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Potential Energy Surface
A 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 energy profile. 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. two bond lengths), the value of the energy (analogy: the height of the land) is a function of two bond lengths (analogy: the coordinates of the position on the ground). The PES concept finds application in fields such as chemistry and physics, especially in the theoretical sub-branches of these subjects. It can be used to theoretically explore properties of structures composed of atoms, for example, finding the minimum energy shape of a molecule or computing the rates of a chemical reaction. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to mass–energy equivalence, any object that has mass whe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Eyring (chemist)
Henry Eyring (February 20, 1901 – December 26, 1981) was a Mexico-born United States theoretical chemist whose primary contribution was in the study of chemical reaction rates and intermediates. History Eyring, a third-generation member of the Church of Jesus Christ of Latter-day Saints (LDS Church), was reared on a cattle ranch in Colonia Juárez, Chihuahua, a Mormon colony, for the first 11 years of his life. His father, Edward Christian Eyring, practiced plural marriage; Edward married Caroline Romney (1893) and her sister Emma Romney (1903), both daughters of Miles Park Romney, the great-grandfather of Mitt Romney. In July 1912, the Eyrings and about 4,200 other immigrants were driven out of Mexico by violent insurgents during the Mexican Revolution and moved to El Paso, Texas. After living in El Paso for approximately one year, the Eyrings relocated to Pima, Arizona, where he completed high school and showed a special aptitude for mathematics and science. He also studied ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harpoon Reaction
A harpoon reaction is a type of chemical reaction, first proposed by Michael Polanyi in 1920, whose mechanism (also called the harpooning mechanism) involves two neutral reactants undergoing an electron transfer over a relatively long distance to form ions that then attract each other closer together. For example, a metal atom and a halogen might react to form a cation and anion, respectively, leading to a combined metal halide. The main feature of these redox reactions is that, unlike most reactions, they have steric factors greater than unity; that is, they take place faster than predicted by collision theory. This is explained by the fact that the colliding particles have greater cross sections than the pure geometrical ones calculated from their radii, because when the particles are close enough, an electron "jumps" (therefore the name) from one of the particles to the other one, forming an anion and a cation which subsequently attract each other. Harpoon reactions usually tak ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Vibration
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. For a diatomic molecule A−B, the vibrational frequency in s−1 is given by \nu = \frac \sqrt , where k is the force constant in dyne/cm or erg/cm2 and μ is the reduced mass given by \frac = \frac+\frac. The vibrational wavenumber in cm−1 is \tilde \;= \frac \sqrt, where c is the speed of light in cm/s. Vibrations of polyatomic molecules are described in terms of normal modes, which are independent of each other, but each normal mode involves simultaneous vibrations of different parts of the molecule. In general, a non-linear molecule with ''N'' atoms has 3''N'' – 6 normal modes of vibration, but a ''linear'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exothermic Reaction
In thermochemistry, an exothermic reaction is a "reaction for which the overall standard enthalpy change Δ''H''⚬ is negative." Exothermic reactions usually release heat. The term is often confused with exergonic reaction, which IUPAC defines as "... a reaction for which the overall standard Gibbs energy change Δ''G''⚬ is negative." A strongly exothermic reaction will usually also be exergonic because Δ''H''⚬ makes a major contribution to Δ''G''⚬. Most of the spectacular chemical reactions that are demonstrated in classrooms are exothermic and exergonic. The opposite is an endothermic reaction, which usually takes up heat and is driven by an entropy increase in the system. Examples Examples are numerous: combustion, the thermite reaction, combining strong acids and bases, polymerizations. As an example in everyday life, hand warmers make use of the oxidation of iron to achieve an exothermic reaction: :4Fe + 3O2 → 2Fe2O3 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Coordinate
In chemistry, a reaction coordinate is an abstract one-dimensional coordinate which represents progress along a reaction pathway. It is usually a geometric parameter that changes during the conversion of one or more molecular entities. In molecular dynamics simulations, a reaction coordinate is called collective variable. These coordinates can sometimes represent a real coordinate system (such as bond length, bond angle...), although, for more complex reactions especially, this can be difficult (and non geometric parameters are used, e.g., bond order). Reaction coordinate is distinct from extent of reaction, a different parameter of reaction progress, which is a measure of the ''composition'' of the reaction system. (Free) energy is often plotted against reaction coordinate(s) to demonstrate in some schematic form the potential energy profile (an intersection of a potential energy surface) associated with the reaction. In the formalism of transition-state theory the reaction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transition State
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. As an example, the transition state shown below occurs during the SN2 reaction of bromoethane with a hydroxide anion: The activated complex of a reaction can refer to either the transition state or to other states along the reaction coordinate between reactants and products, especially those close to the transition state.Peter Atkins and Julio de Paula, ''Physical Chemistry'' (8th ed., W.H. Freeman 2006), p.809 According to the transition state theory, once the reactants have passed through the transition state configuration, they always continue to form products. History of concept The concept of a transition state has been important in many theories of the rates at which chemical reactions occ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Saddle Point
In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. An example of a saddle point is when there is a critical point with a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis. However, a saddle point need not be in this form. For example, the function f(x,y) = x^2 + y^3 has a critical point at (0, 0) that is a saddle point since it is neither a relative maximum nor relative minimum, but it does not have a relative maximum or relative minimum in the y-direction. The name derives from the fact that the prototypical example in two dimensions is a surface that ''curves up'' in one direction, and ''curves down'' in a different direction, resembling a riding saddle or a mountain pass between two peaks forming a landform saddle. In te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reaction Dynamics
Reaction dynamics is a field within physical chemistry, studying why chemical reactions occur, how to predict their behavior, and how to control them. It is closely related to chemical kinetics, but is concerned with individual chemical events on atomic length scales and over very brief time periods. It considers ''state-to-state kinetics'' between reactant and product molecules in specific quantum states, and how energy is distributed between translational, vibrational, rotational, and electronic modes. Laidler, K.J. ''Chemical Kinetics'' (3rd ed., Harper & Row 1987), Chap.12 Experimental methods of reaction dynamics probe the chemical physics associated with molecular collisions. They include crossed molecular beam and infrared chemiluminescence experiments, both recognized by the 1986 Nobel Prize in Chemistry awarded to Dudley Herschbach, Yuan T. Lee, and John C. Polanyi "for their contributions concerning the dynamics of chemical elementary processes", In the crossed beam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Geometry
Molecular geometry is the three-dimensional arrangement of the atoms that constitute a molecule. It includes the general shape of the molecule as well as bond lengths, bond angles, torsional angles and any other geometrical parameters that determine the position of each atom. Molecular geometry influences several properties of a substance including its reactivity, polarity, phase of matter, color, magnetism and biological activity. The angles between bonds that an atom forms depend only weakly on the rest of molecule, i.e. they can be understood as approximately local and hence transferable properties. Determination The molecular geometry can be determined by various spectroscopic methods and diffraction methods. IR, microwave and Raman spectroscopy can give information about the molecule geometry from the details of the vibrational and rotational absorbance detected by these techniques. X-ray crystallography, neutron diffraction and electron diffraction can give molecular ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
