[资源分享] 简单的第一性原理介绍

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什么是第一性原理计算(What are first principles calculations?)
1。What are first principles calculations?

A material is simply a collection of atoms that are bound by chemical reactions. Chemical reactions, in turn, are simply interactions between electrons. These interactions are described by the laws of quantum physics. This means that all material properties (chemical, mechanical, electrical, magnetic, optical, thermal,…) can, in principle, be predicted from nothing more than the atomic number and mass of the atomic species involved, with the aid of quantum physics. This is precisely what first principles calculations attempt to do.

One of the joys of first principles calculations is that a few atomic numbers make abstract quantum concepts come to life in the form of quantitatively accurate, experimentally verifiable predictions - for quantities ranging from the Young modulus of diamond to the absorption spectra of conjugated polymers.

2。How do we do first principles calculations?

Solving the Schrödinger equation by brute mathematical force is extremely demanding computationally and not practical for all but tiny systems. Instead, we use a combination of two physical approximations:

1. We use density functional theory (DFT), for which Prof. Walter Kohn was awarded the 1998 Nobel prize in chemistry. DFT maps the original many-electron problem into an equivalent single-electron problem. It does so by lumping all the many-body quantum phenomena (such as Pauli’s exclusion principle and electron correlation) into a single additive “exchange-correlation” potential, which is a functional of the charge density alone. In principle, this mapping is exact. In practice, the exact functional is unknown and people use approximate forms for the functional, usually (but not always) derived from properties of a uniform electron gas.

2. We use first principles pseudopotential theory. The periodic table tells us that chemical reactivity is governed by valence electrons, with core electrons being chemically inert. Pseudopotentials make use of this basic fact by replacing the inert core electrons with an effective potential. This reduces, sometimes drastically, the number of electrons we need to solve for. Even more importantly, this results in much smoother wave functions for the remaining valence electrons, making the problem much easier to solve numerically.

For the calculation of excited state properties (notably optical ones), we have to move beyond DFT, which is a ground state theory. Our favorite tool is time-dependent DFT –an extension of the original method.

Doesn’t the use of physical approximations mean that we’re not really doing first principles work? No! Our approximations are systematic. All “hidden parameters” within them are determined objectively from theoretical results for properties of the electron gas (DFT) or the isolated atom (pseudopotentials), and not by fitting experiments.

付百度的解释：
第一性原理通常是跟计算联系在一起的，是指在进行计算的时候除了告诉程序你所使用的原子和他们的位置外，没有其他的实验的，经验的或者半经验的参量，且具有很好的移植性。作为评价事物的依据，第一性原理和经验参数是两个极端。第一性原理是某些硬性规定或推演得出的结论，而经验参数则是通过大量实例得出的规律性的数据，这些数据可以来自第一性原理(称为理论统计数据)，也可以来自实验(称为实验统计数据)。
但是就某个特定的问题，第一性原理和经验参数没有明显的界限，必须特别界定。如果某些原理或数据来源于第一性原理，但推演过程中加入了一些假设(这些假设当然是很有说服力的)，那么这些原理或数据就称为“半经验的”。

其他解释：

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。

[ 本帖最后由 fatcharm 于 2008-8-28 11:27 编辑 ]

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