What is First Principle Calculation?

         After the establishment of quantum mechanics, and in accordance with the principle of statistical physics, the macroscopic properties of microscopic state are determined. The difference with classical physics is how to express microscopic state of the system? In classical physics can be simply expressed by position and momentum, but the presentation of framework in quantum mechanics is changed. Because in quantum mechanics, the position and momentum cannot both be accurately measured simultaneously.

How to do it?

Represent in wave functions. Square of the wave function represent the probability of particles appeared, this is statistical interpretation of wave function. Then, how to get the electron’s wave function? This is done by solving the Schrodinger equation.

         However, solving the Schrodinger equation is extremely difficult. Except for a few simple system i.e. Hydrogen atom, Schrodinger equation are difficult to obtain analytical solution. Thereafter, in order to apply the principles of quantum mechanics, Hartree and Fock proposed self-consistent field, which is SCF method. Here, field actually is a mean-field, that is, the potential field where particles in is replaced by a mean potential field, here included one electron approximation.

What is self-consistent field method?

This is no more science, whose interested can look at the Xie Xide band theory of solids. In general, those based on the Hartree-Fock self-consistent field is called first principle methods. This is the first source of the first principle methods, also called ab initio methods.

Why it is called ab initio methods?

Because this method which developed based on the principles of quantum mechanics requires only seven physical constants – the speed of light, Planck’s constant, atomic fine-structure constant, the electron mass, electron charge, nuclear mass, and nuclear charge, then we can calculate almost every properties of materials in ground state.Because not depend on the experiment, so is called ab initio methods.

         In addition, the source said it was from "the first impetus", the religious vocabulary. Newton founded the first impetus, because Newton's first law describes the substance remains stationary or in uniform motion without external force. If the universe was born at the beginning of all things should be static, but had later in the movement, how come it is moving? Newton believed that this is due to pushed of the God, and Newton later years committed to Theological Studies. Modern science believes that universe originated from the Big Bang, but the explosion also need a reason of it. All of these hard to explain things are attributed to "the first impetus" problem of universe.
         Science does not believe in God, we do not know "the first impetus" problem is merely because our scientific knowledge is imperfect. The first push certainly caused by some principle. This could be the "first principles." Einstein later years committed to "grand unified field theory" research, it is hoped to find "the first prinple" of all the physics laws, unfortunately, it was the level of science can not reach at that time. Now too far no answer.
(This paragraph is taken from: http: //baike.baidu.com/view/1278387.htm)

         Another first principle designation is derived from the Kohn-Sham method. Because the square of the wave function is equivalent to the probability of electron appear, then using probability density of electrons as a variable brought a great convenience. If wave functions as a variable, for N particle system, each particle described with a wave function, then would have 3N variables, since each particle has a xyz coordinates, three degrees of freedom, N particles have 3N variables, N is generally Avogadro constant magnitude. Difficult to solve! However, if the electron density is taken as the variable, just to be able to give electron density at any point, which is actually three variables, i.e., Rou (x, y, z), Rou is electron density.

Can electron density to be used as a variable?

Using a 3-dimensional variable to replace a 3N-dimensional variable will it lose information?

Hohenberg and Kohn proved two theorems, the density functional theory, the famous H-K theorem of first principle. Interested go to the website look how to prove.

Theorem along the following lines: a non-degenerate ground state wave function is the only function of the electron density; the second is, if the electron density is determined, then the unique nature of the ground state is determined. Since then, Kohn and Sham (沈吕九) develop this approach, called the density functional theory, Kohn received Nobel Prize in Chemistry for this work. Note: The physicist won the Nobel Prize in Chemistry, another is seemingly physicist Rutherford, the 20th century's greatest experimental physicist.

         In summary, the first principle is the title of ab initio methods based on density functional theory, or based on ab initio Hartree-Fock self-consistent field method.

taken from http://emuch.net/html/201106/3227802.html