Ab initio approach for many-electron systems without invoking orbitals: An integral formulation of density-functional theory

Embedding Quantum Statistical Excitations in a Classical Force Field

Quantum-mechanically driven charge polarization and charge transfer are ubiquitous in biomolecular systems, controlling reaction rates, allosteric interactions, ligand-protein binding, membrane transport, and dynamically driven structural transformations. Molecular dynamics (MD) simulations of these processes require quantum mechanical (QM) information in order to accurately describe their reactive dynamics. However, current techniques-empirical force fields, subsystem approaches, ab initio MD, and machine learning-vary in their ability to achieve a consistent chemical description across multiple atom types, and at scale. Here we present a physics-based, atomistic force field, the ensemble DFT charge-transfer embedded-atom method, in which QM forces are described at a uniform level of theory across all atoms, avoiding the need for explicit solution of the Schrödinger equation or large, precomputed training data sets. Coupling between the electronic and atomistic length scales is effected through an ensemble density functional theory formulation of the embedded-atom method originally developed for elemental materials. Charge transfer is expressed in terms of ensembles of ionic state basis densities of individual atoms, and charge polarization, in terms of atomic excited-state basis densities. This provides a highly compact yet general representation of the force field, encompassing both local and system-wide effects. Charge rearrangement is realized through the evolution of ensemble weights, adjusted at each dynamical time step via chemical potential equalization.

Strategies to build functionals of the density, or functionals of Green's functions: what can we learn?

The many-body problem cannot in general be solved exactly, and one of the most prominent approximations is to build perturbation expansions. A huge variety of expansions are possible, which differ by the quantity to be expanded, the expansion variable, the starting point, and ideas of how to re-sum or terminate the series. Although much has been discussed and much has been done, some choices were made for historical reasons, in particular, limited computation or storage capacities. The present work aims to examine the justification for different choices made in different contexts, by comparing the components of functionals based on Green's functions on the one side, and on the charge density on the other side. Of particular interest will be the question of how to build an optimal starting point for the approximation of non-local quantities, making use of near- or far-sightedness, and daring to consider models beyond the homogeneous electron gas. This will include the use of connector approximations. We will also discuss why it is a good idea to build functionals of the density.

Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.