Toward Accurate Post-Born-Oppenheimer Molecular Simulations on Quantum Computers: An Adaptive Variational Eigensolver with Nuclear-Electronic Frozen Natural Orbitals.

Nuclear quantum effects such as zero-point energy and hydrogen tunneling play a central role in many biological and chemical processes. The nuclear-electronic orbital (NEO) approach captures these effects by treating selected nuclei quantum mechanically on the same footing as electrons. On classical computers, the resources required for an exact solution of NEO-based models grow exponentially with system size. By contrast, quantum computers offer a means of solving this problem with polynomial scaling. However, due to the limitations of current quantum devices, NEO simulations are confined to the smallest systems described by minimal basis sets, whereas realistic simulations beyond the Born-Oppenheimer approximation require more sophisticated basis sets. For this purpose, we herein extend a hardware-efficient ADAPT-VQE method to the NEO framework in the frozen natural orbital (FNO) basis. We demonstrate on H2 and D2 molecules that the NEO-FNO-ADAPT-VQE method reduces the CNOT count by several orders of magnitude relative to the NEO unitary coupled cluster method with singles and doubles while maintaining the desired accuracy. This extreme reduction in the CNOT gate count is sufficient to permit practical computations employing the NEO method─an important step toward accurate simulations involving nonclassical nuclei and non-Born-Oppenheimer effects on near-term quantum devices. We further show that the method can capture isotope effects, and we demonstrate that inclusion of correlation energy systematically improves the prediction of difference in the zero-point energy (ΔZPE) between isotopes.

Nonadiabatic Nuclear-Electron Dynamics: A Quantum Computing Approach.

Coupled quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent representations of electrons and nuclei also exist, which do not rely on any a priori approximation. However, their implementation is hampered by prohibitive scaling. Consequently, quantum computers offer a unique opportunity for extending their use to larger systems. Here, we propose a quantum algorithm for simulating the time-evolution of molecular systems and apply it to proton transfer dynamics in malonaldehyde, described as a rigid scaffold. The proposed quantum algorithm can be easily generalized to include the explicit dynamics of the classically described molecular scaffold. We show how entanglement between electronic and nuclear degrees of freedom can persist over long times if electrons do not follow the nuclear displacement adiabatically. The proposed quantum algorithm may become a valid candidate for the study of such phenomena when sufficiently powerful quantum computers become available.

Application of Quantum Chemical Topology Force Field FFLUX to Condensed Matter Simulations: Liquid Water.

We present here the first application of the quantum chemical topology force field FFLUX to condensed matter simulations. FFLUX offers many-body potential energy surfaces learnt exclusively from ab initio data using Gaussian process regression. FFLUX also includes high-rank, polarizable multipole moments (up to quadrupole moments in this work) that are learnt from the same ab initio calculations as the potential energy surfaces. Many-body effects (where a body is an atom) and polarization are captured by the machine learning models. The choice to use machine learning in this way allows the force field's representation of reality to be improved (e.g., by including higher order many-body effects) with little detriment to the computational scaling of the code. In this manner, FFLUX is inherently future-proof. The "plug and play" nature of the machine learning models also ensures that FFLUX can be applied to any system of interest, not just liquid water. In this work we study liquid water across a range of temperatures and compare the predicted bulk properties to experiment as well as other state-of-the-art force fields AMOEBA(+CF), HIPPO, MB-Pol and SIBFA21. We find that FFLUX finds a place amongst these.

Flexible multipole moments in smooth particle mesh Ewald.

The smooth particle mesh Ewald sum is extended with additional force terms that arise from the so-called flexible multipole moments. These are multipole moments (of any rank) that depend explicitly on atomic positions in some local environment that can be made arbitrarily large. By introducing explicit dependence on atomic positions, flexible multipole moments are polarized by their local environment, allowing both intramolecular and intermolecular polarizations to be captured. Multipolar torques are discussed in detail, and it is shown that they arise naturally in the presented framework. Furthermore, we give details of how we validated our implementation of the flexible smooth particle mesh Ewald sum by considering two mathematical limits of the smooth particle mesh Ewald summation.

DL_FFLUX: A Parallel, Quantum Chemical Topology Force Field.

DL_FFLUX is a force field based on quantum chemical topology that can perform molecular dynamics for flexible molecules endowed with polarizable atomic multipole moments (up to hexadecapole). Using the machine learning method kriging (aka Gaussian process regression), DL_FFLUX has access to atomic properties (energy, charge, dipole moment, etc.) with quantum mechanical accuracy. Newly optimized and parallelized using domain decomposition Message Passing Interface (MPI), DL_FFLUX is now able to deliver this rigorous methodology at scale while still in reasonable time frames. DL_FFLUX is delivered as an add-on to the widely distributed molecular dynamics code DL_POLY 4.08. For the systems studied here (103-105 atoms), DL_FFLUX is shown to add minimal computational cost to the standard DL_POLY package. In fact, the optimization of the electrostatics in DL_FFLUX means that, when high-rank multipole moments are enabled, DL_FFLUX is up to 1.25× faster than standard DL_POLY. The parallel DL_FFLUX preserves the quality of the scaling of MPI implementation in standard DL_POLY. For the first time, it is feasible to use the full capability of DL_FFLUX to study systems that are large enough to be of real-world interest. For example, a fully flexible, high-rank polarized (up to and including quadrupole moments) 1 ns simulation of a system of 10 125 atoms (3375 water molecules) takes 30 h (wall time) on 18 cores.

On the many-body nature of intramolecular forces in FFLUX and its implications.

FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3Natoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to Natoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

A FFLUX Water Model: Flexible, Polarizable and with a Multipolar Description of Electrostatics.

Key to progress in molecular simulation is the development of advanced models that go beyond the limitations of traditional force fields that employ a fixed, point charge-based description of electrostatics. Taking water as an example system, the FFLUX framework is shown capable of producing models that are flexible, polarizable and have a multipolar description of the electrostatics. The kriging machine-learning methods used in FFLUX are able to reproduce the intramolecular potential energy surface and multipole moments of a single water molecule with chemical accuracy using as few as 50 training configurations. Molecular dynamics simulations of water clusters (25-216 molecules) using the new FFLUX model reveal that incorporating charge-quadrupole, dipole-dipole, and quadrupole-charge interactions into the description of the electrostatics results in significant changes to the intermolecular structuring of the water molecules. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Does the Intra-atomic Deformation Energy of Interacting Quantum Atoms Represent Steric Energy?

Invited for this month's cover picture is the group of Paul L. A. Popelier from Manchester Institute of Biotechnology (UK). The cover picture shows the quantum topological atoms in a configuration of the complex HF⋅⋅⋅OH2, where F is green and O is red. Read the full text of their Full Paper at 10.1002/open.201800275.

Does the Intra-Atomic Deformation Energy of Interacting Quantum Atoms Represent Steric Energy?

We show that the mutual, through-space compression of atomic volume experienced by approaching topological atoms causes an exponential increase in the intra-atomic energy of those atoms, regardless of approach orientation. This insight was obtained using the modern energy partitioning method called interacting quantum atoms (IQA). This behaviour is consistent for all atoms except hydrogen, which can behave differently depending on its environment. Whilst all atoms experience charge transfer when they interact, the intra-atomic energy of the hydrogen atom is more vulnerable to these changes than larger atoms. The difference in behaviour is found to be due to hydrogen's lack of a core of electrons, which, in heavier atoms, consistently provide repulsion when compressed. As such, hydrogen atoms do not always provide steric hindrance. In accounting for hydrogen's unusual behaviour and demonstrating the exponential character of the intra-atomic energy in all other atoms, we provide evidence for IQA's intra-atomic energy as a quantitative description of steric energy.