The density-functional (DF) theory provides a simple method for calculating the properties of an interacting system under an external potential by associating it with a corresponding non-interacting system. Here, we find some relations in this non-interacting system, which can enable us to set up the thermodynamical relations for a neutral electron-nucleus mixture in terms of quantities of the non-interacting system and the exchange-correlation effect. In this way, Andersen's force theorems are clearly described and easily proved in conjunction with other types of force theorems, Janak's theorem extended to a finite-temperature system, pressure formulas and some thermodynamical relations. For this purpose, the thermodynamics in the DF theory is presented in a systematic and explicit way.
Closed-form hard-sphere thermodynamics under nanoscale confinement: from equations of state to unmixing forces
Biofisika Institute (CSIC, UPV/EHU), University of the Basque Country (UPV/EHU)（巴斯克大学（UPV/EHU）生物物理研究所）；IKERBASQUE, Basque Foundation for Science（伊克尔巴斯克，巴斯克科学基金会）；Department of Biomedical Engineering, University of California, Davis（加州大学戴维斯分校生物医学工程系）
A polarizable force-field (FF) model for short- and long-alkane chains and amide derivatives was constructed based solely on accurate quantum chemical (QC) calculations. First, the FF model accuracy was accessed by performing molecular dynamics (MD) simulations to calculate liquid-phase thermodynamic and structural properties for alkanes, for which experimental data are available. Second, The FF was then used to perform molecular dynamics simulations to calculate thermodynamic, structural and excess properties of monoamide/dodecane mixtures, namely DEHiBA/dodecane and DEHBA/dodecane. Aggregati…
In nonequilibrium chemical reaction systems, a fundamental relationship between unbalanced kinetic one-way fluxes and thermodynamic chemical driving forces is believed to exists. However this relation has been rigorously demonstrated only in a few cases in which one-way fluxes are well defined. In terms of its stochastic kinetic representation, we formulate the one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. For each kinetic cycle, the logarithm of the ratio of the steady-state forward …
The stability of possible termination structures for the (010) surface of forsterite, $ Mg_2SiO_4 $, is studied using a density functional theory (DFT) based thermodynamic approach. The DFT calculations are used to estimate the surface Gibbs free energy of various surface structures and compare their stability as a function of the chemical environment. Among 9 possible terminations, the SiO-II, M2, O-II terminations are found to be most stable as conditions range from Mg-poor to Mg-rich. This relative stability order remains the same at an elevated temperature. The surface phase diagram obtain…
Nowadays, hydrogen activation by frustrated Lewis pairs (FLPs) and their applications have been demonstrated to be one of emerge research topics in the field of catalysis. Previous studies have shown that the thermodynamics of these reaction is determined by electronic structures of FLPs and solvents. Herein, we investigated the systems consisting of typical FLPs and ionic liquids (ILs), which are well known by their large number of types and excellent solvent effects. The density functional theory (DFT) calculations were performed to study the thermodynamics for H2 activation by both inter- a…
Bridgmanite, a high temperature and pressure form of $MgSiO_3$, is believed to be Earth's most abundant mineral and responsible for the observed seismic anisotropy in the mantle. Little is known about surfaces of bridgmanite but knowledge of the most stable surface terminations is important for understanding various geochemical processes as well as likely slip planes. A density functional theory based thermodynamic approach is used here to establish the range of stability of bridgmanite as well as possible termination structures of the (001), (010), (100) and (011) surfaces as a function of th…
We use density-matrix renormalization group, applied to a one-dimensional model of continuum Hamiltonians, to accurately solve chains of hydrogen atoms of various separations and numbers of atoms. We train and test a machine-learned approximation to $F[n]$, the universal part of the electronic density functional, to within quantum chemical accuracy. Our calculation (a) bypasses the standard Kohn-Sham approach, avoiding the need to find orbitals, (b) includes the strong correlation of highly-stretched bonds without any specific difficulty (unlike all standard DFT approximations) and (c) is so a…
Thermodynamic extension of density-functional theory. I. Basic Massieu function, its Legendre and Massieu-Planck transforms for equilibrium state in terms of density matrix
A general formulation of the equilibrium state of a many-electron system in terms of a (mixed-state, ensemble) density matrix operator in the Fock space, based on the maximum entropy principle, is introduced. Various characteristic functions/functionals are defined and investigated: the basic Massieu function for fully open thermodynamic system (ensemble), the effective action function for the fully closed (isolated) system, and a series of Legendre transforms for partially open/closed ones - the Massieu functions. Convexity and/or concavity properties of these functions are determined, their …
On the assumption that experimentally validated tabulated thermodynamic properties of saturated fluids published by the National Institute of Standards and Technology are accurate, a theoretical thermodynamic cycle can be demonstrated that produces a net-negative entropy generation to the universe. The experimental data on the internal energy can also be used to obtain a simple, empirical equation for the change in internal energy of a real fluid undergoing isothermal expansion and compression. This demonstration provides experimental evidence to the theory that temperature-dependent intermole…
We introduce a family of Maxwellian Demons for which correlations among information bearing degrees of freedom can be calculated exactly and in compact analytical form. This allows one to precisely determine Demon functional thermodynamic operating regimes, when previous methods either misclassify or simply fail due to approximations they invoke. This reveals that these Demons are more functional than previous candidates. They too behave either as engines, lifting a mass against gravity by extracting energy from a single heat reservoir, or as Landauer erasers, consuming external work to remove…
In this work, we use molecular dynamics simulations to study the thermodynamics, structure and dynamics of the Li$_2$CO$_3$-K$_2$CO$_3$ (62:38 mol%) eutectic mixture. We present a new classical non-polarizable force field for this molten salt mixture, optimized using experimental and first principles molecular dynamics simulations as reference data. This simple force field allows efficient molecular simulations of phenomena at long timescales. We use this optimized force field to describe the behavior of the eutectic mixture in the 900-1100 K temperature range, at pressures between 0 and 5 GPa…
Force correcting atom centered potentials for generalized gradient approximated density functional theory: Approaching hybrid functional accuracy for geometries and harmonic frequencies in small chlorofluorocarbons
The Hellmann-Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upwards of 10 eV/Ang in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed a…
We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on equations of motion of current quantities (force balance equations) and is feasible both in the ground-state and the time-dependent setting. This avoids, besides differentiability and causality issues, the optimized-effective-potential procedure of orbital-dependent functionals. We provide straightforward exchange-type approximations for different density funct…
