Total angular momentum quantum numberIn quantum mechanics, the total angular momentum quantum number parametrises the total angular momentum of a given particle, by combining its orbital angular momentum and its intrinsic angular momentum (i.e., its spin). If s is the particle's spin angular momentum and l its orbital angular momentum vector, the total angular momentum j is The associated quantum number is the main total angular momentum quantum number j.
Quantum numberIn quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their corresponding eigenspaces. Together, a specification of all of the quantum numbers of a quantum system fully characterize a basis state of the system, and can in principle be measured together.
Transition state theoryIn 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. TST is used primarily to understand qualitatively how chemical reactions take place.
Azimuthal quantum numberIn quantum mechanics, the azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of quantum numbers that describe the unique quantum state of an electron (the others being the principal quantum number n, the magnetic quantum number m_l, and the spin quantum number m_s). It is also known as the orbital angular momentum quantum number, orbital quantum number, subsidiary quantum number, or second quantum number, and is symbolized as l (pronounced ell).
Spin quantum numberIn physics, the spin quantum number is a quantum number (designated s) that describes the intrinsic angular momentum (or spin angular momentum, or simply spin) of an electron or other particle. It has the same value for all particles of the same type, such as s = 1/2 for all electrons. It is an integer for all bosons, such as photons, and a half-odd-integer for all fermions, such as electrons and protons. The component of the spin along a specified axis is given by the spin magnetic quantum number, conventionally written ms.
Angular momentum operatorIn quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Such an operator is applied to a mathematical representation of the physical state of a system and yields an angular momentum value if the state has a definite value for it.
Magnetic quantum numberIn atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number (ml or m) distinguishes the orbitals available within a given subshell of an atom. It specifies the component of the orbital angular momentum that lies along a given axis, conventionally called the z-axis, so it describes the orientation of the orbital in space.
Chemical reactionA chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. 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 (no change to the elements present), 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.
MolecularityIn chemistry, molecularity is the number of molecules that come together to react in an elementary (single-step) reaction and is equal to the sum of stoichiometric coefficients of reactants in the elementary reaction with effective collision (sufficient energy) and correct orientation. Depending on how many molecules come together, a reaction can be unimolecular, bimolecular or even trimolecular. The kinetic order of any elementary reaction or reaction step is equal to its molecularity, and the rate equation of an elementary reaction can therefore be determined by inspection, from the molecularity.
Angular momentum couplingIn quantum mechanics, the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta is called angular momentum coupling. For instance, the orbit and spin of a single particle can interact through spin–orbit interaction, in which case the complete physical picture must include spin–orbit coupling. Or two charged particles, each with a well-defined angular momentum, may interact by Coulomb forces, in which case coupling of the two one-particle angular momenta to a total angular momentum is a useful step in the solution of the two-particle Schrödinger equation.
Angular momentumIn physics, angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved. Bicycles and motorcycles, flying discs, rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum.
Principal quantum numberIn quantum mechanics, the principal quantum number (symbolized n) is one of four quantum numbers assigned to each electron in an atom to describe that electron's state. Its values are natural numbers (from 1) making it a discrete variable. Apart from the principal quantum number, the other quantum numbers for bound electrons are the azimuthal quantum number l, the magnetic quantum number ml, and the spin quantum number s. As n increases, the electron is also at a higher energy and is, therefore, less tightly bound to the nucleus.
Angular momentum of lightThe angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of the light. While traveling approximately in a straight line, a beam of light can also be rotating (or "spinning, or "twisting) around its own axis. This rotation, while not visible to the naked eye, can be revealed by the interaction of the light beam with matter. There are two distinct forms of rotation of a light beam, one involving its polarization and the other its wavefront shape.
Relativistic angular momentumIn physics, relativistic angular momentum refers to the mathematical formalisms and physical concepts that define angular momentum in special relativity (SR) and general relativity (GR). The relativistic quantity is subtly different from the three-dimensional quantity in classical mechanics. Angular momentum is an important dynamical quantity derived from position and momentum. It is a measure of an object's rotational motion and resistance to changes in its rotation.
Entropy of activationIn chemical kinetics, the entropy of activation of a reaction is one of the two parameters (along with the enthalpy of activation) which are typically obtained from the temperature dependence of a reaction rate constant, when these data are analyzed using the Eyring equation of the transition state theory. The standard entropy of activation is symbolized ΔS‡ and equals the change in entropy when the reactants change from their initial state to the activated complex or transition state (Δ = change, S = entropy, ‡ = activation).
Rate equationIn chemistry, the rate law or rate equation for a chemical reaction is a mathematical equation that links the rate of forward reaction with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders). For many reactions, the initial rate is given by a power law such as where [\mathrm{A}] and [\mathrm{B}] express the concentration of the species \mathrm{A} and \mathrm{B}, usually in moles per liter (molarity, M).
Raman spectroscopyRaman spectroscopy (ˈrɑːmən) (named after Indian physicist C. V. Raman) is a spectroscopic technique typically used to determine vibrational modes of molecules, although rotational and other low-frequency modes of systems may also be observed. Raman spectroscopy is commonly used in chemistry to provide a structural fingerprint by which molecules can be identified. Raman spectroscopy relies upon inelastic scattering of photons, known as Raman scattering.
Reaction rate constantIn chemical kinetics, a reaction rate constant or reaction rate coefficient (k) is a proportionality constant which quantifies the rate and direction of a chemical reaction by relating it with the concentration of reactants. For a reaction between reactants A and B to form a product C, where A and B are reactants C is a product a, b, and c are stoichiometric coefficients, the reaction rate is often found to have the form: Here k is the reaction rate constant that depends on temperature, and [A] and [B] are the molar concentrations of substances A and B in moles per unit volume of solution, assuming the reaction is taking place throughout the volume of the solution.
Molecular vibrationA 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. For a diatomic molecule A−B, the vibrational frequency in s−1 is given by , where k is the force constant in dyne/cm or erg/cm2 and μ is the reduced mass given by .
Potential energy surfaceA potential energy surface (PES) 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 . An example is the Morse/Long-range potential. It is helpful to use the analogy of a landscape: for a system with two degrees of freedom (e.g.
