[docs]: Put a section describing the DFT -1/2 method at the beginning…

… of the introduction

docs/source/introduction.rst

@@ -2,13 +2,31 @@
 Introduction
 ##############
 
+The DFT -1/2 method
+*********************
+DFT-1/2, an alternative way of referring to the LDA -1/2 [1]_ [2]_ and GGA -1/2 [2]_ techniques, 
+is a method that method for approximate self-energy corrections within the framework of conventional Kohn-Sham DFT 
+which can be used not only with the local density approximation (LDA), but also with the generalized gradient approximation (GGA) [11]_ [2]_ [12]_.
+
+The method aims to predict energy gaps results with the same precision [2]_ as the quasiparticle correction [9]_ algorithm, considered 
+the state of the art for calculating energy gap of semiconductors. In addition, the computational effort of the method 
+is equivalent to the standard DFT approach, which allows the technique to be applied to complex systems.
+
+.. figure:: images/dft_05_demonstration.png
+   :width: 400
+
+   Fig 1. Comparison of calculated band gaps with experiment. The red square are the SCF LDA-1/2 (standard
+   LDA-1/2). The crosses are standard LDA. The small gap semiconductors are metals (negative gaps), when calculated with
+   LDA. LDA-1/2 corrects the situation. The band structure calculations were made with the codes VASP [13]_ [14]_ and WIEN2k. [15]_ [2]_
+
+
+
 What is minushalf?
 ********************
 
-Minushalf is a CLI developed by GMSN that aims to automate 
-the application of the DFT -1/2 method. The commands available in this 
-CLI automate both the entire process and each of its steps in order to be 
-used by the user for any purposes.
+Minushalf is a command line interface (CLI) developed by the group of semiconductor materials and nanotechnology (`GMSN <http://www.gmsn.ita.br/>`_) that aims to automate 
+the application of the DFT -1/2 method. The commands available in this  CLI automate both the entire process and each of its steps in order to be 
+used for several purposes.
 
 An intuitive explanation of the DFT -1/2 method
 ************************************************
@@ -34,7 +52,7 @@ this existing relationship, self-energy corrections performed in atoms could pro
 .. figure:: images/cdo_bands.png
    :width: 500
 
-   Fig 1. Orbital character for CdO valence bands. The character :math:`p` is represented
+   Fig 2. Orbital character for CdO valence bands. The character :math:`p` is represented
    in yellow and the character :math:`d` in a magnet [10]_.
 
 
@@ -45,14 +63,7 @@ In this section, calculations were developed using some approximations in order
 intuitively how the potential correction in crystals is made. To access the rigorous demonstration, consult the references [1]_ [2]_ . 
 
 Following the Slater half occupation procedure for atoms, a change in charge density is required
-to obtain the potential for semi-occupation and perform the consistent calculations using the Khon-Shan equation, as well as
-shown in Figure 2.
-
-.. figure:: images/slater-atoms.svg
-   :width: 400
-
-   Fig 2. Flowchart representing the Slater procedure in atoms
-
+to obtain the potential for semi-occupation and perform the consistent calculations using the Khon-Shan equation.
 
 
 Altough in extended systems like crystals a change in charge density in a unit cell would result in an infinitely charged system, which would lead to a 
@@ -63,7 +74,7 @@ to derive the semi-occupied potential.
 Firstly, one have to define the system that corresponds to the semi-occupied potential for a solid. For an atom containing
 :math:`N` electrons in its ground state, the semi-occupied potential is defined as the potential of the atom with :math:`N-\frac{1}{2}` electrons. Similarly, we should 
 consider that the semi-occupied potential of a solid would be the potential generated by a solid with :math:`M-\frac{1}{2}` electrons per primitive cell, where :math:`M` is the number of electrons
-of the unit cell in the ground state, as shown in Figure 3.
+of the unit cell in the ground state, as shown in Figure 2.
 
 .. figure:: images/semi-solid.svg
    :width: 400
@@ -196,16 +207,6 @@ After applying the correction, the optimum cut must be found for each corrected
 we find the final value for the gap. 
 
 
-DFT -1/2 results
-*********************
-
-The results obtained by the application the method have the same precision [2]_ as the GW [9]_ algorithm, considered 
-the state of the art for calculating band gap of semiconductors. In addition, the computational complexity of the method 
-is equivalent to the standard DFT approach, which allows the technique to be applied to complex systems.
-
-
-
-
 References
 ********************
 
@@ -227,4 +228,14 @@ References
 
 .. [9] G. Onida, L. Reining, and A. Rubio, `Rev. Mod. Phys. 74, 601 (2002) <http://dx.doi.org/10.1103/RevModPhys.74.601>`_.
 
-.. [10] C. A. Ataide, R. R. Pelá, M. Marques, L. K. Teles, J. Furthmüller, and F. Bechstedt `Phys. Rev. B 95, 045126 – Published 17 January 2017 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045126>`
+.. [10] C. A. Ataide, R. R. Pelá, M. Marques, L. K. Teles, J. Furthmüller, and F. Bechstedt `Phys. Rev. B 95, 045126 – Published 17 January 2017 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.95.045126>`
+
+.. [11] R. R. Pelá, M. Marques, L. G. Ferreira, J. Furthmüller, and L. K. Teles, `Appl. Phys. Lett. 100, 202408 (2012) <https://doi.org/10.1063/1.3624562>`_.
+
+.. [12] I. Guilhon, D. S. Koda, L. G. Ferreira, M. Marques, and L. K. Teles 1, `Phys. Rev. B 95, 045426 – Published 24 January 2018 <https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.045426>`
+
+.. [13] G. Kresse and J. Furthmüller, `Phys. Rev. B 54, 11169 (1996) <https://doi.org/10.1103/PhysRevB.54.11169>`_.
+
+.. [14] G. Kresse and J. Furthmüller, `Comput. Mater. Sci. 6, 15 (1996) <https://doi.org/10.1016/0927-0256(96)00008-0>`_.
+
+.. [15] P. Blaha, K. Schwarz, P. Sorantin, and S. B. Trickey, `Comput. Phys. Commun <http://dx.doi.org/10.1016/0010-4655(90)90187-6>`_. 59, 399 (1990), see www.wien2k.at.