1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with LaTeX2HTML 2019.2 (Released June 5, 2019) -->
<HTML lang="EN">
<HEAD>
<TITLE>1.3 Pseudopotential generation, in general</TITLE>
<META NAME="description" CONTENT="1.3 Pseudopotential generation, in general">
<META NAME="keywords" CONTENT="pseudo-gen">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=utf-8">
<META NAME="viewport" CONTENT="width=device-width, initial-scale=1.0">
<META NAME="Generator" CONTENT="LaTeX2HTML v2019.2">
<LINK REL="STYLESHEET" HREF="pseudo-gen.css">
<LINK REL="previous" HREF="node4.html">
<LINK REL="next" HREF="node6.html">
</HEAD>
<BODY >
<!--Navigation Panel-->
<A
HREF="node6.html">
<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A>
<A
HREF="node2.html">
<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A>
<A
HREF="node4.html">
<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A>
<A ID="tex2html77"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A
HREF="node6.html">2 Step-by-step Pseudopotential generation</A>
<B> Up:</B> <A
HREF="node2.html">1 Introduction</A>
<B> Previous:</B> <A
HREF="node4.html">1.2 About similar work</A>
<B> <A ID="tex2html78"
HREF="node1.html">Contents</A></B>
<BR>
<BR>
<!--End of Navigation Panel-->
<H2><A ID="SECTION00023000000000000000">
1.3 Pseudopotential generation, in general</A>
</H2>
<P>
<EM>In the following I am assuming that the basic PP theory
is known to the reader. Otherwise, see
Refs.[<A
HREF="node21.html#NC">1</A>,<A
HREF="node21.html#BHS">4</A>,<A
HREF="node21.html#TM">7</A>,<A
HREF="node21.html#fhi98PP">8</A>,<A
HREF="node21.html#RRKJ">9</A>] and references quoted
therein for NC-PP's; Refs.[<A
HREF="node21.html#van">2</A>,<A
HREF="node21.html#PAW">3</A>] for US-PP's and PAWsets.
I am also assuming that the generated PP's are to be used
in separable form [<A
HREF="node21.html#KB">10</A>] with a plane-wave (PW) basis set.
</EM>
<P>
<EM>The PP generation is a three-step process. First, one generates
atomic levels and orbitals with Density-functional theory (DFT).
Second, from atomic results one generates the PP. Third, one checks
whether the reesulting PP is actually working. If not, one tries again in
a different way.
</EM>
<P>
<EM>The first step is invariably done assuming a spherically symmetric
self-consistent Hamiltonian, so that all elementary quantum mechanics
results for the atom apply. The atomic state is defined by the
"electronic configuration", one-electron states are defined by a
principal quantum number and by the angular momentum and are obtained
by solving a self-consistent radial Schrödinger-like (Kohn-Sham)
equation.
</EM>
<P>
<EM>The second step exists in many variants. One can generate ``traditional''
single-projector NC-PP's; multiple-projector US-PP's, or PAW sets.
The crucial step is in all cases the generation of smooth
``pseudo-orbitals'' from atomic all-electron (AE) orbitals.
Two popular pseudization
methods are presently implemented: Troullier-Martins [<A
HREF="node21.html#TM">7</A>]
and Rappe-Rabe-Kaxiras-Joannopoulos [<A
HREF="node21.html#RRKJ">9</A>] (RRKJ).
</EM>
<P>
<EM>The second and third steps are closer to cooking than to science.
There is a
large arbitrariness in the preceding step that one would like to
exploit in order to get the "best" PP, but there is no well-defined
way to do this. Moreover one is often forced to strike a compromise
between transferability (thus accuracy) and hardness (i.e. computer
time). These two steps are the main focus of these notes.
</EM>
<P><HR>
<!--Navigation Panel-->
<A
HREF="node6.html">
<IMG WIDTH="37" HEIGHT="24" ALT="next" SRC="next.png"></A>
<A
HREF="node2.html">
<IMG WIDTH="26" HEIGHT="24" ALT="up" SRC="up.png"></A>
<A
HREF="node4.html">
<IMG WIDTH="63" HEIGHT="24" ALT="previous" SRC="prev.png"></A>
<A ID="tex2html77"
HREF="node1.html">
<IMG WIDTH="65" HEIGHT="24" ALT="contents" SRC="contents.png"></A>
<BR>
<B> Next:</B> <A
HREF="node6.html">2 Step-by-step Pseudopotential generation</A>
<B> Up:</B> <A
HREF="node2.html">1 Introduction</A>
<B> Previous:</B> <A
HREF="node4.html">1.2 About similar work</A>
<B> <A ID="tex2html78"
HREF="node1.html">Contents</A></B>
<!--End of Navigation Panel-->
</BODY>
</HTML>
|
