1\section{Diamond --- MLWFs for the valence bands}
2\label{sec5:diamond}
3\begin{itemize}
4\item Outline: {\it Obtain MLWFs for the valence bands of diamond.}
5\end{itemize}
6
7\begin{figure}[h!]
8\centering
9\includegraphics[width=0.25\columnwidth,trim={45pt 45pt 55pt 55pt},clip]{figure/example05/diamond.png}
10\caption{Unit cell of Diamond crystal plotted with the \xcrysden{} program.}
11\label{fig5.0}
12\end{figure}
13
14
15\begin{enumerate}
16	\item {\it Run pwscf to obtain the ground state of diamond.}
17
18	Convergence of the self-consistent field calculation in Quantum Espresso can be checked at the end of the {\tt scf.out} file. At the very end of the file one should find the line confirming that the job has finished without crashing, e.g.
19	\begin{tcolorbox}[sharp corners,boxrule=0.5pt]
20	{\small
21	\begin{verbatim}
22	=------------------------------------------------------------------------------=
23	   JOB DONE.
24	=------------------------------------------------------------------------------=
25	\end{verbatim}
26	}
27	\end{tcolorbox}
28	Depending on the output verbosity one may or may not find info about WALL times for the calls to the different routines. Just above this block, if present, one may find the info about the convergence of the SCF loop, such as the scf accuracy and the number of iterations to required to achieve it:
29	\begin{tcolorbox}[sharp corners,boxrule=0.5pt]
30	\small{
31	\begin{verbatim}
32    !    total energy              =     -22.58128615 Ry
33         Harris-Foulkes estimate   =     -22.58128615 Ry
34         estimated scf accuracy    <          1.0E-14 Ry
35
36
37         The total energy is the sum of the following terms:
38
39         one-electron contribution =      11.69117931 Ry
40         hartree contribution      =       1.57036314 Ry
41         xc contribution           =      -7.58421586 Ry
42         ewald contribution        =     -28.25861274 Ry
43
44         convergence has been achieved in   9 iterations
45	\end{verbatim}
46	}
47	\end{tcolorbox}
48	\item {\it Run pwscf to obtain the Bloch states on a uniform k-point grid.}
49
50	Similarly for the non-scf calculation one can check that the calculation has been carried out without crashing by looking at the last three line of the {\tt nscf.out} file. A useful information to check is the value of the highest eigenvalue (for insulators and semiconductors) or the value of the Fermi level (for metals). In the diamond we case, we find:
51	\begin{tcolorbox}[sharp corners,boxrule=0.5pt]
52	{\small
53	\begin{verbatim}
54	highest occupied level (ev):    19.3978
55	\end{verbatim}
56	}
57	\end{tcolorbox}
58	\item[5] {\it Run \Wannier{} to compute the MLWFs.}
59
60	The result of the wannierisation, after 20 iterations, may be found at the end of {\tt diamond.wout} file:
61	\begin{tcolorbox}[sharp corners,boxrule=0.5pt]
62	\small{
63	\begin{verbatim}
64	 Final State
65  WF centre and spread    1  ( -0.000000,  0.000000, -0.000000 )     0.58022623
66  WF centre and spread    2  ( -0.806995,  0.806995,  0.000000 )     0.58022623
67  WF centre and spread    3  ( -0.000000,  0.806995,  0.806995 )     0.58022623
68  WF centre and spread    4  ( -0.806995, -0.000000,  0.806995 )     0.58022623
69  Sum of centres and spreads ( -1.613990,  1.613990,  1.613990 )     2.32090491
70
71         Spreads (Ang^2)       Omega I      =     1.954619859
72        ================       Omega D      =     0.000000000
73                               Omega OD     =     0.366285054
74    Final Spread (Ang^2)       Omega Total  =     2.320904912
75 ------------------------------------------------------------------------------
76	\end{verbatim}
77	}
78	\end{tcolorbox}
79	\item[Extra :] {\it Plot the 4 \MLWFs.}
80
81	The resulting 4 $\sigma$-bonding \MLWFs{} are shown in \Fig{fig5.1}
82\end{enumerate}
83	\begin{figure}[h!]
84	\centering
85 	\subfloat[\MLWF{} 1]{\includegraphics[width=0.2\columnwidth,trim={220pt 120pt 220pt 120pt},clip]{figure/example05/diamond_1.png}}
86 	\centering
87 	\subfloat[\MLWF{} 2]{\includegraphics[width=0.2\columnwidth,trim={220pt 120pt 220pt 120pt},clip]{figure/example05/diamond_2.png}}
88	\centering
89 	\subfloat[\MLWF{} 3]{\includegraphics[width=0.2\columnwidth,trim={220pt 120pt 220pt 120pt},clip]{figure/example05/diamond_3.png}}
90    \centering
91 	\subfloat[\MLWF{} 4]{\includegraphics[width=0.2\columnwidth,trim={220pt 120pt 220pt 120pt},clip]{figure/example05/diamond_4.png}}
92 	\caption{4 \MLWFs{} in diamond describing the valence bands plotted using \vesta.}\label{fig5.1}
93	\end{figure}
94