We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by the choice of the free energy and the dynamics of the chemical reaction is determined by the choice of the dissipation. This approach enables us to couple chemical reactions with other effects, such as diffusion and drift in an electric field. As an illustration, we apply our approach to a non-equilibrium reaction-diffusion system in a specific but canonical set-up. We show by numerical simulation that the input-output relation of such a system depends on the choice of the dissipation.
In this letter we analyse an amazing variational approach to chemical reactions. Our results clearly show that the variational expressions are unsuitable for the analysis of empirical data obtained from chemical reactions.
We report on a many-electron wavefunction theory study for the reaction energetics of hydrogen dissociation on the Si(100) surface. We demonstrate that quantum chemical wavefunction based methods using periodic boundary conditions can predict chemically accurate results for the activation barrier and the chemisorption energy in agreement with experimental findings. These highly accurate results for the reaction energetics enable a deeper understanding of the underlying physical mechanism and make it possible to benchmark widely used density functional theory methods.
We investigate the energetics of the atom exchange reaction in the SrF+alkali-metal atom and CaF+alkali-metal atom systems. Such reactions are possible only for collisions of SrF and CaF with the lithium atoms, while they are energetically forbidden for other alkali-metal atoms. Specifically, we focus on SrF interacting with Li, Rb, and Sr atoms and use ab initio methods to demonstrate that the SrF+Li and SrF+Sr reactions are barrierless. We present potential energy surfaces for the interaction of the SrF molecule with the Li, Rb, and Sr atoms in their energetically lowest-lying electronic spi…
A mathematical model for chemical reactions in electrolytes is developed using an Energy variational method consistent with classical thermodynamics. Electrostatics and chemical reactions are included in properly defined energetic and dissipative functionals. The energy variation method is generalized to deal with open systems with inputs of charge, mass, and energy. The open systems can transform input energy of one type into output energy of another type. The generalized method is used to analyze the conversion of electrical current into proton flow by cytochrome c oxidase, an important enzy…
Astrochemical surface reactions are thought to be responsible for the formation of complex organic molecules, which are of potential importance for the origin of life. In a situation, when the chemical composition of dust surfaces is not precisely known, the fundamental knowledge concerning such reactions gains significance. We describe an experimental technique, which can be used to measure the energy released in reactions of a single pair of reactants. These data can be directly compared with the results of quantum chemical computations leading to unequivocal conclusions regarding the reacti…
We explore the energetics of the titular reaction, which current astrochemical databases consider open at typical dense molecular (i.e., dark) cloud conditions. As is common for reactions involving the transfer of light particles, we assume that there are no intersystem crossings of the potential energy surfaces involved. In the absence of any such crossings, we find that this reaction is endoergic and will be suppressed at dark cloud temperatures. Updating accordingly a generic astrochemical model for dark clouds changes the predicted gas-phase abundances of 224 species by greater than a fact…
This work proposes a new variational, thermodynamically consistent model to predict thermal electrokinetics in electric double layer capacitors (EDLCs) by using an energetic variational approach. The least action principle and maximum dissipation principle from the non-equilibrium thermodynamics are employed to develop modified Nernst-Planck equations for non-isothermal ion transport with temperature inhomogeneity. Laws of thermodynamics are employed to derive a temperature evolution equation with heat sources due to thermal pressure and electrostatic interactions. Numerical simulations succes…
We show that isotope-exchange reactions between ground-state alkali-metal, alkaline-earth-metal, and lanthanide heteronuclear dimers consisting of two isotopes of the same atom are exothermic with an energy change in the range of 1-8000$\,$MHz thus resulting in cold or ultracold products. For these chemical reactions there are only one rovibrational and at most several hyperfine possible product states. The number and energetics of open and closed reactive channels can be controlled by the laser and magnetic fields. We suggest a laser-induced isotope- and state-selective Stark shift control to…
On the time scales accessible to atomistic numerical modelling, chemical reactions are considered rare events. Atomistic simulations are typically biased along a low-dimensional representation of a chemical reaction in an atomic structure space, i.e., along the collective variable, to accelerate sampling of these improbable events. However, suitable collective variables are often complicated to guess due to the complexity of the transitions. Therefore, we present an automatic method of generating robust collective variables from atomic representation vectors, using either fixed Behler-Parrinel…
We present a theoretical investigation of the chemical reaction SrF + SrF $\rightarrow$ products, focusing on reactions at ultralow temperatures. We find that bond swapping, SrF + SrF $\rightarrow$ Sr$_2$ + F$_2$, is energetically forbidden at these temperatures. Rather, the only energetically allowed reaction is SrF + SrF $\rightarrow$ SrF$_2$ + Sr, and even then only singlet states of the SrF$_2$ trimer can form. A calculation along a reduced reaction path demonstrates that this abstraction reaction is barrierless, and proceeds by one SrF molecule "handing off" a fluorine atom to the other m…
In light of the recent discovery of ArH+ in the Crab nebula, it is shown through high-level quantum chemical comptuations that the global minima on the Ar+/Ne+ + H2 potential energy surfaces are ArH2+ and NeH2+. Hence, ArH2+ may be a necessary intermediate in the Ar+ + H2 -> ArH+ + H formation reaction proposed in the same work where ArH+ is first reported in the Crab nebula. ArH2+ is also probably an intermediate in the alternative Ar + H+2 -> ArH+ + H reaction. Additionally, it is shown that Ne+ + H2 -> NeH+2 will subsequently most likely yield Ne + H+2 and not NeH+ + H offering a possible r…
Molecule- and particle-based simulations provide the tools to test, in microscopic detail, the validity of classical nucleation theory. In this endeavour, determining nucleation mechanisms and rates for phase separation requires an appropriately defined reaction coordinate to describe the transformation of an out-of-equilibrium parent phase, for which myriad options are available to the simulator. In this article, we describe the application of the variational approach to Markov processes (VAMP) to quantify the suitability of reaction coordinates to study crystallisation from supersaturated co…
Approximate solutions of the chemical master equation and the chemical Fokker-Planck equation are an important tool in the analysis of biomolecular reaction networks. Previous studies have highlighted a number of problems with the moment-closure approach used to obtain such approximations, calling it an ad-hoc method. In this article, we give a new variational derivation of moment-closure equations which provides us with an intuitive understanding of their properties and failure modes and allows us to correct some of these problems. We use mixtures of product-Poisson distributions to obtain a …
We investigate the potential energy surfaces and activation energies for reactions between methyl halide molecules CH$_{3}X$ ($X$ = F, Cl, Br, I) and alkali-metal atoms $A$ ($A$ = Li, Na, K, Rb) using high-level {\it ab initio} calculations. We examine the anisotropy of each intermolecular potential energy surface (PES) and the mechanism and energetics of the only available exothermic reaction pathway, ${\rm CH}_{3}X+A\rightarrow{\rm CH}_{3}+AX$. The region of the transition state is explored using two-dimensional PES cuts and estimates of the activation energies are inferred. Nearly all combi…
Understanding how biological homochirality emerged remains a challenge for the researchers interested in the origin of life. During the last decades, stable non-racemic steady states of nonequilibrium chemical systems have been discussed as a possible response to this problem. In line with this framework, a description of recycled systems was provided in which stable products can be activated back to reactive compounds. The dynamical behaviour of such systems relies on the presence of a source of energy, leading to the continuous maintaining of unidirectional reaction loops. A full thermodynam…
Regions of energy localization referred to as hotspots are known to govern shock initiation and the run-to-detonation in energetic materials. Mounting computational evidence points to accelerated chemistry in hotspots from large intramolecular strains induced via the interactions between the shockwave and microstructure. However, definite evidence mapping intramolecular strain to accelerated or altered chemical reactions has so far been elusive. From a large-scale reactive molecular dynamics simulation of the energetic material TATB, we map molecular temperature and intramolecular strain energ…
We report the results of Molecular Dynamics (MD) simulations and formal modeling of the free energy surfaces and reaction rates of primary charge separation in the reaction center of \textit{Rhodobacter sphaeroides}. Two simulation protocols were used to produce MD trajectories. Standard force field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dyna…
The analysis of a chemical reaction along the ground state potential energy surface in conjunction with an unknown spin state is challenging because electronic states must be separately computed several times using different spin multiplicities to find the lowest energy state. However, in principle, the ground state could be obtained with just a single calculation using a quantum computer without specifying the spin multiplicity in advance. In the present work, ground state potential energy curves for PtCO were calculated as a proof-of-concept using a variational quantum eigensolver (VQE) algo…
Elucidating photochemical reactions is vital to understand various biochemical phenomena and develop functional materials such as artificial photosynthesis and organic solar cells, albeit its notorious difficulty by both experiments and theories. The best theoretical way so far to analyze photochemical reactions at the level of ab initio electronic structure is the state-averaged multi-configurational self-consistent field (SA-MCSCF) method. However, the exponential computational cost of classical computers with the increasing number of molecular orbitals hinders applications of SA-MCSCF for l…
When examining dynamics occurring at non-zero temperatures, both energy and entropy must be taken into account while describing activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called the State Predictive Information Bottleneck (SPIB) to find non-linear reaction coordinates for three systems of varying complexity. The SPIB is able to predict correctly an entropic bottleneck for an analytical flat-energy double-we…
We theoretically characterize interactions, energetics, and chemical reaction paths in ionic two-body and three-body systems of alkali-metal and alkaline-earth-metal atoms in the context of modern experiments with cold hybrid ion-atom mixtures. Using \textit{ab initio} techniques of quantum chemistry such as the coupled-cluster method, we calculate ground-state electronic properties of all diatomic $AB^+$ and most of triatomic $A_2B^+$ molecular ions consisting of Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, and Yb atoms. Different geometries and wave-function symmetries of the ground state are found fo…
We develop a thermodynamic framework for closed and open chemical networks applicable to non-elementary reactions that do not need to obey mass action kinetics. It only requires the knowledge of the kinetics and of the standard chemical potentials, and makes use of the topological properties of the network (conservation laws and cycles). Our approach is proven to be exact if the network results from a bigger network of elementary reactions where the fast-evolving species have been coarse grained. Our work should be particularly relevant for energetic considerations in biosystems where the char…
A wave front propagating through a medium is described using the Ising--Bloch method The reaction-diffusion behaviour of an autocatalysis model of incoming waves from energetic material in a nitroguanidine lens and its interactions with Dirichlet boundaries system are examined. Wave splitting is found to occur for some relative diffusivities through introducing defects into the lens. The system is introduced using a nonlinear method with a Boltzmann--Gibbs distribution of diffusion parameters and forced into a right-hand-side divergence for final analysis. Considering the nonlinearity, the mod…
Recent advancements on the fabrication of organic micro- and nanostructures have permitted the strong collective light-matter coupling regime to be reached with molecular materials. Pioneering works in this direction have shown the effects of this regime in the excited state reactivity of molecular systems and at the same time has opened up the question of whether it is possible to introduce any modifications in the electronic ground energy landscape which could affect chemical thermodynamics and/or kinetics. In this work, we use a model system of many molecules coupled to a surface-plasmon fi…
The Minima Hopping global optimization method uses physically realizable molecular dynamics moves in combination with an energy feedback that guarantees the escape from any potential energy funnel. For the purpose of finding reactions pathways, we argue that Minima Hopping is particularly suitable as a guide through the potential energy landscape and as a generator for pairs of minima that can be used as input structures for methods capable of finding transition states between two minima. For Lennard-Jones benchmark systems we compared this Minima Hopping guided path search method to a known a…
