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Drude Particle
Drude particles are model oscillators used to simulate the effects of electronic polarizability in the context of a classical molecular mechanics force field. They are inspired by the Drude model of mobile electrons and are used in the computational study of proteins, nucleic acids, and other biomolecules. Classical Drude oscillator Most force fields in current practice represent individual atoms as point particles interacting according to the laws of Newtonian mechanics. To each atom, a single electric charge is assigned that doesn't change during the course of the simulation. However, such models cannot have induced dipoles or other electronic effects due to a changing local environment. Classical Drude particles are massless virtual sites carrying a partial electric charge, attached to individual atoms via a harmonic spring. The spring constant and relative partial charges on the atom and associated Drude particle determine its response to the local electrostatic field, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Oscillator
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum and alternating current. Oscillations can be used in physics to approximate complex interactions, such as those between atoms. Oscillations occur not only in mechanical systems but also in dynamic systems in virtually every area of science: for example the beating of the human heart (for circulation), business cycles in economics, predator–prey population cycles in ecology, geothermal geysers in geology, vibration of strings in guitar and other string instruments, periodic firing of nerve cells in the brain, and the periodic swelling of Cepheid variable stars in astronomy. The term ''vibration'' is precisely used to describe a mechanical oscillation. Oscillation, especially rapid oscillation, may be an undesirable phenomenon in pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spring Constant
In physics, Hooke's law is an empirical law which states that the force () needed to extend or compress a spring (device), spring by some distance () Proportionality (mathematics)#Direct_proportionality, scales linearly with respect to that distance—that is, where is a constant factor characteristic of the spring (i.e., its stiffness), and is small compared to the total possible deformation of the spring. The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660. Hooke's equation holds (to some extent) in many other situations where an elasticity (physics), elastic body is Deformation (physics), deformed, such as wind blowing on a tall building, and a musician plucking a string (music), string of a guitar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many Body Dispersion .
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Many may refer to: * grammatically plural in number *an English quantifier used with count nouns indicating a large but indefinite number of; at any rate, more than a few ;Place names * Many, Moselle, a commune of the Moselle department in France * Mány, a village in Hungary * Many, Louisiana, a town in the United States * Many, Masovian Voivodeship, east-central Poland Surname * Moshe Many, Israeli urologist; President of Tel Aviv University, and President of Ashkelon Academic College Ashkelon Academic College ( he, המכללה האקדמית אשקלון, ''HaMiklala HaAkademit Ashkelon'') is a public college in Ashkelon, Israel. The college has two faculties The School of Economics and Social Work for management, logistics, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
London Dispersion Force
London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, fluctuating induced dipole bonds or loosely as van der Waals forces) are a type of intermolecular force acting between atoms and molecules that are normally electrically symmetric; that is, the electrons are symmetrically distributed with respect to the nucleus. They are part of the van der Waals forces. The LDF is named after the German physicist Fritz London. They are the weakest intermolecular force. Introduction The electron distribution around an atom or molecule undergoes fluctuations in time. These fluctuations create instantaneous electric fields which are felt by other nearby atoms and molecules, which in turn adjust the spatial distribution of their own electrons. The net effect is that the fluctuations in electron positions in one atom induce a corresponding redistribution of electrons in other atoms, such that the electron motions become corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electronic Correlation
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how much the movement of one electron is influenced by the presence of all other electrons. Atomic and molecular systems Within the Hartree–Fock method of quantum chemistry, the antisymmetric wave function is approximated by a single Slater determinant. Exact wave functions, however, cannot generally be expressed as single determinants. The single-determinant approximation does not take into account Coulomb correlation, leading to a total electronic energy different from the exact solution of the non-relativistic Schrödinger equation within the Born–Oppenheimer approximation. Therefore, the Hartree–Fock limit is always above this exact energy. The difference is called the ''correlation energy'', a term coined by Löwdin. The concept of the correlation energy was studied earlier by Wigner. A certain amount of electron c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perturbation Theory (quantum Mechanics)
In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates) can be expressed as "corrections" to those of the simple system. These corrections, being small compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one. In effect, it is describing a complicated unsolved system using a simple, solvable system. Approximate Hamiltonians Perturbation theory is an important tool for de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is equal to one event per second. The period is the interval of time between events, so the period is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), the period, —the interval at which the beats repeat—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term ''frequency'' is defined as the number of cycles or vibrations per unit of time. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Harmonic Oscillator
量子調和振動子 は、 古典調和振動子 の 量子力学 類似物です。任意の滑らかな ポテンシャル は通常、安定した 平衡点 の近くで 調和ポテンシャル として近似できるため、最も量子力学における重要なモデル系。さらに、これは正確な 解析解法が知られている数少ない量子力学系の1つである。 author=Griffiths, David J. , title=量子力学入門 , エディション=2nd , 出版社=プレンティス・ホール , 年=2004 , isbn=978-0-13-805326-0 , author-link=David Griffiths (物理学者) , URL アクセス = 登録 , url=https://archive.org/details/introductiontoel00grif_0 One-dimensional harmonic oscillator Hamiltonian and energy eigenstates 粒子の ハミルトニアン は次のとおりです。 \hat H = \frac + \frac k ^2 = \frac + \frac m \omega^2 ^2 \, , ここで、 は粒子の質量、 は力定数、\omega = \sqrt は 動子の [角周波数 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Water Model
In computational chemistry, a water model is used to simulate and thermodynamically calculate water clusters, liquid water, and aqueous solutions with explicit solvent. The models are determined from quantum mechanics, molecular mechanics, experimental results, and these combinations. To imitate a specific nature of molecules, many types of models have been developed. In general, these can be classified by the following three points; (i) the number of interaction points called ''site'', (ii) whether the model is rigid or flexible, (iii) whether the model includes polarization effects. An alternative to the explicit water models is to use an implicit solvation model, also termed a continuum model, an example of which would be the COSMO solvation model or the polarizable continuum model (PCM) or a hybrid solvation model. Simple water models The rigid models are considered the simplest water models and rely on non-bonded interactions. In these models, bonding interactions are imp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lagrangian Mechanics
In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in his 1788 work, '' Mécanique analytique''. Lagrangian mechanics describes a mechanical system as a pair (M,L) consisting of a configuration space M and a smooth function L within that space called a ''Lagrangian''. By convention, L = T - V, where T and V are the kinetic and potential energy of the system, respectively. The stationary action principle requires that the action functional of the system derived from L must remain at a stationary point (a maximum, minimum, or saddle) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using Lagrange's equations. Introduction Suppose there exists a bead sliding around on a wire, or a swinging simple p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Self Consistent Field
The self is an individual as the object of that individual’s own reflective consciousness. Since the ''self'' is a reference by a subject to the same subject, this reference is necessarily subjective. The sense of having a self—or ''selfhood''—should, however, not be confused with subjectivity itself. Ostensibly, this sense is directed outward from the subject to refer inward, back to its "self" (or itself). Examples of psychiatric conditions where such "sameness" may become broken include depersonalization, which sometimes occurs in schizophrenia: the self appears different from the subject. The first-person perspective distinguishes selfhood from personal identity. Whereas "identity" is (literally) sameness and may involve categorization and labeling, selfhood implies a first-person perspective and suggests potential uniqueness. Conversely, we use "person" as a third-person reference. Personal identity can be impaired in late-stage Alzheimer's disease and in other neu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electric Field Gradient
In atomic, molecular, and solid-state physics, the electric field gradient (EFG) measures the rate of change of the electric field at an atomic nucleus generated by the electronic charge distribution and the other nuclei. The EFG couples with the nuclear electric quadrupole moment of quadrupolar nuclei (those with spin quantum number greater than one-half) to generate an effect which can be measured using several spectroscopic methods, such as nuclear magnetic resonance (NMR), microwave spectroscopy, electron paramagnetic resonance (EPR, ESR), nuclear quadrupole resonance (NQR), Mössbauer spectroscopy or perturbed angular correlation (PAC). The EFG is non-zero only if the charges surrounding the nucleus violate cubic symmetry and therefore generate an inhomogeneous electric field at the position of the nucleus. EFGs are highly sensitive to the electronic density in the immediate vicinity of a nucleus. This is because the EFG operator scales as ''r''−3, where ''r'' is the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
