[go: up one dir, main page]
Menu ▾ ▴

[9a5978]: / src / f_psi.f90  Maximize  Restore  History

Download this file

68 lines (63 with data), 3.0 kB 

 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
!*******************************************************************************

!       Copyright (C) 1996-2022 Alan W. Irwin

!

!    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 2 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, write to the Free Software

!    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

!*******************************************************************************

! Note:

! The original version of this routine is in the public domain.  It was

! written in the late 60's or early 70's by Darwin Harwood for the US

! government, and it was brought to the attention of AWI by Forrest J.

! Rogers and Fritz J. Swenson. AWI relicensed the routine under the GPL

! and put in many changes to convert to structured programming and

! real(fp_kind), evaluate partial derivatives, and insert commentary.



! forrest's electron exchange integral subroutine.

! fpsi and its first through third derivatives wrt psi, where

! psi is the Cox and Giuli degeneracy parameter eta.

!

! definition is derived from definitions of fp12 and exct (see their

! commentary):

! fpsi(psi) =

! integral from -inf to psi of square of derivative of fp12(psi') d psi'

! fp12(psi) is C&G F(1/2, psi)/Gamma(3/2).

!

!> This f_psi subroutine calculates an approximation for fpsi(psi) =

!> integral from -inf to psi of square of derivative of fp12(psi') d

!> psi' where fp12(psi) is C&G F(1/2, psi)/Gamma(3/2).  The grand

!> canonical partition function of the exchange effect in the

!> non-relativistic limit can be calculated from this integral. See <a

!> href="http://freeeos.sourceforge.net/exchange.pdf">"The Exchange

!> Paper"</a> for further details.

!>

!> \param[in] psi PARAMETERS NEED DOCUMENTATION

!>

subroutine f_psi(psi, fpsi, dfpsi, d2fpsi, d3fpsi)



  ! Arguments

  real(fp_kind), intent(in) :: psi

  real(fp_kind), intent(out) :: fpsi, dfpsi, d2fpsi, d3fpsi



  ! Local variables

  real(fp_kind) f1, df1, d2f1, d3f1, f2, df2, d2f2, d3f2



  call fp12_calc(psi, f1, df1, d2f1, d3f1)

  ! df2, etc., are derivatives of f2 wrt f1

  call exct_calc(f1, f2, df2, d2f2, d3f2)

  fpsi = f1*f1*f2

  dfpsi = 2._fp_kind*f1*df1*f2 + f1*f1*df2*df1

  d2fpsi = 2._fp_kind*(df1*df1 + f1*d2f1)*f2 +&

       4._fp_kind*f1*df1*df2*df1 +&

       f1*f1*(d2f2*df1*df1 + df2*d2f1)

  d3fpsi = 2._fp_kind*(3._fp_kind*df1*d2f1 + f1*d3f1)*f2 +&

       6._fp_kind*(df1*df1 + f1*d2f1)*df2*df1 +&

       6._fp_kind*f1*df1*(d2f2*df1*df1 + df2*d2f1) +&

       f1*f1*(d3f2*df1*df1*df1 + 3._fp_kind*d2f2*df1*d2f1 + df2*d3f1)

end subroutine f_psi