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
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
|
/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/** @file fun-lb94.c LB94 implementation.
Implementation of Exchange-correlation potential with correct
asymptotic behavior by R. van Leeuwen and E. J. Baerends:
[ van Leeuwen and EJ Baerends, Phys Rev A 49, 2421 (1994)]
See also comments in Gisbergen et al, JCP 105(8) 3142.
(c) P. Salek, oct 2003 - the working implementation.
*/
#include <math.h>
#include <stddef.h>
#define __CVERSION__
#include "functionals.h"
/* INTERFACE PART */
static int lb94_isgga(void) { return 1; }
static int lb94_read(const char* conf_line);
static real lb94_energy(const FunDensProp* dens_prop);
static void lb94_first(FunFirstFuncDrv *ds, real factor,
const FunDensProp* dens_prop);
static void lb94_second(FunSecondFuncDrv *ds, real factor,
const FunDensProp* dens_prop);
static void lb94_third(FunThirdFuncDrv *ds, real factor,
const FunDensProp* dens_prop);
#ifdef FOURTH_ORDER_DERIVATIVES
static void lb94_fourth(FourthFuncDrv *ds, real factor,
const FunDensProp* dens_prop);
#endif
Functional LB94Functional = {"LB94", /* name */
lb94_isgga, /* gga-corrected */
lb94_read, /* set common blocks */
NULL, /* reporter */
lb94_energy,
lb94_first,
lb94_second,
lb94_third
#ifdef FOURTH_ORDER_DERIVATIVES
,lb94_fourth,
#endif
};
/* IMPLEMENTATION PART */
static int
lb94_read(const char* conf_line)
{
fun_set_hf_weight(0.0);
return 1;
}
static const real BETA = 0.05;
static real
lb94_energy(const FunDensProp* dp)
{
return SlaterFunctional.func(dp)+VWNFunctional.func(dp);
}
static void
lb94_first(FunFirstFuncDrv *ds, real factor, const FunDensProp* dp)
{
real rho = dp->rhoa + dp->rhob;
real rho13 = POW(rho, 1.0/3.0);
real grad = dp->grada + dp->gradb;
real rho43=rho*rho13;
real scaled_grad, sg2, vx;
scaled_grad = grad/(rho43>1e-13 ? rho43 : 1e-13);
sg2 = scaled_grad*scaled_grad;
vx = -BETA*rho13*sg2/
(1+3*BETA*scaled_grad*ASINH(scaled_grad));
ds->df1000 += vx*factor;
ds->df0100 += vx*factor;
SlaterFunctional.first(ds, factor, dp);
VWNFunctional.first(ds, factor, dp);
}
static void
lb94_second(FunSecondFuncDrv *ds, real factor, const FunDensProp* dp)
{
/* according to the authors, it is equivalent to ALDA for LR and higher.
* See comments in Gisbergen et al, JCP 105(8) 3142. */
#if 0
real
x1 = POW(dp->gradb,2.0)+2.0*dp->gradab+POW(dp->grada,2.0),
x2 = dp->rhob+dp->rhoa,
x3 = 1/POW(x2,2.333333333333334),
x4 = sqrt(x1),
x5 = 1/POW(x2,1.333333333333333),
x6 = asinh(x4*x5),
x7 = 0.15*x4*x5*x6+1.0,
x8 = 1/x7,
x9 = -0.05*x1*x3*x8,
x10 = 1/POW(x2,2.666666666666667),
x11 = 1/sqrt(x1*x10+1.0),
x12 = 1/POW(x7,2.0),
x13 = 0.11666666666667*x1*x8/POW(x2,3.333333333333334)
+0.05*x1*x12*x3*(-0.2*x4*x3*x6-0.2*x1*x11/POW(x2,3.666666666666667)),
x14 = 1/x4,
x15 = 0.05*x1*x3*(0.15*dp->grada*x14*x5*x6+0.15*dp->grada*x10*x11)*x12
-0.1*dp->grada*x3*x8,
x16 = 0.05*x1*x3*(0.15*dp->gradb*x14*x5*x6+0.15*dp->gradb*x10*x11)*x12
-0.1*dp->gradb*x3*x8;
ds->df1000 += x9*factor;
ds->df0100 += x9*factor;
ds->df2000 += x13*factor;
ds->df0200 += x13*factor;
ds->df1100 += x13*factor;
ds->df1010 += x15*factor;
ds->df1001 += x16*factor;
ds->df10001 += (0.05*x1*x3*(0.15*x14*x5*x6+0.15*x10*x11)*x12-0.1*x3*x8)
*factor;
ds->df0110 += x15*factor;
ds->df0101 += x16*factor;
#endif
SlaterFunctional.second(ds, factor, dp);
VWNFunctional.second(ds, factor, dp);
}
static void
lb94_third(FunThirdFuncDrv *ds, real factor, const FunDensProp* dp)
{
SlaterFunctional.third(ds, factor, dp);
VWNFunctional.third(ds, factor, dp);
}
#ifdef FOURTH_ORDER_DERIVATIVES
static void
lb94_fourth(FourthFuncDrv *ds, real factor, const FunDensProp* dp)
{
SlaterFunctional.fourth(ds, factor, dp);
VWNFunctional.fourth(ds, factor, dp);
}
#endif
|
