problem.

Properties of the water to boron nitride interaction: From zero to two dimensions with benchmark accuracy

Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation, and second order Møller-Plesset theory. These wavefunction based correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is -107±7 meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions, but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.

Evidence for stable square ice from quantum Monte Carlo

Recent experiments on ice formed by water under nanoconfinement provide evidence for a two-dimensional (2D) “square ice” phase. However, the interpretation of the experiments has been questioned and the stability of square ice has become a matter of debate. Partially this is because the simulation approaches employed so far (force fields and density functional theory) struggle to accurately describe the very small energy differences between the relevant phases. Here we report a study of 2D ice using an accurate wave-function based electronic structure approach, namely diffusion Monte Carlo (DMC). We find that at relatively high pressure, square ice is indeed the lowest enthalpy phase examined, supporting the initial experimental claim. Moreover, at lower pressures, a “pentagonal ice” phase (not yet observed experimentally) has the lowest enthalpy, and at ambient pressure, the “pentagonal ice” phase is degenerate with a “hexagonal ice” phase. Our DMC results also allow us to evaluate the accuracy of various density functional theory exchange-correlation functionals and force field models, and in doing so we extend the understanding of how such methodologies perform to challenging 2D structures presenting dangling hydrogen bonds.