Abstract coordinate depicting chemical reaction progress
Diagram of a catalytic reaction, showing the energy level as a function of the reaction coordinate. For a catalyzed reaction, the activation energy is lower.
In chemistry, a reaction coordinate[1] is an abstract one-dimensional coordinate chosen to represent progress along a reaction pathway. Where possible it is usually a geometric parameter that changes during the conversion of one or more molecular entities, such as bond length or bond angle. For example, in the homolytic dissociation of molecular hydrogen, an apt choice would be the coordinate corresponding to the bond length. Non-geometric parameters such as bond order are also used, but such direct representation of the reaction process can be difficult, especially for more complex reactions.
In computer simulations collective variables are employed for a target-oriented sampling approach. Plain simulations fail to capture so called rare events, because they are not feasible to occur in realistic computation times. This often stems from to high energy barriers separating the reactants from products, or any two states of interest. A collective variable is as the name states only a set, a collection, of individual variables (xi) contracted into one:
CV = A{xi},
with A a transformation matrix. The collective variables reduce many variables to a lower-dimensional set of variables, that still describe the crucial characteristics of the system. Many collective variables than span the reaction coordinate with a continuous function ξ:
An example is the complexation of two molecules. The distance between both of them is the collective variable, where the atomic positions are the individual variables xi and the reaction coordinate ξ would be the full path of association and dissociation. By applying a bias to the collective variables the simulation can be 'steered' towards the desired destination. These kind of simulations are called enhanced simulations. Special collective variables that help to distinguish reactants from products are also known as order parameters, terminology that originates in work on phase transitions.[3]Reaction coordinates are special order parameters that describe the entire pathway from reactants through transition states and on to products. Depending on the application, reaction coordinates may be defined by using chemically intuitive variables like bond lengths, or splitting probabilities (also called committors), or using the eigenfunction corresponding to the reactant-to-product transition as a progress coordinate.[4]
A reaction coordinate parameterizes reaction process at the level of the molecular entities involved. It differs from extent of reaction, which measures reaction progress in terms of the composition of the reaction system.
In the formalism of transition-state theory the reaction coordinate for each reaction step is one of a set of curvilinear coordinates obtained from the conventional coordinates for the reactants, and leads smoothly among configurations, from reactants to products via the transition state. It is typically chosen to follow the path defined by potential energy gradient – shallowest ascent/steepest descent – from reactants to products.[1]
In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. This state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.
Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. Chemical thermodynamics involves not only laboratory measurements of various thermodynamic properties, but also the application of mathematical methods to the study of chemical questions and the spontaneity of processes.
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. When chemical reactions occur, the atoms are rearranged and the reaction is accompanied by an energy change as new products are generated. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei, and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
In chemistry, an activated complex represents a collection of intermediate structures in a chemical reaction when bonds are breaking and forming. The activated complex is an arrangement of atoms in an arbitrary region near the saddle point of a potential energy surface. The region represents not one defined state, but a range of unstable configurations that a collection of atoms pass through between the reactants and products of a reaction. Activated complexes have partial reactant and product character, which can significantly impact their behaviour in chemical reactions.
Molecular modelling encompasses all methods, theoretical and computational, used to model or mimic the behaviour of molecules. The methods are used in the fields of computational chemistry, drug design, computational biology and materials science to study molecular systems ranging from small chemical systems to large biological molecules and material assemblies. The simplest calculations can be performed by hand, but inevitably computers are required to perform molecular modelling of any reasonably sized system. The common feature of molecular modelling methods is the atomistic level description of the molecular systems. This may include treating atoms as the smallest individual unit, or explicitly modelling protons and neutrons with its quarks, anti-quarks and gluons and electrons with its photons.
In chemistry, the transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the state corresponding to the highest potential energy along this reaction coordinate. It is often marked with the double dagger (‡) symbol.
In physical organic chemistry, a kinetic isotope effect (KIE) is the change in the reaction rate of a chemical reaction when one of the atoms in the reactants is replaced by one of its isotopes. Formally, it is the ratio of rate constants for the reactions involving the light (kL) and the heavy (kH) isotopically substituted reactants (isotopologues):
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency towards further change. For a given set of reaction conditions, the equilibrium constant is independent of the initial analytical concentrations of the reactant and product species in the mixture. Thus, given the initial composition of a system, known equilibrium constant values can be used to determine the composition of the system at equilibrium. However, reaction parameters like temperature, solvent, and ionic strength may all influence the value of the equilibrium constant.
A potential energy surface (PES) or energy landscape describes the energy of a system, especially a collection of atoms, in terms of certain parameters, normally the positions of the atoms. The surface might define the energy as a function of one or more coordinates; if there is only one coordinate, the surface is called a potential energy curve or energy profile. An example is the Morse/Long-range potential.
Hammond's postulate, is a hypothesis in physical organic chemistry which describes the geometric structure of the transition state in an organic chemical reaction. First proposed by George Hammond in 1955, the postulate states that:
If two states, as, for example, a transition state and an unstable intermediate, occur consecutively during a reaction process and have nearly the same energy content, their interconversion will involve only a small reorganization of the molecular structures.
Enzyme catalysis is the increase in the rate of a process by a biological molecule, an "enzyme". Most enzymes are proteins, and most such processes are chemical reactions. Within the enzyme, generally catalysis occurs at a localized site, called the active site.
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1 and wavelengths of approximately 30 to 3 µm.
In chemistry, transition state theory (TST) explains the reaction rates of elementary chemical reactions. The theory assumes a special type of chemical equilibrium (quasi-equilibrium) between reactants and activated transition state complexes.
In the field of computational chemistry, energy minimization is the process of finding an arrangement in space of a collection of atoms where, according to some computational model of chemical bonding, the net inter-atomic force on each atom is acceptably close to zero and the position on the potential energy surface (PES) is a stationary point. The collection of atoms might be a single molecule, an ion, a condensed phase, a transition state or even a collection of any of these. The computational model of chemical bonding might, for example, be quantum mechanics.
In theoretical chemistry, an energy profile is a theoretical representation of a chemical reaction or process as a single energetic pathway as the reactants are transformed into products. This pathway runs along the reaction coordinate, which is a parametric curve that follows the pathway of the reaction and indicates its progress; thus, energy profiles are also called reaction coordinate diagrams. They are derived from the corresponding potential energy surface (PES), which is used in computational chemistry to model chemical reactions by relating the energy of a molecule(s) to its structure.
More O’Ferrall–Jencks plots are two-dimensional representations of multiple reaction coordinate potential energy surfaces for chemical reactions that involve simultaneous changes in two bonds. As such, they are a useful tool to explain or predict how changes in the reactants or reaction conditions can affect the position and geometry of the transition state of a reaction for which there are possible competing pathways.
George Simms Hammond was an American scientist and theoretical chemist who developed "Hammond's postulate", and fathered organic photochemistry,–the general theory of the geometric structure of the transition state in an organic chemical reaction. Hammond's research is also known for its influence on the philosophy of science. His research garnered him the Norris Award in 1968, the Priestley Medal in 1976, the National Medal of Science in 1994, and the Othmer Gold Medal in 2003. He served as the executive chairman of the Allied Chemical Corporation from 1979 to 1989.
Metadynamics is a computer simulation method in computational physics, chemistry and biology. It is used to estimate the free energy and other state functions of a system, where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Alessandro Laio and Michele Parrinello in 2002 and is usually applied within molecular dynamics simulations. MTD closely resembles a number of newer methods such as adaptively biased molecular dynamics, adaptive reaction coordinate forces and local elevation umbrella sampling. More recently, both the original and well-tempered metadynamics were derived in the context of importance sampling and shown to be a special case of the adaptive biasing potential setting. MTD is related to the Wang–Landau sampling.
The inverse electron demand Diels–Alder reaction, or DAINV or IEDDA is an organic chemical reaction, in which two new chemical bonds and a six-membered ring are formed. It is related to the Diels–Alder reaction, but unlike the Diels–Alder reaction, the DAINV is a cycloaddition between an electron-rich dienophile and an electron-poor diene. During a DAINV reaction, three pi-bonds are broken, and two sigma bonds and one new pi-bond are formed. A prototypical DAINV reaction is shown on the right.
In theoretical chemistry, the Empirical Valence Bond (EVB) approach is an approximation for calculating free-energies of a chemical reaction in condensed-phase. It was first developed by Israeli chemist Arieh Warshel, and was inspired by the way Marcus theory uses potential surfaces to calculate the probability of electron transfer.
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