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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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philip M
Philip, also Phillip, is a male given name, derived from the Greek (''Philippos'', lit. "horse-loving" or "fond of horses"), from a compound of (''philos'', "dear", "loved", "loving") and (''hippos'', "horse"). Prominent Philips who popularized the name include kings of Macedonia and one of the apostles of early Christianity. ''Philip'' has many alternative spellings. One derivation often used as a surname is Phillips. It was also found during ancient Greek times with two Ps as Philippides and Philippos. It has many diminutive (or even hypocoristic) forms including Phil, Philly, Lip, Pip, Pep or Peps. There are also feminine forms such as Philippine and Philippa. Antiquity Kings of Macedon * Philip I of Macedon * Philip II of Macedon, father of Alexander the Great * Philip III of Macedon, half-brother of Alexander the Great * Philip IV of Macedon * Philip V of Macedon New Testament * Philip the Apostle * Philip the Evangelist Others * Philippus of Croton (c. 6th ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N2ground
N, or n, is the fourteenth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''en'' (pronounced ), plural ''ens''. History One of the most common hieroglyphs, snake, was used in Egyptian writing to stand for a sound like the English , because the Egyptian word for "snake" was ''djet''. It is speculated by many that Semitic people working in Egypt adapted hieroglyphics to create the first alphabet, and that they used the same snake symbol to represent N, because their word for "snake" may have begun with that sound. However, the name for the letter in the Phoenician, Hebrew, Aramaic and Arabic alphabets is ''nun'', which means "fish" in some of these languages. The sound value of the letter was —as in Greek, Etruscan, Latin and modern languages. Use in writing systems represents a dental or alveolar nasal in virtually all languages that use the Latin alp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Chemistry
Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions to physical and chemical properties of molecules, materials, and solutions at the atomic level. These calculations include systematically applied approximations intended to make calculations computationally feasible while still capturing as much information about important contributions to the computed wave functions as well as to observable properties such as structures, spectra, and thermodynamic properties. Quantum chemistry is also concerned with the computation of quantum effects on molecular dynamics and chemical kinetics. Chemists rely heavily on spectroscopy through which information regarding the quantization of energy on a molecular scale can be obtained. Common methods are infra-red (IR) spectroscopy, nuclear magnetic r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chemical Bonding
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding. Strong chemical bonding arises from the sharing or transfer of electrons between the participating atoms. Since opposite electric charges attract, the negatively charged electrons surrounding the nucleus and the positively charged protons within a nucleus attract each other. An electron positioned between two nuclei will be attracted to both of them, and the nuclei will be attracted toward electrons in this position. This attraction constitu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Mechanics
Molecular mechanics uses classical mechanics to model molecular systems. The Born–Oppenheimer approximation is assumed valid and the potential energy of all systems is calculated as a function of the nuclear coordinates using Force field (chemistry), force fields. Molecular mechanics can be used to study molecule systems ranging in size and complexity from small to large biological systems or material assemblies with many thousands to millions of atoms. All-atomistic molecular mechanics methods have the following properties: * Each atom is simulated as one particle * Each particle is assigned a radius (typically the van der Waals radius), polarizability, and a constant net charge (generally derived from quantum calculations and/or experiment) * Bonded interactions are treated as ''springs'' with an equilibrium distance equal to the experimental or calculated bond length Variants on this theme are possible. For example, many simulations have historically used a ''united-atom'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Frequency
In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit time (for example, in rotation) or the rate of change of the phase of a sinusoidal waveform (for example, in oscillations and waves), or as the rate of change of the argument of the sine function. Angular frequency (or angular speed) is the magnitude of the pseudovector quantity angular velocity.(UP1) One turn is equal to 2''π'' radians, hence \omega = \frac = , where: *''ω'' is the angular frequency (unit: radians per second), *''T'' is the period (unit: seconds), *''f'' is the ordinary frequency (unit: hertz) (sometimes ''ν''). Units In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. The unit hertz (Hz) is dimensionally equivalent, but by conventi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavenumber
In the physical sciences, the wavenumber (also wave number or repetency) is the '' spatial frequency'' of a wave, measured in cycles per unit distance (ordinary wavenumber) or radians per unit distance (angular wavenumber). It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (''ordinary frequency'') or radians per unit time (''angular frequency''). In multidimensional systems, the wavenumber is the magnitude of the '' wave vector''. The space of wave vectors is called '' reciprocal space''. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, electron diffraction, and elementary particle physics. For quantum mechanical waves, the wavenumber multiplied by the reduced Planck's constant is the '' canonical momentum''. Wavenumber can be used to specify quantities other than spatial frequency. For example, in optical spectroscopy, it is of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensional Analysis
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as miles vs. kilometres, or pounds vs. kilograms) and tracking these dimensions as calculations or comparisons are performed. The conversion of units from one dimensional unit to another is often easier within the metric or the SI than in others, due to the regular 10-base in all units. ''Commensurable'' physical quantities are of the same kind and have the same dimension, and can be directly compared to each other, even if they are expressed in differing units of measure, e.g. yards and metres, pounds (mass) and kilograms, seconds and years. ''Incommensurable'' physical quantities are of different kinds and have different dimensions, and can not be directly compared to each other, no matter what units they are expressed in, e.g. metres and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matrix (mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and, un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laguerre Polynomial
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre's equation: xy'' + (1 - x)y' + ny = 0 which is a second-order linear differential equation. This equation has nonsingular solutions only if is a non-negative integer. Sometimes the name Laguerre polynomials is used for solutions of xy'' + (\alpha + 1 - x)y' + ny = 0~. where is still a non-negative integer. Then they are also named generalized Laguerre polynomials, as will be done here (alternatively associated Laguerre polynomials or, rarely, Sonine polynomials, after their inventor Nikolay Yakovlevich Sonin). More generally, a Laguerre function is a solution when is not necessarily a non-negative integer. The Laguerre polynomials are also used for Gaussian quadrature to numerically compute integrals of the form \int_0^\infty f(x) e^ \, dx. These polynomials, usually denoted , , …, are a polynomial sequence which may be defined by the Rodrigues formula ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenstate
In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces. Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum. For example, when dealing with the energy spectrum of the electron in a hydrogen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
