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It is common in science to define the relationship between two physical quantities. For instance, in mathematics, a rate is the ratio between two related quantities in different units. Example of rate quantities is heart rate and flux. A particular case is a variation of a physical quantity "per unit of time", which is a case of a rate concept, such as speed. In chemistry, the rate with which chemical reactions occurs is a constant parameter of the velocity of the reaction that describes the "speed" with which reagent varies in time. The study of the velocity of chemical reactions is a branch of chemistry denoted as chemical kinetics. Chemical kinetics employs kinematics, as a subfield of classical physics, to study the velocity of the chemical reactions (collision theory is derived from this type of approach). Quantum rate theories arise as a way of using quantum rather than classical mechanics to study the physical chemistry meaning of the reaction rate constant. Therefore, the use of quantum physics (including quantum mechanics) to provide a meaning for the reaction rate constant is referred to as a quantum rate theory. Accordingly, any chemical rate theory (see, for example, transition state theory) that uses quantum physics for describing temporal changes in chemical processes and reactions can be classified as a quantum rate theory. This includes, for example, the electron transfer rate in quantum electrochemistry, where the electron transfer rate constant (see also Marcus theory as an example of a semi-classical approach for calculating the rate constant of electrochemical reactions) is simply calculated as the ratio between the conductance quantum and the quantum capacitance. This is the simplest quantum rate concept that defines one of the most fundamental frequency (energy divided by the Planck constant) concept defined in nature. It defines the characteristic time for moving a single electron from a quantum state to another and complies with Planck's law (a law that is considered as the born of quantum mechanics). It also equates to the electric current produced by a single electron moving between quantum states per unit of charge. This electron quantum rate serves as the most basic example of particle rate (as the velocity of the electron in the quantum channel per unit of length of the channel) common to both physics and chemistry. The rate of electron transfer or quantum transport between any quantum state, particularly in the latter case in which it can be used to determine the rate constant of electron transfer between orbital states, is important for calculating the velocity of electrochemical reactions.
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