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Birge–Sponer Method
In molecular spectroscopy, the Birge–Sponer method or Birge–Sponer plot is a way to calculate the dissociation energy of a molecule. By observing transitions between as many vibrational energy levels as possible, for example through electronic or infrared spectroscopy, the difference between the energy levels, \Delta G_=G(v+1)-G(v) can be calculated. This sum will have a maximum at v_, representing the point of bond dissociation; summing over all the differences up to this point gives the total energy required to dissociate the molecule, i.e. to promote it from the ground state to an unbound state. This can be written: D_0=\sum_^ \Delta G_ where D_0 is the dissociation energy. If a Morse potential is assumed, plotting \Delta G_ against v+1/2 should give a straight line, from which it is easy to extract v_ from the intercept with the x-axis. In practice, such plots often give curves because of unaccounted anharmonicity in the potential; furthermore, the low population of the h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectroscopy
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associated with a spectral signature in the context of the Laser Interferometer Gravitational-Wave Observatory (LIGO) In simpler terms, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Historically, spectroscopy originated as the study of the wavelength dependence of the absorption by gas phase matter of visible light dispersed by a prism. Spectroscopy, primarily in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of astronomy, chemistry, materials science, and physics, allowing the composition, physical structure and e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dissociation Energy
The bond-dissociation energy (BDE, ''D''0, or ''DH°'') is one measure of the strength of a chemical bond . It can be defined as the standard enthalpy change when is cleaved by homolysis to give fragments A and B, which are usually radical species. The enthalpy change is temperature-dependent, and the bond-dissociation energy is often defined to be the enthalpy change of the homolysis at 0 K ( absolute zero), although the enthalpy change at 298 K (standard conditions) is also a frequently encountered parameter. As a typical example, the bond-dissociation energy for one of the C−H bonds in ethane () is defined as the standard enthalpy change of the process : , : ''DH''°298() = Δ''H°'' = 101.1(4) kcal/mol = 423.0 ± 1.7 kJ/mol = 4.40(2) eV (per bond). To convert a molar BDE to the energy needed to dissociate the bond ''per molecule'', the conversion factor 23.060 kcal/mol (96.485 kJ/mol) for each eV can be used. A variety of experi ... [...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] |
Infrared Spectroscopy
Infrared spectroscopy (IR spectroscopy or vibrational spectroscopy) is the measurement of the interaction of infrared radiation with matter by absorption, emission, or reflection. It is used to study and identify chemical substances or functional groups in solid, liquid, or gaseous forms. It can be used to characterize new materials or identify and verify known and unknown samples. The method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer (or spectrophotometer) which produces an infrared spectrum. An IR spectrum can be visualized in a graph of infrared light absorbance (or transmittance) on the vertical axis vs. frequency, wavenumber or wavelength on the horizontal axis. Typical units of wavenumber used in IR spectra are reciprocal centimeters, with the symbol cm−1. Units of IR wavelength are commonly given in micrometers (formerly called "microns"), symbol μm, which are related to the wavenumber in a reciprocal way. A com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the ''local'' or ''relative'' extrema), or on the entire domain (the ''global'' or ''absolute'' extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions. As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum. Definition A real-valued function ''f'' defined on a domain ''X'' has a global (or absolute) maximum point at ''x''∗, if for all ''x'' in ''X''. Similarly, the function has a global (or absolute) minimum point at ''x''∗, if for all ''x'' in ''X''. The value of the function at a m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ground State
The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state. In quantum field theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate. Many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator that acts non-trivially on a ground state and commutes with the Hamiltonian of the system. According to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state; thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a perfect crystal lattice, have a unique ground state and therefore have zero entropy at absolute zero. It is also possible for the highest excited state to have absolute zero temper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Morse Potential
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the vibrational structure of the molecule than the quantum harmonic oscillator because it explicitly includes the effects of bond breaking, such as the existence of unbound states. It also accounts for the anharmonicity of real bonds and the non-zero transition probability for overtone and combination bands. The Morse potential can also be used to model other interactions such as the interaction between an atom and a surface. Due to its simplicity (only three fitting parameters), it is not used in modern spectroscopy. However, its mathematical form inspired the MLR ( Morse/Long-range) potential, which is the most popular potential energy function used for fitting spectroscopic data. Potential energy function The Morse potential energy function is of the form :V(r) = D_e ( 1-e^ )^2 Here r is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero Of A Function
In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function f, is a member x of the domain of f such that f(x) ''vanishes'' at x; that is, the function f attains the value of 0 at x, or equivalently, x is the solution to the equation f(x) = 0. A "zero" of a function is thus an input value that produces an output of 0. A root of a polynomial is a zero of the corresponding polynomial function. The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree, and that the number of roots and the degree are equal when one considers the complex roots (or more generally, the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by f(x)=x^2-5x+6 has the two roots (or zeros) that are 2 and 3. f(2)=2^2-5\times 2+6= 0\textf(3)=3^2-5\times 3+6=0. If the function maps real numbers to real numbers, then it ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franck–Condon Principle
The Franck–Condon principle (named for James Franck and Edward Condon) is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions (the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy). The principle states that during an electronic transition, a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly. Overview The Franck–Condon principle has a well-established semiclassical interpretation based on the original contributions of James Franck. Electronic transitions are relatively instantaneous compared with the time scale of nuclear motions, therefore if the molecule is to move to a new vibrational level during the electronic transition, this new vibrational level must be instantaneously compatible with the nuclear positions and momenta of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extrapolation
In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Extrapolation may also mean extension of a method, assuming similar methods will be applicable. Extrapolation may also apply to human experience to project, extend, or expand known experience into an area not known or previously experienced so as to arrive at a (usually conjectural) knowledge of the unknownExtrapolation entry at Merriam–Webster (e.g. a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Raymond Thayer Birge
Raymond Thayer Birge (March 13, 1887 – March 22, 1980) was an American physicist. Career Born in Brooklyn, New York, into an academic scientific family, Birge obtained his doctorate from the University of Wisconsin in 1913. In the same year he married Irene A. Walsh. The Birges had two children, Carolyn Elizabeth (Mrs. E. D. Yocky) and Robert Walsh, Associate Director of the Lawrence Berkeley National Laboratory in 1973-1981. After five years as an instructor at Syracuse University, he became a member of the physics department at University of California, Berkeley, where he remained until he retired, as chairman, in 1955. On his arrival at Berkeley, Birge sought collaboration with the Berkeley College of Chemistry, then under the leadership of Gilbert N. Lewis. However, Birge's championing of the Bohr atom led him into conflict with the chemists who defended Lewis' earlier theory of the cubical atom. Birge was unafraid of scientific controversy and persevered with his cour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hertha Sponer
Hertha Sponer (1 September 1895 – 27 February 1968) was a German physicist and chemist who contributed to modern quantum mechanics and molecular physics and was the first woman on the physics faculty of Duke University. She was the older sister of philologist and resistance fighter Margot Sponer. Life and career Sponer was born in Neisse (Nysa), Prussian Silesia, and obtained her high school degree in Neisse. She spent a year at the University of Tübingen, after which she enrolled at the University of Göttingen where she received her PhD in 1920 under the supervision of Peter Debye. During her time at the University of Tübingen, she was an assistant of James Franck. In 1921 she, along with a few others, was among the first women to obtain a PhD in physics in Germany along with the right to teach science at a German university. In October 1925 she received a Rockefeller Foundation fellowship to stay at University of California, Berkeley, where she remained for a year. Durin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
