【VIP专享】第一性原理简介

认知升级之第一性原理一、本文概述1、认知升级的重要性认知升级是人类思维方式的核心转变，它对于个人和社会的发展具有重要意义。

随着科技的迅速发展和全球化的推进，我们所处的环境变得越来越复杂，面对的问题也越来越具有挑战性。

在这样的背景下，只有不断升级我们的认知，才能更好地适应这个快速变化的世界。

认知升级的重要性体现在以下几个方面。

首先，认知升级可以帮助我们更好地理解周围的事物和现象。

在现代社会，信息量庞大且更新速度极快，只有不断提升我们的认知水平，才能更好地把握和理解这些信息，从而做出更为明智的决策。

其次，认知升级有助于我们克服认知偏差和惯性思维。

人们在思考问题时常常受到惯性思维和认知偏差的影响，导致做出错误的判断或决策。

通过认知升级，我们可以克服这些思维障碍，以更加客观、全面的视角看待问题。

再者，认知升级能够提高我们的学习能力和创新思维。

随着认知水平的提升，我们能够更好地吸收新知识和掌握新技能，从而提高自己的学习能力和创新思维。

这对于个人的职业发展和社会的创新进步都具有重要的推动作用。

最后，认知升级有助于我们更好地应对未来的挑战和不确定性。

随着科技的发展和社会的变革，未来的挑战和不确定性将更加复杂和多变。

通过认知升级，我们可以培养更为深刻的洞察力和预见性，以更好地应对未来的挑战和不确定性。

总之，认知升级对于个人和社会的发展具有重要意义。

只有不断提升我们的认知水平，才能更好地适应这个快速变化的世界，并在未来的挑战中立于不败之地。

2、第一性原理的定义与理解第一性原理是指在一个系统中，将所有因素考虑进去后，得出的一种最基本、最本质的结论或推论。

这个概念最早由古希腊哲学家亚里士多德提出，他认为第一性原理是自明的、不可证明的，是一切其他知识的基础。

在现代哲学、数学、物理学等学科中，第一性原理被广泛应用，成为一种重要的思维方式和方法论。

第一性原理的定义可以从不同的角度来阐述。

从哲学的角度来看，第一性原理可以被理解为一种本源性的真理，是其他一切知识的基础。

第一性原理是什么第一性原理怎么用1什么是第一性原理根据原子核和电子互相作用的原理及其基本运动规律，运用，从具体要求出发，经过一些近似处理后直接求解的算法，称为第一性原理。

广义的第一原理包括两大类，以Hartree-Fock自洽场计算为基础的从头算和（DFT计算。

从定义可以看出第一性原理涉及到量子力学、、Hartree-Fock自洽场、等许多对我来说很陌生的物理化学定义。

因此我通过向师兄请教和上网查资料一点点的了解并学习这些知识。

2第一性原理的作用以密度泛函理论（DFT）为基础以及在此基础上发展起来的简单而具有一定精度的局域密度近似（LDA）和广义梯度近似（GGA）的第一性原理电子结构计算方法，与传统的解析方法一样，不但能够给出描述体系微观电子特性的物理量如波函数、态密度、费米面、电子间互作用势等，以及在此基础上所得到的体现体系宏观物理特性的参量如结合能、电离能、比热、电导、光电子谱、穆斯堡尔谱等等，而且它还可以帮助人们预言许多新的物理现象和物理规律。

密度泛函计算的一些结果能够与实验直接进行比较一些应用程序的发展乃至商业软件的发布，导致了基于密度泛函理论的第一原理计算方法的广泛应用。

密度泛函理论（DFT）为第一性原理中的一类，在物理系、化学、材料科学以及其他工程领域中，密度泛函理论（DFT及其计算已经快速发展成为材料建模模拟的一种“标准工具”。

密度泛函理论可以计算预测固体的晶体结构、晶格参数、能带结构、态密度（DOS、光学性能、磁性能以及原子集合的总能等等。

3第一性原理怎么用目前我所学到的利用第一性原理的软件为Material Studio 、VASP软件。

其中Materials Studio （简称MS是专门为材料科学领域研究者幵发的一款可运行在PC上的模拟软件。

使化学及材料科学的研究者们能更方便地建立三维结构模型，并对各种晶体、无定型以及高分子材料的性质及相关过程进行深入的研究。

模拟的内容包括了催化剂、聚合物、固体及表面、晶体与衍射、化学反应等材料和化学研究领域的主要课题。

第一性原理发展简史（2）——霍恩贝格-科恩定理与里兹变分法•关于第一性原理这个词语在1900前哲学与数学中使用的问题很多人追问文中一段话出处，其实严格意义上逐字逐句的表述应该算作者原创，并不是直接引用，但是这样论述并非是毫无根据的。

这段内容最初是作者学生时代一门课程老师所述，写文章时已经默认这是本领域中学界的一个共识。

今天的文字资料中第一性原理(first principle)一般已经默认就是指计算材料学中的第一性原理计算，个别国家特别是德国、奥地利等德语区为了学术严谨起见则更愿意使用ab-initia（又译为从头算），美国、澳大利亚、英国等英语区国家则是二者并用，中文环境下由于历史原因主要是源自外文翻译与编辑，因此主流说法认为汉语环境“第一性原理”仅指代计算材料学。

上期之所以说1900年前第一性原理主要用于哲学、数学、理论物理，根据与逻辑如下：亚里士多德时代已经诞生了第一性原理(firstprinciple)的定义，而计算材料学的源头——量子力学诞生于1900年之后。

1900年以前的哲学、数学著作中时常可以见到first principle 这一术语的使用，当然这些著作今天流通的修订本或者是再编版已不再使用第一性原理的表述：哲学中往往用priori-principle替代之前的第一性原理表述；数学中今天已经统一使用规范术语“公理”（axioms）表述，因此今天再说第一性原理涵盖哲学、数学已经有些不合时宜。

另外第一性原理这个词语本身的使用一定程度上也体现了欧洲16世纪以来，人文主义的兴起初期理论、知识是以人为本、以人为核心的，它的出发点是希望不依赖（那时认为是上帝或神创造的）物质实验、测量建立起一个完全由人的意识引出的（与神学足以抗衡的）理论体系。

这一点上与中华神话《夸父逐日》的精髓类似，反映出人类在探索自然时不屈、奋进的精神。

•关于分子动力学是否属于第一性原理此处的分子动力学特指molecule dynamics，简称MD，中文环境中由于各种原因“分子动力学”可一词可能涵盖其他意义，如作者接触过的物理化学中的分子马达领域将相关的内容称为分子动力学。

第一性原理在混沌大学，到底要学什么？怎么学？•思维模型•刻意练习混沌大学三大思维模型1.非连续性2.第一原理3.第二曲线“用第一性原理，跨越非连续性，发现第二曲线”《世界觀: 現代年輕人必懂的科學哲學和科學史》第1讲『第一性原理』Part 1常人的逻辑思维，有且仅有两种：归纳法、演绎法。

一、归纳法归纳法是人类最基础、最常见的用智方式，借助感觉和经验来积累知识，从特殊到一般。

几千年来，我们一直使用这个简单的归纳推理，99%人类知识建立在基于经验的归纳法上。

无师自通，也理所当然。

培根《新工具》提倡科学的归纳法，迄今，归纳法仍是常规科学的主要工具。

创业者最擅长归纳法，比如商业计划书中的上升曲线。

休谟是经验论者，他相信“知识源于感觉经验”。

但他第一个发现了归纳法的谬误：即使所有前提都正确，结论依然可能错误。

归纳法是对经验事实的简约处理，仅能收集部分信息，却得出普遍判断。

归纳法有一特征：“只能证伪，不能证明”。

换句话说，归纳法得出的知识一定是错误的，就像我们的眼睛看到外界的事实，一定会进行简约化和扭曲一样。

归纳法，我们的逻辑对经验事实进行处理的结果，也一定是简约和扭曲的。

既然每个人的经验都来自归纳法，你必须承认自己的认知有可能是错的。

——这就是“可证伪性” 的态度。

为什么我们要用归纳法呢？我们是要求存，而不是求真。

二、演绎法常人的思维逻辑只有两种，归纳法有根本问题，演绎法是不是好一点呢？•归纳法：从具象到抽象。

•演绎法：从抽象到抽象。

可以从已知思想推出未知思想。

演绎法的一大特征/好处：你可以从已知的知识里面推演出未知的知识来。

1%的人类知识来自演绎法，但这却是最重要的那一小部分知识。

哲科思维的重要特征“假设与检验” 或者“假设与证明”所有大科学家都是演绎法。

——张守晟抽象思维演绎法的坏处是速度慢；好处是可迁移性。

可迁移性：抽象东西，它生下来就是抽象的，抽象的东西可以从不同领域里边来迁移。

一旦在逻辑上导通一个共同的抽象概念，与此相关的所有具象问题，立即全部化解。

第一性原理是什么？第一性原理有什么用？第一性原理怎么用？怎样将第一性原理与实践结合起来？什么是第一性原理？1原理，量子力学根据原子核和电子互相作用的原理及其基本运动规律，运用第一性称为经过一些近似处理后直接求解薛定谔方程的算法，从具体要求出发，计算为基础的从头算。

广义的第一原理包括两大类，以Hartree-Fock自洽场原理DFT）计算。

密度泛函理论和（自从定义可以看出第一性原理涉及到量子力学、薛定谔方程、Hartree-Fock因此我通过向师兄密度泛函理论等许多对我来说很陌生的物理化学定义。

洽场、请教和上网查资料一点点的了解并学习这些知识。

2第一性原理的作用为基础以及在此基础上发展起来的简单而具有一定精(DFT)以密度泛函理论,的第一性原理电子结构计算方法和广义梯度近似(GGA)度的局域密度近似(LDA)不但能够给出描述体系微观电子特性的物理量如波函与传统的解析方法一样,以及在此基础上所得到的体现体系宏,数、态密度、费米面、电子间互作用势等,穆斯堡尔谱等等比热、电导、观物理特性的参量如结合能、电离能、光电子谱、密度泛函计算的一些而且它还可以帮助人们预言许多新的物理现象和物理规律。

．导致了,结果能够与实验直接进行比较,一些应用程序的发展乃至商业软件的发布基于密度泛函理论的第一原理计算方法的广泛应用。

为第一性原理中的一类，在物理系、化学、材料科学以(DFT)密度泛函理论）及其计算已经快速发展成为材料建模DFT及其他工程领域中，密度泛函理论（模拟的一种“标准工具”。

密度泛函理论可以计算预测固体的晶体结构、晶格参数、能带结构、态密度（DOS）、光学性能、磁性能以及原子集合的总能等等。

3第一性原理怎么用？其中ASP、软件。

V目前我所学到的利用第一性原理的软件为Material Studio）是专门为材料科学领域研究者开发的一款可运行在MSMaterials Studio（简称使化学及材料科学的研究者们能更方便地建立三维结构模型，上的模拟软件。

Condensed matter physicsFrom Wikipedia, the free encyclopediaCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the constituents are strong. The most familiar examples of condensed phases are solids and liquids, which arise from the bonding and electromagnetic force between atoms. More exotic condensed phases include the superfluid and the Bose-Einstein condensate found in certain atomic systems at very low temperatures, the superconducting phase exhibited by conduction electrons in certain materials, and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics. Much progress has also been made in theoretical condensed matter physics. By one estimate, one third of all American physicists identify themselves as condensed matter physicists. Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term "condensed matter physics" was apparently coined by Philip Anderson and Volker Heine when they renamed their research group at Cavendish Laboratory - previously "solid-state theory" - in 1967. In 1978, the Division of Solid State Physics at the American Physical Society was renamed as the Division of Condensed Matter Physics. Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.One of the reasons for calling the field "condensed matter physics" is that many of the concepts and techniques developed for studying solids actually apply to fluid systems. For instance, the conduction electrons in an electrical conductor form a type of quantum fluid with essentially the same properties as fluids made up of atoms. In fact, the phenomenon of superconductivity, in which the electrons condense into a new fluid phase in which they can flow without dissipation, is very closely analogous to the superfluid phase found in helium 3 at low temperatures.Fermi energyThe Fermi energy is a concept in quantum mechanics usually referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature. This article requires a basic knowledge of quantum mechanics.IntroductionIn quantum mechanics, a group of particles known as fermions (for example, electrons, protons and neutrons are fermions) obey the Pauli exclusion principle. This principle states that two identical fermions can not be in the same quantum state. The states are labeled by a set of quantum numbers. In a system containing many fermions (like electrons in a metal) each fermion will have a different set of quantum numbers. To determine the lowest energy a system of fermions can have, we first group the states in sets with equal energy and order these sets by increasing energy. Starting with an empty system, we then add particles one at a time, consecutively filling up the unoccupied quantum states with lowest-energy. When all the particles have been put in, the Fermi energy is the energy of the highest occupied state. What this means is that even if we have extracted all possible energy from a metal by cooling it down to near absolute zero temperature (0 kelvins), the electrons in the metal are still moving around, the fastest ones would be moving at a velocity that corresponds to a kinetic energy equal to the Fermi energy. This is the Fermi velocity. The Fermi energy is one of the important concepts of condensed matter physics. It is used, for example, to describe metals, insulators, and semiconductors. It is a very important quantity in the physics of superconductors, in the physics of quantum liquids like low temperature helium (both normal 3He and superfluid 4He), and it is quite important to nuclear physics and to understand the stability of white dwarf stars against gravitational collapse.The Fermi energy (E F) of a system of non-interacting fermions is the increase in the ground state energy when exactly one particle is added to the system. It can also be interpreted as the maximum energy of an individual fermion in this ground state. The chemical potential at zero temperature is equal to the Fermi energy.Illustration of the concept for a one dimensional square wellThe one dimensional infinite square well is a model for a one dimensional box. It is a standard model-system in quantum mechanics for which the solution for a single particle is well known. The levels are labeled by a single quantum number n and the energies are given by.Suppose now that instead of one particle in this box we have N particles in the box and that these particles are fermions with spin 1/2. Then only two particles can have the same energy i.e. two particles can have theenergy of , or two particles can have energy E2 = 4E1 and so forth. The reason that two particles can have the same energy is that a spin-1/2 particle can have a spin of 1/2 (spin up) or a spin of -1/2 (spin down), leading to two states for each energy level. When we look at the total energy of this system, the configuration for which the total energy is lowest (the ground state), is the configuration where all the energy levels up to n=N/2 are occupied and all the higher levels are empty. The Fermi energy is therefore.The three-dimensional caseThe three-dimensional isotropic case is known as the fermi sphere.Let us now consider a three-dimensional cubical box that has a side length L (see infinite square well). This turns out to be a very good approximation for describing electrons in a metal. The states are nowlabeled by three quantum numbers nx , ny, and nz. The single particleenergies aren x, n y, n z are positive integers.There are multiple states with the same energy, for example E100 = E010 = E001. Now let's put N non-interacting fermions of spin 1/2 into this box. To calculate the Fermi energy, we look at the case for N is large.If we introduce a vector then each quantum state corresponds to a point in 'n-space' with EnergyThe number of states with energy less than Efis equal to the number of states that lie within a sphere of radius in the region of n-spacewhere nx , ny, nzare positive. In the ground state this number equals thenumber of fermions in the system.The free fermions that occupy the lowest energy states form a sphere in momentum space. The surface of this sphere is the Fermi surface.the factor of two is once again because there are two spin states, the factor of 1/8 is because only 1/8 of the sphere lies in the region where all n are positive. We findso the Fermi energy is given byWhich results in a relationship between the fermi energy and the number of particles per volume (when we replace L2 with V2/3):The total energy of a fermi sphere of N0 fermions is given byTypical fermi energies White dwarfsStars known as White dwarfs have mass comparable to our Sun, but have a radius about 100 times smaller. The high densities means that the electrons are no longer bound to single nuclei and instead form a degenerate electron gas. The number density of electrons in a White dwarf are on the order of 1036 electrons/m3. This means their fermi energy is:Another typical example is that of the particles in a nucleus of an atom. The radius of the nucleus is roughly:where A is the number of nucleons.The number density of nucleons in a nucleus is therefore:Now since the fermi energy only applies to fermions of the same type, one must divide this density in two. This is because the presence of neutrons does not affect the fermi energy of the protons in the nucleus, and vice versa.So the fermi energy of a nucleus is about:The radius of the nucleus admits deviations around the value mentioned above, so a typical value for the fermi energy usually given is 38 MeV.Fermi levelThe Fermi level is the highest occupied energy level at absolute zero, that is, all energy levels up to the Fermi level are occupied by electrons. Since fermions cannot exist in identical energy states (see the exclusion principle), at absolute zero, electrons pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. [1] In this state (at 0 K), the average energy of an electron is given by:where E f is the Fermi energy.The Fermi momentum is the momentum of fermions at the Fermi surface. The Fermi momentum is given by:where m e is the mass of the electron.This concept is usually applied in the case of dispersion relations between the energy and momentum that do not depend on the direction. In more general cases, one must consider the Fermi energy.The Fermi velocity is the velocity of fermions at the Fermi surface. It is defined by:where m e is the mass of the electron.Below the Fermi temperature, a substance gradually expresses more and more quantum effects of cooling. The Fermi temperature is defined by:where k is the Boltzmann constant.Quantum mechanicsAccording to quantum mechanics, fermions -- particles with a half-integer spin, usually 1/2, such as electrons -- follow the Pauli exclusion principle, which states that multiple particles may not occupy the same quantum state. Consequently, fermions obey Fermi-Dirac statistics. The ground state of a non-interacting fermion system is constructed bystarting with an empty system and adding particles one at a time, consecutively filling up the lowest-energy unoccupied quantum states. When the desired number of particles has been reached, the Fermi energy is the energy of the highest occupied molecular orbital (HOMO). Within conductive materials, this is equivalent to the lowest unoccupied molecular orbital (LUMO); however, within other materials there will be a significant gap between the HOMO and LUMO on the order of 2-3 eV.Pinning of Fermi levelWhen the energy density of surface states is very high (>1013/cm2), the position of the Fermi level is determined by the neutral level of the Surface states [2] and becomes independent of Work Function [3] variations.Free electron gasIn the free electron gas, the quantum mechanical version of an ideal gas of fermions, the quantum states can be labeled according to their momentum. Something similar can be done for periodic systems, such as electrons moving in the atomic lattice of a metal, using something called the "quasi-momentum" or "crystal momentum" (see Bloch wave). In either case, the Fermi energy states reside on a surface in momentum space known as the Fermi surface. For the free electron gas, the Fermi surface is the surface of a sphere; for periodic systems, it generally has a contorted shape (see Brillouin zones). The volume enclosed by the Fermi surface defines the number of electrons in the system, and the topology is directly related to the transport properties of metals, such as electrical conductivity. The study of the Fermi surface is sometimes called Fermiology. The Fermi surfaces of most metals are well studied both theoretically and experimentally.The Fermi energy of the free electron gas is related to the chemical potential by the equationwhere E F is the Fermi energy, k is the Boltzmann constant and T is temperature. Hence, the chemical potential is approximately equal to the Fermi energy at temperatures of much less than the characteristic Fermi temperature E F/k. The characteristic temperature is on the order of 105K for a metal, hence at room temperature (300 K), the Fermi energy and chemical potential are essentially equivalent. This is significant since it is the chemical potential, not the Fermi energy, which appears in Fermi-Dirac statistics.ReferencesKroemer, Herbert; Kittel, Charles (1980). Thermal Physics (2nd ed.). W.H. Freeman Company. ISBN 0-7167-1088-9.Table of fermi energies, velocities, and temperatures for various elements.a discussion of fermi gases and fermi temperatures.Fermi Surface:In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state.TheoryFormally speaking, the Fermi surface is a surface of constant energy in-space where is the wavevector of the electron. At absolute zerotemperature the Fermi surface separates the unfilled electronic orbitals from the filled ones. The energy of the highest occupied orbitals is known as the Fermi energy E F which, in the zero temperature case, resides on the Fermi level. The linear response of a metal to an electric, magnetic or thermal gradient is determined by the shape of the Fermi surface, because currents are due to changes in the occupancy of states near the Fermi energy. Free-electron Fermi surfaces are spheres of radiusdetermined by the valence electron concentration whereis the reduced Planck's constant. A material whose Fermi level falls in a gap between bands is an insulator or semiconductor depending on the size of the bandgap. When a material's Fermi level falls in a bandgap, there is no Fermi surface.A view of the graphite Fermi surface at the corner H points of the Brillouin zone showing the trigonal symmetry of the electron and hole pockets.Materials with complex crystal structures can have quite intricate Fermi surfaces. The figure illustrates the anisotropic Fermi surface of graphite, which has both electron and hole pockets in its Fermi surfacedue to multiple bands crossing the Fermi energy along the direction. Often in a metal the Fermi surface radius k F is larger than the size of the first Brillouin zone which results in a portion of the Fermi surface lying in the second (or higher) zones. As with the band structure itself,the Fermi surface can be displayed in an extended-zone scheme whereis allowed to have arbitrarily large values or a reduced-zone scheme wherewavevectors are shown modulo where a is the lattice constant. Solidswith a large density of states at the Fermi level become unstable at low temperatures and tend to form ground states where the condensation energy comes from opening a gap at the Fermi surface. Examples of such ground states are superconductors, ferromagnets, Jahn-Teller distortions and spin density waves.The state occupancy of fermions like electrons is governed by Fermi-Dirac statistics so at finite temperatures the Fermi surface is accordingly broadened. In principle all fermion energy level populations are bound by a Fermi surface although the term is not generally used outside of condensed-matter physics.Experimental determinationde Haas-van Alphen effect. Electronic Fermi surfaces have been measured through observation of the oscillation of transport properties in magnetic fields H, for example the de Haas-van Alphen effect (dHvA) andthe Shubnikov-De Haas effect (SdH). The former is an oscillation in magnetic susceptibility and the latter in resistivity. The oscillations are periodic versus 1 / H and occur because of the quantization of energy levels in the plane perpendicular to a magnetic field, a phenomenon first predicted by Lev Landau. The new states are called Landau levels and areseparated by an energy where ωc = eH / m*c is called the cyclotron frequency, e is the electronic charge, m*is the electron effective mass and c is the speed of light. In a famous result, Lars Onsager proved that the period of oscillation ΔH is related to the cross-section of the Fermisurface (typically given in ) perpendicular to the magnetic fielddirection by the equation . Thus the determination of the periods of oscillation for various applied field directions allows mapping of the Fermi surface.Observation of the dHvA and SdH oscillations requires magnetic fields large enough that the circumference of the cyclotron orbit is smaller than a mean free path. Therefore dHvA and SdH experiments are usually performed at high-field facilities like the High Field Magnet Laboratory in Netherlands, Grenoble High Magnetic Field Laboratory in France, the Tsukuba Magnet Laboratory in Japan or the National High Magnetic Field Laboratory in the United States.Fermi surface of BSCCO measured by ARPES. The experimental data shown as an intensity plot in yellow-red-black scale. Green dashed rectagle represents the Brillouin zone of the CuO2 plane of BSCCO.Angle resolved photoemission.The most direct experimental technique to resolve the electronic structure of crystals in the momentum-energy space (see reciprocal lattice), and, consequently, the Fermi surface, is the angle resolved photoemission spectroscopy (ARPES). An example of the Fermi surface of superconducting cuprates measured by ARPES is shown in figure.Two photon positron annihilation.With positron annihilation the two photons carry the momentum of the electron away; as the momentum of a thermalized positron is negligible, in this way also information about the momentum distribution can be obtained. Because the positron can be polarized, also the momentum distribution for the two spin states in magnetized materials can be obtained. Another advantage with De Haas-Van Alphen-effect is that the technique can be applied to non-dilute alloys. In this way the first determination of a smeared Fermi surface in a 30% alloy has been obtained in 1978.ReferencesN. Ashcroft and N.D. Mermin, Solid-State Physics, ISBN 0-03-083993-9. W.A. Harrison, Electronic Structure and the Properties of Solids, ISBN 0-486-66021-4.VRML Fermi Surface DatabaseBrillouin zoneFrom Wikipedia, the free encyclopediaJump to: navigation, searchBrillouin zoneIn mathematics and solid state physics, the first Brillouin zone is a uniquely defined primitive cell of the reciprocal lattice in the frequency domain. It is found by the same method as for the Wigner-Seitz cell inthe Bravais lattice. The importance of the Brillouin zone stems from the Bloch wave description of waves in a periodic medium, in which it is found that the solutions can be completely characterized by their behavior in a single Brillouin zone.Taking the surfaces at the same distance from one element of the lattice and its neighbours, the volume included is the first Brillouin zone. Another definition is as the set of points in k-space that can be reached from the origin without crossing any Bragg plane.There are also second, third, etc., Brillouin zones, corresponding to a sequence of disjoint regions (all with the same volume) at increasing distances from the origin, but these are used more rarely. As a result, the first Brillouin zone is often called simply the Brillouin zone. (In general, the n-th Brillouin zone consist of the set of points that can be reached from the origin by crossing n− 1 Bragg planes.)A related concept is that of the irreducible Brillouin zone, which is the first Brillouin zone reduced by all of the symmetries in the point group of the lattice.The concept of a Brillouin zone was developed by Leon Brillouin (1889-1969), a French physicist.Critical pointsFirst Brillouin zone of FCC lattice showing symmetry labels for high symmetry lines and points Several points of high symmetry are of special interest – these are called critical points.[1]Symbol DescriptionΓCenter of the Brillouin zoneSimple cubeM Center of an edgeR Corner pointX Center of a faceFace-centered cubicK Middle of an edge joining two hexagonal facesL Center of a hexagonal faceU Middle of an edge joining a hexagonal and a square faceW Corner pointX Center of a square faceBody-centered cubicH Corner point joining four edgesN Center of a faceP Corner point joining three edgesHexagonalA Center of a hexagonal faceH Corner pointK Middle of an edge joining two rectangular facesL Middle of an edge joining a hexagonal and a rectangular faceM Center of a rectangular faceReferences1.^ Harald Ibach & Hans Lüth, Solid-State Physics, An Introduction to Principles of MaterialsScience, corrected second printing of the second edition, 1996, Springer-Verlag, ISBN3-540-58573-72.Charles Kittel, Introduction to Solid State Physics (Wiley: New York, 1996).3.Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).4.Léon Brillouin Les électrons dans les métaux et le classement des ondes de de Brogliecorrespondantes Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences, 191, 292 (1930). (original article)Bloch waveFrom Wikipedia, the free encyclopediaA Bloch wave or Bloch state, named after Felix Bloch, is the wavefunction of a particle (usually, an electron) placed in a periodic potential. It consists of the product of a plane wave envelope function and a periodicfunction (periodic Bloch function) which has the same periodicity as the potential:Bloch wave in siliconThe result that the eigenfunctions can be written in this form for a periodic system is called Bloch's theorem. The corresponding energyeigenvalue is Єn (k)= Єn(k + K), periodic with periodicity K of a reciprocallattice vector. Because the energies associated with the index n vary continuously with wavevector k we speak of an energy band with band index n. Because the eigenvalues for given n are periodic in k, all distinct values of Єn(k) occur for k-values within the first Brillouin zone of the reciprocal lattice.More generally, a Bloch-wave description applies to any wave-like phenomenon in a periodic medium. For example, a periodic dielectric in electromagnetism leads to photonic crystals, and a periodic acoustic medium leads to phononic crystals. It is generally treated in the different forms of the dynamical theory of diffraction.The plane wave wavevector (or Bloch wavevector) k (multiplied by the reduced Planck's constant, this is the particle's crystal momentum) is unique only up to a reciprocal lattice vector, so one only needs to consider the wavevectors inside the first Brillouin zone. For a given wavevector and potential, there are a number of solutions, indexed by n, to Schrödinger's equation for a Bloch electron. These solutions, called bands, are separated in energy by a finite spacing at each k; if there is a separation that extends over all wavevectors, it is called a (complete) band gap. The band structure is the collection of energy eigenstates within the first Brillouin zone. All the properties of electrons in a periodic potential can be calculated from this band structure and the associated wavefunctions, at least within the independent electron approximation.A corollary of this result is that the Bloch wavevector k is a conserved quantity in a crystalline system (modulo addition of reciprocal latticevectors), and hence the group velocity of the wave is conserved. This means that electrons can propagate without scattering through a crystalline material, almost like free particles, and that electrical resistance in a crystalline conductor only results from things like imperfections that break the periodicity.It can be shown that the eigenfunctions of a particle in a periodic potential can always be chosen in this form by proving that translation operators (by lattice vectors) commute with the Hamiltonian. More generally, the consequences of symmetry on the eigenfunctions are described by representation theory.The concept of the Bloch state was developed by Felix Bloch in 1928, to describe the conduction of electrons in crystalline solids. The same underlying mathematics, however, was also discovered independently several times: by George William Hill (1877), Gaston Floquet (1883), and Alexander Lyapunov (1892). As a result, a variety of nomenclatures are common: applied to ordinary differential equations, it is called Floquet theory (or occasionally the Lyapunov-Floquet theorem). Variousone-dimensional periodic potential equations have special names, for example, Hill's equation:[1],where the θ's are constants. Hill's equation is very general, as the θ-related terms may viewed as a Fourier series expansion of a periodic potential. Other much studied periodic one-dimensional equations are the Kronig-Penney model and Mathieu's equation.References1.^ W Magnus and S Winkler (2004). Hill's Equation. Courier Dover, p. 11. ISBN0-0486495655.Further reading∙Charles Kittel, Introduction to Solid State Physics (Wiley: New York, 1996).∙Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).∙Felix Bloch, "Über die Quantenmechanik der Elektronen in Kristallgittern," Z. Physik52, 555-600 (1928).∙George William Hill, "On the part of the motion of the lunar perigee which is a function of the mean motions of the sun and moon," Acta. Math.8, 1-36 (1886). (This work wasinitially published and distributed privately in 1877.)∙Gaston Floquet, "Sur les équations différentielles linéaires à coefficients périodiques,"Ann. École Norm. Sup.12, 47-88 (1883).∙Alexander Mihailovich Lyapunov, The General Problem of the Stability of Motion (London: Taylor and Francis, 1992). Translated by A. T. Fuller from Edouard Davaux'sFrench translation (1907) of the original Russian dissertation (1892).Retrieved from "/wiki/Bloch_wave"Density of statesFrom Wikipedia, the free encyclopediaIn statistical and condensed matter physics, the density of states (DOS) of a system describes the number of states at each energy level that are available to be occupied. A high DOS at a specific energy level means that there are many states available for occupation. A DOS of zero means that no states can be occupied at that energy level.ExplanationWaves, or wave-like particles, can only exist within quantum mechanical (QM) systems if the properties of the system allow the wave to exist. In some systems, the interatomic spacing and the atomic charge of the material allows only electrons of certain wavelengths to exist. In other systems, the crystalline structure of the material allows waves to propagate in one direction, while suppressing wave propagation in another direction. Waves in a QM system have specific wavelengths and can propagate in specific directions, and each wave occupies a different mode, or state. Because many of these states have the same wavelength, and therefore share the same energy, there may be many states available at certain energy levels, while no states are available at other energy levels. For example, the density of states for electrons in a semiconductor is shown in red in Fig. 2. For electrons at the conduction band edge, very few states are available for the electron to occupy. As the electron increases in energy, the electron density of states increases and more states become available for occupation. However, because thereare no states available for electrons to occupy within the bandgap, electrons at the conduction band edge must lose at least E g of energy in order to transition to another available mode. The density of states can be calculated for electron, photon, or phonon in QM systems. The DOS is usually represented by one of the symbols g, ρ, D, n, or N, and can be given as a function of either energy or wavevector k. To convert between energy and wavevector, the specific relation between E and k must be known.For example, the formula for electrons isAnd for photons, the formula isDerivationThe density of states is dependent upon the dimensional limits of the object itself. The role dimensions play is evident from the units of DOS (Energy-1Volume-1). In the limit that the system is 2 dimensional a volume becomes an area and in the limit of 1 dimension it becomes a length. It is important to note that the volume being referenced is the volume of k-space,the space enclosed by the constant energy surface of the system derived through a dispersion relation that relates E to k. An example of a specific k-space is given in Fig. 1. It can be seen that the dimensionality of the system itself will confine the momentum of particles inside the system.Figure 1: Constant energy surface k-space for electrons in a 3 dimensional crystalline material with isotropic effective mass.The calculation for DOS starts by counting the N allowed states at a certain k that are contained within [k, k+dk] inside the volume of the system. This is done by dividing the whole k-space volume V k at an arbitrary k, by a volume increment dΩ(area for 2D, length for 1D) in k-space that。

第一性原理计算简述第一性原理，英文First Principle，是一个计算物理或计算化学专业名词，广义的第一性原理计算指的是一切基于量子力学原理的计算。

我们知道物质由分子组成，分子由原子组成，原子由原子核和电子组成。

量子力学计算就是根据原子核和电子的相互作用原理去计算分子结构和分子能量（或离子），然后就能计算物质的各种性质。

从头算（ab initio）是狭义的第一性原理计算，它是指不使用经验参数，只用电子质量，光速，质子中子质量等少数实验数据去做量子计算。

但是这个计算很慢，所以就加入一些经验参数，可以大大加快计算速度，当然也会不可避免的牺牲计算结果精度。

那为什么使用“第一性原理”这个字眼呢？据说这是来源于“第一推动力”这个宗教词汇。

第一推动力是牛顿创立的，因为牛顿第一定律说明了物质在不受外力的作用下保持静止或匀速直线运动。

如果宇宙诞生之初万事万物应该是静止的，后来却都在运动，是怎么动起来的呢？牛顿相信这是由于上帝推了一把，并且牛顿晚年致力于神学研究。

现代科学认为宇宙起源于大爆炸，那么大爆炸也是有原因的吧。

所有这些说不清的东西，都归结为宇宙“第一推动力”问题。

科学不相信上帝，我们不清楚“第一推动力”问题只是因为我们科学知识不完善。

第一推动一定由某种原理决定。

这个可以成为“第一原理”。

爱因斯坦晚年致力与“大统一场理论”研究，也是希望找到统概一切物理定律的“第一原理”，可惜，这是当时科学水平所不能及的。

现在也远没有答案。

但是为什么称量子力学计算为第一性原理计算？大概是因为这种计算能够从根本上计算出来分子结构和物质的性质，这样的理论很接近于反映宇宙本质的原理，就称为第一原理了。

广义的第一原理包括两大类，以Hartree-Fork自洽场计算为基础的ab initio从头算，和密度泛函理论（DFT）计算。

也有人主张，ab initio专指从头算，而第一性原理和所谓量子化学计算特指密度泛函理论计算。

根据原子核和电子互相作用的原理及其基本运动规律，运用量子力学原理，从具体要求出发，经过一些近似处理后直接求解薛定谔方程的算法，习惯上称为第一原理。

认识“第一性原理”【833】第一次听说“第一性原理”就是通过帅老师的《优势成长》这本书。

第一性原理，又称“第一原理”，是古希腊哲学家亚里士多德提出的一个哲学术语。

举个例子来说明一下，什么是第一性原理：几何中的“第一性原理”，我们最熟悉的是：两点之间，直线最短。

生物学中的“第一性原理”：物竞天择，适者生存。

经济学中的“第一性原理”：供求理论。

帅老师在书中讲到，“第一性原理”是所有学科的本质和根基，与此同时，也是深度思考的基石和方向。

大多数人做事都缺乏创新，别人做什么他也跟风去做，先模仿然后再想办法超越，这样不是不行，只是这样做多数的结果都是微小的迭代和发展。

可是，如果能够学会用“第一性原理”来思考问题的话，那么就可以尝试着用物理的角度看待世界，意思就是，一层一层拨开事物的表象，去看清事物的本质，然后再从本质一层一层往上走。

“教主”乔布斯曾表示，只有能看到事物本质的人，才拥有改变世界的力量。

他在苹果公司所坚持的“第一性原理”就是“简洁”，也正是在这个原理指导下，苹果公司产品不断升级。

所以，我们在学习的时候，或者想要去做点什么的时候，也要思考，这件事情的“第一性原理”是什么。

比如说，大家很喜欢的“吐槽大会”，大家看着很上瘾，而且一期看下来嘴巴都没有合上过。

还有“奇葩说”，那些辩手辩论起来，真是越看越上瘾，越听越过瘾。

为什么？为什么看书会瞌睡，看这样的辩论赛和吐槽大会就不犯困，而且超级兴奋。

因为你永远都不知道他们接下来会说什么，尤其是吐槽大会，他们的台词基本上都是远远超出我们的预估和期待的，所以，越听就越好奇他们接下来会如何吐槽。

无论是吐槽大会、奇葩说、还是脱口秀，你会发现，他们能逗乐你，一方面是技巧和方法使然，更重要的是，他们都秉承了一个原则，也是幽默的第一性原理：突破期待。

所以，我们要学会去思考事物的本质——只有先认识了本质，后续的方法技巧才有用。

END。

第一性原理是什么意思1. 简介第一性原理（First Principles）是科学研究的基础。

它指的是通过分析和理解系统的最基本原理来推导其他的现象和规律。

第一性原理是一种从根本上解决问题的方法，它能够帮助科学家和研究人员在没有任何已有经验或假设的情况下，从最基本的原理出发，推导出一系列的结论和规律。

第一性原理可以应用于各个领域，例如物理学、化学、工程学、经济学等等。

通过应用第一性原理，我们可以深入理解事物的本质，并从中推导出新的解决方案和创新。

本文将从两个方面来介绍第一性原理的含义和应用。

首先，我们将探讨第一性原理的概念和基本原则。

然后，我们将介绍第一性原理在科学研究和创新中的重要性和应用案例。

2. 第一性原理的概念第一性原理的概念可以追溯到古希腊哲学家亚里士多德的思想。

他认为，探索问题的最基本原则是通过分析和理解事物的本质和基本属性。

这种思维方法被称为“分析思维”。

在现代科学研究中，第一性原理的概念得到了进一步发展。

它强调了通过分析和理解事物的基本元素和相互关系，来推导其他现象和规律。

换句话说，第一性原理是一种从首要元素出发的推理方法，它基于逻辑和推理，而不是依赖于经验或假设。

3. 第一性原理的基本原则第一性原理的应用需要遵循一些基本的原则：（1）避免传统思维模式的束缚第一性原理要求摒弃传统思维模式的束缚，不盲从于以往的经验和假设。

它鼓励科学家和研究人员去探索系统的本质和基本原理，而不是局限于已有的认知框架。

（2）分解问题为最基本的元素第一性原理要求将复杂的问题分解为最基本的元素。

通过分析和理解这些基本元素，我们可以深入研究问题的本质，并从中推导出新的知识和规律。

（3）基于逻辑和推理进行推导第一性原理强调基于逻辑和推理进行推导和证明。

通过严谨的思维和推理过程，我们可以得出准确和可靠的结论，并进行进一步的推导和应用。

4. 第一性原理在科学研究中的应用第一性原理在科学研究中具有广泛的应用价值，下面将介绍几个常见的应用案例：（1）物理学中的第一性原理在物理学中，第一性原理被广泛应用于研究基本粒子、能量传递、量子力学等领域。

第一性原理简介精选文档TTMS system office room 【TTMS16H-TTMS2A-TTMS8Q8-1什么是第一性原理？ 根据原子核和电子互相作用的原理及其基本运动规律，运用，从具体要求出发，经过一些近似处理后直接求解的算法，称为第一性原理。

广义的第一原理包括两大类，以Hartree-Fock 自洽场计算为基础的从头算和（DFT ）计算。

从定义可以看出第一性原理涉及到量子力学、、Hartree-Fock自洽场、等许多对我来说很陌生的物理化学定义。

因此我通过向师兄请教和上网查资料一点点的了解并学习这些知识。

2第一性原理的作用以密度泛函理论(DFT)为基础以及在此基础上发展起来的简单而具有一定精度的局域密度近似(LDA)和广义梯度近似(GGA)的第一性原理电子结构计算方法,与传统的解析方法一样,不但能够给出描述体系微观电子特性的物理量如波函数、态密度、费米面、电子间互作用势等,以及在此基础上所得到的体现体系宏观物理特性的参量如结合能、电离能、比热、电导、光电子谱、穆斯堡尔谱等等,而且它还可以帮助人们预言许多新的物理现象和物理规律。

密度泛函计算的一些结果能够与实验直接进行比较,一些应用程序的发展乃至商业软件的发布,导致了基于密度泛函理论的第一原理计算方法的广泛应用。

密度泛函理论(DFT)为第一性原理中的一类，在物理系、化学、材料科学以及其他工程领域中，密度泛函理论（DFT）及其计算已经快速发展成为材料建模模拟的一种“标准工具”。

密度泛函理论可以计算预测固体的晶体结构、晶格参数、能带结构、态密度（DOS）、光学性能、磁性能以及原子集合的总能等等。

3第一性原理怎么用？目前我所学到的利用第一性原理的软件为Material Studio、VASP软件。

其中Materials Studio（简称MS）是专门为材料科学领域研究者开发的一款可运行在PC上的模拟软件。

使化学及材料科学的研究者们能更方便地建立三维结构模型，并对各种晶体、无定型以及高分子材料的性质及相关过程进行深入的研究。